Mathematics Curriculum
Form 2
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
1
Directorate for Quality and Standards in Education
Curriculum Management and eLearning Department
To access the pages click on the page title below
MATHEMATICS CURRICULUM UNITS – FORM 2
MTH 8.1
MTH 8.2
MTH 8.3
MTH 8.4
MTH 8.5
MTH 8.6
MTH 8.7
MTH 8.8
MTH 8.9
MTH 8.10
MTH 8.11
MTH 8.12
MTH 8.13
MTH 8.14
MTH 8.15
Factors, Multiples and Using a Calculator
Angles
Fractions
Decimal Numbers
Percentages
Area and Volume
Triangles and Quadrilaterals
Constructions
Directed Numbers and Sequences
Expressions and Formulae
Statistics and Probability
Ratio and Proportion
Transformations
Solving Equations
Coordinates and Straight Line Graphs
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
2
Subject:
Unit code and title:
Strand 1:
MATHEMATICS
MTH 8.1 Factors, Multiples & the Use of Calculator (Levels 7.1 – 8.1)
Number
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Recognise and find common factors and multiples of up to three numbers.
2. Recognise prime numbers and write numbers as a product of their prime factors.
3. Find the least common multiple and highest common factor (up to three numbers) and solve simple problems using LCM and HCF.
4. Use the four rules for calculations with integers including the correct use of operations and the use of brackets.
5. Make efficient use of the basic functions on a calculator; including the fraction, bracket, square, cube, square root and cube root keys.
Key Words
Factors, multiples, prime, prime
factors, LCM, HCF, product,
power/index, index form
Squares, cubes, square root,
cube root
BIDMAS, order of operations,
brackets
Points to Note
Resources
Three main teaching approaches are being recommended to promote a FOM B2, Students’ Book, Practice Book,
student centred learning environment.
Resource Pack - Chapters 13 and 25
Exposition: the teacher states the objectives of the lesson and may use ICT
Internet Links:
software for students to practise new knowledge. This is consolidated by
www.mathsnet.net/js/primefinder.html
setting students tasks that offer students the opportunity to apply
http://newdream.net/~sage/old/numbers/
mathematics to a variety of real life situations.
primeodd.htm
Discovery: the teacher can set group tasks in which students discuss and
construct mathematical knowledge. Students may become active learners Other Resources:
while testing hypotheses and/or making generalisations.
 Number cards
Exploration: the teacher integrates an inquiry based learning approach
that enhances the students’ understanding of concepts. These tasks might
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
3
Teaching Objective
Examples of teaching experiences and activities
Indicators of Learning outcomes
The teacher will teach students
to:
The teacher can prepare cards with sets of numbers (say 5, 9 and 12; 6, 10
and 13; 15, 21 and 35) and distribute them to groups of students (students
preferably working in pairs or in threes).
Students will be able to recognise and find
common factors and common multiples of
three numbers.
(Level 8.1)
1. Recognise and find common
factors and multiples, up to
three numbers.
5
9
12
6
10
13
15
21
35
4
7
12
The teacher can ask students to investigate the multiplication table and
the factors of the numbers in each set. They are then asked to identify any
common factors and multiples for each set.
2. Recognise prime numbers
and write numbers as a
product of their prime
factors.
Students will be able to find common
factors and common multiples of two
numbers.
(Level 7.3)
Students will be able to find all the factors
of given numbers up to 100 and list all the
multiples of the numbers from 1 to 12.
(Level 7.2)
For a more challenging whole class task, the teacher can then present
students with slightly larger numbers.
Students will be able to find all the factors
of given numbers up to 50 and list all the
multiples of the numbers from 1 to 10.
(Level 7.1)
As an introductory activity, the teacher can give each student a card
consisting of a number and a phrase (as the ones shown below).
Students will understand that prime
numbers are the building blocks of all
natural numbers and be able to check
which numbers less than 100 are prime.
(Level 8.1)
17
8
A prime between
30 and 35
A factor
of 60
31
6
A factor
of 56
A prime factor
of 34
The teacher selects a student (at random) to read the phrase and asks the
others to find who has the answer. That student then calls out the answer
and the phrase so that the game continues.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will understand the definition of a
prime number and be able to identify and
distinguish between factors and prime
factors.
(Level 7.3)
Students will be able to use prime numbers
4
Working in groups, students are then asked to list the prime numbers up
to 100 and come up with a definition.
Use this discussion point, to ask the class to find the prime factors of
numbers and to write these numbers as a product of prime factors.
The link www.mathsnet.net/js/primefinder.html can be used by students
to check out the prime factors of any given number.
3. Find the least common
multiple and highest
common factor (up to
three numbers) and solve
simple problems using
LCM and HCF.
The teacher can present students with the situation on page 114 – three
buses first depart from a stop at 9.00 a.m. with bus A leaving every 8
minutes, bus B every 10 minutes and C every 12 minutes. Students are
asked to find out the next time at which one could catch any of the buses –
hence introducing the least common multiple.
Using the card game illustrated in teaching objective 1, the teacher can ask
students to find the highest common factor of the set of numbers
displayed in their cards.
The teacher can then introduce other real-life situations involving the use
of LCM and HCF. For example:
4. Use the four rules for
calculations with integers
including the correct use
of operations and the use
of brackets.

Designing a box which can be completely filled with containers of
different size

Tiling a room with the largest possible tile
The teacher can assign groups of students with answers (say, 25, 13.5 etc.)
and asked to create their own questions involving the four rules with the
use of brackets.
The student group presentation can serve as an exercise for the other
students in the class to work out and argue about the correct order of the
operations used.
Note: The teacher can initially ask students to formulate questions
involving at least two operations and then move on to three or more
operations depending on the students’ ability.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
to write numbers as a product of prime
factors.
(Level 7.2)
Students will be able to identify all the
prime numbers up to 50.
(Level 7.1)
Students will be able to solve simple
problems involving the use of HCF.
(Level 8.1)
Students will be able to solve simple
problems involving the use of LCM.
(Level 7.3)
Students will be able to find the HCF and
LCM of two numbers.
(Level 7.2)
Students will be able to find the LCM of
two numbers.
(Level 7.1)
Students will be able to use the four rules
for calculations including the correct use of
operations and brackets.
(Level 8.1)
Students will be able to use the four rules
for calculations with integers including the
correct use of operations and brackets.
(Level 7.3)
Students will be able to use the correct
5
order of the four basic rules with integers
including the use of brackets for
calculations involving up to three
operations.
(Level 7.2)
Students will be able to use the correct
order of the four basic rules with integers
for calculations involving two operations.
(Level 7.1)
5. Make efficient use of the
basic functions on a
calculator; including the
fraction, bracket, square,
cube, square root and
cube root keys.
Students use their calculator to input a sequence of three basic functions
(e.g.: fraction, addition and square) which they manipulate to come up
with as many different questions as possible. For example:
1. (10 + ⅝)2
2. 10 + (⅝)2
3. 102 + ⅝
Students will explore different ways of using functions and understand and
appreciate that they will lead to different answers.
The teacher might leave it free for groups of students to select their own
basic functions or else decide beforehand to assign them specific functions
to work with.
Students will be able to use the required
key calculator functions in complex
calculations involving fractions, brackets
squares, cubes, square roots and cube
roots.
(Level 8.1)
Students will be able to make efficient use
of the basic calculator functions in simple
calculations involving fractions, brackets,
squares, cubes and square roots.
(Level 7.3)
Students will be able to make efficient use
of the basic calculator functions in simple
calculations involving fractions, brackets,
squares and cubes.
(Level 7.2)
Students will be able to make efficient use
of the basic calculator functions in simple
calculations involving squares and cubes.
(Level 7.1)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
6
Subject:
Unit code and title:
Strand 1:
MATHEMATICS
MTH 8.1 Factors, Multiples & the Use of Calculator (Levels 6.3 – 7.3)
Number
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Recognise and find common factors and multiples of two numbers.
2. Recognise prime numbers and write numbers as a product of their prime factors.
3. Find the least common multiple (LCM) and highest common factor (HCF) of two numbers and solve simple problems using LCM and HCF.
4. Use the four rules for calculations with integers including the correct use of operations and the use of brackets.
5. Make efficient use of the basic functions on a calculator; including the fraction, bracket, square, cube, square root and cube root keys.
Key Words
Factors, multiples, prime, prime
factors, LCM, HCF, product,
power/index, index form
Squares, cubes, square root
BIDMAS, order of operations,
brackets
Points to Note
Resources
Three main teaching approaches are being recommended to promote a FOM B1, Students’ Book, Practice Book,
student centred learning environment.
Resource Pack - Chapters 13 and 25
Exposition: the teacher states the objectives of the lesson and may use ICT
Internet Links:
software for students to practise new knowledge. This is consolidated by
www.mathsnet.net/js/primefinder.html
setting students tasks that offer students the opportunity to apply
http://newdream.net/~sage/old/numbers/
mathematics to a variety of real life situations.
primeodd.htm
Discovery: the teacher can set group tasks in which students discuss and
construct mathematical knowledge. Students may become active learners Other Resources:
while testing hypotheses and/or making generalisations.
 Number cards
Exploration: the teacher integrates an inquiry based learning approach
that enhances the students’ understanding of concepts. These tasks might
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
7
Teaching Objective
Examples of teaching experiences and activities
Indicators of Learning outcomes
The teacher will teach students
to:
The teacher can prepare cards with sets of numbers (say 3 and 10; 6 and
11; 10 and 17) and distribute them to groups of students (students
preferably working in pairs or in threes).
Students will be able to find common
factors and common multiples of two
numbers.
(Level 7.3)
1. Recognise and find
common factors and
multiples of two numbers.
3
10
6
11
10
17
4
12
The teacher can ask students to investigate the multiplication table and
the factors of the numbers in each set. They are then asked to identify any
common factors and multiples for each set.
2. Recognise prime numbers
and write numbers as a
product of their prime
factors.
Students will be able to find all the factors
of given numbers up to 100 and list all the
multiples of the numbers from 1 to 12.
(Level 7.2)
Students will able to find all the factors of
given numbers up to 50 and list all the
multiples of the numbers from 1 to 10.
(Level 7.1)
For a more challenging whole class task, the teacher can then present
students with slightly larger numbers.
Students will be able to find all the factors
of numbers up to 25 and list all the
multiples of 2, 3, 5 and 10.
(Level 6.3)
As an introductory activity, the teacher can give each student a card
consisting of a number and a phrase (as the ones shown below).
Students will understand the definition of a
prime number and be able to identify and
distinguish between factors and prime
factors.
(Level 7.3)
17
8
A prime between
30 and 35
A factor
of 60
31
6
A factor
of 56
A prime factor
of 34
The teacher selects a student (at random) to read the phrase and asks the
others to find who has the answer. That student then calls out the answer
and the phrase so that the game continues.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to use prime numbers
to write numbers as a product of prime
factors.
(Level 7.2)
Students will be able to identify all the
prime numbers up to 50.
8
Working in groups, students are then asked to list the prime numbers up
to 100 and come up with a definition.
Use this discussion point, to ask the class to find the prime factors of
numbers and to write these numbers as a product of prime factors.
The link www.mathsnet.net/js/primefinder.html can be used by students
to check out the prime factors of any given number.
3. Find the least common
multiple (LCM) and highest
common factor (HCF) of
two numbers and solve
simple problems using
LCM and HCF.
The teacher can present students with the situation similar to that on page
112. Two buses first depart from a stop at 9.00 a.m. with bus A leaving
every 5 minutes and bus B every 8 minutes. Students are asked to find out
the next time at which one could catch any of the buses – hence
introducing the least common multiple.
Using the card game illustrated in teaching objective 1, the teacher can ask
students to find the highest common factor of the set of numbers
displayed in their cards.
The teacher can then introduce other real-life situations involving the use
of LCM and HCF. For example:
4. Use the four rules for
calculations with integers
including the correct use
of operations and the use
of brackets

LCM – Flashing lights at different intervals

HCF – Tiling a room with the largest possible tile
The teacher can assign groups of students with answers (say, 25, 13.5 etc.)
and asked to create their own questions involving the four rules with the
use of brackets.
The student group presentation can serve as an exercise for the other
students in the class to work out and argue about the correct order of the
operations used.
Note: The teacher can initially ask students to formulate questions
involving at least two operations and then move on to three or more
operations depending on the students’ ability.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
(Level 7.1)
Students will be able to identify the prime
numbers up to 35.
(Level 6.3)
Students will be able to solve simple
problems involving the use of LCM.
(Level 7.3)
Students will be able to find the HCF and
LCM of two numbers.
(Level 7.2)
Students will be able to find the LCM of
two numbers.
(Level 7.1)
Students will be able to find common
factors and common multiples of two
numbers.
(Level 6.3)
Students will be able to use the four rules
for calculations with integers including the
correct use of operations and brackets.
(Level 7.3)
Students will be able to use the correct
order of the four basic rules with integers
including the use of brackets for
calculations involving up to three
operations.
9
(Level 7.2)
Students will be able to use the correct
order of the four basic rules with integers
for calculations involving two operations.
(Level 7.1)
Students will be able to use the correct
order of the four basic rules for
calculations involving two operations one
of which includes the use of brackets.
(Level 6.3)
5. Make efficient use of the
basic functions on a
calculator; including the
fraction, bracket, square,
cube, square root and
cube root keys.
Students use their calculator to input a sequence of three basic functions
(e.g.: fraction, addition and square) which they manipulate to come up
with as many different questions as possible. For example:
1. (10 + ⅝)2
2. 10 + (⅝)2
3. 102 + ⅝
Students will explore different ways of using functions and understand and
appreciate that they will lead to different answers.
The teacher might leave it free for groups of students to select their own
basic functions or else decide beforehand to assign them specific functions
to work with.
Students will be able to make efficient use
of the basic calculator functions in simple
calculations involving fractions, brackets,
squares, cubes and square roots.
(Level 7.3)
Students will be able to make efficient use
of the basic calculator functions in simple
calculations involving fractions, brackets,
squares and cubes.
(Level 7.2)
Students will be able to make efficient use
of the basic calculator functions in simple
calculations involving squares and cubes.
(Level 7.1)
Students will be able to make efficient use
of the basic calculator functions in simple
calculations.
(Level 6.3)
Subject:
MATHEMATICS
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Form 2
10
Unit code and title:
Strand 1:
MTH 8.1 Factors, Multiples & the Use of Calculator (Levels 5.3 – 7.1)
Number
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Order a set of numbers and round numbers to the nearest unit, 10, 100 and 1000.
2. Recognise factors, multiples, prime, square and cube numbers.
3. Use brackets correctly to help with multiplication and use tests of divisibility restricted to multiples of 2, 3, 5 and 10.
Key Words
Ordering, rounding, nearest
unit, nearest 10, nearest 100,
nearest 1000
Factors, multiples, prime,
square, cube
Brackets
Divide
Points to Note
Resources
Three main teaching approaches are being recommended to promote a FOM B Gold, Students’ Book, Practice
student centred learning environment.
Book, Resource Pack - Chapters 2, 13 and
22
Exposition: the teacher states the objectives of the lesson and may use ICT
software for students to practise new knowledge. This is consolidated by
Internet Links:
setting students tasks that offer students the opportunity to apply
http://hoodamath.com/games
mathematics to a variety of real life situations.
www.math-play.com
Discovery: the teacher can set group tasks in which students discuss and www.helpingwithmath.com
construct mathematical knowledge. Students may become active learners
while testing hypotheses and/or making generalisations.
Other Resources:
 Number cards
Exploration: the teacher integrates an inquiry based learning approach
 Geo-boards
that enhances the students’ understanding of concepts. These tasks might
 Multilink cubes
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
11
Teaching Objective
Examples of teaching experiences and activities
Indicators of Learning outcomes
The teacher will teach students
to:
The teacher provides groups of students with sets of cards containing sets
of numbers in context. For example:
Students will be able to order a set of
numbers between 0 and 9999 and round
numbers to the nearest unit, 10, 100 and
1000.
(Level 7.1)
1. Order a set of numbers
and round numbers to the
nearest unit, 10, 100 and
1000.

A list of weights (in kg) of five different objects – students place
the weights in descending order and round each weight to the
nearest unit;
2.3 kg

5.4 kg
2.7 kg
35°C
19°C
42°C
33°C
A list of five distances (in m) – students place the distances in
descending order and round each to the nearest 100;
847 m

1.9 kg
A list of five temperatures – students place the set in ascending
order and round each temperature to the nearest 10;
27°C

1.6 kg
349 m
470 m
625 m
577 m
A list of five population sizes of Maltese towns/villages – students
place the populations in ascending order and round each to the
nearest 1000.
7328
11347
9837
13725
10219
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to order a set of
numbers between 0 and 999, and round
numbers to the nearest unit, 10 and 100.
(Level 6.3)
Students will be able to order a set of 3digit numbers and round numbers to the
nearest unit and 10.
(Level 6.2)
Students will be able to order a set of 2digit numbers on a number line, and round
numbers to the nearest 10.
(Level 6.1)
Students will be able to order a set of
numbers between 0 and 100, putting them
in ascending and/or descending order.
(Level 5.3)
12
2. Recognise factors,
multiples, prime, square
and cube numbers.
Factor Feeder at http://hoodamath.com/games/factorfeeder.php is a
game that students can play to practise finding factors. This game also
tests the students’ speed recognition of factors.
Using a spreadsheet, students can also become familiar with generating
multiples.
‘Factors and Multiples Jeopardy Game’ available online at
http://www.math-play.com/math-jeopardy.html is an excellent game for
practicing and reviewing factors and multiples.
At www.helpingwithmath.com/resources/games/prime/prime01.html
students can practise classifying numbers into prime and composite.
Geo-boards can be provided for students to form different squares using
rubber bands. The squares can be investigated in understanding the
meaning of a square number.
Multilink cubes can be given to students to construct and hence
investigate cubes. The teacher can use the students’ constructs/models to
relate cube numbers to the volume (number of cubes used) of the cubes.
Students will be able to list all the multiples
of numbers up to 10, factors of given
numbers up to 50, identify prime numbers
up to 50 and square/cube numbers up to
100.
(Level 7.1)
Students will be able to list all the multiples
of 2, 5 and 10, the factors of given
numbers up to 30, identify the prime
numbers up to 35 and square numbers up
to 50.
(Level 6.3)
Students will be able to find some factors
of given numbers up to 30 and identify the
prime and square numbers up to 30.
(Level 6.2)
Students will be able to list the multiples of
2, 5 and 10 and identify the first five prime
and square numbers.
(Level 6.1)
Students will be able to list the factors of
numbers up to 12 and the multiples of 2, 5
and 10.
(Level 5.3)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
13
3. Use brackets correctly to
help with multiplication
and use tests of divisibility
restricted to multiples of
2, 3, 5 and 10.
Using the interactive white-board, the teacher can present students with
prices of different items (the teacher might want to use those provided on
page 188). The teacher can then ask students to choose any two items
they wish from the list and work out their total cost.
For example: Student A chooses 2 raspberry rocket and 2 fruity fun icecreams. Hence, total cost is presented as:
2 × cost of raspberry ice-cream + 2 × cost of fruity fun ice-cream
Or 2 × (cost of raspberry ice-cream + cost of fruity fun ice-cream)
First remind students of the multiples of 2, 3, 5 and 10 using tables or
otherwise. Then the teacher can set groups of students on an investigative
task – choosing a set of 30 numbers ranging from 1 to 100 and:

Find which of their numbers are divisible by 2, by 3, by 5 and by 10
– grouping numbers using a table;

Determine how they can tell if a number is divisible by 2, by 3, by 5
or by 10;

Test their method/conjecture.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to use brackets
correctly to help with multiplication of two
2-digit numbers and use tests of divisibility
restricted to multiples of 2, 3, 5 and 10.
(Level 7.1)
Students will be able to use brackets
correctly to help with multiplying a 2-digit
number with a single digit and use tests of
divisibility restricted to 2, 5 and 10.
(Level 6.3)
Students will be able to list common
multiples of say 2 and 5, 5 and 10, and 2
and 10.
(Level 6.2)
Students will be able to list the multiples of
2, 5 and 10.
(Level 6.1)
Students will be able to list the multiples of
2 and 10.
(Level 5.3)
14
Subject:
Mathematics
Unit code and title: MTH 8.1 Factors, Multiples & the use of Calculator (Levels 1 - 4)
Strand 1:
Number
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives at attainment Level 5 and 6
The teacher will teach the students to:
1. Order a set of numbers and round numbers to the nearest unit, 10, 100 and 1000.
2. Recognise factors, multiples, prime, square and cube numbers.
3. Use brackets correctly to help with multiplication and use tests of divisibility restricted to multiples of 2, 3, 5 and 10.
Objectives at attainment levels 1, 2, 3, 4
The teacher will teach the students to:
1.1 Order a set of numbers within a specific range and round it to the nearest 10 and 100.
2.1 Develop the idea of factors through the use of sets of objects.
3.1a Create equal sets of objects, express it as repeated addition of and then as a multiplication sum.
3.1b Share a number of items into equal groups and then include the concept of left overs.
Key Words
Points to Note
Resources
In order, smallest, largest,
nearest, close to, number,
groups, count on, move on,
jump on, move forward,
share, equal amounts.
In addition to the points to note recommended for students
performing at Level 5 or higher, it is very important for the teacher to
allow time for the students to respond. This response can take the
form of unaided and/or aided means of communication and the
teacher needs to provide adequate scaffolding techniques to enable
the students to respond affectively or intentionally.
Teaching Objective
Examples of teaching experiences and activities
New Maths Frame Working-Step Up Workbook.
Oxford Framework Maths 7
Software: Ilearn Maths, Calculator, Excel
Worksheets
Internet Links:
http://www.ictgames.com/dragonmap.html
http://www.bbc.co.uk/schools/starship/maths
/games/number_jumbler/small_sound/standard.
shtml
http://www.oswego.org/ocsdweb/games/BillyBug/bugcoord.html
http://hotmath.com/hotmath_help/games/ctf/ct
f_hotmath.swf
Indicators of Learning Outcomes
The teacher will teach the
Pairs or groups of students are given different numbers to order. For
Students will be able to order a set of numbers,
For additional examples at Level 1, refer to handbook.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
15
students to:
1.1 Order a set of numbers
within a specific range and
round it to the nearest 10
and 100.
e.g. 13, 18, 26, 29. Then they place them on a 100 square number
grid. For each number, the teacher encourages the students to count
the farthest they are from the previous and the next multiple ten.
They colour the closest multiple of ten to that number.
On a 1 to 10 grid, the students order the numbers. They pick a
number and point to which end it’s the closest.
Students have a set of coloured numbers (those closest to 0 in one
colour and those closest to 10 in another) and simply match the
numbers together.
Students are exposed to the idea of ordering objects by stacking
objects.
2.1 Develop the idea of
factors through the use of
sets of objects.
Starter: Students are presented with a number line up to 20. Teachers
give out some instructions like colour the number 2 red and the
number 3, green to check whether students have number recognition.
Others can experience this multi-sensorially.
The teacher presents a set of cards from 0 to 10. They are asked to
start counting in 2’s and make sets of 2, 3 and 5. The teacher will
point out the difference between the odd and even sets of numbers.
Students will talk about the number of sets they have, e.g. 2 sets of 2.
The teacher points to a set of flashcards from 1 to 10. S/he starts
counting by saying out one number in a loud voice and another
number in a quiet voice. Then the students colour the numbers said in
a loud voice in red whilst the others in blue. Students will build towers
to represent the respective sets.
The teacher presents a coloured square grid. S/he asks one student to
walk on the blue numbers and another one to walk only on the red
numbers. The square grid activity can be lowered down to clapping
count, compare and decide on the closest
multiple of ten.
(Level 4)
Students will be able to order a set of numbers up
to 10, choose a number and point to the closest
end.
(Level 3)
Students will match the numbers correctly and at
the same time notice the differences between
the ends.
(Level 2)
Students are involved in ordering of objects
through stacking.
(Level 1)
Students will order a set of numbers and count
on and back in one’s, two’s etc. whilst talking
about the sequence.
(Level 4)
Students will be able to count the number of
objects in an odd or even set.
(Level 3)
Students will match diagrams or objects that have
the same amount of numbers (odd with odd and
even with even).
(Level 2)
Students will observe, notice and if possible
indicate anticipation for clapping or beating.
(Level 1)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
16
3.1a. Create equal sets of
objects, express them as
repeated addition of and
then as a multiplication
sum.
the blue numbers the child walks on and to beating a drum when the
child walks on the red numbers.
Starter: Students are presented with a number of objects or a
worksheet and they are asked to group objects in 2, 3 and 5. Teacher
will check whether they know how to create equal sets. Eventually,
s/he checks whether they can find the sum either using repeated
addition or otherwise.
Students will be able to group equal sets of
objects and translate the pictorial representation
into repeated addition and then into a
multiplication sum.
(Level 4)
Students will be asked to make sets of equal amounts, e.g. 3 sets of 3
or 8 sets of 1, and count the total. They will discuss how they worked
out the total and possibly find a quicker method of calculation than
repeated addition.
Students will be able to make equal sets of
objects up to 5 and check their work by rote
counting.
(Level 3)
Students will be involved in a similar activity to the above but the
number of objects in a set is limited to 5. At a lower level, the
students will be involved in matching equal sets of objects and at a
further lower level, the students will drop equal amount of objects
into two containers.
3.1b Share a number of items
into equal groups and then
include the concept of left
overs.
Students will be able to match equal sets of
objects.
(Level 2)
Students will be involved in grabbing and
dropping equal amounts of objects into two
containers and they follow the movement of the
object.
(Level 1)
Starter: The teacher shows the process of sharing equally a quantity of Students will separate a group of objects into
objects using two containers and lets the students discuss what s/he is three equal groups and they will be able to use
doing so s/he can understand the knowledge that the students have
this knowledge in everyday calculations.
about sharing. Same activity will be extended to include left overs.
(Level 4)
Students are organising a tea party and they have invited 3 close
friends at home. Mum has prepared a number of items and they help Students will separate a group of objects into two
equal groups.
her by distributing the items on the plates with each plate has to
(Level 3)
contain an equal number of items. Students can talk about the
process.
Students will separate a fixed number of objects
The teacher shows a picture of a circle with a number of objects in it
in equal amounts.
which the students have to reproduce a similar one through matching.
(Level 2)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
17
Students use the number of items given to make two equal groups
like the one shown.
Same activity can be presented on a touch screen and the students
drag the objects between two groups.
Students observe the other groups in the sharing activity and they
might be involved by grasping and releasing the objects.
Students will experience and may be involved in
separating a set of interlocking objects.
(Level 1)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
18
Subject:
Unit code and title:
Strand 3:
MATHEMATICS
MTH 8.2 Angles (Levels 7.1 – 8.1)
Shape, Space and Measures
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Estimate the size of an angle and use a protractor to measure and draw angles up to 360°.
2. Solve problems involving angles at a point, angles on a straight line and vertically opposite angles; solve problems involving parallel lines.
3. Find unknown angles in triangles and quadrilaterals.
4. Understand a proof that the exterior angle of a triangle is equal to the sum of the two interior opposite angles.
Key Words
Degrees, acute, obtuse, right
and reflex angles, revolution,
protractor, estimate, measure.
Points to Note
Angles at a point, angles on a
straight line, vertically opposite
angles, exterior angles, interior
angles, proof.
Exposition: the teacher states the objectives of the lesson and may use ICT
software for students to practise new knowledge. This is consolidated by
setting students tasks that offer students the opportunity to apply
mathematics to a variety of real life situations.
Parallel lines, intersecting lines,
corresponding angles, alternate
angles, interior angles between
parallel lines, supplementary
angles.
Discovery: the teacher can set group tasks in which students discuss and
construct mathematical knowledge. Students may become active learners
while testing hypotheses and/or making generalisations.
Triangle (equilateral, isosceles,
scalene, right-angled) and
quadrilateral.
Resources
FOM B2, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to promote a
Resource Pack - Chapter 3
student centred learning environment.
Exploration: the teacher integrates an inquiry based learning approach that
enhances the students’ understanding of concepts. These tasks might
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Show-me boards
Protractors and rulers
Dynamic Geometry Software (Cabrigeometre or GeoGebra -free download
for teachers and students)
Internet Links:
http://www.amblesideprimary.com/ambl
eweb/mentalmaths/angleshapes.html
http://www.mathwarehouse.com/interac
tive/
19
Teaching Objective
The teacher will teach the
students to:
1. Estimate the size of an angle
and use a protractor to
measure and draw angles up
to 360°.
Examples of teaching experiences and activities
Mental Starter: The teacher asks questions to find out what students already
know about angles: - What is an angle? - How do you measure an angle?
The teacher reinforces the fact that an angle is an amount of turn, and that
one whole revolution amounts to 360°. The class revises the vocabulary
‘acute, right, obtuse, reflex angles, straight line, whole turn/revolution’. The
students use their show-me board to draw the type of angle indicated by
the teacher. In this way students are also learning to estimate the size of
angles.
The teacher draws two intersecting lines on the board. Students are asked
to identify the type of angles formed between the two lines and estimate
their size.
Game for angle estimation:
http://www.mathplayground.com/alienangles.html
The teacher draws an angle on the (interactive) whiteboard and asks a
student to come out and explain how a protractor can be used to measure
and draw angles, and what common mistakes they need to look out for.
Indicators of Learning outcomes
Students will be able to estimate,
measure and draw angles up to 360°.
(Level 8.1)
Students will be able to estimate,
measure and draw angles up to 180°.
(Level 7.3)
Students will be able to estimate and
measure angles up to 180°.
(Level 7.2)
Students will be able to estimate angles
up to 180°.
(Level 7.1)
Students are asked how they would draw angles of 200°, 320° and discuss
different methods that can be used to draw reflex angles.
Pair-work on the use of the protractor: A set of cards is given to each pair
of students. These cards show different angles, including reflex angles. One
student will draw the angle showing that amount of degrees on the back
side of the card. The other student will measure the angle using a protractor
and will then check that the answer is correct. The student doing the
checking must check the accuracy of the other student’s drawing. The
students’ roles will be reversed for each card.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
20
2. Solve problems involving
angles at a point, angles on a
straight line and vertically
opposite angles; solve
problems involving parallel
lines.
Students are asked to draw examples of angles at a point, vertically opposite
angles and angles on a straight line on their show-me boards. They can
discuss in pairs angle facts concerned.
Investigation using Dynamic Geometry Software:
Students, working in pairs, are given one diagram that includes parallel lines,
angles on a straight line, angles at a point, vertically opposite angles. The
students measure the angles formed using Dynamic Geometry Software.
Students can manipulate the diagram to change the angles, leaving the lines
parallel. Discussion of results follows.
Students will be able to find missing
angles in geometric diagrams by forming
and solving algebraic equations.
(Level 8.1)
Students will be able to solve simple
problems involving angles at a point,
angles on a straight line, vertically
opposite angles, and angles formed by a
transversal on parallel lines.
(Level 7.3)
Students will be able to identify vertically
opposite angles and angles formed by a
transversal on parallel lines in diagrams.
(Level 7.2)
Students will be able to calculate missing
angles using the facts that angles at a
point add up to 360° and angles on a
straight line are supplementary.
(Level 7.1)
3. Find unknown angles in
triangles and quadrilaterals.
a) Angles in a Triangle
Students are each asked to draw a triangle and measure the angles using a
protractor. Compare the answers. (This activity can also be done through
Dynamic Geometry Software, where students manipulate a triangle to
produce different angles.)
Students discuss a geometrical proof for the angle sum of triangles. A
possible proof: Draw a triangle and extend one of the sides. Construct a line
parallel to one of the sides. Use alternate angles, corresponding angles and
angles on a straight line to prove that the angle sum of triangle is 180.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to find the interior
angles in regular polygons.
(Level 8.1)
Students will be able to work out missing
angles in complex diagrams involving
triangles and quadrilaterals.
(Level 7.3)
Students will be able to understand that
the angle sum of a quadrilateral is 360
21
An alternative proof is found on FOM B2 p.26.
and to find missing angles.
(Level 7.2)
a
b
a
b
Students will be able to find unknown
angles in any type of triangle.
(Level 7.1)
b) Angles in a quadrilateral
Students are asked to use the sum of angles in a triangle to deduce the sum
of the angles in a quadrilateral, by drawing a diagonal in a quadrilateral thus
dividing it into two triangles. Discuss ‘special quadrilaterals’ like squares and
rectangles.
Consolidation and practice: Finding missing angles of quadrilaterals and
triangles, including isosceles and equilateral triangles. Students can also be
asked to create their own examples and give them to their class partners to
solve.
the work done on angles and triangles:
http://www.bbc.co.uk/schools/ks2bitesize/maths/shape_space/angles/play
_popup.shtml
4. Understand a proof that the
exterior angle of a triangle is
equal to the sum of the two
interior opposite angles.
Problem-solving task (in pairs): Students are given a task where they are
asked to find the missing interior angles and exterior angle of a triangle
where one side is extended. Students then discuss why the exterior angle of
a triangle is equal to the sum of the two interior opposite angles. Encourage
the students to write down their reasoning.
Students discuss their observations as a whole class and deduce a general
proof.
Students apply the theorem to find missing exterior or interior angles in
triangles.
Concluding activity: Teacher divides class in groups. Each group produces a
poster to highlight all that they have learnt about angles. The posters are
then presented to the rest of the class.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to write a general
proof that the exterior angle of a triangle
is equal to the sum of the two interior
opposite angles.
(Level 8.1)
Students will be able to understand a
proof that the exterior angle of a triangle
is equal to the sum of the two interior
opposite angles.
(Level 7.3)
Students will be able to find the value of
an exterior angle of a triangle given the
22
two interior opposite angles
(Level 7.2)
Students will know that in a triangle an
exterior and its adjacent interior angle
add up to 180°.
(Level 7.1)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
23
Subject:
Unit code and title:
Strand 3:
MATHEMATICS
MTH 8.2 Angles (Levels 6.3 – 7.3)
Shape, Space and Measures
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Estimate the size of an angle and use a protractor to measure and draw angles up to 180°.
2. Solve problems involving angles at a point, angles on a straight line and vertically opposite angles; solve problems involving parallel lines.
3. Find unknown angles in triangles and quadrilaterals.
4. Understand a proof that the exterior angle of a triangle is equal to the sum of the two interior opposite angles.
Key Words
Degrees, acute, obtuse, right
and reflex angles, revolution,
protractor, estimate, measure.
Points to Note
Angles at a point, angles on a
straight line, vertically opposite
angles, exterior angles, interior
angles, proof.
Exposition: the teacher states the objectives of the lesson and may use ICT
software for students to practise new knowledge. This is consolidated by
setting students tasks that offer students the opportunity to apply
mathematics to a variety of real life situations.
Parallel lines, intersecting lines,
corresponding angles, alternate
angles, interior angles between
parallel lines, supplementary
angles.
Discovery: the teacher can set group tasks in which students discuss and
construct mathematical knowledge. Students may become active learners
while testing hypotheses and/or making generalisations.
Triangle (equilateral, isosceles,
scalene, right-angled) and
quadrilateral.
Resources
FOM B1, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to promote a
Resource Pack - Chapter 3
student centred learning environment.
Exploration: the teacher integrates an inquiry based learning approach that
enhances the students’ understanding of concepts. These tasks might
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Show-me boards
Protractors and rulers
Dynamic Geometry Software (Cabrigeometre or GeoGebra -free download
for teachers and students)
Internet Links:
http://www.amblesideprimary.com/ambl
eweb/mentalmaths/angleshapes.html
http://www.mathwarehouse.com/interac
tive/
http://www.bbc.co.uk/schools/ks2bitesiz
e/maths/
24
Teaching Objective
The teacher will teach the
students to:
1. Estimate the size of an angle
and use a protractor to
measure and draw angles up
to 180°.
Examples of teaching experiences and activities
Mental Starter: The teacher asks questions to find out what students already
know about angles:
- What is an angle? - How do you measure an angle?
The teacher reinforces the fact that an angle is an amount of turn, and that
one whole revolution amounts to 360°. The class revises the vocabulary
‘acute, right, obtuse, reflex angles, straight line, whole turn/revolution’. The
students can use the show-me board to draw the type of angle which is
indicated by the teacher. In this way students are also learning to estimate
the size of angles.
The teacher draws two intersecting lines on the board. Students are asked
to identify the type of angles formed between the two lines and estimate
their size.
Game for angle estimation:
http://www.mathplayground.com/alienangles.html
Indicators of Learning outcomes
Students will be able to estimate,
measure and draw angles up to 180°.
(Level 7.3)
Students will be able to estimate and
measure angles up to 180°.
(Level 7.2)
Students will be able to estimate angles
up to 180°.
(Level 7.1)
Students will distinguish between acute,
right, obtuse and reflex angles.
(Level 6.3)
The teacher draws an angle on the (interactive) whiteboard and asks a
student to come out and explain how a protractor can be used to measure
and draw angles, and what common mistakes they need to look out for.
Pair-work on the use of the protractor:
A set of cards is given to each pair of students. These cards show different
acute and obtuse angles. One student will draw the angle showing that
amount of degrees on the back side of the card. The other student will
measure the angle using a protractor and will then check that the answer is
correct. The student doing the checking must check the accuracy of the
other student’s drawing. The students’ roles will be reversed for each card.
2. Solve problems involving
angles at a point, angles on a
straight line and vertically
opposite angles; solve
problems involving parallel
The teacher asks the students to draw examples of angles at a point,
vertically opposite angles and angles on a straight line on their show-me
boards. They can discuss in pairs the angle facts concerned.
Investigation using Dynamic Geometry Software:
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to solve simple
problems involving angles at a point,
angles on a straight line, vertically
opposite angles, and angles formed by a
transversal on parallel lines.
25
lines.
Students working in pairs are given one diagram that includes parallel lines,
angles on a straight line, angles at a point, vertically opposite angles. The
students measure the angles formed using Dynamic Geometry Software.
Students can manipulate the diagram to change the angles, leaving the lines
parallel. Discussion of results follow.
(Level 7.3)
Students will be able to identify vertically
opposite angles and angles formed by a
transversal on parallel lines in diagrams.
(Level 7.2)
Students will be able to calculate missing
angles using the facts that angles at a
point add up to 360° and angles on a
straight line are supplementary.
(Level 7.1)
Students will be able to identify parallel
lines in diagrams.
(Level 6.3)
3. Find unknown angles in
triangles and quadrilaterals.
a) Angles in a Triangle
Students are each asked to draw a triangle and measure the angles using a
protractor. Compare the answers. (This activity can also be done through
Dynamic Geometry Software, where students manipulate a triangle to
produce different angles.)
Students discuss a geometrical proof for the angle sum of triangles. A
possible proof: Draw a triangle and extend one of the sides. Construct a line
parallel to one of the sides. Use alternate angles, corresponding angles and
angles on a straight line to prove that the angle sum of triangle is 180.
a
b
a
b
b) Angles in a quadrilateral
Students are asked to use the sum of angles in a triangle to deduce the sum
of the angles in a quadrilateral, by drawing a diagonal in a quadrilateral thus
dividing it into two triangles. Discuss ‘special quadrilaterals’ like squares and
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to work out missing
angles in complex diagrams involving
triangles and quadrilaterals.
(Level 7.3)
Students will be able to understand that
the angle sum of a quadrilateral is 360
and find missing angles.
(Level 7.2)
Students will be able to find unknown
angles in any type of triangle.
(Level 7.1)
Students will be able to find unknown
angles in scalene triangles.
(Level 6.3)
26
rectangles.
Consolidation and practice: Finding missing angles of quadrilaterals and
triangles, including isosceles and equilateral triangles. Students can also be
asked to create their own examples and give them to their class partners to
solve.
Students can use the following game to consolidate the work done on angles
and triangles:
http://www.bbc.co.uk/schools/ks2bitesize/maths/shape_space/angles/play
_popup.shtml
4. Understand a proof that the
exterior angle of a triangle is
equal to the sum of the two
interior opposite angles.
Problem-solving task (in pairs): Students are given a task where they are
asked to find the missing interior angle and exterior angle of a triangle
where one side is extended. Students then discuss why the exterior angle of
a triangle is equal to the sum of the two interior opposite angles. Encourage
the students to write down their reasoning.
Students discuss their observations as a whole class and deduce a general
proof.
Students apply the theorem to find missing exterior or interior angles in
triangles.
Concluding activity: Teacher divides class in groups. Each group produces a
poster to highlight all that they have learnt about angles. The posters are
then presented to the rest of the class.
Students will be able to understand a
proof that the exterior angle of a triangle
is equal to the sum of the two interior
opposite angles.
(Level 7.3)
Students will be able to find the value of
an exterior angle of a triangle given the
two interior opposite angles
(Level 7.2)
Students will know that in a triangle an
exterior and its adjacent interior angle
add up to 180°.
(Level 7.1)
Students will know that angles in a
triangle add up to 180°, and angles on a
straight line add up to 180°.
(Level 6.3)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
27
Subject:
Unit code and title:
Strand 3:
MATHEMATICS
MTH 8.2 Angles (Levels 5.3 – 7.1)
Shape, Space and Measures
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Understand that a revolution is divided into 360 parts called degrees; estimate the size of an angle and distinguish between acute, right, obtuse and
reflex angle.
2. Use a protractor to measure and draw angles up to 180.
3. Solve problems involving angles at a point and angles on a straight line.
4. Find unknown angles in triangles.
Key Words
Whole turn, revolution,
degrees.
Acute, right, obtuse and reflex
angles.
Protractor, estimate, measure.
Angles at a point, angles on a
straight line.
Triangles: equilateral, isosceles,
scalene, right-angled.
Points to Note
Resources
FOM B Gold, Students’ Book, Resource
Three main teaching approaches are being recommended to promote a
Pack - Chapter 3
student centred learning environment.
Exposition: the teacher states the objectives of the lesson and may use ICT
software for students to practise new knowledge. This is consolidated by
setting students tasks that offer students the opportunity to apply
mathematics to a variety of real life situations.
Discovery: the teacher can set group tasks in which students discuss and
construct mathematical knowledge. Students may become active learners
while testing hypotheses and/or making generalisations.
Exploration: the teacher integrates an inquiry based learning approach that
enhances the students’ understanding of concepts. These tasks might
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Show-me boards,
Protractors and rulers
Dynamic Geometry Software (Cabrigeometre or GeoGebra -free download
for teachers and students)
Internet links:
http://www.amblesideprimary.com/amblewe
b/mentalmaths/protractor.html
http://www.mathplayground.com/alienangles.html
http://www.bbc.co.uk/schools/ks2bitesize/maths
http://www.echalk.co.uk/Maths/angleEstimat
or/EstimatingAngles.htm
http://www.bbc.co.uk/schools/ks2bitesize/m
aths/shape_space/angles/play.shtml
http://www.bbc.co.uk/keyskills/flash/kfa/kfa.shtml
28
Teaching Objective
The teacher will teach the
students to:
1. Understand that a revolution
is divided into 360 parts
called degrees; estimate the
size of an angle and
distinguish between acute,
right, obtuse and reflex
angle.
Examples of teaching experiences and activities
Students are asked: ‘What is an angle?’ Using Dynamic Geometry Software
on the interactive whiteboard (or the ilearn maths toolbox software) the
teacher draws and marks an angle and sets it at 0. A student is asked to
come out and turn one of the ‘arms’ to form an angle.
The teacher sets Dynamic Geometry Software to show the size in degrees of
a marked angle. A student comes out and turns one arm of the angle to
show the increasing size of the angle in degrees. This will also show that one
whole revolution/one whole turn amounts to 360°.
Class activity: Students are asked to start opening their arms and form an
angle of 90°. What is this angle called? Right angle. This is repeated for 180°
(a straight line) and 270°.
This activity is extended to revise the terms ‘acute angle’, ‘obtuse angle’ and
‘reflex angle’ by showing such angle using their arms and demonstrating this
on the whiteboard. For each type of angle students are asked to give an
estimate for their angle.
Game for angle estimation: www.mathplayground.com/alienangles.html
Card-matching game: Students work in pairs. They are presented with a set
of cards which they need to match in sets of 3 – one card showing a drawn
angle, another showing the amount of degrees(through estimation only) and
the third indicating the type of angle (right, acute, obtuse, reflex, straight
line, whole turn). Once matched, the sets of cards are placed in order of size
on their desks.
2. Use a protractor to measure
and draw angles up to 180.
The teacher draws an angle on the (interactive) whiteboard and asks a
student to come out and explain how a protractor can be used to measure
and draw angles. Different students take turns in estimating an angle,
identifying the type of angle and then measuring it on the whiteboard.
Discuss common mistakes they need to look out for when using a
protractor.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Indicators of Learning outcomes
Students will be able to estimate angles
up to 180°.
(Level 7.1)
Students will distinguish between acute,
right, obtuse and reflex angles.
(Level 6.3)
Students will know that a revolution is
made up of 360.
(Level 6.2)
Students will understand that a whole
turn is equivalent to 4 right angles and
half a turn is equivalent to 2 right angles
(Level 6.1)
Students will be able to recognise right
angles in 2D shapes and understand that
a right angle is a quarter turn.
(Level 5.3)
Students will be able to use a protractor
to measure and draw angles up to 180°.
(Level 7.1)
Students will be able to use a protractor
to measure angles up to 180°.
(Level 6.3)
29
Pair-work on the use of protractor:
A set of cards is given to each pair of students. These cards show different
acute and obtuse angles. One student will draw the angle showing that
amount of degrees on the back side of the card. The other student will
measure the angle using a protractor and will then check that the answer is
correct. The student doing the checking must check the accuracy of the
other student’s drawing. The students’ roles will be reversed for each card.
Suitable websites for estimating and measuring angles:
http://www.echalk.co.uk/Maths/angleEstimator/EstimatingAngles.htm
http://www.amblesideprimary.com/ambleweb/mentalmaths/protrac
tor.html
http://www.bbc.co.uk/schools/ks2bitesize/maths/shape_space/angle
s/play.shtml
http://www.bbc.co.uk/keyskills/flash/kfa/kfa.shtml
http://www.bbc.co.uk/apps/ifl/schools/ks2bitesize/maths/quizengine
?quiz=angles&templateStyle=maths
http://www.interactivestuff.org/match/maker.phtml?featured=1&id=13
http://www.edu.dudley.gov.uk/numeracy/Primary/Easter%20CD/pro
grams/angle_challenge.swf
3. Solve problems involving
angles at a point and angles
on a straight line.
Students are asked to draw a straight line on their show-me board, then
mark and indicate the amount of degrees on the line.
Students work in pairs: Students are given a set of 8 card sectors (each card
marked with its measured angle) and they have to choose two/three of
them which make up a straight line. Encourage different combinations.
Class discussion to share the students’ different responses and discuss why
the angles form a straight line. Students discuss how they could find one
missing angle if the other angle/s on a straight line are known.
The same activity above is repeated for angles at a point. Students share
their combinations and discuss why the form one revolution and how they
could find one missing angle if the other angles are given.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to use a protractor
to measure and draw angles in multiples
of 5 up to 180.
(Level 6.2)
Students will be able to use a protractor
to measure and draw angles in multiples
of 10 up to 180.
(Level 6.1)
Students will be able to measure and
draw angles of 90 and 180.
(Level 5.3)
Students will be able to calculate missing
angles using the facts that angles at a
point add up to 360° and angles on a
straight line are supplementary.
(Level 7.1)
Students will be able to work missing
angles in diagrams involving angles at a
point.
(Level 6.3)
Students will be able to identify angles at
a point in given diagrams.
30
Activity in pairs using Dynamic Geometry Software: Students are given a set
of diagrams involving angles on a straight line or angles at a point. Students
have to first calculate the missing angles on a straight line/at a point. They
then check their answer by measuring the angle using the software.
Students can manipulate the diagrams on screen to create their own
examples.
(Level 6.2)
Students will be able to work out missing
angles in diagrams involving angles on a
straight line.
(Level 6.1)
Students will be able to identify angles on
a straight line in given diagrams.
(Level 5.3)
4. Find unknown angles in
triangles.
Students are asked to come out and draw different triangles on the
(interactive whiteboard). Class distinguishes between different types of
triangles – scalene, isosceles and equilateral.
Activity in pairs using protractor and paper or using Dynamic geometry
software:
Students are asked to draw a triangle and measure the angles. They put
their data in a table and discuss in pairs their observations on the sum of the
angles. This is repeated for different triangles. Class discussion to compare
the students’ answers, is held.
Investigation: Students draw a triangle on a piece of paper and cut out the
triangle. They shade and cut out the three angles, and fit them together.
The angles will form a straight line.
Concluding activity: Teacher divides class in groups. Each group produces a
poster to highlight all that they have learnt about angles. The posters are
then presented to the rest of the class.
Students will be able to find unknown
angles in any type of triangle.
(Level 7.1)
Students will be able to find unknown
angles in scalene triangles.
(Level 6.3)
Students will be able to understand that
the angles in a triangle add up to 180.
(Level 6.2)
Students will be able to identify different
types of triangles (scalene, isosceles,
right-angled and equilateral triangles).
(Level 6.1)
Students will be able to distinguish
triangles from other shapes.
(Level 5.3)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
31
Subject:
Mathematics
Unit code and title: MTH 8.2 Angles (Levels 1 - 4)
Strand 3:
Shape, Space & Measures
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives at attainment Level 5 and 6
The teacher will teach the students to:
1. Understand that a revolution is divided into 360 parts called degrees; estimate the size of an angle, and distinguish between acute, right, obtuse
and reflex angle.
2. Use a protractor to measure and draw angles up to 180°.
3. Solve problems involving angles at a point and angles on a straight line.
4. Find unknown angles in triangles.
Objectives at attainment levels 1, 2, 3, 4 (The mainstream objective 2 is beyond level 4 and below.)
The teacher will teach the students to:
1.1 Start tracking objects within their field of awareness and distinguish between whole turn and half turn movement and indicate whether an angle is a
right angle, less than half a turn or more.
3.1 Become aware of the angle positions in a shape.
4.1 Move around a square by following given directions.
Key Words
Points to Note
Resources
Angle, right angle, estimate,
measure, less than, greater
than, half turn, whole turn.
In addition to the points to note recommended for students performing at
Level 5 or higher, it is very important for the teacher to allow time for the
students to respond. This response can take the form of unaided and/or
aided means of communication and the teacher needs to provide adequate
scaffolding techniques to enable the students to respond affectively or
intentionally.
Visual cards, plasticine, salt, sand tray, touch
screen, interactive whiteboard, big mac or
any other adapted mouse.
New Maths Frame Working Step Up
Workbook.
Oxford Framework Maths 7
Software: Ilearn Maths, Calculator, Excel
Worksheets, Protractor and compass on the
IWB.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
32
Teaching Objective
The teacher will teach the
students to:
1.1 Start tracking objects
within their field of
awareness and
distinguish between
whole and half turn
movement and indicate
whether an angle is a
right angle, less than half
a turn or more.
Examples of teaching experiences and activities
Starter: The teacher starts the lesson by marking a point on the IWB and
then, using the online compass the teacher draws a line from that point.
During this time, she will observe whether some students can track a
moving object whilst listening to others who will talk about the different
diagrams. This will be the starter activity to help the teacher identify where
the students are in their learning. Also, the teacher uses the ilearn maths
software to show the whole and half turn of the angle. Students will talk
about it.
Students are presented with a timer which is timed to make a whole turn. At
the starting point a piece of blu tac is fixed to the timer. Meanwhile they are
asked to continue an activity to their liking but when the timer rings they
have to stop. This activity can be extended to other situations like a child
walking in a path – they have to show and talk about the whole path back to
the starting point. Moreover, different angle movements are shown on the
IWB and they talk about whether the angles shown are smaller/greater,
less/more than half a turn.
Students are presented with a series of V strokes representing acute, obtuse
and reflex without mentioning the terminology. They are to focus on the
similarities and differences and talk about them like some VVV are wider
than the others. Some students are then asked to draw similar shapes in
imitation and to sort them according to the angle. Students will be shown an
angle and given three pictures at a time they have to compare and match
which angle is the same as the picture shown.
Indicators of Learning outcomes
Students will mark or tick the right angles,
sort the shapes into categories of right angle,
and those that are bigger/smaller than a right
angle.
(Level 4)
Students will talk about and write whether
the angle given has made a whole or half
turn.
(Level 3)
Students will be able to fill angle points with
colour and sort pictures according to angle
category.
(Level 2)
Students will follow an object, visually,
moving past their midline.
(Level 1)
Students are given various pictures with dotted lines around them. They use
finger painting to join the dots thus showing the whole turn that one makes
from end to the other. Students will sort objects or pictures containing right
angles, acute and obtuse angles (terminology not mentioned).
The adult rests her elbow with palms together, as if she is praying, and then
starts to move one palm and then both palms are open to different degrees
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
33
in opposite directions. Students follow this open and close movement.
3.1 Become aware of the
angle positions in a
shape.
Links that can be used are:
http://www.primaryresources.co.uk/online/powerpoint/rightangles.swf
http://www.mathsisfun.com/flash.php?path=/geometry/images/anglesdrag
http://www.skola.gov.mt/maths/Spreadsheets_for_Primary/Measuring_An
gles.xls
http://www.bbc.co.uk/apps/ifl/schools/ks2bitesize/maths/quizengine?quiz=
angles&templateStyle=maths
http://www.bbc.co.uk/schools/ks2bitesize/maths/shape_space/angles/play.
shtml
Starter: Various shapes are drawn on the IWB and the students have to
circle the vertices.
Students use straws to make a shape and they have to colour the turning
points. Then they are given other shapes and they have to mark the angles.
Eventually, they will count the angles and comment about their sizes.
Students are given shapes with marked angles and they have to match the
shapes with the same coloured angles and same number of angles.
4.1 Move around a square
by following given
directions.
Students will mark the angles in a shape and
write the number of angles as well as talk
about the size of these angles.
(Level 4)
Students will match and talk about their
choice of shapes with the same angles. E.g.
same inside angle colour. They can also count
how many angles each shape has.
(Level 3)
Students will be presented with the same shape but in various sizes and they
sort the shapes according to the size.
Students will sort shapes by their size.
(Level 2)
Students will experience the angle turns in a shape.
Students will encounter and experience
activities related with the shape and its
space.
(Level 1)
Starter: Students are given a grid and asked particular questions about
Students will follow the trail according to the
directional movement like up, down, left, right, forward and backwards.
instructions given thus showing
Students are presented with a number grid or letter or shape grid. They are
understanding of directionality.
given particular instructions like start at 1 move 3 up, then 2 right etc.
(Level 4)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
34
Previous activity can be adapted to include just the instructions, go on
number 1 then number 5 and the students find their way about whilst
counting their moves.
Students will be given a four by four grid and they point to the named
object.
Students are presented with an eye track board with two pictures. They
skim and stop to focus on the named object.
E.g.
Students will show that they can follow
instructions to go to a particular point after
they have taken a certain path.
(Level 3)
Students will skim through the pictures and
show the position of a requested object by
pointing or otherwise.
(Level 2)
Students will look at the board, skim through
it and focus on the requested object.
(Level 1)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
35
Subject:
Unit code and title:
Strand 1:
MATHEMATICS
MTH 8.3 Fractions (Levels 7.1 – 8.1)
Number
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Write a fraction that is equivalent to another fraction and change improper fractions to mixed numbers and vice-versa.
2. Add and/or subtract two fractions, including mixed numbers.
3. Arrange fractions in ascending /descending order; understand that the reciprocal of a number is its multiplicative inverse.
4. Multiply and divide one fraction by another fraction, excluding mixed numbers.
5. Solve problems involving fractions.
Key Words
Fraction, equivalent, proper,
improper, mixed number,
ascending, descending,
common denominator, least
common multiple, L.C.M.,
reciprocal, multiplicative
inverse.
Points to Note
Resources
Three main teaching approaches are being recommended to promote a FOM B2, Students’ Book, Practice Book,
student centred learning environment.
Resource Pack - Chapter 10, Chapter 13,
Chapter 23 and Chapter 25.
Exposition: the teacher states the objectives of the lesson and may use ICT
software for students to practice new knowledge. This is consolidated by Interactive Whiteboard Activities.
setting students tasks that offer students the opportunity to apply i-learn Maths toolbox from IWB software.
mathematics to a variety of real life situations.
i-learn Maths lessons from IWB folder.
Discovery: the teacher can set group tasks in which students discuss and Fraction Magnets, Fraction Tiles,
construct mathematical knowledge. Students may become active learners Fractions Circles, Fraction Strips, Apple
while testing hypotheses and/or making generalisations.
Fractions, Fraction Puzzle Cards (Pizza and
Cake), Fractions Kit, Fractions Lotto,
Exploration: the teacher integrates an inquiry based learning approach that Fraction Dominoes, Fraction Number
enhances the students’ understanding of concepts. These tasks might Fans, Fraction Bars.
employ the processes of reasoning, problem solving, investigations, Internet Links:
connecting ideas and concepts, and expressing results by using the precise www.mathgoodies.com/lessons/toc_vol4.shtm
www.mathsisfun.com
language of mathematics.
www.mathopolis.com
www.ixl.com
www.ictgames.com
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
36
Teaching Objective
The teacher will teach the
students to:
1. Write a fraction that is
equivalent to another
fraction and change
improper fractions to mixed
numbers and vice-versa.
Examples of teaching experiences and activities
Using any of the resources listed in the resource list and the IWB i-learn
Maths toolbox, the teacher can create games or group work to investigate
equivalent fractions. These resources also lend themselves to illustrate
mixed numbers and improper fractions.
Interactive activities for this objective can be practiced at:
http://www.ixl.com/math/grade-5/equivalent-fractions
http://www.mathsisfun.com/equivalent_fractions.html
http://www.math-aids.com/Fractions/
Worksheets WS 51S, 52E, 53S and 54E from Chapter 10, FOM B2 teacher’s
pack can be used for this objective.
2. Add and/or subtract two
fractions, including mixed
numbers.
Using any of the resources listed in the resource list and the IWB i-learn
Maths toolbox, the teacher can create games or group work to investigate
addition and subtraction of fractions. These resources also lend themselves
to be used for mixed numbers and improper fractions.
Lesson n8_3 from i-learn Maths lessons from IWB folder can be used for
adding fractions.
Interactive activities for this objective can be practiced at:
http://www.ixl.com/math/grade-5
http://www.mathsisfun.com/fractions_addition.html
http://www.mathsisfun.com/fractions_subtraction.html
http://www.math-aids.com/Fractions/
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Indicators of Learning outcomes
Students will be able to write a fraction
that is equivalent to another fraction and
change improper fractions to mixed
numbers and vice-versa.
(Level 8.1)
Students will be able to write a fraction
that is equivalent to another fraction and
change improper fractions to mixed
numbers.
(Level 7.3)
Students will be able to write a fraction
that is equivalent to another fraction.
(Level 7.2)
Students will be able to compare
equivalent fractions using fraction charts
etc.
(Level 7.1)
Students will be able to add and subtract
mixed numbers in parts: first the wholes,
then the fractions.
(Level 8.1)
Students will be able to add and subtract
mixed numbers by expressing them as
improper fractions, using both equivalent
fractions and L.C.M.
(Level 7.3)
Students will be able to add and subtract
two fractions with different
37
http://www.ixl.com/math/grade-5/least-common-denominator
Worksheets WS 51S, 52E, 53S and 54E from Chapter 10, and WS 62S from
Chapter 13 on L.C.M., FOM B2 teacher’s pack can be used for this objective.
3. Arrange fractions in
ascending/descending order;
understand that the
reciprocal of a number is its
multiplicative inverse.
Use activities and resources for equivalent fractions to arrange in ascending
or descending order.
Interactive activities for this objective can be practiced at:
http://www.ixl.com/math/grade-5/order-fractions-from-least-to-greatest
http://www.ixl.com/math/grade-5/compare-fractions-and-mixed-numbers
http://www.ixl.com/math/grade-5/reciprocals
http://www.mathopolis.com/games/ordering-frac.php
http://www.mathsisfun.com/reciprocal-fraction.html
http://www.ictgames.com/equivalence.html
Worksheet WS 62S from Chapter 13, FOM B2 teacher’s pack can be used for
practising finding L.C.Ms.
Worksheet WS 96S from Chapter 23, FOM B2 teacher’s pack can be used for
work with reciprocals.
denominators, using equivalent fractions.
(Level 7.2)
Students will be able to add and
subtract two fractions with same
denominator.
(Level 7.1)
Students will be able to manipulate
reciprocals as multiplicative inverses of
fractions and whole numbers.
(Level 8.1)
Students will be able to understand that
multiplication and division are functions
1
opposite to each other and that 𝑥 and x
are multiplicative inverses of each other,
called reciprocals of each other.
(Level 7.3)
Students will be able to arrange fractions
(denominators having common multiples)
in ascending/descending order using
LCM.
(Level 7.2)
Students will be able to arrange a set of
fractions (with denominators 2, 5 or 10)
on a number line from 0 to 1 (divided in
tenths).
(Level 7.1)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
38
4. Multiply and divide one
fraction by another fraction,
excluding mixed numbers.
Using fraction bars and blocks, the teacher demonstrates, then the students
investigate dividing a fraction by a whole number. From this the students
are lead to work division of a fraction by multiplying it with the
multiplicative inverse of the divisor.
Practice of the above by various worksheets and exercises.
Worksheets WS 95S and 96S from Chapter 23, FOM B2 teacher’s pack can
be used for this objective.
Interactive activities for this objective can be found at:
http://www.mathsisfun.com/numbers/fractions-division-wholenumbers.html
http://www.mathsisfun.com/fractions_multiplication.html
http://www.mathsisfun.com/fractions_division.html
http://www.ixl.com/math/grade-5/multiply-two-fractions
http://www.ixl.com/math/grade-5/divide-fractions
5. Solve problems involving
fractions.
Students in pairs or in groups discuss different problems and work together
to find proper solutions. Various worksheets and exercises may be used.
Worksheets WS 52E, 53S, 54E, 62S and 95S from FOM B2 teacher’s pack
may be used for this objective.
The following sites may be used:
http://www.ixl.com/math/grade-5/add-subtract-multiply-and-dividefractions-and-mixed-numbers-word-problems
http://www.primaryresources.co.uk/maths/pdfs/9harryfrac.pdf
http://math.about.com/library/fractionsa.pdf
Additional practice can be done by using National Tests style questions,
FOM B2 teacher’s pack, pages 263 – 271.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to multiply and
divide one fraction by another fraction
without using the calculator; numerators
and denominators may or may not be
simplified.
(Level 8.1)
Students will be able to multiply and
divide one fraction by another fraction
without using the calculator, numerators
and denominators can be simplified.
(Level 7.3)
Students will be able to multiply one
fraction by another without the use of the
calculator.
(Level 7.2)
Students will be able to simplify fractions
by cancelling.
(Level 7.1)
Students will be able to solve problems in
addition and subtraction involving mixed
numbers, and multiplication and division
involving fractions but not mixed
numbers.
(Level 8.1)
Students will be able to solve problems in
finding fractions of a quantity.
(Level 7.3)
Students will be able to solve simple
problems in addition and subtraction of
39
fractions with different denominators.
(Level 7.2)
Students will be able to solve simple
problems in addition and subtraction of
fractions with same denominator.
(Level 7.1)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
40
Subject:
Unit code and title:
Strand 1:
MATHEMATICS
MTH 8.3 Fractions (Levels 6.3 – 7.3)
Number
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Write a fraction that is equivalent to another fraction and reduce a fraction to its simplest form by cancelling common factors.
2. Add and/or subtract two fractions.
3. Arrange fractions in ascending / descending order.
4. Work out the fraction of a quantity.
5. Solve simple problems involving fractions.
Key Words
Fraction, equivalent, improper,
reduce, simplest form,
cancelling common factors,
mixed number, ascending
order, descending order.
Points to Note
Resources
FOM B1, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to promote a
Resource Pack - Chapter 10, Chapter 13
student centred learning environment.
and Chapter 25.
Exposition: the teacher states the objectives of the lesson and may use ICT Interactive Whiteboard Activities.
software for students to practice new knowledge. This is consolidated by i-learn Maths toolbox from IWB software.
setting students tasks that offer students the opportunity to apply i-learn Maths lessons from IWB folder.
mathematics to a variety of real life situations.
Fraction Magnets, Fraction Tiles,
Discovery: the teacher can set group tasks in which students discuss and Fractions Circles, Fraction Strips, Apple
construct mathematical knowledge. Students may become active learners Fractions, Fraction Puzzle Cards (Pizza and
while testing hypotheses and/or making generalisations.
Cake), Fractions Kit, Fractions Lotto,
Fraction Dominoes, Fraction Number
Exploration: the teacher integrates an inquiry based learning approach that Fans, Fraction Bars.
enhances the students’ understanding of concepts. These tasks might Internet Links:
employ the processes of reasoning, problem solving, investigations, www.mathgoodies.com/lessons/toc_vol4.shtm
connecting ideas and concepts, and expressing results by using the precise www.mathsisfun.com
language of mathematics.
www.mathopolis.com
www.ixl.com
www.ictgames.com
http://www.bbc.co.uk/skillswise/maths/games
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
41
Teaching Objective
The teacher will teach the
students to:
1. Write a fraction that is
equivalent to another
fraction and reduce a
fraction to its simplest form
by cancelling common
factors.
Examples of teaching experiences and activities
Using any of the resources listed in the resource list and the IWB i-learn
Maths toolbox, the teacher can create games or group work to investigate
equivalent fractions.
Interactive activities for this objective can be practiced at:
http://www.ixl.com/math/grade-5/equivalent-fractions
http://www.mathsisfun.com/equivalent_fractions.html
http://www.math-aids.com/Fractions/
Worksheets WS 51S and 52E, from Chapter 10, FOM B1 teacher’s pack can
be used for this objective.
Worksheets WS 51S and 52E from Chapter 10, FOM B2 teacher’s pack can
be used for this objective.
Lessons n2_18 and n2_19 from i-learn Maths lessons from IWB folder can be
used for this objective.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Indicators of Learning outcomes
Students will be able to express whole
numbers and fractions into different
equivalent fractions.
(Level 7.3)
Students will be able to reduce a fraction
to its simplest form by cancelling
common factors.
(Level 7.2)
Students will be able to use equivalent
fractions in comparing/ordering fractions.
(Level 7.1)
Students will be able to write equivalent
fractions by multiplying or dividing
numerator and denominator by a scale
factor.
(Level 6.3)
42
2. Add and/or subtract two
fractions.
Using any of the resources listed in the resource list and the IWB i-learn
Maths toolbox, the teacher can create games or group work to investigate
addition and subtraction of fractions.
Lesson n8_3 from i-learn Maths lessons from IWB folder can be used for
adding fractions.
Interactive activities for this objective can be practiced at:
http://www.ixl.com/math/grade-5
http://www.mathsisfun.com/fractions_addition.html
http://www.mathsisfun.com/fractions_subtraction.html
http://www.math-aids.com/Fractions/
http://www.ixl.com/math/grade-5/least-common-denominator
Worksheets WS 53S and 54E from Chapter 10 and WS 67E from Chapter 13
on L.C.M., FOM B1 teacher’s pack can be used for this objective.
3. Arrange fractions in
ascending/descending order.
Worksheets WS 51S and 52E from Chapter 10 and WS 62S from Chapter 13
on L.C.M., FOM B2 teacher’s pack can be used for this objective.
Use activities and resources for equivalent fractions to arrange in ascending
or descending order.
Lesson n2_17 from i-learn Maths lessons from IWB folder can be used for
arranging halves on a number line.
Lesson n7_2 from i-learn Maths lessons from IWB folder can be used for
comparing and ordering fractions.
Interactive activities for this objective can be practiced at:
http://www.ixl.com/math/grade-5/order-fractions-from-least-to-greatest
http://www.mathopolis.com/games/ordering-frac.php
http://www.ictgames.com/equivalence.html
Worksheet WS 67E from Chapter 13, FOM B1 teacher’s pack can be used for
practising finding L.C.Ms.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to add and subtract
improper fractions, using both equivalent
fractions and L.C.M.
(Level 7.3)
Students will be able to add and subtract
two fractions with different denominators
using equivalent fractions.
(Level 7.2)
Students will be able to add and subtract
two fractions with same denominators.
(Level 7.1)
Students will be able to add and subtract
two fractions through fraction circles and
picture cards.
(Level 6.3)
Students will be able to arrange a set of
fractions in ascending/descending order.
(Level 7.3)
Students will be able to arrange fractions
(denominators having common multiples)
in ascending/descending order using
LCM.
(Level 7.2)
Students will be able to arrange a set of
fractions (with denominators 2, 5 or 10)
on a number line from 0 to 1 (divided in
tenths).
(Level 7.1)
43
4. Work out the fraction of a
quantity.
Worksheet WS 62S from Chapter 13, FOM B2 teacher’s pack can be used for
practising finding L.C.Ms.
Students will be able to understand that
numerators can be used to put fractions
in ascending/descending order when
there is a common denominator.
(Level 6.3)
Using any of the resources listed in the resource list and the IWB i-learn
Maths toolbox, the teacher can create games or group work to investigate
and work out fractions of quantities.
Lesson n2_15 from i-learn Maths lessons from IWB folder can be used for
finding fractions of quantities.
Lesson n2_16 from i-learn Maths lessons from IWB folder can be used for
finding fractions of shapes.
Interactive activities for this objective can be found at:
http://www.ixl.com/math/grade-5/multiply-two-fractions
http://www.mathsisfun.com/fractions_multiplication.html
http://www.bbc.co.uk/skillswise/maths/games
Students will be able to multiply one
fraction by another fraction without using
the calculator.
(Level 7.3)
A selection of questions from the following worksheets can be used for
practice:
FOM B1 teacher’s pack, WS 55E from Chapter 10
FOM B2 teacher’s pack, WS 95S and WS 96S from Chapter 23.
5. Solve simple problems
involving fractions.
Students in pairs or in groups discuss different problems and work together
to find proper solutions. Various worksheets and exercises may be used.
Worksheets WS 51S, 52E, 53S and 54Efrom Chapter 10 of FOM B1 teacher’s
pack may be used for this objective.
Worksheets WS 52E, 53S from Chapter 10, WS 62S from Chapter 13 and 95S
from Chapter 23, FOM B2 teacher’s pack may be used for this objective.
The following sites may be used (exclude questions involving mixed
numbers):
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to multiply one
fraction by another using the calculator.
(Level 7.2)
Students will be able to work out the
fraction of a quantity (whole number),
without the use of a calculator.
(Level 7.1)
Students will be able to find half, a
quarter, a tenth and a fifth of an integer.
(Level 6.3)
Students will be able to solve problems in
finding fractions of any quantity.
(Level 7.3)
Students will be able to solve simple
problems in addition and subtraction of
fractions with different denominators.
(Level 7.2)
Students will be able to solve simple
44
http://www.ixl.com/math/grade-5/add-subtract-multiply-and-dividefractions-and-mixed-numbers-word-problems
http://www.primaryresources.co.uk/maths/pdfs/9harryfrac.pdf
http://math.about.com/od/fractionsrounding1/ss/teachfraction_3.htm
Additional practice can be done by using National Tests style questions,
FOM B1 teacher’s pack, pages 281– 287.
Additional practice can be done by using National Tests style questions,
FOM B2 teacher’s pack, pages 263 – 271.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
problems in addition and subtraction of
fractions with common denominators.
(Level 7.1)
Students will be able to solve problems in
finding fractions of quantities (integers).
(Level 6.3)
45
Subject:
MATHEMATICS
Unit code and title: MTH 8.3 Fractions (Levels 5.3 – 7.1)
Strand 1:
Number
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Write a fraction that is equivalent to another fraction and reduce a fraction to its simplest form by cancelling common factors.
2. Add and subtract two fractions that have a common denominator.
3. Work out the fraction of a quantity (integer).
4. Solve simple problems involving fractions.
Key Words
Fraction, equivalent, improper,
reduce, simplest form,
cancelling common factors,
common denominator.
Points to Note
Resources
FOM B Gold, Students’ Book, Resource
Three main teaching approaches are being recommended to promote a
Pack - Chapter 10.
student centred learning environment.
Interactive Whiteboard Activities.
Exposition: the teacher states the objectives of the lesson and may use ICT i-learn Maths toolbox from IWB software.
software for students to practise new knowledge. This is consolidated by i-learn Maths lessons from IWB folder.
setting students tasks that offer students the opportunity to apply
mathematics to a variety of real life situations.
Fraction Magnets, Fraction Tiles,
Fractions Circles, Fraction Strips, Apple
Discovery: the teacher can set group tasks in which students discuss and Fractions, Fraction Puzzle Cards (Pizza and
construct mathematical knowledge. Students may become active learners Cake), Fractions Kit, Fractions Lotto,
while testing hypotheses and/or making generalisations.
Fraction Dominoes, Fraction Number
Fans, Fraction Bars.
Exploration: the teacher integrates an inquiry based learning approach that
enhances the students’ understanding of concepts. These tasks might Internet Links:
employ the processes of reasoning, problem solving, investigations, www.mathsisfun.com
connecting ideas and concepts, and expressing results by using the precise www.mathopolis.com www.ictgames.com
www.ixl.com http://nrich.maths.org
language of mathematics.
http://www.bbc.co.uk/skillswise/maths/games
http://www.math-drills.com/fractions/
www.primaryresources.co.uk/maths/mathsB6.htm
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
46
Teaching Objective
Examples of teaching experiences and activities
Indicators of Learning outcomes
The teacher will teach the
students to:
Using any of the resources listed in the resource list and the IWB i-learn
Maths toolbox, the teacher can create games or group work to investigate
equivalent fractions.
Interactive activities for this objective can be practised at:
http://www.ixl.com/math/grade-5/equivalent-fractions
http://www.mathsisfun.com/equivalent_fractions.html
http://www.math-aids.com/Fractions/
http://nrich.maths.org/4519
Students will be able to use equivalent
fractions in comparing/ordering fractions.
(Level 7.1)
1. Write a fraction that is
equivalent to another
fraction and reduce a
fraction to its simplest form
by cancelling common
factors.
Task sheet 10.1 and worksheet WS 10.1 for Chapter 10, FOM B Gold
teacher’s pack can be used for this objective.
Worksheets WS 51S and 52E, from Chapter 10, FOM B1 teacher’s pack can
be used for this objective.
Worksheets WS 51S and 52E from Chapter 10, FOM B2 teacher’s pack can
be used for this objective.
Lessons n2_18 and n2_19 from i-learn Maths lessons from IWB folder can be
used for this objective.
2. Add and subtract two
fractions that have a
common denominator.
Using any of the resources listed in the resource list and the IWB i-learn
Maths toolbox, the teacher can create games or group work to investigate
addition and subtraction of fractions.
Lesson n8_3 from i-learn Maths lessons from IWB folder can be used for
adding fractions.
Interactive activities for this objective can be practiced at:
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to write equivalent
fractions by multiplying or dividing
numerator and denominator by a scale
factor.
(Level 6.3)
Students will be able to write equivalent
fractions by multiplying numerator and
denominator by a scale factor.
(Level 6.2)
Students will be able to write equivalent
fractions involving halves, fourths, fifths
and tenths.
(Level 6.1)
Students will be able to write equivalent
fractions using pictures, fraction cards
and blocks.
(Level 5.3)
Students will be able to add and subtract
two fractions with same denominators.
(Level 7.1)
Students will be able to add and subtract
two fractions through fraction circles and
picture cards.
(Level 6.3)
47
http://www.ixl.com/math/grade-5/add-and-subtract-fractions-with-like
denominators
http://www.mathsisfun.com/fractions_addition.html
http://www.mathsisfun.com/fractions_subtraction.html
http://www.math-aids.com/Fractions/
Task sheet 10.2 and worksheet WS 10.2 for Chapter 10, FOM B Gold
teacher’s pack can be used for this objective.
Worksheet WS 53S from Chapter 10, FOM B1 teacher’s pack can be used for
this objective.
3. Work out the fraction of a
quantity (integer).
Worksheets WS 51S and 52E from Chapter 10, FOM B2 teacher’s pack can
be used for this objective.
Using any of the resources listed in the resource list and the IWB i-learn
Maths toolbox, the teacher can create games or group work to investigate
and work out fractions of quantities.
Lesson n2_15 from i-learn Maths lessons from IWB folder can be used for
finding fractions of quantities.
Lesson n2_16 from i-learn Maths lessons from IWB folder can be used for
finding fractions of shapes.
Interactive activities for this objective can be found at:
http://www.ixl.com/math/grade-5/multiply-fractions-by-whole-numbersihttp://www.ixl.com/math/grade-5/multiply-fractions-by-whole-numbersiihttp://www.bbc.co.uk/skillswise/maths/games
http://nrich.maths.org/1102
http://www.math-drills.com/fractions/parts_of_a_group_001.pdf
Task sheet 10.3 and worksheet WS 10.3 for Chapter 10, FOM B Gold
teacher’s pack can be used for this objective.
A selection of questions from the following worksheet can be used for
practice:
FOM B1 teacher’s pack, WS 55E from Chapter 10
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to add two fractions
through fraction circles and picture cards.
(Level 6.2)
Students will be able to add and subtract
halves, fourths, fifths and tenths, each
time with the same denominator.
(Level 6.1)
Students will be able to add and subtract
halves, fourths, fifths and tenths through
fraction circles and picture cards.
(Level 5.3)
Students will be able to work out the
fraction of a quantity (whole number),
without the use of a calculator.
(Level 7.1)
Students will be able to find half, a
quarter, a tenth and a fifth of an integer.
(Level 6.3)
Students will be able to find half, a
quarter and a tenth of an integer.
(Level 6.2)
Students will be able to work out half and
a quarter of an integer.
(Level 6.1)
Students will be able to manipulate
picture cards and blocks to work out the
fraction of a quantity. (Level 5.3)
48
4. Solve simple problems
involving fractions.
Students in pairs or in groups discuss different problems and work together
to find proper solutions. Various worksheets and exercises may be used.
A selection of questions from the following worksheets can be used for
practice:
Task sheet 10.4 and worksheet WS 10.4 for Chapter 10, FOM B Gold
teacher’s pack.
Worksheets WS 51S, 52E and 54E from Chapter 10 of FOM B1 teacher’s
pack.
Worksheets WS 52E from Chapter 10, and 95S from Chapter 23, FOM B2
teacher’s pack.
The following sites may be used:
http://www.ixl.com/math/grade-1/fractions-word-problems
http://www.ixl.com/math/grade-5/add-and-subtract-fractions-with-likedenominators-word-problems
http://www.ixl.com/math/grade-5/multiply-fractions-by-whole-numbersword-problems
http://www.primaryresources.co.uk/maths/pdfs/9harryfrac.pdf
http://math.about.com/od/fractionsrounding1/ss/teachfraction_3.htm
Additional practice can be done by using National Tests style questions,
FOM B Gold teacher’s pack, pages 338–343.
Additional practice can be done by using National Tests style questions,
FOM B1 teacher’s pack, pages 281– 287.
Additional practice can be done by using National Tests style questions,
FOM B2 teacher’s pack, pages 263 – 271.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to solve simple
problems in addition and subtraction of
fractions with common denominators.
(Level 7.1)
Students will be able to solve problems in
finding fractions of quantities (integers).
(Level 6.3)
Students will be able to solve simple
problems in addition and subtraction of
fractions.
(Level 6.2)
Students will be able to solve simple
problems involving addition of two
fractions.
(Level 6.1)
Students will be able to identify two
simple fractions with a total of 1.
(Level 5.3)
49
Subject:
Mathematics
Unit code and title: MTH 8.3 Fractions (Level 1-4)
Strand 1:
Number
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives at attainment Level 5 and 6
The teacher will teach the students to:
1. Write a fraction that is equivalent to another fraction and reduce a fraction to its simplest form by cancelling common factors.
2. Add and subtract two fractions that have a common denominator.
3. Work out the fraction of a quantity (integer).
4. Convert fractions to percentages and decimals and vice-versa.
5. Solve simple fractions involving fractions.
Objectives at attainment levels 1, 2, 3, 4 (The mainstream objectives 3, 4 and 5 are beyond the attainment level 4.)
The teacher will teach the students to:
1.1. Identify the shapes with equal shaded parts and to share a group of objects until it cannot be shared anymore.
2.1 Students will use simple addition and subtraction facts to work out the number of parts of two equal partitioned shapes.
Key Words
Points to Note
Shaded/coloured parts,
In addition to the points to note recommended for students performing at
share the number of objects Level 5 or higher, it is very important for the teacher to allow time for the
equally.
students to respond. This response can take the form of unaided and/or
aided means of communication and the teacher needs to provide adequate
scaffolding techniques to enable the students to respond affectively or
intentionally.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Resources
New Maths Frame Working-Step Up
Workbook.
Oxford Framework Maths 7
Ilearn Maths, Calculator, Excel Worksheets
www.math-drills.com/fractions.shtml
www.numeracyworld.com/fractionsworksheets.php
http://math.about.com/od/worksheets/a/fra
ctions.htm
www.superteacherworksheets.com/fractions
.html
http://edhelper.com/fractions.htm
www.mathsisfun.com/worksheets/fractions.
php
50
Teaching Objective
The teacher will teach
students to:
1.1. Identify the shapes
with equal shaded
parts and to share a
group of objects until it
cannot be shared
anymore.
Examples of teaching experiences and activities
Starter: Students are shown two circles, one divided in two whilst the other
divided into four parts. Circle 1 has one part shaded whilst circle 2 has two
parts shaded. Students will talk about the shaded parts. Then they cut them
in parts and discuss whether the parts can be shared equally amongst a
number of people.
Students are shown more examples of the above type to talk about and
write the number of shaded parts. Then they have to create two shapes
divided into two different parts but with the same shaded parts. The
students are given a number of parts, e.g. 8 and 7 which they need to share
amongst a group. They observe and discuss that an even number can be
shared equally whilst an odd number cannot.
Students will be given the same shapes as above and told to colour like one
out of two, two out of four etc.
At an even lower level, the students can match the shapes that go together
according to their coloured parts. The students will follow the teacher’s
instructions and count whilst sharing the objects.
2.1 Use simple addition and
subtraction facts to work
out the number of parts
of two equal partitioned
shapes.
At a further basic level, the students observe and experience how a pizza is
divided into two or four parts but yet having the same portion.
Starter: Students will be shown two shapes divided into equal parts and they
have to tell the total number of shaded parts.
Above activity is extended to other shapes with students counting the
number of shaded parts in shape 1 then shape 2 and add the total. They can
try writing the fraction simply by filling the top and the bottom box aided by
visual prompts. Similarly, they can find the unshaded parts by subtraction.
At a lower level, the above activity can be limited to shading and counting
on up to 6.
Indicators of Learning outcomes
Students will be able to identify and talk
about the shaded fraction. They become
aware of equivalent fractions.
(Level 4)
Students will be able to apply the concept of
counting to colour the same part of a shape.
(Level 3)
Students will be able to match shapes by
their number of parts.
(Level 2)
Students will be able to encounter and
experience the cutting shapes in different
parts.
(Level 1)
Students will be able to use simple addition
facts to work out the number of shaded parts
of two shapes. Conversely, they will use
subtraction to find out the unshaded parts.
(Level 4)
Students will be able to use number value to
count the parts and colour accordingly.
(Level 3)
Students will be able to identify the odd one
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
51
Students can be given 2 circles and a rectangle and they have to point to the
odd one out.
out by pointing.
(Level 2)
Students will be able to observe and focus on
the activity that it is taking place.
(Level 1)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
52
Subject:
Unit code and title:
Strand 1:
MATHEMATICS
MTH 8.4 Decimals (Levels 7.1 – 8.1)
Number
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Recognise and use the symbols <, >, ≤ and ≥ to compare two quantities. Use the number line to illustrate simple cases of inequalities.
2. Read decimal numbers from number lines and scales; read and use scales in practical situations.
3. Arrange decimal numbers in order of size.
4. Round numbers to a given number of decimal places and carry out rough estimates to check accuracy.
5. Change fractions into decimals and vice versa; recognise recurring and non recurring decimals.
Key Words
Decimal, number line, scales,
rounding numbers, decimal
places, rough estimate,
accuracy, recurring decimal,
non-recurring decimal, fraction,
less than, greater than, less or
equal to, greater or equal to,
inequalities, symbols, ascending
order, descending order.
Points to Note
Resources
FOM B2, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to promote a
Resource Pack – Chapters 2 & 5
student centred learning environment.
From Teachers’ laptop:
C:\Documents and Settings\teacher\My
Exposition: the teacher states the objectives of the lesson and may use ICT
Documents\Maths Excel Lessons
software for students to practise new knowledge. This is consolidated by
setting students tasks that offer students the opportunity to apply Interactive Whiteboard Activities.
mathematics to a variety of real life situations.
i-learn Maths toolbox from IWB software.
i-learn Maths lessons from IWB folder.
Discovery: the teacher can set group tasks in which students discuss and
Place value flipchart and abacus stand for
construct mathematical knowledge. Students may become active learners
decimals; Number lines; Scales and dials;
while testing hypotheses and/or making generalisations.
Base 10 unit blocks, strips of 10, Chart of
numbers up to 100 and blocks of 1000.
Exploration: the teacher integrates an inquiry based learning approach that
enhances the students’ understanding of concepts. These tasks might Internet Links:
www.ixl.com
employ the processes of reasoning, problem solving, investigations, www.mathsisfun.com
connecting ideas and concepts, and expressing results by using the precise http://www.bbc.co.uk
www.ictgames.com
language of mathematics.
http://teachingimage.com
http://www.primaryresources.co.uk/maths/
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
53
Teaching Objective
Examples of teaching experiences and activities
Indicators of Learning outcomes
The teacher will teach the
students to:
Games can be held in groups or pairs, using the symbols <, >, ≤ and ≥ to
compare two quantities. The use of different number lines from i-learn
Maths toolbox from IWB software can be very helpful. Other cardboard
number lines can also be used.
Students will be able to illustrate simple
cases of inequalities on a number line.
(Level 8.1)
1.
Recognise and use the
symbols <, >, ≤ and ≥ to
compare two quantities.
Use the number line to
illustrate simple cases of
inequalities.
Interactive activities for this objective can be practised at:
http://www.ixl.com/math/grade-5/decimal-number-lines
http://www.ixl.com/math/grade-5/compare-decimal-numbers
http://www.ixl.com/math/grade-5/compare-decimals-and-fractions
http://www.mathsisfun.com/numbers/number-line-zoom.html
http://www.ictgames.com/equivalence.html
http://teachingimage.com/decimal-worksheets/decimal-number-lines-2.pdf
Worksheets WS 14S and 15E from Chapter 2, FOM B2 teacher’s pack can be
used for this objective.
2.
Read decimal numbers
from number lines and
scales; read and use scales
in practical situations.
Interactive activities with different scales and measures can be done with
the help of the i-learn Maths toolbox from IWB software.
Students in groups or pairs can practise measuring their height, their weight,
the weight of different objects, volume of liquids in measuring cylinders and
writing their observations using appropriate units.
Interactive activities for this objective can be practised at:
http://www.mathsisfun.com/measure/index.html
http://www.ictgames.com/weight.html
http://www.primaryresources.co.uk/maths/mathsE1.htm
http://www.bbc.co.uk/schools/teachers/ks2_activities/maths/measures.shtml
Worksheet WS 10S from Chapter 2, FOM B2 teacher’s pack can be used for
this objective.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to recognise and use
the symbols ≤ and ≥ for integers, decimals
and fractions.
(Level 7.3)
Students will be able to recognise and use
the symbols < and > for integers and
decimals.
(Level 7.2)
Students will be able to compare integers
and decimals and determine which is
larger or smaller.
(Level 7.1)
Students will be able to read multiple
dials to get one reading.
(Level 8.1)
Students will be able to read from scales
such as speedometer, ampere meter,
altimeter and air speed indicator.
(Level 7.3)
Students will be able to read decimal
numbers up to three places of decimals
from number lines and scales.
(Level 7.2)
54
Students will be able to read decimal
numbers up to two places of decimals
from scales measuring length, weight,
capacity, speed and fuel gauge.
(Level 7.1)
3.
Arrange decimal numbers
in order of size.
Games can be held in groups or pairs, using the symbols <, >, ≤ and ≥ to
compare two quantities at a time from a set of given quantities. The use of
different number lines from i-learn Maths toolbox from IWB software can be
very helpful. Other cardboard number lines can also be used. Finally the set
of quantities can be arranged in ascending/descending order.
Lesson n7_1_place _value/sheet 4 from i-learn Maths lessons from IWB
folder can be used for this objective.
Interactive activities for this objective can be practised at:
http://www.ixl.com/math/grade-5/put-assorted-decimals-fractions-andmixed-numbers-in-order
http://www.ixl.com/math/grade-5/put-decimal-numbers-in-order
http://www.mathsisfun.com/ordering_decimals.html
http://www.mathsisfun.com/numbers/ordering-game.php?m=Dec-Tricky
http://www.ictgames.com/equivalence.html
Worksheet WS 12S and 13E from Chapter 2, FOM B2 teacher’s pack can be
used for this objective.
4.
Round numbers to a given
number of decimal places
and carry out rough
estimates to check
accuracy.
From Teachers’ laptop:
C:\Documents and Settings\teacher\My Documents\Maths Excel Lessons:
2 lessons/games on rounding numbers, including decimal places, can be
used.
Base 10 blocks set and decimal abacus can be used to work in groups to
build decimal numbers and round them to any decimal place.
Interactive activities with different number tools can be done with the help
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to find a number
between any two given decimal numbers.
(Level 8.1)
Students will be able to arrange any set of
decimal numbers in ascending and
descending order.
(Level 7.3)
Students will be able to arrange numbers
in ascending and descending order up to
3 decimal places.
(Level 7.2)
Students will be able to arrange numbers
in ascending and descending order up to
2 decimal places.
(Level 7.1)
Students will be able to recognise the
difference between decimal places and
significant figures.
(Level 8.1)
Students will be able to carry rough
estimates to check accuracy.
(Level 7.3)
55
of the i-learn Maths toolbox from IWB software to illustrate rounding
decimal numbers.
Interactive activities for this objective can be practiced at:
http://www.ixl.com/math/grade-7/round-decimals
http://www.ixl.com/math/grade-5/estimate-products-with-decimals
http://www.ixl.com/math/grade-5/estimate-sums-and-differences-ofdecimals
http://www.mathsisfun.com/rounding-numbers.html
http://www.primaryresources.co.uk/maths/mathsB6b.htm
Students will be able to round numbers to
a given number of decimal places.
(Level 7.2)
Students will be able to round numbers to
one decimal place.
(Level 7.1)
Worksheets WS 28S, 29E and 30E from Chapter 5, FOM B2 teacher’s pack
can be used for this objective.
5.
Change fractions into
decimals and vice versa;
recognise recurring and
non-recurring decimals.
From Teachers’ laptop:
C:\Documents and Settings\teacher\My Documents\Maths Excel Lessons:
Decimal expansion lesson to illustrate recurring patterns in decimals for
particular fractions.
Students will be able to recognise that
particular fractions have specific recurring
decimal patterns.
(Level 8.1)
Students work in pairs to match equivalent cards of fractions and decimals.
Students will be able to change fractions
to decimals.
(Level 7.3)
Interactive activities for this objective can be practised at:
http://www.ixl.com/math/grade-5/convert-fractions-to-decimals
http://www.ixl.com/math/grade-5/convert-decimals-to-fractions
http://www.ixl.com/math/grade-5/repeating-decimals
http://www.mathsisfun.com/converting-decimals-fractions.html
http://www.mathsisfun.com/converting-fractions-decimals.html
http://www.mathsisfun.com/worksheets/decimals.php
http://www.primaryresources.co.uk/maths/docs/making_decimal_fractions
_EC.doc
Investigation on recurring decimals, Ch 5 FOM B2 can be tackled.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to change decimals,
with a finite number of decimal places to
fractions in their lowest terms.
(Level 7.2)
Students will be able to change decimals
with up to 3 decimal places to fractions in
their lowest terms.
(Level 7.1)
56
Subject:
MATHEMATICS
Form 2
Unit code and title:
MTH 8.4 Decimals (Levels 6.3 – 7.3)
Strand 1:
Number
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Recognise and use the symbols <, >, ≤ and ≥ to compare two quantities.
2. Read decimal numbers from number lines and scales; read and use scales in practical situations.
3. Arrange decimal numbers in order of size.
4. Round numbers to a given number of decimal places and carry out rough estimates to check accuracy.
5. Change fractions into decimals and vice versa; recognise recurring and non-recurring decimals.
Key Words
Decimal, number line, scales,
rounding numbers, decimal
places, rough estimate,
accuracy, recurring decimal,
non-recurring decimal, fraction,
less than, greater than, less or
equal to, greater or equal to,
inequalities, symbols, ascending
order, descending order.
Points to Note
Resources
FOM B1, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to promote a
Resource Pack – Chapters 2 & 5
student centred learning environment.
FOM B2 Resource Pack – Chapters 2 & 5
From Teachers’ laptop:
Exposition: the teacher states the objectives of the lesson and may use ICT
C:\Documents and Settings\teacher\My
software for students to practice new knowledge. This is consolidated by
Documents\Maths Excel Lessons
setting students tasks that offer students the opportunity to apply
mathematics to a variety of real life situations.
Interactive Whiteboard Activities.
i-learn Maths toolbox from IWB software.
Discovery: the teacher can set group tasks in which students discuss and i-learn Maths lessons from IWB folder.
construct mathematical knowledge. Students may become active learners
Place value flipchart and abacus stand for
while testing hypotheses and/or making generalisations.
decimals; Number lines; Scales and dials;
Base 10 unit blocks, strips of 10, Chart of
Exploration: the teacher integrates an inquiry based learning approach that
numbers up to 100 and blocks of 1000.
enhances the students’ understanding of concepts. These tasks might
employ the processes of reasoning, problem solving, investigations, Internet Links:
www.ixl.com
connecting ideas and concepts, and expressing results by using the precise www.mathsisfun.com
http://www.bbc.co.uk
language of mathematics.
www.ictgames.com
http://teachingimage.com
http://www.primaryresources.co.uk/maths/
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
57
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
58
Teaching Objective
Examples of teaching experiences and activities
Indicators of Learning outcomes
The teacher will teach the
students to:
Games can be held in groups or pairs, using the symbols <, >, ≤ and ≥ to
compare two quantities. The use of different number lines from i-learn
Maths toolbox from IWB software can be very helpful. Other cardboard
number lines can also be used.
Students will be able to recognise and use
the symbols ≤ and ≥ for integers, decimals
and fractions.
(Level 7.3)
Interactive activities for this objective can be practised at:
http://www.ixl.com/math/grade-5/decimal-number-lines
http://www.ixl.com/math/grade-5/compare-decimal-numbers
http://www.ixl.com/math/grade-5/compare-decimals-and-fractions
http://www.mathsisfun.com/numbers/number-line-zoom.html
http://www.ictgames.com/equivalence.html
http://teachingimage.com/decimal-worksheets/decimal-number-lines-2.pdf
Students will be able to recognise and use
the symbols < and > for integers and
decimals.
(Level 7.2)
1.
Recognise and use the
symbols <, >, ≤ and ≥ to
compare two quantities.
Worksheets WS 14S and 15E from Chapter 2, FOM B2 teacher’s pack can be
used for this objective.
Students will be able to compare integers
and decimals and determine which is
larger or smaller.
(Level 7.1)
Students will be able to compare two
pictorial quantities and determine which
is larger or smaller.
(Level 6.3)
2.
Read decimal numbers
from number lines and
scales; read and use scales
in practical situations.
Interactive activities with different scales and measures can be done with
the help of the i-learn Maths toolbox from IWB software.
Students in groups or pairs can practise measuring their height, their weight,
the weight of different objects, volume of liquids in measuring cylinders and
writing their observations using appropriate units.
Interactive activities for this objective can be practised at:
http://www.mathsisfun.com/measure/index.html
http://www.ictgames.com/weight.html
http://www.primaryresources.co.uk/maths/mathsE1.htm
http://www.bbc.co.uk/schools/teachers/ks2_activities/maths/measures.shtml
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to read from scales
such as speedometer, ampere meter,
altimeter and air speed indicator.
(Level 7.3)
Students will be able to read decimal
numbers up to three places of decimals
from number lines and scales.
(Level 7.2)
Students will be able to read decimal
numbers up to two places of decimals
59
Worksheet WS 8S and 9E from Chapter 2, FOM B1 teacher’s pack can be
used for this objective.
from number lines and scales measuring
length, weight, capacity, speed and fuel
gauge.
(Level 7.1)
Students will be able to read decimal
numbers up to one decimal place from
number lines and scales measuring
length, weight, capacity, speed and fuel
gauge.
(Level 6.3)
3.
Arrange decimal numbers
in order of size.
Games can be held in groups or pairs, using the symbols <, >, ≤ and ≥ to
compare two quantities at a time from a set of given quantities. The use of
different number lines from i-learn Maths toolbox from IWB software can be
very helpful. Other cardboard number lines can also be used. Finally the set
of quantities can be arranged in ascending/descending order.
Lesson n7_1_place _value/sheet 4 from i-learn Maths lessons from IWB
folder can be used for this objective.
Interactive activities for this objective can be practised at:
http://www.ixl.com/math/grade-5/put-assorted-decimals-fractions-andmixed-numbers-in-order
http://www.ixl.com/math/grade-5/put-decimal-numbers-in-order
http://www.mathsisfun.com/ordering_decimals.html
http://www.mathsisfun.com/numbers/ordering-game.php?m=Dec-Tricky
http://www.ictgames.com/equivalence.html
Worksheet WS 12S and 13E from Chapter 2, FOM B2 teacher’s pack can be
used for this objective.
Worksheet WS 10S and 11E from Chapter 2, FOM B1 teacher’s pack can be
used for this objective.
4.
Round numbers to a given
From Teachers’ laptop:
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to arrange any set of
decimal numbers in ascending and
descending order.
(Level 7.3)
Students will be able to arrange numbers
in ascending and descending order up to
3 decimal places.
(Level 7.2)
Students will be able to arrange numbers
in ascending and descending order up to
2 decimal places.
(Level 7.1)
Students will be able to arrange numbers
in ascending and descending order up to
1 decimal place.
(Level 6.3)
Students will be able to carry rough
60
number of decimal places
and carry out rough
estimates to check
accuracy.
C:\Documents and Settings\teacher\My Documents\Maths Excel Lessons:
2 lessons/games on rounding numbers, including decimal places, can be
used.
Base 10 blocks set and decimal abacus can be used to work in groups to
build decimal numbers and round them to any decimal place.
Interactive activities with different number tools can be done with the help
of the i-learn Maths toolbox from IWB software to illustrate rounding
decimal numbers.
Interactive activities for this objective can be practised at:
http://www.ixl.com/math/grade-7/round-decimals
http://www.ixl.com/math/grade-5/estimate-products-with-decimals
http://www.ixl.com/math/grade-5/estimate-sums-and-differences-ofdecimals
http://www.mathsisfun.com/rounding-numbers.html
http://www.primaryresources.co.uk/maths/mathsB6b.htm
estimates to check accuracy.
(Level 7.3)
Students will be able to round numbers to
a given number of decimal places.
(Level 7.2)
Students will be able to round numbers to
one decimal place.
(Level 7.1)
Students will be able to round numbers to
the nearest whole.
(Level 6.3)
Worksheets WS 28S, 29E and 30E from Chapter 5, FOM B2 teacher’s pack
can be used for this objective.
Worksheet WS 30S, 31E, 32S, 33E, 35E and 36S from Chapter 5, FOM B1
teacher’s pack can be used for this objective.
5.
Change fractions into
decimals and vice versa;
recognise recurring and
non-recurring decimals.
From Teachers’ laptop:
C:\Documents and Settings\teacher\My Documents\Maths Excel Lessons:
Decimal expansion lesson to illustrate recurring patterns in decimals for
particular fractions.
Students work in pairs to match equivalent cards of fractions and decimals.
Interactive activities for this objective can be practised at:
http://www.ixl.com/math/grade-5/convert-fractions-to-decimals
http://www.ixl.com/math/grade-5/convert-decimals-to-fractions
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to change fractions
to decimals.
(Level 7.3)
Students will be able to change decimals,
with a finite number of decimal places, to
fractions in their lowest terms.
(Level 7.2)
Students will be able to change decimals
61
http://www.ixl.com/math/grade-5/repeating-decimals
http://www.mathsisfun.com/converting-decimals-fractions.html
http://www.mathsisfun.com/converting-fractions-decimals.html
http://www.mathsisfun.com/worksheets/decimals.php
http://www.primaryresources.co.uk/maths/docs/making_decimal_fractions
_EC.doc
Investigation on recurring decimals, Ch 5 FOM B1 can be tackled.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
with up to 3 decimal places to fractions in
their lowest terms.
(Level 7.1)
Students will be able to change decimals
with up to 2 decimal places to fractions in
their lowest terms.
(Level 6.3)
62
Subject:
Unit code and title:
Strand 1:
MATHEMATICS
MTH 8.4 Decimals (Levels 5.3 – 7.1)
Number
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Read decimal numbers from number lines and scales; read and use scales in practical situations up to two decimal places.
2. Arrange decimal numbers in order of size.
3. Add and subtract decimal numbers.
4. Round numbers to one decimal place.
5. Multiply and divide decimal numbers by an integer.
6. Work out simple problems on multiplication and division of decimals.
Key Words
Decimal, scales, rounding
numbers, decimal places,
fractions of 10, 100 and 1000,
less than, greater than,
ascending order, descending
order, integer.
Points to Note
Resources
FOM B Gold, Students’ Book, Resource
Three main teaching approaches are being recommended to promote a
Pack – Chapters 2 & 5
student centred learning environment.
FOM B1, B2 Resource Pack – Ch 2 & 5
SKILLSHEETS 2011 v2 CD.
Exposition: the teacher states the objectives of the lesson and may use ICT
software for students to practise new knowledge. This is consolidated by From Teachers’ laptop:
setting students tasks that offer students the opportunity to apply C:\Documents and Settings\teacher\My
mathematics to a variety of real life situations.
Documents\Maths Excel Lessons
Interactive Whiteboard Activities.
Discovery: the teacher can set group tasks in which students discuss and
i-learn Maths toolbox from IWB software.
construct mathematical knowledge. Students may become active learners
i-learn Maths lessons from IWB folder.
while testing hypotheses and/or making generalisations.
Place value flipchart, abacus stand;
Exploration: the teacher integrates an inquiry based learning approach that number lines; scales and dials; Base 10
enhances the students’ understanding of concepts. These tasks might blocks, strips of 10, charts of 100 coins.
employ the processes of reasoning, problem solving, investigations, Internet Links:
connecting ideas and concepts, and expressing results by using the precise www.mathsisfun.com www.ixl.com
language of mathematics.
www.mathopolis.com www.ictgames.com
http://teachingimage.com www.bbc.co.uk
http://www.primaryresources.co.uk/maths/
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
63
Teaching Objective
Examples of teaching experiences and activities
Indicators of Learning outcomes
The teacher will teach the
students to:
Interactive activities with different scales and measures can be done with
the help of the i-learn Maths toolbox from IWB software.
Students in groups or pairs can practise measuring their height, their weight,
the weight of different objects, volume of liquids in measuring cylinders and
writing their observations using appropriate units.
Students will be able to read decimal
numbers up to two places of decimals
from number lines and scales measuring
length, weight, capacity, speed and fuel
gauge.
(Level 7.1)
1.
Read decimal numbers
from scales; read and use
scales in practical
situations up to two
decimal places.
Interactive activities for this objective can be practised at:
http://www.mathsisfun.com/measure/index.html
http://www.ictgames.com/weight.html
http://www.primaryresources.co.uk/maths/mathsE1.htm
http://www.bbc.co.uk/schools/teachers/ks2_activities/maths/measures.sht
ml
Worksheet WS 8S and 9E from Chapter 2, FOM B1 teacher’s pack can be
used for this objective.
Task sheet 2.4 and worksheet 2.4 from Chapter 2, FOM B Gold teacher’s
pack can be used for this objective.
Students will be able to read decimal
numbers up to one decimal place from
number lines and scales measuring
length, weight, capacity, speed and fuel
gauge.
(Level 6.3)
Students will be able to read decimal
numbers up to one decimal place from a
number line.
(Level 6.2)
Students will be able to read scales
involving half unit and quarter unit
intervals.
(Level 6.1)
Students will be able to read scales
involving half unit intervals.
(Level 5.3)
2.
Arrange decimal numbers
in order of size.
Games can be held in groups or pairs to compare two quantities at a time
from a set of given quantities to determine which is greater and which is
less. The use of different number lines from i-learn Maths toolbox from IWB
software can be very helpful. Other cardboard number lines can also be
used. Finally the set of quantities can be arranged in ascending/descending
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to arrange numbers
in ascending and descending order up to
2 decimal places.
(Level 7.1)
64
order.
Lesson n7_1_place _value/sheet 4 from i-learn Maths lessons from IWB
folder can be used for this objective.
Interactive activities for this objective can be practised at:
http://www.ixl.com/math/grade-5/put-decimal-numbers-in-order
http://www.mathsisfun.com/ordering_decimals.html
http://www.mathsisfun.com/numbers/ordering-game.php?m=Dec-Tricky
http://www.ictgames.com/equivalence.html
When using the above links or worksheets suggested below, one can either
restrict examples with two decimal places or venture to investigate
examples with three decimal places.
Worksheet WS 12S and 13E from Chapter 2, FOM B2 teacher’s pack can be
used for this objective.
Worksheet WS 10S and 11E from Chapter 2, FOM B1 teacher’s pack can be
used for this objective.
3. Add and subtract decimal
numbers.
The Base 10 unit blocks, strips of 10, sheets of 100 and blocks of 1000 value
set and abacus for decimals can be used to work in groups or pairs to
practise addition and subtraction of decimal quantities.
The same can be done using i-learn Maths toolbox from IWB software and
decimal number lines.
From Teachers’ laptop:
C:\Documents and Settings\teacher\My Documents\Maths Excel Lessons
The lesson Decimals + & - can be used for this objective.
Lesson n7_1_place _value/sheet 2 from i-learn Maths lessons from IWB
folder can be used for this objective.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to arrange numbers
in ascending and descending order up to
1 decimal place.
(Level 6.3)
Students will be able to arrange decimal
numbers represented as wholes, halves
and quarters, in ascending and
descending order.
(Level 6.2)
Students will be able to arrange decimal
numbers represented as wholes and
halves, in ascending and descending
order.
(Level 6.1)
Students will be able to arrange integers,
in ascending and descending order.
(Level 5.3)
Students will be able to add and subtract
decimal numbers with 2 decimal places.
(Level 7.1)
Students will be able to subtract decimals
with 1 decimal place, involving change
over place value (borrowing).
(Level 6.3)
Students will be able to add decimal
numbers with 1 decimal place, involving
carrying over.
(Level 6.2)
65
Interactive activities for this objective can be practised at:
http://www.bbc.co.uk/schools/ks2bitesize/maths/number/decimals/play.shtml
http://www.bbc.co.uk/schools/ks2bitesize/maths/number/decimals/read3.shtml
http://www.mathsisfun.com/adding-decimals.html
http://www.mathsisfun.com/subtracting-decimals.html
http://www.mathopolis.com/games/estimate-subtracttenths.php
http://www.mathopolis.com/games/estimate-addtenths.php
http://www.ixl.com/math/grade-5/add-and-subtract-decimal-numbers
http://teachingimage.com/decimal-worksheets.php
Students will be able to subtract decimals
with 1 decimal place, not involving
change over place value (borrowing).
(Level 6.1)
Students will be able to add decimal
numbers with 1 decimal place, not
involving carrying over.
(Level 5.3)
Task sheet 5.1 and worksheet WS 5.1 from Chapter 5, FOM B Gold teacher’s
pack can be used for this objective.
4.
Round numbers to one
decimal place.
In the following suggested activities, one can either restrict examples and
work to one/two decimal places or venture to investigate examples with
three decimal places.
Students will be able to round numbers to
one decimal place.
(Level 7.1)
From Teachers’ laptop:
C:\Documents and Settings\teacher\My Documents\Maths Excel Lessons:
2 lessons/games on rounding numbers, including decimal places, can be
used.
Base 10 blocks set and decimal abacus can be used to work in groups to
build decimal numbers and round them to any decimal place wanted.
Students will be able to round numbers to
the nearest hundred.
(Level 6.3)
Interactive activities with different number tools can be done with the help
of the i-learn Maths toolbox from IWB software to illustrate rounding
decimal numbers.
Interactive activities for this objective can be practiced at:
http://www.ixl.com/math/grade-7/round-decimals
http://www.mathsisfun.com/rounding-numbers.html
http://www.primaryresources.co.uk/maths/mathsB6b.htm
http://www.ictgames.com/helipad%20hops7.html
Worksheet WS 28S from Chapter 5, FOM B2 teacher’s pack can be used for
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to round numbers to
the nearest ten.
(Level 6.2)
Students will be able to round numbers to
the nearest whole.
(Level 6.1)
Students will be able to understand that
the decimal system uses a base of ten.
(Level 5.3)
66
this objective.
Worksheet WS 32S from Chapter 5, FOM B1 teacher’s pack can be used for
this objective.
Task sheet 2.3 and worksheet WS 2.3 from Chapter 2, and Task sheet 5.2
and worksheet WS 5.2 from Chapter 5 FOM B Gold teacher’s pack can be
used for this objective.
5.
Multiply and divide decimal Base 10 blocks set and decimal strips can be used to work in groups to build
numbers by an integer.
decimal numbers and multiply/divide them by any integer..
The i-learn Maths toolbox from IWB software (function machine) can be
used to generate work with multiplication and division by an integer.
Interactive activities for this objective can be practised at:
http://www.ixl.com/math/grade-5/multiply-a-decimal-by-a-one-digitwhole-number
http://www.ixl.com/math/grade-6/divide-decimals-by-whole-numbers
http://teachingimage.com/decimal-worksheets/multiplication-ofdecimals.pdf
http://teachingimage.com/decimal-worksheets/division-of-decimals.pdf
http://www.primaryresources.co.uk/maths/docs/double_halve_decimals.doc
Task sheets 5.3 and 5.4 and worksheets WS 5.3 and 5.4 from Chapter 5 FOM
B Gold teacher’s pack can be used for this objective.
Students will be able to multiply and
divide any decimal number by an integer.
(Level 7.1)
Students will be able to multiply decimal
numbers up to 2 decimal places by an
integer.
(Level 6.3)
Students will be able to multiply decimal
numbers up to 1 decimal place by an
integer.
(Level 6.2)
Students will be able to multiply and
divide decimal numbers by 10, 100 and
1000.
(Level 6.1)
Students will be able to multiply and
divide decimal numbers by 10.
(Level 5.3)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
67
6. Work out simple problems
on multiplication and
division of decimals.
Groups of students can play at shopping. A temporary shop can be set in
class with empty boxes and tins. Each group is given an amount of plastic
coins with which they can do the shopping. Each group member takes in
turn to play the shopkeeper. Each group practises and records in writing
work with multiplying and dividing amounts of money involving decimals.
The following internet sites may be used for this objective:
http://www.ixl.com/math/grade-5/multiply-decimals-and-whole-numbersword-problems
http://www.ixl.com/math/grade-5/multiply-money-amounts-wordproblems
http://www.ixl.com/math/grade-6/divide-money-amounts-word-problems
http://www.ixl.com/math/grade-6/divide-decimals-by-whole-numbersword-problems
http://www.primaryresources.co.uk/maths/mathsD2.htm
http://www.primaryresources.co.uk/maths/mathsD1.htm
Investigation at page 47 FOM B Gold and word problems from pages 44 to
49 of the same book can be used to practice multiplication and division of
decimals.
Skillsheets 2011: Money Basics MB29 and MB30 can be used to practice
multiplication and division of decimals
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to work out simple
worded problems involving both
multiplication and division of quantities.
(Level 7.1)
Students will be able to work out simple
worded problems involving division of
decimals.
(Level 6.3)
Students will be able to work out simple
worded problems involving multiplication
of decimals.
(Level 6.2)
Students will be able to decide which
operation to use to solve a simple worded
problem.
(Level 6.1)
Students will be able to decide which
operation to use given a simple practical
situation.
(Level 5.3)
68
Subject:
Mathematics
Unit code and title: MTH 8.4 Decimals (Levels 1 - 4)
Strand 1:
Number
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives at attainment Level 5 and 6
The teacher will teach the students to:
1. Read decimal numbers on the number line and from scales; read and use scales in practical situations up to two decimal places.
2. Arrange decimal numbers in order of size.
3. Add and subtract decimal numbers.
4. Round numbers to one decimal place.
5. Multiply and divide decimal numbers by 10, 100 and 1000.
6. Work out simple problems on multiplication and division of decimals.
Objectives at attainment levels 1, 2, 3, 4 (The mainstream objectives 4 & 6 are beyond level 4 so they are not included in the list below.)
The teacher will teach the students to:
1.1. Read numbers on a number line; read and use scales in practical situations.
2.1 Arrange one set of numbers in order of size from ascending/descending.
3.1 Add and subtract simple numbers.
5. 1Group and count in tens and apply this to solve simple problems like rounding to 10.
Key Words
Closest, nearest, scales,
heavy, light, add, subtract,
farther, nearer, order
numbers from smallest to
largest and vice versa,
what’s next?
Points to Note
In addition to the points to note recommended for students performing at
Level 5 or higher, it is very important for the teacher to allow time for the
students to respond. This response can take the form of unaided and/or
aided means of communication and the teacher needs to provide adequate
scaffolding techniques to enable the students to respond effectively or
intentionally.
Resources
New Maths Frame Working Step Up
Workbook.
Oxford Framework Maths 7
Various scales and dials; Base 10 unit blocks,
strips of 10, sheets of 100 and blocks of 1000
value set.
For further examples about level 1 refer to the handbook.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
69
Teaching Objective
The teacher will teach the
students to:
Examples of teaching experiences and activities
Starter: The teacher shows a number line with missing numbers and the
students have to fill in the right numbers.
1.1 Read numbers on a
number line; read and
use scales in practical
situations
Students will be involved in a game using a 1 to 20 number line. E.g. teacher
says “Which number is even and the sum of its digits is 3? Can you find it?
Show it!” Eventually, the students will use the scales, either a real one or the
one on the ilearn to read the scales and find the number on the number
line.
Indicators of Learning outcomes
Students will be able to use their knowledge
of mathematical facts to find and read
numbers on a number line.
(Level 4)
Students will be able to recognise and read
numbers on a scale and find them on the
number line. (Level 3)
Previous activity can be adapted to the use of scales with simple numbers up Students will be able to match different scale
to ten. The students read the number from the scales and then colour it on
readings.
the number line.
(Level 2)
At a lower level, the students can match same scale readings.
At a lower level, the students will observe the change in numbers on the
scale as soon as an object is placed on the scale.
2.1 Arrange one set of
numbers in order of size
from ascending/
descending order.
Starter: Students are given two sequences with different numbers and put
to order them from the smallest to the largest and vice-versa.
Students are given a 30 number grid with some missing numbers and the
students have to identify the missing numbers and write them, or else
choose from a number bank. Then, the students are given random
sequences and they have to put them in order from the smallest to largest
and vice-versa. The students can make use of sites that involve ordering of
numbers.
http://www.primaryresources.co.uk/maths/
www.ictgames.com
At a lower level, the students can be given a 1 to 10 number grid and the
students say the numbers, point and drag the missing numbers using the
ilearn software. Then, three numbers can be chosen randomly and they
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to observe the process
of cause and effect when an item is placed on
the scale.
(Level 1)
Students will be able to choose the correct
missing number and put a sequence in order
of size in both ascending and descending
form.
(Level 4)
Students will be able to order a set of three
numbers in ascending order.
(Level 3)
Students will be able to match sequences of
ordered numbers together.
(Level 2)
Students will maintain eye contact whilst
70
have to put them in order.
listening to a voice saying the numbers.
(Level 1)
At Level 2, the students can match strips of ordered numbers in pairs.
At Level 1, the students will simply listen with focus when a number is
clicked on the computer and its name is read.
3.1 Add and subtract simple
numbers.
Starter: Students are presented with a set of scores of from a game, which
highlight the fact that when we win, points are added and when we lose
points are taken away.
In a birthday party situation, the students count the number of plates and
cups needed for the whole group. The teacher shows the class different
coloured cups, e.g. 2 red and 3 blue, how many cups altogether? Students
choose the food they want to eat. They count the items on their plate whilst
the student next to them counts theirs and they have to work out how many
items they have altogether. When they start eating the food they can check
again how many items are left and how many they have altogether.
5.1 Group and count in
ten’s and apply this to
solve simple problems
like rounding to 10.
Students count how many plates, cups and napkins are needed. Teacher
reads a story about a party situation which is about two girls/boys who took
2 cheesecakes and a nugget. Students represent this situation visually and
they count the pictures to find the total amount. Alternatively the story can
be elaborated to show the situation when they ate the items. Relating to the
above situation students’ hand is held and they point and touch the object
whilst hearing the number one being named. They observe the
disappearance of an object and the adult counts again to expose them to a
new amount.
Starter: Students are shown a group of twenty or more objects and they
have to group them in tens.
Students use counting on or pairs that make ten to work out and solve
simple word problems or just numerical problems involving the create verb.
E.g. given the numbers 2, 4, 6 and 8 create a sum.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to work out simple
totals by adding two’s, three’s, five’s and
taking away by the same quantities and write
simple sum representations e.g.1 4 + 3 or
100 + 3.
(Level 4)
Students will be able to indicate one more
and count total. Also, they will observe taking
away one and count the total.
(Level 3)
Students will be able to match same number
of objects.
(Level 2)
Students will be able to observe the
movement of an object and its
disappearance.
(Level 1)
Students will be able to create problems
themselves and self-check like counting in
threes or fives for numerical representations
given by the teacher.
(Level 4)
71
Students have to group and circle ten objects.
Students will match cards containing the same sums and then use individual
cards to match them on the number line thus reproducing the sum.
Students will be involved in putting objects in a container and taking out
objects from a container.
Students will be able to count and group ten
objects.
(Level 3)
Students will be able to match problem
statement cards and represent them on the
number line through matching.
(Level 2)
Students will be able to participate in tipping
objects into a container.
(Level 1)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
72
Subject:
Unit code and title:
Strand 1:
MATHEMATICS
MTH 8.5 Percentages (Levels 7.1 – 8.1)
Number
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will:
1. Change percentages to fractions and decimals and vice-versa.
2. Express one quantity as a percentage of another.
3. Work out the percentage of a quantity.
4. Work out the percentage increase and decrease.
Key Words
Fraction, equivalent fraction,
decimal, percentage, convert,
quantity, percentage
increase, percentage
decrease.
Points to Note
Resources
FOM B2, Students’ Book, Practice
Three main teaching approaches are being recommended to promote a student
Book, Resource Pack - Chapters 10
centred learning environment.
and 18.
Exposition: the teacher states the objectives of the lesson and may use ICT
software for students to practise new knowledge. This is consolidated by setting
students tasks that offer students the opportunity to apply mathematics to a
variety of real life situations.
From Teachers’ laptop:
C:\Documents and
Settings\teacher\My
Documents\Maths Excel Lessons
Discovery: the teacher can set group tasks in which students discuss and Internet Links:
construct mathematical knowledge. Students may become active learners while http://www.bbc.co.uk
testing hypotheses and/or making generalisations.
http://www.mathsisfun.com
Exploration: the teacher integrates an inquiry based learning approach that
enhances the students’ understanding of concepts. These tasks might employ the
processes of reasoning, problem solving, investigations, connecting ideas and
concepts, and expressing results by using the precise language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
73
Teaching Objective
The teacher will teach
students to:
1. Change percentages to
fractions and decimals and
vice-versa.
Examples of teaching experiences and activities
Using euro coins and notes the students are asked about the relationship
between them.
Examples - Express:
1. 10 cent as a decimal and as a percentage of 20 cent;
2. 10 cent as a decimal and as a percentage of 1 euro;
3. 20 cent as a decimal and as a percentage of 5 euro.
The above quantities can be inputted in a spreadsheet:
Indicators of Learning outcomes
Students will be able to change mixed
numbers to percentages and decimals
and vice versa.
(Level 8.1)
Students will be able to change
fractions and decimals to percentages
without the use of calculator.
(Level 7.3)
Students will be able to change
percentages to fractions and decimals
without the use of calculator.
(Level 7.2)
As a challenge the students may be asked to solve problems.
Example: Mary has €5.50 in her money box. She spends €1.10 at the tuck shop.
What fraction of her money is left? Express this as a decimal and as a percentage.
Students practise converting fractions to decimals and percentages on this online
game. The students can play the game individually or in teams.
This game gives the students the opportunity to try different answers and learn
from their own mistakes.
http://www.math-play.com/Fractions-Decimals-Percents-Jeopardy/fractionsdecimals-percents-jeopardy.html
2. Express one quantity as a
percentage of another.
Through this activity the students express one quantity as a percentage of the
other. The students are divided in groups of three. Each group uses a measuring
tape to find:
1. the length of a student’s desk as a percentage of the length of the
classroom;
2. the area occupied by the desks as a percentage of the whole classroom;
3. the area occupied by the teachers’ desk as a percentage of the whole
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to change
percentages to fractions and decimals
and vice versa using calculator when
necessary.
(Level 7.1)
Students will be able to solve complex
problems involving a quantity as a
percentage of another.
(Level 8.1)
Students will be able to solve simple
problems involving a quantity as a
74
classroom;
4. the area of the students’ desk as a percentage of the teacher’s desk;
Each group presents the results obtained, possibly through the use of a
spreadsheet. The students can then discuss their results.
percentage of another.
(Level 7.3)
Students will be able to express one
quantity as a percentage of another by
calculation and/or spreadsheet
software.
(Level 7.2)
Students will be able to express one
quantity as a percentage of another.
(Level 7.1)
3. Work out the percentage
of a quantity.
Students are organised in groups. They record the price of ten items on sale at the
school tuck shop.
Students are asked to calculate different percentage values (e.g. 50%, 25%, 80%)
of the recorded prices. These calculations are done using pencil and paper or by
1
33 %
3 etc.).
the help of a calculator for more complex percentages (e.g.
The recorded prices are then inputted on a spreadsheet to verify their results.
Students will be able to solve
problems which involve finding the
percentage of a quantity, where the
percentage is a mixed number.
(Level 8.1)
Students will be able to solve
problems which involve finding the
percentage of a quantity, using
integral values.
(Level 7.3)
Students will be able to work out
more complex examples which involve
finding the percentage of a quantity.
(Level 7.2)
Through the following sites the students reinforce percentage of quantities:
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to work out the
75
http://www.bbc.co.uk/schools/ks3bitesize/maths/number/percentages/revise3.s
html
http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=157039-850-X&chapter=4&lesson=2
percentage of a quantity where the
percentage and/or the quantity is a
multiple of 5.
(Level 7.1)
http://yteach.com/page.php/resources/view_all?id=percentage_decimal_fractio
n_value_page_1
4. Work out the percentage
increase and decrease.
http://www.homeschoolmath.net/teaching/percent/percent_of_number_mental
_math.php
Students record the price of ten items on sale at the school tuck shop. The
students compare these prices with those shown on a new price list provided by
another vendor.
When the prices differ, the percentage increase or decrease is found using pencil
and paper, calculator or spreadsheet software.
Students will be able to solve
problems which involve percentage
increase/decrease where the
percentage is a mixed number.
(Level 8.1)
Students will be able to solve
problems which involve percentage
increase/decrease using integral
values.
(Level 7.3)
The students are divided in groups.
Each member of the group gives the information requires to work out one of the
following tasks:
 The amount of money you spend at the tuck shop on Monday and on
Friday.
 The amount of pocket money you received last year and this year.
 The number of hours you usually spend chatting on a weekday and on a
Sunday.
 The number of hours you usually spend doing your homework on a
weekday and on a Saturday.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to work out the
new amount after a percentage
increase/decrease.
(Level 7.2)
Students will be able to work out the
percentage increase/decrease of a
quantity.
(Level 7.1)
76
The percentage increase or decrease is found using pencil and paper, calculator
or spreadsheet software.
The following sites enable the students to reinforce solving percentage increase /
decrease:
http://www.mathgoodies.com/lessons/percent/change.html
http://www.themathpage.com/arith/percent-increase-or-decrease.htm
http://www.mangahigh.com/en/maths_games/number/percentages/percentage
_increase_and_decrease_calculator?localeset=en
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
77
Subject:
Unit code and title:
Strand 1:
MATHEMATICS
MTH 8.5 Percentages (Levels 6.3 – 7.3)
Number
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will:
1. Change percentages to fractions and decimals and vice-versa.
2. Express one quantity as a percentage of another.
3. Work out the percentage of a quantity.
4. Work out the percentage increase and decrease.
Key Words
Fraction, equivalent fraction,
decimal, convert, percentage
increase, percentage decrease.
Points to Note
Resources
FOM B1, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to promote a
Resource Pack – Chapters 10 and 18.
student centred learning environment.
From Teachers’ laptop:
Exposition: the teacher states the objectives of the lesson and may use ICT C:\Documents and Settings\teacher\My
software for students to practise new knowledge. This is consolidated by Documents\Maths Excel Lessons
setting students tasks that offer students the opportunity to apply
mathematics to a variety of real life situations.
Internet Links:
Discovery: the teacher can set group tasks in which students discuss and http://www.bbc.co.uk
construct mathematical knowledge. Students may become active learners
while testing hypotheses and/or making generalisations.
http://www.mathsisfun.com
Exploration: the teacher integrates an inquiry based learning approach that
enhances the students’ understanding of concepts. These tasks might
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
78
Teaching Objective
The teacher will teach students
to:
1. Change percentages to
fractions and decimals and
vice-versa.
Examples of teaching experiences and activities
Using euro coins and notes the students are asked about the relationship
between them.
Examples: Express:
1. 10 cent as a decimal and as a percentage of 20 cent;
2. 10 cent as a decimal and as a percentage of 1 euro;
3. €2.50 as a decimal and as a percentage of 5 euro.
The above results can be inputted in the spreadsheet:
Indicators of Learning outcomes
Students will be able to change fractions
and decimals to percentages without the
use of calculator.
(Level 7.3)
Students will be able to change
percentages to fractions and decimals
without the use of calculator.
(Level 7.2)
Students will be able to change
percentages to fractions and decimals
and vice versa using calculator when
necessary.
(Level 7.1)
Students practise converting fractions to decimals and percentages on this
online game. The students can play the game individually or in teams.
This game gives the students the opportunity to try different answers and
learn from their own mistakes.
http://www.math-play.com/Fractions-Decimals-PercentsJeopardy/fractions-decimals-percents-jeopardy.html
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to change fractions
with a factor of 100 as denominator, to
decimals and vice versa.
(Level 6.3)
79
2. Express one quantity as a
percentage of another.
Through this activity the students express one quantity as a percentage of
the other. The students carry out a survey of their favourite sports among
their classmates. The students express their results as percentages.
For example in a class of 30 students, 6 prefer volleyball.
6
 100  20%
30
So 20% of the class prefer volleyball.
The percentages are worked out using pencil and paper and checked with
the help of a calculator.
Finally, the data gathered is inputted in the spreadsheet. This allows
students to come up with a formula which can express one quantity as a
percentage of the other. The spreadsheet gives the students the
opportunity to represent their data as a bar chart or a pie chart. This enables
the students to compare the results pictorially.
3. Workout the percentage of a
quantity.
Students are organised in groups. They record the price of five items on sale
at the school tuck shop.
Students are asked to calculate different percentage values (e.g. 50%, 25%,
80%) of the recorded prices. These calculations are done using pencil and
paper or by the help of a calculator.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to solve simple
problems involving a quantity as a
percentage of another.
(Level 7.3)
Students will be able to express one
quantity as a percentage of another by
calculation and/or spreadsheet software.
(Level 7.2)
Students will be able to express one
quantity as a percentage of another.
(Level 7.1)
Students will be able to express quantities
out of multiples of 100 as a percentage.
(Level 6.3)
Students will be able to solve problems
which involve finding the percentage of a
quantity, using integral values.
(Level 7.3)
Students will be able to work out more
complex examples which involve finding
80
The recorded prices items are then inputted on a spreadsheet in the
computer lab to verify their results.
the percentage of a quantity.
(Level 7.2)
Students will be able to work out the
percentage of a quantity where the
percentage and/or the quantity is a
multiple of 5.
(Level 7.1)
Through the following sites the students reinforce percentage of quantities:
http://www.bbc.co.uk/schools/ks3bitesize/maths/number/percentages/revi
se3.shtml
Students will be able to work out the
percentage of a quantity where the
percentage and/or the quantity is a
multiple of 10.
(Level 6.3)
http://www.glencoe.com/sec/math/studytools/cgibin/msgQuiz.php4?isbn=1-57039-850-X&chapter=4&lesson=2
4. Work out the percentage
increase / decrease.
Students record the price of five items on sale at the school tuck shop. The
students compare these prices with those shown on a new price list
provided by another vendor.
When the prices differ, the percentage increase or decrease is found using
pencil and paper, calculator or spreadsheet software.
Students will be able to solve problems
which involve percentage
increase/decrease using integral values.
(Level 7.3)
Students will be able to work out the new
amount after a percentage
increase/decrease.
(Level 7.2)
Students will be able to work out the
percentage increase/decrease of a
quantity.
(Level 7.1)
The students are divided in groups.
Students will be able to work out the
Each member of the group gives the information requires to work out one of percentage increase / decrease of a
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
81
the following tasks:
 The amount of money you spend at the tuck shop on Monday and
on Friday.
 The amount of pocket money you received last year and this year.
 The number of hours you usually spend chatting on a weekday and
on a Sunday.
 The number of hours you usually spend doing your homework on a
weekday and on a Saturday.
quantity where the percentage and/or
the quantity is a multiple of 10.
(Level 6.3)
The percentage increase or decrease is found using pencil and paper,
calculator or spreadsheet software.
The following sites enable the students to reinforce solving percentage
increase / decrease:
http://www.mathgoodies.com/lessons/percent/change.html
http://www.themathpage.com/arith/percent-increase-or-decrease.htm
http://www.mangahigh.com/en/maths_games/number/percentages/perce
ntage_increase_and_decrease_calculator?localeset=en
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
82
Subject:
Unit code and title:
Strand 1:
MATHEMATICS
MTH 8.5 – Percentages (Levels 5.3 – 7.1)
Number
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will:
1. Change percentages to fractions and decimals and vice-versa.
2. Express one quantity as a percentage of another.
3. Work out the percentage of a quantity.
Key Words
Percentage , fraction ,
equivalent fractions.
Points to Note
Resources
FOM B Gold, Students’ Book, Resource
Three main teaching approaches are being recommended to promote a
Pack – Chapters 10 and 18
student centred learning environment.
From Teachers’ laptop:
Exposition: the teacher states the objectives of the lesson and may use ICT C:\Documents and Settings\teacher\My
software for students to practise new knowledge. This is consolidated by Documents\Maths Excel Lessons
setting students tasks that offer students the opportunity to apply
mathematics to a variety of real life situations.
Discovery: the teacher can set group tasks in which students discuss and
construct mathematical knowledge. Students may become active learners
while testing hypotheses and/or making generalisations.
Exploration: the teacher integrates an inquiry based learning approach that
enhances the students’ understanding of concepts. These tasks might
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
83
Teaching Objective
The teacher will teach students
to:
Examples of teaching experiences and activities
Using euro coins and notes the students are asked about the relationship
between them.
1. Change percentages to
fractions and decimals and
vice-versa.
Examples: Express:
1. 10 cent as a decimal and as a percentage of 20 cent;
2. 10 cent as a decimal and as a percentage of 50 cent;
3. €2.50 as a decimal and as a percentage of 5 euro.
Students practise converting fractions to decimals and percentages on this
online game. The students can play the game individually or in teams.
This game gives the students the opportunity to try different answers and
learn from their own mistakes.
http://www.math-play.com/Fractions-Decimals-PercentsJeopardy/fractions-decimals-percents-jeopardy.html
Indicators of Learning outcomes
Students will be able to change
percentages to fractions and decimals
and vice versa using calculator when
necessary.
(Level 7.1)
Students will be able to change fractions
with a factor of 100 as denominator, to
decimals and vice versa.
(Level 6.3)
Students will be able to change fractions
with a factor of 100 as denominator, to
percentages and vice versa.
(Level 6.2)
Students will be able to change integral
percentages to fractions and simplify
when necessary.
(Level 6.1)
2. Express one quantity as a
percentage of another.
Through this activity the students express one quantity as a percentage of
the other. The students carry out a survey of their favourite season among
their classmates. The students express their results as percentages.
For example in a class of 30 students, 6 prefer winter.
6
 100  20%
30
So 20% of the class prefer winter.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to list all the factors
of 100.
(Level 5.3)
Students will be able to express one
quantity as a percentage of another.
(Level 7.1)
Students will be able to express quantities
out of multiples of 100 as a percentage.
(Level 6.3)
84
The percentages are worked out using pencil and paper and checked with
the help of a calculator.
Students will be able to express quantities
out of factors of 100 as percentages.
(Level 6.2)
Students will be able to express quantities
out of 10 as percentages.
(Level 6.1)
3. Work out the percentage of
a quantity.
Students are organised in groups. They record the price of 5 items on sale at
the school tuck shop.
Students are asked to calculate different percentage values (e.g. 50%, 25%,
80%) of the recorded prices. These calculations are done using pencil and
paper or by the help of a calculator.
Through the following sites the students reinforce percentage of quantities:
http://www.bbc.co.uk/schools/ks3bitesize/maths/number/percentages/revi
se3.shtml
http://www.glencoe.com/sec/math/studytools/cgibin/msgQuiz.php4?isbn=1-57039-850-X&chapter=4&lesson=2
Students will be able to express quantities
out of 100 as percentages.
(Level 5.3)
Students will be able to work out the
percentage of a quantity where the
percentage and/or the quantity is a
multiple of 5.
(Level 7.1)
Students will be able to work out the
percentage of a quantity where the
percentage and/or the quantity is a
multiple of 10. (Level 6.3)
Students will be able to work out the
percentage of a quantity where the
percentage is a multiple of 10.
(Level 6.2)
Students will be able to work out the
percentage of a quantity which is a
multiple of 100. (Level 6.1)
Students will be able to appreciate that
100% represents the total amount.
(Level 5.3)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
85
Subject:
MATHEMATICS
Unit code and title: MTH 8.5 Percentages (Levels 1 - 4)
Strand 1:
Number
Form 2
Duration: 9 sessions of 40 minutes (6 hours)
Objectives at attainment levels 5 and 6
The teacher will teach the students to:
1. Change percentages to fractions and decimals and vice-versa. (Fractions are restricted to denominators that are factors of 100).
2. Express one quantity as a percentage of another.
3. Work out the percentage of a quantity.
The mainstream objective 1b (changing fractions to decimals and vice versa) and objective 3 are beyond attainment level 4 and below.
Objectives at attainment levels 1,2,3,4.
The teacher will teach the students to:
1.1 Develop the basic idea of percentages as the number of parts out of 10 and out of 100.
2.1 Identify the percentage and represent it as a number of parts out of a whole.
Key Words
Decimal , scales , round numbers ,
decimal places , rough estimate ,
accuracy , recurring decimal , nonrecurring decimal , percentage ,
fraction , percentage increase ,
percentage decrease.
Points to Note
In addition to the points to note recommended for students
performing at Level 5 or higher, it is very important for the teacher
to allow time for the students to respond. This response can take
the form of unaided and/or aided means of communication and
the teacher needs to provide adequate scaffolding techniques to
enable the students to respond affectively or intentionally.
For additional examples at Level 1, refer to the handbook.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Resources
New Maths Frame Working-Step Up
Workbook.
Oxford Framework Maths 7
Software: Ilearn Maths, Calculator,
Excel Worksheets
From Teachers’ laptop:
C:\Documents and
Settings\teacher\My
Documents\Maths Excel Lessons
86
Teaching Objective
The teacher will teach the students
to:
Examples of teaching experiences and activities
Starter: The teacher encourages the students to form talk
partners or groups to discuss the idea of parts and wholes.
1.1 Develop the basic idea of
percentages as the number of
parts out of 10 and out of 100.
Students will work on a grid (hard copy) or on the ilearn
software and colour or shade a number of parts. Then they
talk about the number of shaded parts out of the whole grid.
They can have a grid with 10 parts or 100 parts. The idea is to
end up with statements like 4 out of 10 or 4 out of 100 and
then 40%.
At level 3, the students will count the number out of ten parts
and circle their answer from a choice of two numbers.
At level 2, the students will match strips representing the
same number of shaded parts.
2.1 Identify the percentage and
represent it as a number of
parts out of a whole.
At level 1, the students will be involved in sensory activities
like using finger paint to paint a number of parts or else they
can use ICT skills like touch screen and the cause and effect
when they touch a box on the grid.
For further activities at attainment level 1 refer to the
handbook.
Starter: Given a statement like 50 out of 100, the students will
discuss and talk about its meaning.
The activities for this objective are the converse of the
activities in the previous objective.
Students are given statements like 30%, they discuss its
meaning, (30 out of 100) and colour the number of parts on a
grid or on a block graph. Same activities can be carried out on
a block graph.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Indicators of Learning Outcomes
Students will be able to count the
number of parts out of a whole number
and talk about it.
(Level 4)
Students will count and choose the
number matching the number of shaded
parts.
(Level 3)
Students will sort and match same
number of parts together.
(Level 2)
Students will be involved in sensory
activities by touching a screen to click on
the parts and drag them to form a
whole picture.
(Level 1)
Students will understand, interpret
mathematical statements and be able to
communicate them through drawing.
(Level 4)
Students will understand verbal
mathematical statements by marking,
shading, colouring or moving on in a
grid.
(Level 3)
87
At level 3, the students will work on the same activity but with
a reduced number of parts, say 10, and work out by colouring
or pointing to the number of parts out of 10.
Students will be able to point out the
odd one out of a selection of three.
(Level 2)
At level 2, the students will be given strips with coloured parts
and they have to identify the odd one out does not have the
same number of coloured parts.
Students will follow and focus on a line
of movement from one direction to the
next.
(Level 1)
At level 1, the students will be involved in sensory activities of
the type following a line of movement as the adult moves her
finger on things and then stops.
For further activities at attainment level 1 refer to the
handbook.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
88
Subject:
Unit code and title:
Strand 3:
MATHEMATICS
MTH 8.6 Area and Volume (Levels 7.1 – 8.1)
Shape, Space & Measures
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach students to:
1. Use the formula to find the area of a triangle; derive & use the formula to find the area of a parallelogram.
2. Calculate the area of compound shapes.
3. Work out the surface area of a cube and cuboid.
4. Find the volume of compound shapes involving cubes and cuboids.
5. Understand that the prism is a solid with uniform cross-section; find the volume of a prism using V= area of cross-section  length.
Key Words
Units, area, triangle, obtuseangled triangle, right-angled
triangle, parallelogram,
perpendicular height,
compound shapes, volume,
cube, cuboid, surface area,
cross-section, area of crosssection, prism.
Points to Note
Resources
FOM B2, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to promote a
Resource Pack – Chapter 17
student centred learning environment.
From Teachers’ laptop:
Exposition: the teacher states the objectives of the lesson and may use ICT C:\Documents and Settings\teacher\My
software for students to practice new knowledge. This is consolidated by Documents\Maths Excel Lesson
setting students tasks that offer students the opportunity to apply
mathematics to a variety of real life situations.
Solid shapes
Folding geometry shapes
Discovery: the teacher can set group tasks in which students discuss and
construct mathematical knowledge. Students may become active learners Internet Links:
while testing hypotheses and/or making generalisations.
http://www.cimt.plymouth.ac.uk
http://www.suffolkmaths.co.uk
Exploration: the teacher integrates an inquiry based learning approach that http://www.learner.org/interactives/geo
enhances the students’ understanding of concepts. These tasks might metry/area_surface.html
employ the processes of reasoning, problem solving, investigations, http://www.brainingcamp.com
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
89
Teaching Objective
The teacher will teach the
students to:
1. Use the formula to find the
area of a triangle; derive &
use the formula to find the
area of a parallelogram.
Examples of teaching experiences and activities
Review how to find the area of a rectangle, and the properties of the
parallelogram. Use different cardboard cut parallelograms and distribute to
students who will be divided into groups of three. Ask them to try and find a
single straight cut in order to form a rectangle.
=
Then lead students to discover the formula A= bh.
Introduce the three types of triangles; obtuse, acute, and right-angled. Use
identical pairs of cardboard cut triangles to show that together they will
always form a parallelogram. Then lead students to derive the formula:
Area = ½(base)(height). Students will then work with different triangles and
their measurements in order to find the area. Discuss why knowing how to
find the area of a triangle is important. Help the students realize that a
carpenter or architect will need to know this information.
Use the following site to practice using the formula to calculate the area of
different triangles.
http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i9/bk7_9i5.htm
2. Calculate the area of
compound shapes.
Students suggest different ways how compound shapes can be divided into
squares/rectangles. The area of the composite shape is then calculated
using different suggested arrangements, concluding that the result is the
same.
Students are given compound shapes which can be split into right-angled
triangles and squares/rectangles and the area is again calculated.
Students are given compound shapes which can be split into triangles which
need not be right-angled and squares/rectangles and the area is again
calculated.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Indicators of Learning outcomes
Students will be able to derive the
formula A = ½bh for the area of a triangle
(Level 8.1)
Students will be able to derive the
formula A = bh for the area of a
parallelogram.
(Level 7.3)
Students will be able to use the formulae
to find the area of a parallelogram and a
triangle.
(Level 7.2)
Students will be able to work out the area
of a triangle given the area of a rectangle
or parallelogram.
(Level 7.1)
Students will be able to find the area of
compound shapes formed of
squares/rectangles and triangles which
need not be right-angled, using formulae.
(Level 8.1)
Students will be able to find the area of
compound shapes which can be split into
right-angled triangles and
squares/rectangles, using formulae.
(Level 7.3)
90
Students can access these sites:
http://www.suffolkmaths.co.uk/pages/Lesson%20Resources/Shape/20%20
Mensuration/Questions%20-%20Composite%20Shapes%2056.pdf
3. Work out the surface area
of a cube and cuboid.
Students will be able to find the area of
compound shapes which can be split into
squares/rectangles, using formulae.
(Level 7.2)
http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i9/bk7_9i4.htm
Students will be able to find the area of
compound shapes which can be split into
right-angled triangles and
squares/rectangles by counting squares.
(Level 7.1)
Teacher shows a couple simple of applications of the surface area of a cube
and cuboid. For example: Melanie wants to make a coin box, the shape of a
cube with an edge 10 cm long or a pencil box whose shape is cuboid where
the length, width and height are 20 cm, 7 cm and 2 cm respectively
Teacher shows cardboard models of the cube and the cuboid and asks
students how many squares/rectangles are needed to build the cube and
the cuboid. Teacher asks students the area of each square and rectangle and
guides students in finding the surface area of the cube and cuboid. Teacher
will gradually introduce the formal method using the formula.
Students will be able to derive the
formulae for the surface area of a cube, A
= 6l2 and a cuboid, A = 2(lb+lw+bw)
(Level 8.1)
Students will be able to find: the side of a
cube given the surface area; a side of a
cuboid given the surface area and the
other two sides.
(Level 7.3)
Teacher gives examples and solves them together with students.
Teacher can use these sites to demonstrate the concept of surface area of a
cuboid.
http://www.learner.org/interactives/geometry/area_surface.html
4. Find the volume of
compound shapes involving
cubes and cuboids.
Students will be able to use the formulae
to find the surface area of a cuboid.
(Level 7.2)
http://www.brainingcamp.com/resources/math/surfacearea/interactive.php
Students will be able to use the formulae
to find the surface area of a cube.
(Level 7.1)
The students are divided in groups. The teacher provides each group with a
worksheet involving compound shapes made up of cubes and cuboids.
Students have to split the shapes in cuboids (or cubes), find the dimensions
of each and finally calculate the total volume of the compound shape.
Students will be able to find the volume
of compound shapes involving more than
2 components (cubes/cuboids).
(Level 8.1)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
91
Students play a domino game involving compound shapes. The students
have to match the compound shape on one domino to its volume on
another domino.
The students may practice finding the volume of compound shapes involving
cubes and cuboids on the site:
http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i22/bk7_22i3.
htm
5. Understand that the prism
is a solid with uniform
cross-section; find the
volume of a prism using V=
area of cross-section 
length.
Show students three dimensional models of a number of solids. Define a
prism and ask them to identify the prisms. Discuss with students which face
of the prism is the cross-section and how to identify the perpendicular
length.
Pick out the rectangular prism and deduce that V = b  h  l = (b  h)  l =
area of cross-section  length. Explain how this formula works out for all
prisms.
Practice finding the volume of triangular prisms using the following site:
http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i22/bk7_22i6.
htm
Students will be able to find the volume
of compound shapes involving 2
components (cubes/cuboids).
(Level 7.3)
Students will be able to identify the
dimensions of the components
(cubes/cuboids) of a compound shape.
(Level 7.2)
Students will be able to identify the
components (cubes/cuboids) making up a
compound shape.
(Level 7.1)
Students will be able to derive the
formula: V= area of cross-section 
length.
(Level 8.1)
Students will be able to find the length of
a prism given the volume and crosssectional area.
(Level 7.3)
Students will be able to find the volume
of a prism where the cross section is a
triangle or a parallelogram.
(Level 7.2)
Students will be able to find the volume
of a prism where the cross section is a
square or a rectangle.
(Level 7.1)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
92
Subject:
Unit code and title:
Strand 3:
MATHEMATICS
MTH 8.6 Area and Volume (Levels 6.3 – 7.3)
Shape, Space & Measure
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach students to:
1.
Use the formula to find the area of a triangle; derive & use the formula to find the area of a parallelogram.
2.
Calculate the area of compound shapes.
3.
Work out the surface area of a cube and cuboid.
4.
Find the volume of compound shapes involving cubes and cuboids.
5.
Understand that the prism is a solid with uniform cross-section; find the volume of a prism using V= area of cross-section  length.
Key Words
Units, area, triangle, obtuseangled triangle, right-angled
triangle, parallelogram,
perpendicular height,
compound shapes, volume,
cube, cuboid, surface area,
cross-section, area of crosssection, prism.
Points to Note
Resources
FOM B1, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to promote a
Resource Pack – Chapter 17
student centred learning environment.
From Teachers’ laptop:
Exposition: the teacher states the objectives of the lesson and may use ICT C:\Documents and Settings\teacher\My
software for students to practice new knowledge. This is consolidated by Documents\Maths Excel Lessons
setting students tasks that offer students the opportunity to apply
mathematics to a variety of real life situations.
Internet Links:
http://www.cimt.plymouth.ac.uk
Discovery: the teacher can set group tasks in which students discuss and http://www.suffolkmaths.co.uk
construct mathematical knowledge. Students may become active learners http://www.learner.org/interactives/geo
while testing hypotheses and/or making generalisations.
metry/area_surface.html
http://www.brainingcamp.com
Exploration: the teacher integrates an inquiry based learning approach that
enhances the students’ understanding of concepts. These tasks might
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
93
Teaching Objective
The teacher will teach the
students to:
1. Use the formula to find
the area of a triangle;
derive & use the
formula to find the area
of a parallelogram.
2. Calculate the area of
compound shapes.
Examples of teaching experiences and activities
Review how to find the area of a rectangle, and the properties of the
parallelogram. Use different cardboard cut parallelograms and distribute
them to students who will be divided into groups of three. Ask them to try
and find a single straight cut in order to form a rectangle.
=
Then lead students to discover the formula A= bh.
Introduce the three types of triangles; obtuse, acute, and right-angled. Use
identical pairs of cardboard cut triangles to show that together they will
always form a parallelogram. Then lead students to derive the formula:
Area = ½(base)(height). Students will then work with different triangles in
order to find the area. Discuss why knowing how to find the area of a
triangle is important. Help the students realize that a carpenter or architect
will need to know this information.
Use the following site to practice using the formula to calculate the area of
different triangles.
http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i9/bk7_9i5.htm
Students suggest different ways how compound shapes can be divided into
squares/rectangles. The area of the composite shape is then calculated
using different suggested arrangements, concluding that the result is the
same.
Students are given compound shapes which can be split into right-angled
triangles and squares/rectangles and the area is again calculated.
Students are given compound shapes which can be split into triangles which
need not be right-angled and squares/rectangles and the area is again
calculated.
Indicators of Learning outcomes
Students will be able to derive the
formula A = bh for the area of a
parallelogram.
(Level 7.3)
Students will be able to use the formulae
to find the area of a parallelogram and a
triangle.
(Level 7.2)
Students will be able to work out the area
of a triangle given the area of a rectangle
or parallelogram.
(Level 7.1)
Students will be able to find the area of a
rectangle/square by adding unit squares
(Level 6.3)
Students will be able to find the area of
compound shapes which can be split into
right-angled triangles and
squares/rectangles, using formulae.
(Level 7.3)
Students will be able to find the area of
compound shapes which can be split into
squares/rectangles, using formulae.
(Level 7.2)
Students will be able to find the area of
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
94
Students can access these sites:
http://www.suffolkmaths.co.uk/pages/Lesson%20Resources/Shape/20%20
Mensuration/Questions%20-%20Composite%20Shapes%2056.pdf
compound shapes which can be split into
right-angled triangles and
squares/rectangles by counting squares.
(Level 7.1)
http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i9/bk7_9i4.htm
Students will be able to find the area of
compound shapes which can be split in
squares / rectangles, by counting squares
on a grid.
(Level 6.3)
3. Work out the surface
area of a cube and
cuboid.
Teacher shows a couple simple of applications of the surface area of a cube
and cuboid. For example: Melanie wants to make a coin box, the shape of a
cube with an edge 10 cm long or a pencil box whose shape is cuboid where
the length, width and height are 20 cm, 7 cm and 2 cm respectively
Teacher shows cardboard models of the cube and the cuboid and asks
students how many squares/rectangles are needed to build the cube and
the cuboid. Teacher asks students the area of each square and rectangle and
guides students in finding the surface area of the cube and cuboid. Teacher
will gradually introduce the formal method using the formula.
Students will be able to find: the side of a
cube given the surface area; a side of a
cuboid given the surface area and the
other two sides.
(Level 7.3)
Students will be able to use the formulae
to find the surface area of a cuboid.
(Level 7.2)
Teacher gives examples and solves them together with students.
Teacher can use these sites to demonstrate the concept of surface area of a
cuboid.
http://www.learner.org/interactives/geometry/area_surface.html
http://www.brainingcamp.com/resources/math/surfacearea/interactive.php
4. Find the volume of
compound shapes
involving cubes and
cuboids.
The students are divided in groups. The teacher provides each group with a
worksheet involving compound shapes made up of cubes and cuboids.
Students have to split the shapes in cuboids (or cubes), find the dimensions
of each and finally calculate the total volume of the compound shape.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to use the formulae
to find the surface area of a cube.
(Level 7.1)
Students will be able to find the surface
area of cubes and cuboids by adding the
areas of each face.
(Level 6.3)
Students will be able to find the volume
of compound shapes involving 2
components (cubes/cuboids).
(Level 7.3)
95
Students play a domino game involving compound shapes. The students
have to match the compound shape on one domino to its volume on
another domino.
The students may practice finding the volume of compound shapes involving
cubes and cuboids on the site:
http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i22/bk7_22i3.
htm
Students will be able to identify the
dimensions of the components
(cubes/cuboids) of a compound shape.
(Level 7.2)
Students will be able to identify the
components (cubes/cuboids) making up a
compound shape.
(Level 7.1)
Students will be able to calculate the
volume of simple compound shapes given
the description of its 2 components.
(Level 6.3)
5. Understand that the prism
is a solid with uniform
cross-section; find the
volume of a prism using V=
area of cross-section 
length.
Show students three dimensional models of a number of solids. Define a
prism and ask them to identify the prisms. Discuss with students which face
of the prism is the cross-section and how to identify the perpendicular
length.
Pick out the rectangular prism and deduce that V = b  h  l = (b  h)  l =
area of cross-section  length. Explain how this formula works out for all
prisms.
Practice finding the volume of triangular prisms using the following site:
http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i22/bk7_22i6.
htm
Students will be able to find the length of
a prism given the volume and crosssectional area.
(Level 7.3)
Students will be able to find the volume
of a prism where the cross section is a
triangle or a parallelogram.
(Level 7.2)
Students will be able to find the volume
of a prism where the cross section is a
square or a rectangle.
(Level 7.1)
Students are able to identify prisms, their
cross-section and length.
(Level 6.3)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
96
Subject:
MATHEMATICS
Unit code and title: MTH 8.6 Area & Volume (Levels 5.3 – 7.1)
Strand 3:
Shape, Space & Measures
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach students to:
1. Find the perimeter of simple shapes by adding side lengths.
2. Use the formula to find the area of a rectangle; find the area of simple shapes made up of rectangles.
3. Find the volume of cubes and cuboids by counting cubes/using formula.
4. Find the volume of compound shapes involving cubes and cuboids.
Key Words
Units, area, triangle,
parallelogram, compound
shape, volume, cube, cuboid.
Points to Note
Resources
FOM B Gold, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to promote
Resource Pack – Chapter 17
a student centred learning environment.
Exposition: the teacher states the objectives of the lesson and may use From Teachers’ laptop:
ICT software for students to practise new knowledge. This is C:\Documents and Settings\teacher\My
consolidated by setting students tasks that offer students the Documents\Maths Excel Lessons
opportunity to apply mathematics to a variety of real life situations.
Internet Links:
Discovery: the teacher can set group tasks in which students discuss http://www.whiteboardmaths.com
and construct mathematical knowledge. Students may become active http://www.mathsisfun.com/cuboid.html
learners while testing hypotheses and/or making generalisations.
http://www.bbc.co.uk/skillswise
http://www.cimt.plymouth.ac.uk/projects
Exploration: the teacher integrates an inquiry based learning approach http://pbskids.org
that enhances the students’ understanding of concepts. These tasks http://www.teacherled.com/resources/isoexpl
might employ the processes of reasoning, problem solving, ode/isoexplodeload.html
investigations, connecting ideas and concepts, and expressing results http://www.superteacherworksheets.com
by using the precise language of mathematics.
http://www.eduplace.com
http://www.teachingideas.co.uk/maths
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
97
Teaching Objective
Examples of teaching experiences and activities
Indicators of Learning outcomes
The teacher will teach the
students to:
The teacher discusses the following practical examples with the whole
class to elicit the meaning of perimeter:
 length of ribbon needed to surround a photo (in centimetre),
 buying skirting for the classroom (in metre)
 buying fencing for a field (in metre).
The students can be asked beforehand to bring a photo and a ribbon.
Each student is asked to surround it with the ribbon and hence find the
perimeter of the photo
Students are placed in groups of three. Students are given different
cardboard-made composite shapes (irregular polygons – length of
sides must be whole numbers). Students must in turn have the
following roles: using a ruler, one student measures the sides of the
shape, another one checks the measurement and the third student
writes the measurement on a piece of paper. Then together they must
add the sides to find the perimeter of the shape.
Students will be able to find the perimeter of
flat shapes by adding the lengths of all sides;
practice their addition skills as they learn how
to find the perimeter of a figure
(Level 7.1)
The teacher divides the students into two groups. Then he/she projects
the site on the interactive whiteboard by clicking
http://www.bgfl.org/bgfl/custom/resources_ftp/clientftp/ks2/maths/p
erimeter_and_area/index.html (under perimeter). The teacher asks
each leader of each group to give the answers in the form of a quiz.
Students will be able to understand that
perimeter is a linear measurement. Restrict to
cm and mm.
(Level 6.1)
1. Find the perimeter of
simple shapes by
adding side lengths.
Students will be able to find the perimeter of
composite shapes drawn on a grid, by counting
unit squares on each side of each flat shape.
(Level 6.3)
Students will be able to find the perimeter of
rectangles/squares drawn on a grid, by
counting unit squares on each side.
(Level 6.2)
Students will be able to understand the notion
of perimeter as adding all sides.
(Level 5.3)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
98
2. Use the formula to find
the area of a rectangle;
find the area of simple
shapes made up of
rectangles.
Define area: When we think of the area of something, we think how
much ground (or surface) it is covering (or would cover). Area is always
measured in squares of some size. People often use square
centimetres, and square metres for measuring area.
We use the superscript “2” with a unit of length to indicate the
“squaring”. For example 120 cm2 means 120 square centimetres.
Teacher gives out cardboard cut rectangles of different sizes to
students. They will be asked to measure and mark the lengths and
breadth. Then they draw horizontal and vertical lines to form a grid on
each rectangle. Counting these squares gives the area of each
rectangle. Help students realize that one doesn’t necessarily need to
draw and count squares but they can simply multiply the length by the
breadth. Hence deduce the formula Area = length  breadth.
Show students more examples of finding the area of some rectangles,
squares and compound shapes made up of squares and rectangles.
Students will be able to find the area of
compound shapes made up of unmarked
squares and rectangles using the formula.
(Level 7.1)
Students will be able to find the area of
compound shapes made up of squares and
rectangles indicated on the shape and by using
the formula.
(Level 6.3)
Students will be able to solve a worded
problem on finding the area of a rectangle by
using the formula.
(Level 6.2)
Students will Students will be able to find the
area of a rectangle by using the formula.
(Level 6.1)
Students will be able to find the area of a
rectangle drawn on a grid by counting squares.
(Level 5.3)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
99
3. Find the volume of
cubes and cuboids by
counting cubes/using
formula.
The students draw the net of a cuboid on centimetre squared paper
and add the flaps to make a solid shape from their net. The dimensions
of their cuboid are obtained by counting the number of 1 cm squares
on each edge. The number of cubes making up the cuboid is equivalent
to value of the volume of the cuboid obtained by calculation.
Students view the following power point on volume
http://www.whiteboardmaths.com/content/samples/df11683bb425d8
a08bd5ba406797ba1c.ppt
The students bring to school a number of boxes, such as cereal
packets, pasta packets etc. and they measure the lengths of the sides
and find the volume of the box.
The students may use this site as a volume calculator or the can find
the dimensions of a cuboid given the volume.
http://www.mathsisfun.com/cuboid.html
The site
http://www.bbc.co.uk/skillswise/numbers/measuring/volume/index.s
html provides the teacher with notes, online tests and worksheets on
finding the volume of a cube and cuboid.
The students may practice finding the volume of a cuboid using the
formula on the site:
http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i22/bk7
_22i3.htm
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to solve worded problems
involving finding the volume of a cuboid as part
of the solution. E.g. How many cubes of
volume 4 cm3 can be filled with sand from a
cuboid which is 2 cm  4 cm  8 cm
(Level 7.1)
Students will be able to solve worded problems
involving finding the volume of a cuboid.
(Level 6.3)
Students will be able to find the volume of a
cuboid using the formula.
(Level 6.2)
Students will be able to understand that
volume is measured in unit cubes
(Level 6.1)
Students will be able to understand the
concept of volume as the amount of space
occupied by the solid shape.
(Level 5.3)
100
4. Find the volume of
compound shapes
involving cubes and
cuboids.
The following websites show how to find the volume of a compound
shape by counting the cubes inside:
http://pbskids.org/curiousgeorge/video/video_pop.html?clip=interstiti
als/108B&title=Volume%20and%20Shapes&ar=16:9&filetype=wmv&b
andwidth=_hi
Working in pairs on a computer the students investigate the volume of
compound shapes by counting cubes, by accessing the following
website:
http://www.teacherled.com/resources/isoexplode/isoexplodeload.html
The worksheets from the following websites:
http://www.superteacherworksheets.com/geometry/volume-cubeseasy.pdf,
http://www.eduplace.com/math/mthexp/g3/challenge/pdf/cm_g3_f_
2.pdf and
http://www.teachingideas.co.uk/maths/files/volumeofcubes.pdf can
be done in class as group work, pair work or individually. These could
be printed and be given as homework as well.
Students will be able to identify the
components (cubes and cuboids) making up a
compound shape and find its volume.
(Level 7.1)
Students will be able to calculate the volume of
simple compound shapes given the description
of its components
(Level 6.3)
Students will be able to find the volume of the
compound shapes by adding the volume of the
different components.
(Level 6.2)
Students will be able to identify the 2
components (cubes or cuboids) making up the
compound shape.
(Level 6.1)
Students will be able to find the volume of a
compound shape by counting cubes.
(Level 5.3)
Subject:
Mathematics
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Form 2
101
Unit code and title: MTH 8.6 Area & Volume (Levels 1 - 4)
Strand 3:
Shape, Space & Measures
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives at attainment Level 5 and 6
The teacher will teach the students to:
1. Find the perimeter of simple shapes by adding side lengths.
2. Use formula to find the area of a rectangle; find the area of simple shapes made up of rectangles.
3. Find the volume of cubes and cuboids by counting cubes/using formula.
4. Find the volume of compound shapes involving cubes and cuboids.
Objectives at attainment levels 1, 2, 3, 4
The teacher will teach the students to:
1.1 Recognise the space enclosed by the boundary and use simple addition facts to find the total space enclosed.
2.1 Be familiar with standard measurement tools.
3.1 Use simple addition or multiplication or doubling facts to work out the area.
4.1 Explore and compare the use of the space in a 3D shape.
Key Words
Counting, squares, length,
add, side, double, bigger,
smaller, greater and larger.
Points to Note
In addition to the points to note recommended for students performing at
Level 5 or higher, it is very important for the teacher to allow time for the
students to respond. This response can take the form of unaided and/or
aided means of communication and the teacher needs to provide adequate
scaffolding techniques to enable the students to respond effectively or
intentionally.
Resources
New Maths Frame Working-Step Up
Workbook.
Oxford Framework Maths 7
For further examples at attainment levels refer to the handbook.
Perimeter and Area
http://www.brainpopjr.com/math/measure
ment/area/grownups.weml#teachers
http://www.studyzone.org/testprep/math4/k
/squaresp.cfm
http://www.brainpopjr.com/math/measure
ment/area/activity/
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Software: Ilearn Maths, Calculator, Excel
Worksheets
102
Teaching Objective
The teacher will teach
students to:
Examples of teaching experiences and activities
Starter: Students are given shapes or pictures and they are asked to point,
talk about the length and width of each shape.
1.1. Students will recognise
about the space
enclosed by the
boundary and use
simple addition facts to
find the total space
enclosed.
Students are presented with a shape divided into squares and they have to
count the boxes covering the length and the boxes covering the width. Then
they can compare the sizes and talk about the space covered. Eventually,
they record the length of the sides and add them up.
Students are presented with shape objects and they are asked to count the
number of sides per object and talk about the differences in the number of
sides such that a shape with a larger boundary is covering more space. At
this level, the number of blocks inside the shapes will be limited to a total of
10 squares so the students can use rote counting.
At level 3, students will be shown the same objects but varying in size and
they talk which shape requires the largest and the smallest number of
cubes.
At level 2, the students will surround or fill a shape with cubes or other
objects.
2.1 Students will be familiar
with standard
measurement tools.
At level 1, the students will put objects through object holes.
Using
http://www.priorywoods.middlesbrough.sch.uk/page_viewer.asp?page=Fre
e Program Resources&pid=161 the students just observe the different
shapes on the screen and they maintain attention for a short period of time.
The shapes on the screen are also presented to the students to observe and
manipulate.
Starter: Students are presented with a ruler and they are left to explore it.
Different students with roughly different palm hand sizes are asked to
measure the length and width of their table by counting with their palms.
Since they will end up with different answers they can discuss the reliability
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Indicators of Learning outcomes
Students will use simple addition facts to
work out the perimeter of the shape.
(Level 4)
Students will use rote counting up to ten to
find the total perimeter and possibly
compare the perimeter of two shapes by
indicating the larger/smaller one.
(Level 3)
Students will develop awareness of distance
and direction when placing objects in the
surrounding path.
(Level 2)
Students will grab an object and with support
put it in a peg hole.
(Level 1)
Students will be able to investigate and
discuss the disadvantages of non-standard
and the advantages of standard
measurement tools.
(Level 4)
103
of using a non-standard tool of measurement. Together with the teacher
they talk the possibility of having a standard tool which will give the same
answer.
Students are presented with the same chocolate brand but which differ in
size. Teacher shows them 2 bars of each and they discuss which one they
would prefer. This will give them the idea of bigger and smaller.
Students will sort the same object but with varying sizes into different sets.
3.1 Students will use simple
addition or
multiplication or
doubling facts to work
out the area.
Students will compare sizes and recognise
differences in size.
(Level 3)
Students will develop knowledge of size and
begin to group a set of objects by size.
(Level 2)
At level 1, students will be involved in palm printing to get the idea of the
object size.
Students will participate and focus their
attention on their hand movement along a
line.
(Level 1)
Starter: Students are shown a coloured rectangular grid and they have to
calculate the inside space. E.g. a 4 X 3 grid boxes.
Students will use and apply their knowledge
of counting in 2’s, 3’s, 5’s and 10’s to
calculate the area of a shape.
(Level 4)
As a follow up to the above, the students will discuss how we can calculate
the inside space if the rectangle is without grid boxes. They can be led to the
concept of counting in 3’s or in 4’s.
Students are presented with a grid containing coloured squares. They have
to count the number of coloured squares on the grid. Then, they can have a
try to draw their own shape given the number of squares to be coloured like
draw a square or rectangle and draw the lines inside them.
Students are presented with squared shapes and they have to match like
with like through one to one correspondence.
Students are presented with different shapes like shoe box, match box, a
cone shape. They are asked to put their hand in and take out the objects
inside whilst feeling the differences in the structure of the shape.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will become aware of the space
different objects cover through counting.
(Level 3)
Students will match shapes with the same
area.
(Level 2)
Students will pour in and remove contents
from a container whilst feeling the different
texture of the shape.
(Level 1)
104
4.1 Students explore and
compare the use of the
space in a 3D shape.
Starter: Students are presented with two different 3D shapes. They explore,
manipulate and talk about them.
Students are given a range of cubes and cuboids. With adult support they
are asked to engage in structured play to form a shape made up of a cuboid
and a cube or else two cuboids or two cubes. Then they fill the shapes made
with small cubes and they count the cubes needed. They can use different
colours for the two shapes and they work out a simple addition sum to find
out the total.
Students are presented with solid shapes. They play with them to fit them
together. They will investigate how to fit small boxes inside larger cardboard
boxes and discuss how they fit in.
Students become aware of the difference in spaces e.g. how many tennis
balls would fit into a small box or a large box. They realise that bigger
containers would need more items.
Students will use addition facts in problem
solving situations about shapes.
(Level 4)
Students will start to compare sizes and
quantities in relation to shapes.
(Level 3)
Students will start developing knowledge of
shape and its size in terms of the amount
needed to fill a space.
(Level 2)
Students will be able to react to the auditory
responses made by adults.
(Level 1)
The adult plays with the students by talking through a open cylinder from
both ends, blow from a straw whilst students listen and experience and
notice the differences in sound pitch.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
105
Subject:
Unit code and title:
Strand 3:
MATHEMATICS
MTH 8.7 Triangles and Quadrilaterals (Levels 7.1 – 8.1)
Shape, Space & Measures
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Classify triangles and quadrilaterals by identifying their geometric properties through line and/or rotational symmetry.
2. Identify tessellating shapes and cover a given area with tessellating shapes.
3. Make accurate drawings of triangles.
4. Draw simple scale drawings from given data and interpret scale drawings.
5. Draw scale drawings to solve problems involving angles of elevation and depression.
Key Words
Triangles: scalene, isosceles,
equilateral, right-angled
Points to Note
Quadrilaterals: square,
rectangle, trapezium, rhombus,
parallelogram, kite
From Teachers’ laptop:
Exposition: the teacher states the objectives of the lesson and may use ICT C:\Documents and Settings\teacher\My
software for students to practise new knowledge. This is consolidated by Documents\Maths Excel Lessons
setting students tasks that offer students the opportunity to apply
- Quadrilaterals.xls
mathematics to a variety of real life situations.
From Teachers’ laptop:
Discovery: the teacher can set group tasks in which students discuss and C:\Documents and Settings\teacher\My
construct mathematical knowledge. Students may become active learners Documents\Maths PowerPoint Shows
while testing hypotheses and/or making generalisations.
- Construct a Triangle (SSS).pps
- Construct a Triangle (ASA).pps
Exploration: the teacher integrates an inquiry based learning approach
- Construct a Triangle (SAS).pps
that enhances the students’ understanding of concepts. These tasks might
- Quadrilaterals.pps
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise Internet Link:
language of mathematics.
http://nrich.maths.org
Line symmetry, rotational
symmetry
Tessellations
Scale, scale drawing, angle of
elevation, angle of depression
Resources
FOM B2, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to promote a
Resource Pack – Chapters 7 and 12
student centred learning environment.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
106
Teaching Objective
The teacher will teach the
students to:
1. Classify triangles and
quadrilaterals by
identifying their
geometric properties
through line and/or
rotational symmetry.
Examples of teaching experiences and activities
The teacher divides the class into groups of 3 and asks them to look at the
decision tree diagram available on page 102.
The students need to follow the decision boxes provided to classify
triangles into: scalene, isosceles, equilateral, scalene right-angled and
isosceles right-angled.
For the more able students, the teacher might consider giving them the
task on page 103. In this case students need to fill in the questions in the
decision boxes to elicit the geometric properties of triangles.
A second group activity could involve students in classifying quadrilaterals.
However, this time, the students’ task involves producing their own
decision tree diagram to classify quadrilaterals – square, rectangle,
rhombus, parallelogram, trapezium, arrowhead and kite.
This activity is more challenging – is more open and requires more
insightful reasoning skills. Thus the teacher must plan time for a plenary
(the students’ presentation and discussion) of the decision tree diagrams
presented. Each group needs to be given time to present their work, that
is, present their explorations and explanations. Other students should be
encouraged to challenge the format, the questions and the classification
presented by each group.
Otherwise the teacher can use the Maths Excel Lesson ‘Quadrilateral.xls’
and the PowerPoint presentation ‘Quadrilaterals.pps’ available on the
teacher’s laptop. Through pair work students can elicit the geometric
properties of different quadrilaterals and this can be followed by a wholeclass discussion. Here the teacher might also make use of geo-sticks.
Allowing students to assemble the different shapes can help them
discovering the essential properties.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Indicators of Learning outcomes
Students will be able to classify triangles
and quadrilaterals by identifying their
geometric properties through line and
rotational symmetry.
(Level 8.1)
Students will be able to classify triangles
and distinguish between square, rectangle,
rhombus and parallelogram by identifying
some geometric properties including line
or rotational symmetry.
(Level 7.3)
Students will be able to distinguish
between isosceles, equilateral and scalene
triangles and between a square and a
rectangle using their geometric properties.
(Level 7.2)
Students will be able to classify triangles
and quadrilaterals according to number of
sides, length of sides, right angles and size
of angles.
(Level 7.1)
107
2. Identify tessellating
shapes and cover a
given area with
tessellating shapes.
The teacher starts the lesson by showing a few examples of tessellating
shapes and patterns, and later asking students to find real-life
applications, such as, tessellations used in pavements and tiles, and
tessellations in nature, for example, the honeycomb, pineapples and
snakes’ skin.
Working in a computer lab, the teacher sets students working in pairs on
the activity available at http://nrich.maths.org/6069 .
Here the students investigate the tessellation properties of a number of
polygons – they can also draw some of these tessellations on isometric
paper.
After this initial task, the teacher presents students with the problem
available at http://nrich.maths.org/4831.
The students are asked to show whether the convex hexagon below
tessellates or not.
Students will be able to create tessellating
shapes and use it to cover a given area,
such as tiling a room.
(Level 8.1)
Students will be able to draw tessellating
shape and select the appropriate
arrangement to cover a given area, such as
tiling a room.
(Level 7.3)
Students will identify shapes that need to
be rotated to tessellate and be able to
continue a pattern with such shapes.
(Level 7.2)
Students will be able to identify shapes
that need to be rotated to tessellate.
(Level 7.1)
Note:
A + B + C = 180°
x=y
Eventually, the teacher can extend this activity by challenging the whole
class to show whether it is possible to tessellate all convex hexagons
and/or to find a counter example.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
108
3. Make accurate
drawings of triangles.
The teacher starts this lesson by asking groups of students to find out the
information they would require in order to draw an accurate triangle.
After this 5 minute activity, the teacher can ask each group of students to
justify their choice.
The teacher can then use students’ responses to introduce the main
teaching activity below.
Using the Maths PowerPoint shows available on the teacher’s laptop, that
is:
- Construct a Triangle (SSS).pps
- Construct a Triangle (ASA).pps
- Construct a Triangle (SAS).pps
The teacher can again set students to work in pairs on a computer to view
and practice the step by step presentations in making accurate drawings of
different triangles using ruler and protractor.
For the more able students, the teacher could also challenge them to draw
triangles using ruler and compasses only.
Students will be able to make accurate
drawings of triangles given (a) the length of
the three sides using ruler and compasses;
(b) the length of one side and two angles
using ruler and compasses and/or
protractor; and (c) two sides and the
included angle using ruler and compasses
and/or protractor.
(Level 8.1)
Students will be able to make accurate
drawings of triangles given (a) the length of
the three sides using ruler and compasses
only; (b) the length of one side and two
angles using ruler and protractor; and (c)
two sides and the included angle using
ruler and protractor.
(Level 7.3)
Students will be able to make accurate
drawings of triangles given (a) the length of
one side and two angles using ruler and
protractor; and (b) two sides and the
included angle using ruler and protractor.
(Level 7.2)
Students will be able to make an accurate
drawing of triangles given two sides and
the included angle using ruler and
protractor.
(Level 7.1)
4. Draw simple scale
drawings from given
The teacher provides groups of students with the actual measurements of
a particular area/field, such as, the classroom, the school’s hall, the
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to draw scale
drawings from given data and use scale
109
data and interpret scale
drawings.
teacher’s staffroom and the school’s football pitch, netball court and/or
tennis court.
Note: Ideally students take on-site measurements themselves.
Each group will use the given/taken measurements to decide on the most
convenient scale to use to draw their scale drawing on an A4 blank sheet
of paper.
The teacher can then ask students to use their scale drawing to work out
the actual distances of other lengths not indicated in the original given
data.
The teacher might want to conclude this activity by asking each group to
present their work to the whole class.
drawings to find actual distances and
areas.
(Level 8.1)
Students will be able to draw simple scale
drawings from given data and interpret
scale drawings.
(Level 7.3)
Students will be able to draw and interpret
simple scale drawings, that is, involving
positive integer lengths and ratios.
(Level 7.2)
Students will be able to draw and interpret
scale drawings using a ratio of 1cm to
represent 1m and/or 1 km.
(Level 7.1)
5. Draw scale drawings to
solve problems
involving angles of
elevation and
depression.
A practical hands-on group activity involves students in using a clinometer
to work out the height of a building (the school) or a vertical object (a tree
or a flagpole) – from ground level and from an elevated level.
The students are asked to draw a sketch diagram of each situation and
take the necessary measurements using measuring tape and the
clinometer.
Hence, students draw scale drawings and finally work out the height of the
building and/or object.
The teacher can ask the different groups of students to compare their
measurements and their final answers, encouraging them to discuss and
justify their accuracy in working out results.
Students will be able to draw scale
drawings to solve complex problems
involving angles of elevation and
depression.
(Level 8.1)
Students will be able to draw scale
drawings to solve simple problems
involving angles of elevation and
depression.
(Level 7.3)
Students will be able to draw a scale
drawing to solve a simple problem
involving an unknown height (e.g.: finding
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
110
the height of a tree).
(Level 7.2)
Students will be able to solve a simple
problem from a given scale drawing
involving angles of elevation.
(Level 7.1)
Subject:
MATHEMATICS
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Form 2
111
Unit code and title:
Strand 3:
MTH 8.7 Triangles and Quadrilaterals (Levels 6.3 – 7.3)
Shape, Space & Measures
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Classify triangles and quadrilaterals by identifying their geometric properties through line and/or rotational symmetry.
2. Identify tessellating shapes and cover a given area with tessellating shapes.
3. Make accurate drawing of triangles.
4. Draw simple scale drawings from given data and interpret scale drawings.
Key Words
Triangles: scalene, isosceles,
equilateral, right-angled
Points to Note
Quadrilaterals: square,
rectangle, trapezium, rhombus,
parallelogram, kite
From Teachers’ laptop:
Exposition: the teacher states the objectives of the lesson and may use ICT C:\Documents and Settings\teacher\My
software for students to practice new knowledge. This is consolidated by Documents\Maths Excel Lessons
setting students tasks that offer students the opportunity to apply
- Quadrilaterals.xls
mathematics to a variety of real life situations.
From Teachers’ laptop:
Discovery: the teacher can set group tasks in which students discuss and C:\Documents and Settings\teacher\My
construct mathematical knowledge. Students may become active learners Documents\Maths PowerPoint Shows
while testing hypotheses and/or making generalisations.
- Construct a Triangle (SSS).pps
- Construct a Triangle (ASA).pps
Exploration: the teacher integrates an inquiry based learning approach
- Construct a Triangle (SAS).pps
that enhances the students’ understanding of concepts. These tasks might
- Quadrilaterals.pps
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise Internet Links:
language of mathematics.
www.mathcats.com/explore/tessellations/tess
Line symmetry, rotational
symmetry
Tessellations
Scale, scale drawing
Resources
FOM B1, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to promote a
Resource Pack – Chapter 7 and 12
student centred learning environment.
animals.html
http://www.youtube.com/watch?v=T6L6bE_bTMo
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
112
Teaching Objective
The teacher will teach the
students to:
1. Classify triangles and
quadrilaterals by
identifying their
geometric properties
through line and/or
rotational symmetry.
Examples of teaching experiences and activities
The teacher divides the class into groups of 3 and asks them to look at the
decision tree diagram available on page 100.
The students need to follow the decision boxes provided to classify
triangles into: scalene, isosceles, equilateral, scalene right-angled and
isosceles right-angled.
For the more able students, the teacher might consider giving them the
task on page 102. In this case students need to fill in the questions in the
decision boxes to elicit the geometric properties of triangles.
A second group activity could involve students in classifying quadrilaterals.
However, this time, the students’ task involves producing their own
decision tree diagram to classify quadrilaterals – square, rectangle,
rhombus, parallelogram, trapezium, arrowhead and kite.
This activity is more challenging – is more open and requires more
insightful reasoning skills. Thus the teacher must plan time for a plenary
(the students’ presentation and discussion) of the decision tree diagrams
presented. Each group needs to be given time to present their work, that
is, present their explorations and explanations. Other students should be
encouraged to challenge the format, the questions and the classification
presented by each group.
Otherwise the teacher can use the Maths Excel Lesson ‘Quadrilateral.xls’
and the PowerPoint presentation ‘Quadrilaterals.pps’ available on the
teacher’s laptop. Through pair work students can elicit the geometric
properties of different quadrilaterals and this can be followed by a wholeclass discussion. Here the teacher might also make use of geo-sticks.
Allowing students to assemble the different shapes can help them
discovering the essential properties.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Indicators of Learning outcomes
Students will be able to classify triangles
and distinguish between square, rectangle,
rhombus and parallelogram by identifying
some geometric properties including line
or rotational symmetry.
(Level 7.3)
Students will be able to distinguish
between isosceles, equilateral and scalene
triangles and between a square and a
rectangle using their geometric properties.
(Level 7.2)
Students will be able to classify triangles
and quadrilaterals according to number of
sides, length of sides, right angles and size
of angles.
(Level 7.1)
Students will be able to name triangles and
quadrilaterals given their properties.
(Level 6.3)
113
2. Identify tessellating
shapes and cover a
given area with
tessellating shapes.
The teacher might start the lesson by first showing a few examples of
tessellating shapes and patterns, and later asking students to find real-life
applications, such as, tessellations used in pavements and tiles,
tessellations in nature, for example, the honeycomb, pineapples and
snakes’ skin.
Students will be able to draw tessellating
shape and select the appropriate
arrangement to cover a given area, such as
tiling a room.
(Level 7.3)
Working in a computer lab, the teacher then sets students working in pairs
on the activity available at http://nrich.maths.org/6069 .
Here the students investigate which polygons tessellate which they can
also draw on isometric paper.
Students will identify shapes that need to
be rotated to tessellate and be able to
continue a pattern with such shapes.
(Level 7.2)
After this initial task, the teacher uses the link below to present students
with a video animation on the study of how the artist M.C. Escher created
his tessellating lizards from hexagons.
http://www.youtube.com/watch?v=T6L6bE_bTMo
Students will be able to identify shapes
that need to be rotated to tessellate.
(Level 7.1)
Following this presentation, students are asked to design their own
tessellating shapes and patterns from different polygons.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will identify shapes that do not
need to be rotated to tessellate and be
able to continue a pattern with such
shapes.
(Level 6.3)
114
3. Make accurate
drawings of triangles
The teacher starts this lesson by asking groups of students to find out the
information they would require in order to draw an accurate triangle.
After this 5 minute activity, the teacher can ask each group of students to
justify their choice.
The teacher can then use students’ responses to introduce the main
teaching activity below.
Using the Maths PowerPoint shows available on the teacher’s laptop, that
is:
- Construct a Triangle (SSS).pps
- Construct a Triangle (ASA).pps
- Construct a Triangle (SAS).pps
The teacher can again set students to work in pairs on a computer to view
and practice the step by step presentations in making accurate drawing of
different triangles using ruler and protractor.
For the more able students, the teacher could also challenge them to draw
triangles using ruler and compasses only.
Students will be able to make accurate
drawings of triangles given (a) the length of
the three sides using ruler and compasses
only; (b) the length of one side and two
angles using ruler and protractor; and (c)
two sides and the included angle using
ruler and protractor.
(Level 7.3)
Students will be able to make accurate
drawings of triangles given (a) the length of
one side and two angles using ruler and
protractor; and (b) two sides and the
included angle using ruler and protractor.
(Level 7.2)
Students will be able to make an accurate
drawing of triangles given two sides and
the included angle using ruler and
protractor.
(Level 7.1)
Students will be able to make an accurate
drawing of triangles given the length of the
three sides using ruler and compasses.
(Level 6.3)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
115
4. Draw simple scale
drawings from given
data and interpret scale
drawings.
The teacher provides groups of students with the actual measurements of
a particular area/field, such as, the classroom, the school’s hall, the
teacher’s staffroom and the school’s football pitch, netball court and/or
tennis court.
Students will be able to draw simple scale
drawings from given data and interpret
scale drawings.
(Level 7.3)
Note: Ideally students take on-site measurements themselves.
Each group will use the given measurements to decide on the most
convenient scale to use to draw their scale drawing. This could initially be
done on 1 cm squared paper and later on an A4 blank sheet of paper.
The teacher can then ask students to use their scale drawing to work out
the actual distances of other lengths not indicated in the original given
data.
Students will be able to draw and interpret
simple scale drawings, that is, involving
positive integer lengths and ratios.
(Level 7.2)
The teacher might want to conclude this activity by asking each group to
present their work to the whole class.
Students will be able to draw and interpret
scale drawings using a ratio of 1cm to
represent 1m and/or 1 km.
(Level 7.1)
Students will be able to read a simple scale
drawing (in the ratio 1:2, 1: 5 and 1:10).
(Level 6.3)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
116
Subject:
Unit code and title:
Strand 3:
MATHEMATICS
MTH 8.7 Triangles and Quadrilaterals (Levels 5.3 – 7.1)
Shape, Space & Measures
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Classify triangles and quadrilaterals by identifying their geometric properties through line and/or rotational symmetry.
2. Identify tessellating shapes and cover a given area with tessellating shapes.
3. Draw simple scale drawings from given data and interpret scale drawings.
4. Use squared paper to draw nets of solid shapes and use isometric paper to draw solids.
Key Words
Triangles: scalene, isosceles,
equilateral, right-angled
Points to Note
Quadrilaterals: square,
rectangle, trapezium, rhombus,
parallelogram, kite
From Teachers’ laptop:
Exposition: the teacher states the objectives of the lesson and may use ICT C:\Documents and Settings\teacher\My
software for students to practice new knowledge. This is consolidated by Documents\Maths Excel Lessons
setting students tasks that offer students the opportunity to apply
- Quadrilaterals.xls
mathematics to a variety of real life situations.
Line symmetry, rotational
symmetry
Tessellations
Scale, scale drawing
Nets, cube, cuboid,
Resources
Three main teaching approaches are being recommended to promote a FOM B Gold, Students’ Book, Practice
Book, Resource Pack – Chapters 12 & 24
student centred learning environment.
C:\Documents and Settings\teacher\My
Discovery: the teacher can set group tasks in which students discuss and Documents\Maths PowerPoint Shows
construct mathematical knowledge. Students may become active learners
- Quadrilaterals.pps
while testing hypotheses and/or making generalisations.
Exploration: the teacher integrates an inquiry based learning approach
that enhances the students’ understanding of concepts. These tasks might
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Internet Links:
http://nrich.maths.org
http://www.youtube.com/watch?v=NYGIh
Z_HWfg
Other Resources:
 Folding Geometry Shapes
 Skillsheets Measurement (scale
drawing and maps)
117
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
118
Teaching Objective
The teacher will teach the
students to:
1. Classify triangles and
quadrilaterals by
identifying their
geometric properties
through line and/or
rotational symmetry.
Examples of teaching experiences and activities
The teacher divides the class into pairs. Using geo-sticks or geo-boards the
students are asked to construct different triangles and then investigate
different properties. This involves students in measuring the sides and the
angles of the triangles.
Through a whole class discussion and presentation the students classify
the different triangles into: scalene, isosceles, equilateral and right-angled.
During another activity the students can draw the same triangles on
squared paper to investigate line symmetry. Using a pin and a soft board,
the students can also investigate rotational symmetry.
Indicators of Learning outcomes
Students will be able to classify triangles
and quadrilaterals according to number of
sides, length of sides, right angles and size
of angles.
(Level 7.1)
A second group activity could involve students in classifying quadrilaterals.
Similar to the previous one, students construct and classify quadrilaterals –
square, rectangle, rhombus, parallelogram, trapezium and kite.
The use of geo-sticks can facilitate students’ understanding since through
the different quadrilaterals formed, students can compare the shapes and
elicit the key geometric properties – here it is crucial for the teacher to
provide the necessary assistance for students to manage their way
through the task, making interventions as to what students should be
looking at.
Students will be able to distinguish
between regular and irregular triangles and
regular and irregular quadrilaterals using
length of sides and size of angles.
(Level 6.2)
Otherwise the teacher can use the Maths Excel Lesson ‘Quadrilateral.xls’
and the PowerPoint presentation ‘Quadrilaterals.pps’ available on the
teacher’s laptop. Through pair work students can elicit the geometric
properties of different quadrilaterals and this can be followed by a wholeclass discussion. Again here the teacher might also make use of geo-sticks
as this helps them to discover the essential properties.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to name triangles and
quadrilaterals given their properties.
(Level 6.3)
Students will be able to identify and draw
lines of symmetry in triangles and
quadrilaterals.
(Level 6.1)
Students will be able to distinguish
between equilateral, isosceles and scalene
triangles, squares and rectangles from the
number of sides and length of the sides.
(Level 5.3)
119
2. Identify tessellating
shapes and cover a
given area with
tessellating shapes.
The teacher might start the lesson by first showing a few examples of
tessellating shapes and patterns, and later asking students to find real-life
applications, such as, tessellations used in pavements and tiles,
tessellations in nature, for example, the honeycomb, pineapples and
snakes’ skin.
Working in a computer lab, the teacher then sets students working in pairs
on the activity available at http://nrich.maths.org/6069 .
Here the students investigate which polygons tessellate which they can
also draw on isometric paper.
After this initial task, the teacher uses the link below to present students
with a video animation on the study of how the artist M.C. Escher created
his tessellating flying horses.
http://www.youtube.com/watch?v=NYGIhZ_HWfg
The tessellation of the flying horse is based on the simple geometric shape
of a square and only involves sliding parts from one side to the other
(which practically anyone should be able to do).
Following this presentation, students are asked to design their own
tessellating shapes, tiles and/or wallpapers.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to identify shapes
that need to be rotated to tessellate.
(Level 7.1)
Students will identify shapes that do not
need to be rotated to tessellate and be
able to continue a pattern with such
shapes.
(Level 6.3)
Students will be able to identify shapes
that do not need to be rotated to
tessellate.
(Level 6.2)
Students will be able to understand the
meaning of regular and non-regular
tessellations.
(Level 6.1)
Students will be able to understand the
meaning of the term tessellation.
(Level 5.3)
120
3. Draw simple scale
drawings from given
data and interpret scale
drawings.
The teacher provides groups of students with the actual measurements of
a particular area/field, such as, the classroom, the school’s hall, the
teacher’s staffroom and the school’s football pitch, netball court and/or
tennis court.
Students will be able to draw and interpret
scale drawings using a ratio of 1cm to
represent 1m and/or 1 km.
(Level 7.1)
Note: Ideally students take on-site measurements themselves.
Each group will be guided to decide on the most convenient scale to use to
do their scale drawing. It is suggested that student do their drawing on 1
cm squared paper.
Students will be able to read a simple scale
drawing (in the ratio 1:2, 1: 5 and 1:10).
(Level 6.3)
The teacher can then ask students to use their scale drawing to work out
the actual distances (by counting squares) of any length not indicated in
the original given data.
Students will be able to understand the
general notion of ratios in the form: 1 cm
to represent 1 m or 1 km.
(Level 6.2)
Students will be able to understand that
scale drawings are accurate drawing
representing larger areas.
(Level 6.1)
Students will be able to draw simple
shapes with a given set of measurements
(in cm).
(Level 5.3)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
121
4. Use squared paper to
draw nets of solid
shapes and use
isometric paper to draw
solids.
The teacher can initially set students in groups and provide each group
with a set of ‘Folding Geometry Shapes’ that includes a number of prisms
and pyramids.
The teacher can also provide each group with a set of cards containing the
names of the different solid shapes. While investigating the nets of the
shapes included in the set, students are asked to label the shapes and then
draw a table that includes the number of faces, vertices and edges for
each shape.
For the next activity, using the interactive whiteboard, the students can
then be presented with the solid shapes again, and asked to match these
to their nets.
Following this activity, the teacher can ask students to work again in
groups on:
 Drawing the nets of a number of shapes on squared paper, and
 Drawing solids using isometric paper
The students can be asked to present/display their work on a chart and
also be encouraged to construct solid shapes from the nets presented.
Students will be able to draw solid shapes
using isometric paper and their nets on
squared paper.
(Level 7.1)
Students will be able to draw prisms using
isometric paper and their nets on squared
paper.
(Level 6.3)
Students will be able to draw the cube and
cuboid using isometric paper and their
respective nets on squared paper.
(Level 6.2)
Students will be able to draw the nets of a
cube and a cuboid on squared paper.
(Level 6.1)
Students will be able to draw the net of a
cube on squared paper.
(Level 5.3)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
122
Subject:
Mathematics
Unit code and title: MTH 8.7 Triangles and Quadrilaterals (Levels 1-4)
Strand 3:
Shape, Space & Measures
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives at attainment Levels 5 and 6
The teacher will teach the students to:
1. Classify triangles and quadrilaterals by identifying their geometric properties through line and rotational symmetry.
2. Identify tessellating shapes and cover a given area with tessellating shapes.
3. Draw simple scale drawings from given data and interpret scale drawings.
4. Use squared paper to draw nets of solid shapes and use isometric paper to draw solids.
Objectives at attainment Levels 1, 2, 3, 4
The teacher will teach the students to:
1.1 Differentiate between different types of the same shape and between the properties of a rectangle and a square.
2.1 Complete a tessellation based on two coloured squares.
3.1 measure and compare the lengths of objects and the distance between two objects.
Key Words
Squares, rectangles,
sides, opposite sides,
faces, pattern, turns,
same, line and rotational
symmetry, tesselation,
scale drawing.
Points to Note
In addition to the points to note recommended for students performing at
Level 5 or higher, it is very important for the teacher to allow time for the
students to respond. This response can take the form of unaided and/or
aided means of communication and the teacher needs to provide
adequate scaffolding techniques to enable the students to respond
affectively or intentionally.
For further examples about level 1 refer to the handbook.
Resources
New Maths Frame Working Step Up Workbook.
Oxford Framework Maths 7
Teacher Excel Worksheets as on Maths Website.
Other links:
http://www.bbc.co.uk/schools/ks2bitesize/maths
/shape_space/
http://kent.skoool.co.uk/content/keystage3/maths/
http://www.learnalberta.ca/content/mejhm/inde
x.html?
http://www.mathcats.com/explore/tessellations/
tesshouses.html
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
123
Teaching Objective
The teacher will teach
the students to:
1.1 Differentiate
between different
types of the same
shape and between
the properties of a
rectangle and a
square.
Examples of teaching experiences and activities
Starter: Students are shown various models and they have to select the
ones made up of triangles. Then they are shown a rectangle and a square
and they have to talk about what they know about these two shapes.
Students talk about the sizes of different triangles and count how many
they have of each size. Similarly, students are shown rectangles and
squares in different orientation like horizontal, vertical and tilted and the
students have to colour the opposite sides and the angles that are equal.
They talk about the length of the sides and maybe the symmetrical
properties.
Students are given a template of a model made up of different triangle
sizes and they have to choose the right triangle size to reproduce the
model. Alternatively, they can colour triangles differently according to a
given template.
Indicators of Learning outcomes
Students will talk about the different shapes using
terms like bigger, longer sides and wider,
opposite sides and other properties.
(Level 4)
Students will identify the right shape size to
match the ones on the template.
(Level 3)
Students will sort and match the shapes according
to the size.
(Level 2)
Students will be involved in a sensorial experience
of shapes.
(Level 1)
Students are given three different types of triangles and other shapes and
they have to sort them accordingly.
Students are involved into a multisensory experience like sponge painting
activity about rectangles and squares. They are given actual rectangles and
squares to manipulate and explore them.
2.1 Complete a
tessellation based on
two coloured shapes.
Starter: Students are shown a pattern and they have to say what’s next
and continue it.
Students are given a grid with two coloured squares. The teacher gives two
instructions like –create a pattern using the first coloured squares, then
none and then the second coloured square.
Students are given a tessellating shape and they have to choose the
identical shape from a choice of three and talk about it.
Students will be presented with a 4X4 grid and they will be involved in the
Students will create a tessellating pattern by
following the given instructions.
(Level 4)
Students will recognise an equal tessellating
shape from a selection and possibly explain their
choice in a very simple way.
(Level 3)
Students will create a simple tessellation through
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
124
3.1 Measure and
compare the lengths
of objects and the
distance between two
objects.
creation of a simple tessellation through copying and imitation of the
teacher’s moves.
Students will press switches to create an exposure and a feel of a
tessellating pattern.
These activities can be reinforced through the above tessellation link.
a process of copying by imitation.
(Level 2)
Starter: Students are presented with a group of big and small objects.
Teacher asks them to point, sort or talk about them so she can take stock
of what they know and proceed from there.
Students will use objects to find the length and
width and talk about the size differences.
(Level 4)
Students are given a grid with a small and a big square drawn on it.
Teacher asks them to count the number of cubes covered by the square
and eventually they will compare them and talk about their sizes.
Similarly, students are given two locations within their immediate
environment and they have to compare the distances.
Students will recognise and choose the
smaller/shorter and then the largest/tallest from
a set.
(Level 3)
Students are given a set of objects and they choose the smaller/shorter
and put them in order of size according to their length.
Students will be able to sort objects according to their size. Teachers use a
magnifier or a visualiser to enlarge objects.
Subject:
Students will be exposed to a sequence of moves
by pressing switches.
(Level 1)
Students will make sets of objects by size.
(Level 2)
Students will become aware that things can be
enlarged.
(Level 1)
MATHEMATICS
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Form 2
125
Unit code and title: MTH 8.8 Constructions (Levels 7.1 – 8.1)
Strand 3:
Shape, Space & Measures
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach students to:
1. Use ruler and compasses only to construct a perpendicular at a point on a line.
2. Use ruler and compasses only to construct a perpendicular from a point to a line.
3. Use ruler and compasses only to construct the perpendicular bisector of a line segment.
4. Use ruler and compasses only to construct the bisector of an angle.
5. Construct squares and rectangles using ruler and compasses only.
Key Words
ruler, straight-edge,
compasses, protractor,
point,
line, line segment,
sketch, draw,
construct, construction,
bisect, bisection,
arc,
intersect, intersection,
perpendicular,
perpendicular bisector,
angle bisector,
right-angle,
square, rectangle, triangle
Teaching Objective
Points to Note
Resources
Three main teaching approaches are being recommended to promote a
student centred learning environment.
FOM B2, Students’ Book, Practice Book,
Resource Pack ‐ Chapter 7
Exposition: the teacher states the objectives of the lesson and may use ICT
software for students to practice new knowledge. This is consolidated by Compasses, ruler, Cabri-Geometre II,
setting students tasks that offer students the opportunity to apply GeoGebra, MW Logo, IWB compasses,
mathematics to a variety of real life situations.
IWB ruler
Discovery: the teacher can set group tasks in which students discuss and
construct mathematical knowledge. Students may become active learners
while testing hypotheses and/or making generalisations.
Exploration: the teacher integrates an inquiry based learning approach that
enhances the students’ understanding of concepts. These tasks might
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Examples of teaching experiences and activities
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Indicators of Learning Outcomes
126
The teacher will teach students
to:
1. Use ruler and compasses
only to construct a
perpendicular at a point on a
line.
As an introduction to the topic the teacher explains difference between a
ruler and a straight-edge and then explains historical importance of straightedge and compasses constructions in Euclidean geometry. Teacher needs to
show link between constructions of geometrical objects using straight-edge
and compasses only and Euclid’s first three postulates: (1) A straight line
can be drawn from any point to any other point; (2) A straight line can be
extended indefinitely in any direction; and, (3) It is possible to describe a
circle with any centre and radius.
As remote preparation before the lesson, teacher asks pupils to view
animated construction of a perpendicular at a point on a line using ruler and
compasses only from the following website:
http://www.mathsisfun.com/geometry/constructions.html
Teacher uses exposition approach and IWB compasses and IWB ruler to
teach the steps required to construct a perpendicular at a point on a line.
Teacher adopts exploration approach and encourages pupils to construct a
line which is parallel to a given line using ruler and compasses only.
Teacher adopts exploration approach and encourages pupils to construct a
right angled triangle of given dimensions using ruler and compasses only.
At the computer lab teacher adopts exploration approach and encourages
pupils to use Cabri-Geometre to construct a perpendicular at a point on a
line without using the Perpendicular Line tool.
Students will be able to use ruler and
compasses only to construct a
perpendicular at a point on a line and will
be able to give adequate verbal
justifications why the procedure works.
(Level 8.1)
Students will be able to use ruler and
compasses only to construct a
perpendicular at a point on a line.
(Level 7.3)
Students will be able to use ruler and
protractor to construct a perpendicular at
a point on a line.
(Level 7.2)
Students will be able to use ruler only to
make a reasonable accurate sketch of a
perpendicular at a point on a line.
(Level 7.1)
For HW teacher adopts exploration approach and encourages pupils to use
GeoGebra to use the Perpendicular Line tool in order to construct right
angled triangles of various given dimensions starting from a given point on a
line segment.
2. Use ruler and compasses
Note: In order to cater for diversity the construction of a perpendicular at a
point on a line using ruler and compasses should only be introduced after
teacher has reminded pupils how to use protractor and ruler in order to
construct a perpendicular at a point on a line and how to make a reasonable
accurate sketch of this construction.
As remote preparation before the lesson, teacher asks pupils to view
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to use ruler and
127
only to construct a
perpendicular from a point
to a line.
animated construction of a perpendicular from a point to a line using ruler
and compasses only from the following website:
http://www.mathsisfun.com/geometry/constructions.html
Teacher uses exposition approach and IWB compasses and IWB ruler to
teach the steps required to construct a perpendicular from a point to a line.
Teacher adopts exploration approach and encourages pupils to construct a
line passing through a point which is parallel to a given line using ruler and
compasses only.
At the computer lab teacher adopts exploration approach and encourages
pupils to use Cabri-Geometre to construct a perpendicular from a point to a
line without using the Perpendicular Line tool.
For HW teacher adopts exploration approach and encourages pupils to use
GeoGebra to use the Perpendicular Line tool in order to construct right
angled triangles of various given sizes starting from a point not on a given
line.
Note: In order to cater for diversity the construction of a perpendicular from
a point to a line using ruler and compasses should only be introduced after
teacher has reminded pupils how to use protractor and ruler in order to
construct a perpendicular from a point to a line and how to make a
reasonable accurate sketch of this construction.
3. Use ruler and compasses
only to construct the
perpendicular bisector of a
line segment.
As remote preparation before the lesson, teacher asks pupils to view
animated construction of the perpendicular bisector of a line segment using
ruler and compasses only from the following website:
http://www.mathsisfun.com/geometry/constructions.html
Teacher uses exposition approach and IWB compasses and IWB ruler to
teach the steps required to construct the perpendicular bisector of a line
segment.
At the computer lab teacher adopts exploration approach and encourages
pupils to use Cabri-Geometre to construct the perpendicular bisector of a
line segment without using the Perpendicular Bisector tool.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
compasses only to construct a
perpendicular from a point to a line and
will be able to give adequate verbal
justifications why the procedure works.
(Level 8.1)
Students will be able to use ruler and
compasses only to construct a
perpendicular from a point to a line.
(Level 7.3)
Students will be able to use ruler and
protractor only to construct a
perpendicular from a point to a line.
(Level 7.2)
Students will be able to use ruler only to
make a reasonable accurate sketch of a
perpendicular from a point to a line.
(Level 7.1)
Students will be able to use ruler and
compasses only to construct the
perpendicular bisector of a line segment
and will be able to give adequate verbal
justifications why the procedure works.
(Level 8.1)
Students will be able to use ruler and
compasses only to construct the
perpendicular bisector of a line segment.
(Level 7.3)
128
For HW teacher adopts exploration approach and encourages pupils to use
GeoGebra to construct the perpendicular bisector of two non parallel chords
of a circle and to note whether they intersect or not.
Note: In order to cater for diversity the construction of the perpendicular
bisector of a line segment using ruler and compasses should only be
introduced after teacher has reminded pupils how to use protractor and
ruler in order to construct the perpendicular bisector of a line segment and
how to make a reasonable accurate sketch of this construction.
4. Use ruler and compasses
only to construct the
bisector of an angle.
As remote preparation before the lesson, teacher asks pupils to view
animated construction of the bisector of an angle using ruler and compasses
only from the following website:
http://www.mathsisfun.com/geometry/constructions.html
Teacher uses exposition approach and IWB compasses and IWB ruler to
teach the steps required to construct the bisector of an angle.
At the computer lab teacher adopts exploration approach and encourages
pupils to use Cabri-Geometre to construct the bisector of an angle without
using the Angle Bisector tool.
For HW teacher adopts exploration approach and encourages pupils to use
ruler and compasses only in order to construct the bisector of a number of
given angles and to check their work by using GeoGebra to construct the
bisector of these angles using the Angle Bisector tool.
Note: In order to cater for diversity the construction of an angle bisector
using ruler and compasses should only be introduced after teacher has
reminded pupils how to use protractor and ruler in order to construct the
bisector of an angle and how to make a reasonable accurate sketch of this
construction.
5. Construct squares and
Teacher adopts exploration approach and sets tasks that challenge pupils to
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to use ruler and
protractor only to construct the
perpendicular bisector of a line segment.
(Level 7.2)
Students will be able to use ruler only to
make a reasonable accurate sketch of the
perpendicular bisector of a line segment.
(Level 7.1)
Students will be able to use ruler and
compasses only to construct the bisector
of an angle and will be able to give
adequate verbal justifications why the
procedure works.
(Level 8.1)
Students will be able to use ruler and
compasses only to construct the bisector
of an angle.
(Level 7.3)
Students will be able to use ruler and
protractor only to construct the bisector
of an angle.
(Level 7.2)
Students will be able to use ruler only to
make a reasonable sketch of the bisector
of an angle.
(Level 7.1)
Students will be able to use ruler and
129
rectangles using ruler and
compasses only.
apply previously learnt knowledge and skills to construct squares and
rectangles of given dimensions using ruler and compasses only.
For HW teacher adopts the exploration approach and encourages pupils to
use GeoGebra to construct squares and rectangles of given dimensions.
At the computer lab teacher adopts exploration approach and encourages
pupils to use MW Logo to construct squares and rectangles of given
dimensions using first the FD, BK, RT, LT commands and then the REPEAT
command. Teacher asks pupils to reflect on the rotational symmetry and
reflective symmetry of these shapes and the connection between these
properties and the list of Logo commands that create the shapes.
For the more gifted pupils - For HW teacher adopts the exploration
approach and encourages pupils to use ruler and compasses only to
construct a rhombus of given side length and whose internal angles are 45˚,
135˚, 45˚ and 135˚.
Note: In order to cater for diversity the construction of squares and
rectangles using ruler and compasses should only be introduced after
teacher has reminded pupils how to use protractor and ruler in order to
construct a square and a rectangle and how to make a reasonable accurate
sketch of this construction.
Subject:
MATHEMATICS
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
compasses only to construct squares and
rectangles and will be able to give
adequate verbal justifications why the
procedures work.
(Level 8.1)
Students will be able to use ruler and
compasses only to construct squares and
rectangles.
(Level 7.3)
7.2 Students will be able to use ruler and
protractor only to construct squares and
rectangles.
(Level 7.2)
Students will be able to use ruler only to
make reasonable accurate sketches of
squares and rectangles.
(Level 7.1)
Form 2
130
Unit code and title: MTH 8.8 Constructions (Levels 6.3 – 7.1)
Strand 3:
Shape, Space & Measures
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach students to:
1. Use ruler and compasses only to draw an angle of 60˚.
2. Use ruler and compasses only to draw an angle of 90˚.
3. Use ruler and compasses only to construct the perpendicular bisector of a line segment.
4. Use ruler and compasses only to construct the bisector of an angle.
5. Construct squares and rectangles using ruler, compasses and protractor only.
Key Words
Points to Note
Resources
ruler, straight-edge,
compasses, protractor,
point,
line, line segment,
sketch, draw,
construct, construction,
bisect, bisection,
arc,
intersect, intersection,
perpendicular,
perpendicular bisector,
angle bisector,
right-angle,
square, rectangle, triangle.
Three main teaching approaches are being recommended to promote a
FOM B1, Students’ Book, Practice Book,
student centred learning environment.
Resource Pack ‐ Chapter 7
Teaching Objective
Examples of teaching experiences and activities
Exposition: the teacher states the objectives of the lesson and may use ICT Compasses, ruler, Cabri-Geometre II,
software for students to practice new knowledge. This is consolidated by GeoGebra, MS Logo, IWB compasses, IWB
setting students tasks that offer students the opportunity to apply ruler
mathematics to a variety of real life situations.
Discovery: the teacher can set group tasks in which students discuss and
construct mathematical knowledge. Students may become active learners
while testing hypotheses and/or making generalisations.
Exploration: the teacher integrates an inquiry based learning approach that
enhances the students’ understanding of concepts. These tasks might
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Indicators of Learning Outcomes
131
The teacher will teach students
to:
1. Use ruler and compasses
only to draw angles of 60˚.
As an introduction to the topic the teacher explains difference between a
ruler and a straight-edge and then explains historical importance of straightedge and compasses constructions in Euclidean geometry. Teacher needs to
show link between constructions of geometrical objects using straight-edge
and compasses only and Euclid’s first three postulates: (1) A straight line
can be drawn from any point to any other point; (2) A straight line can be
extended indefinitely in any direction; and, (3) It is possible to describe a
circle with any centre and radius.
As remote preparation before the lesson, teacher asks pupils to view
animated construction of a 60˚ angle using ruler and compasses only from
the following website:
http://www.mathsisfun.com/geometry/constructions.html
Teacher can use the exposition approach and IWB compasses and IWB ruler
to teach the steps required to construct an angle of 60˚.
Teacher can adopt the exploratory approach and asks pupils to construct an
equilateral triangle of given side length using ruler and compasses only.
At the computer lab teacher can adopt the exploratory approach and
encourages pupils to use Cabri-Geometre to construct an equilateral triangle
of given side length using the Line Segment, Compass and Intersection
Points tools.
2. Use ruler and compasses
only to draw angles of 90˚.
Note: In order to cater for diversity the construction of a 60˚ using ruler and
compasses should only be introduced after teacher has reminded pupils
how to use ruler and appropriate set square in order to construct an angle
of 60˚ and how to make a reasonable accurate sketch of this construction.
As remote preparation before the lesson, teacher asks pupils to view
animated construction of a perpendicular at a point on a line using ruler and
compasses only from the following website:
http://www.mathsisfun.com/geometry/constructions.html
Teacher can use the exposition approach and IWB compasses and IWB ruler
to teach the steps required to construct an angle of 90˚.
Teacher can adopt the exploratory approach and encourages pupils to
construct a right angled triangle of given dimensions using ruler and
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to use ruler and
compasses only to construct an angle of
60˚.
(Level 7.3)
Students will be able use ruler and
protractor to construct an angle of 60˚.
(Level 7.2)
Students will be able to use ruler and
appropriate set square only to construct
an angle of 60˚.
(Level 7.1)
Students will be able to use ruler only to
make a reasonable accurate sketch of an
angle of 60˚.
(Level 6.3)
Students will be able to use ruler and
compasses only to construct an angle of
90˚.
(Level 7.3)
Students will be able use ruler and
protractor to construct an angle of 90˚.
(Level 7.2)
132
compasses only.
For HW teacher can adopt the exploratory approach and encourages pupils
to use GeoGebra to use the Perpendicular Line and Circle with Centre and
Radius tools in order to construct right angled triangles of various given sizes
starting from a given point on a line segment.
Note: In order to cater for diversity the construction of a 90˚ using ruler and
compasses should only be introduced after teacher has reminded pupils
how to use ruler and appropriate set square in order to construct an angle
of 90˚ and how to make a reasonable accurate sketch of this construction.
3. Use ruler and compasses
only to construct the
perpendicular bisector of a
line segment.
As remote preparation before the lesson, teacher asks pupils to view
animated construction of the perpendicular bisector of a line segment using
ruler and compasses only from the following website:
http://www.mathsisfun.com/geometry/constructions.html
Teacher can use the exposition approach and IWB compasses and IWB ruler
to teach the steps required to construct the perpendicular bisector of a line
segment.
At the computer lab teacher can adopt the discovery approach and directs
pupils to use Cabri-Geometre to construct the perpendicular bisector of a
line segment without using the Perpendicular Bisector tool.
For HW teacher can adopt the discovery approach and directs pupils to use
GeoGebra to construct the perpendicular bisector of two non-parallel
chords of a circle and to note whether they intersect or not.
4. Use ruler and compasses
Note: In order to cater for diversity the construction of the perpendicular
bisector of a line segment using ruler and compasses should only be
introduced after teacher has reminded pupils how to use protractor and
ruler in order to construct the perpendicular bisector of a line segment and
how to make a reasonable accurate sketch of this construction.
As remote preparation before the lesson, teacher asks pupils to view
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to use ruler and
appropriate set square only to construct
an angle of 90˚.
(Level 7.1)
Students will be able to use ruler only to
make a reasonable accurate sketch of an
angle of 90˚.
(Level 6.3)
Students will be able to use ruler and
compasses only to construct the
perpendicular bisector of a line segment.
(Level 7.3)
Students will be able to use ruler and
protractor only to construct the
perpendicular bisector of a line segment.
(Level 7.2)
Students will be able to use ruler only to
make a sketch of the perpendicular
bisector of a line segment.
(Level 7.1)
Students will be able to recognise that a
line is the perpendicular bisector of a line
segment by measuring the angles the line
makes with the line segment using a
protractor. (Level 6.3)
Students will be able to use ruler and
133
only to construct the
bisector of an angle.
animated construction of the bisector of an angle using ruler and compasses
only from the following website:
http://www.mathsisfun.com/geometry/constructions.html
Teacher can use the exposition approach and IWB compasses and IWB ruler
to teach the steps required to construct the bisector of an angle.
At the computer lab teacher can adopt the discovery approach and directs
pupils to use Cabri-Geometre to construct the bisector of an angle without
using the Angle Bisector tool.
compasses only to construct the bisector
of an angle.
(Level 7.3)
For HW teacher can adopt the exploration approach and asks pupils to use
ruler and compasses only in order to construct the bisector of a number of
given angles and to check their work by using GeoGebra to construct the
bisector of these angles using the Angle Bisector tool.
Students will be able to use ruler only to
make a sketch of the bisector of an angle.
(Level 7.1)
Note: In order to cater for diversity the construction of an angle bisector
using ruler and compasses should only be introduced after teacher has
reminded pupils how to use protractor and ruler in order to construct the
bisector of an angle and how to make a reasonable accurate sketch of this
construction.
5. Construct squares and
rectangles using ruler,
protractor and compasses
only.
Teacher can set tasks using the exploration approach that challenge pupils
to apply previously learnt knowledge and skills to construct squares and
rectangles of given dimensions using ruler, compasses and protractor only.
For HW teacher can adopt the discovery approach and asks pupils to use
GeoGebra to construct squares and rectangles of given dimensions.
At the computer lab teacher can adopt the exploration approach and
encourages pupils to use MW Logo to construct squares and rectangles of
given dimensions using first the FD, BK, RT, LT commands and then the
REPEAT command. Teacher asks pupils to reflect on the rotational symmetry
and reflective symmetry of these shapes and the connection between these
properties and the list of Logo commands that create the shapes.
Note: In order to cater for diversity the construction of squares and
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to use ruler and
protractor only to construct the bisector
of an angle.
(Level 7.2)
Students will be able to recognise that a
line is the bisector of an angle by
measuring the angles the line makes with
the arms of the angle using a protractor.
(Level 6.3)
Students will be able to use ruler and
compasses only to construct squares and
rectangles of given dimensions.
(Level 7.3)
Students will be able to use ruler and
protractor only to construct squares and
rectangles of given dimensions.
(Level 7.2)
Students will be able to use ruler and
appropriate set square only to construct
squares and rectangles of given
dimensions.
134
rectangles using ruler and compasses should only be introduced after
teacher has reminded pupils how to use protractor and ruler in order to
construct a square and a rectangle and how to make a reasonable accurate
sketch of this construction.
Subject:
MATHEMATICS
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
(Level 7.1)
Students will be able to use ruler only to
make reasonable accurate sketches of
squares and rectangles of given
dimensions.
(Level 6.3)
Form 2
135
Unit code and title: MTH 8.8 Constructions (Levels 5.3 – 7.1)
Strand 3:
Shape, Space & Measures
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach students to:
1. Construct triangles given the length of the sides using ruler and protractor only.
2. Construct triangles given the length of one side and two angles using ruler and protractor only.
3. Construct triangles given the length of two sides and the included angle using ruler and protractor only.
4. Use ruler and protractor only to draw an angle of 60˚.
5. Use ruler and protractor only to draw an angle of 90˚.
6. Construct squares and rectangles using ruler and protractor only.
Key Words
ruler, straight-edge,
protractor,
point,
line, line segment,
sketch, draw,
construct, construction,
intersect, intersection,
right-angle,
square, rectangle, triangle,
Teaching Objective
The teacher will teach
Points to Note
Three main teaching approaches are being recommended to
promote a student centred learning environment.
Exposition: the teacher states the objectives of the lesson and
may use ICT software for students to practice new knowledge.
This is consolidated by setting students tasks that offer
students the opportunity to apply mathematics to a variety of
real life situations.
Discovery: the teacher can set group tasks in which students
discuss and construct mathematical knowledge. Students may
become active learners while testing hypotheses and/or
making generalisations.
Exploration: the teacher integrates an inquiry based learning
approach that enhances the students’ understanding of
concepts. These tasks might employ the processes of
reasoning, problem solving, investigations, connecting ideas
and concepts, and expressing results by using the precise
language of mathematics.
Resources
Examples of teaching experiences and activities
Teacher can adopt the discovery approach and sets tasks
Indicators of Learning Outcomes
Students will be able to construct a triangle given the
FOM B Gold, Students’ Book, Practice Book, Resource
Pack ‐ Chapter 7
Ruler, Protractor
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
136
students to:
where students are asked to construct triangles of given
dimensions (three sides) using ruler and protractor only.
1. Construct triangles given
the length of the sides
using ruler and protractor
only.
length of the sides using ruler and protractor only with
continual teacher guidance.
(Level 7.1)
Students will be able to produce a reasonably accurate
sketch of a triangle given the length of the sides using
ruler only.
(Level 6.3)
Students will be able to produce a reasonably accurate
sketch of a triangle given the length of the sides using
ruler only with teacher guidance.
(Level 6.2)
Students will be able to produce a reasonably accurate
sketch of a triangle given the length of the sides using
ruler only with continual teacher guidance.
(Level 6.1)
2. Construct triangles given
the length of one side and
two angles using ruler and
protractor only.
Teacher can adopt the discovery approach and sets tasks
where students are asked to construct triangles of given
dimensions (one side and two angles) using ruler and
protractor only.
Students will be able to produce a rough sketch of a
triangle given the length of the sides using a freehand
approach.
(Level 5.3)
Students will be able to construct a triangle given the
length of one side and two angles using ruler and
protractor only with continual teacher guidance.
(Level 7.1)
Students will be able to produce a reasonably accurate
sketch of a triangle given the length of one side and two
angles using ruler only.
(Level 6.3)
Students will be able to produce a reasonably accurate
sketch of a triangle given the length of one side and two
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
137
angles using ruler only with teacher guidance.
(Level 6.2)
Students will be able to produce a reasonably accurate
sketch of a triangle given the length of one side and two
angles using ruler only with continual teacher guidance.
(Level 6.1)
3. Construct triangles given
the length of two sides and
the included angle using
ruler and protractor only.
Teacher can introduce the topic using the available MS
PowerPoint presentations. Teacher can then adopt the
discovery approach and sets tasks where students are asked
to construct triangles of given dimensions (two sides and the
included angle) using ruler and protractor only.
Students will be able to produce a rough sketch of a
triangle given the length of one side and two angles using
a freehand approach.
(Level 5.3)
Students will be able to construct a triangle given the
length of two sides and the included angle using ruler and
protractor only with continual teacher guidance.
Level 7.1)
Students will be able to produce a reasonably accurate
sketch of a triangle given the length of two sides and the
included angle using ruler only. (Level 6.3)
Students will be able to produce a reasonably accurate
sketch of a triangle given the length of two sides and the
included angle using ruler only with teacher guidance.
(Level 6.2)
Students will be able to produce a reasonably accurate
sketch of a triangle given the length of two sides and the
included angle using ruler only with continual teacher
guidance. (Level 6.1)
Students will be able to produce a rough sketch of a
triangle given the length of two sides and the included
angle using a freehand approach.
(Level 5.3)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
138
4. Use ruler and protractor
only to draw angles of 60˚.
Teacher can adopt the exploratory approach and asks pupils
to construct an equilateral triangle of given side length using
ruler and protractor only.
Students will be able use ruler and protractor to construct
an angle of 60˚ with continual teacher guidance.
(Level 7.1)
Students will be able to use ruler only to make a
reasonable accurate sketch of an angle of 60˚.
(Level 6.3)
Students will be able to use ruler only to make a
reasonable accurate sketch of an angle of 60˚ with
teacher guidance.
(Level 6.2)
Students will be able to use ruler only to make a
reasonable accurate sketch of an angle of 60˚ with
continual teacher guidance.
(Level 6.1)
5. Use ruler and protractor
only to draw angles of 90˚.
Teacher can adopt the exploratory approach and encourages
pupils to construct a right angled triangle of given dimensions
using ruler and protractor only.
Students will be able to produce a rough sketch of an
angle of 60˚using a freehand approach.
(Level 5.3)
Students will be able use ruler and protractor to construct
an angle of 90˚ with continual teacher guidance.
(Level 7.1)
Students will be able to use ruler only to make a
reasonable accurate sketch of an angle of 90˚.
(Level 6.3)
Students will be able to use ruler only to make a
reasonable accurate sketch of an angle of 90˚ with
continual teacher guidance.
(Level 6.2)
Students will be able to use ruler only to make a
reasonable accurate sketch of an angle of 90˚ with
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
139
6. Construct squares and
rectangles using ruler and
protractor only.
Teacher can set tasks using the exploration approach that
challenge pupils to apply previously learnt knowledge and
skills to construct squares and rectangles of given dimensions
using ruler and protractor only.
At the computer lab teacher can adopt the exploration
approach and encourages pupils to use MW Logo to construct
squares and rectangles of given dimensions using first the FD,
BK, RT, LT commands and then the REPEAT command
continual teacher guidance.
(Level 6.1)
Students will be able to produce a rough sketch of an
angle of 90˚using a freehand approach.
(Level 5.3)
Students will be able to use ruler and protractor only to
construct squares and rectangles of given dimensions
with continual teacher guidance.
(Level 7.1)
Students will be able to use ruler only to make reasonable
accurate sketches of squares and rectangles of given
dimensions.
(Level 6.3)
Students will be able to use ruler only to make reasonable
accurate sketches of squares and rectangles of given
dimensions with teacher guidance.
(Level 6.2)
Students will be able to use ruler only to make reasonable
accurate sketches of squares and rectangles of given
dimensions with continual teacher guidance.
(Level 6.1)
Students will be able to produce rough sketches of
squares and rectangles of given dimensions using a
freehand approach.
(Level 5.3)
Subject:
Mathematics
Unit code and title: MTH 8.8 Constructions (Level 1-4)
Form 2
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
140
Strand 3:
Shape, Space & Measures
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives at attainment Level 5 and 6
The teacher will teach the students to:
1. Construct triangles given the length of the sides using ruler and compasses only.
2. Construct triangles given the length of one side and two angles, two sides and the included angle.
3. Use ruler and compasses only to draw angles of 60° and 90°.
4. Construct squares and rectangles using ruler and compasses for lengths and protractor for angles.
Objectives at attainment levels 1, 2, 3, 4 (The above objectives are beyond attainment level 4, so slightly different but related objectives have been included.)
The teacher will teach the students to:
1.1 Measure and compare the lengths of objects and the distance between two objects.
2.1 Make and describe patterns using construction kits.
Key Words
Big and small, bigger and
smaller, long and short, longer
and shorter, more, less,
what’s next, continue the
pattern, model.
Points to Note
In addition to the points to note recommended for students performing
at Level 5 or higher, it is very important for the teacher to allow time for
the students to respond. This response can take the form of unaided
and/or aided means of communication and the teacher needs to provide
adequate scaffolding techniques to enable the students to respond
affectively or intentionally.
Resources
New Maths Frame Working - Step Up Workbook.
Oxford Framework Maths 7
Maths Excel Worksheets.
Internet Links:
http://www.ngflcymru.org.uk/vtc/big_small/eng/Introduction/
http://www.onlinemathlearning.com/heavy-andlight.html
http://www.icteachers.co.uk/resources/resources_n
umeracy.htm
Teaching Objective
Examples of teaching experiences and activities
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Indicators of Learning outcomes
141
The teacher will teach the
students to:
1.1 Measure and compare the
lengths of objects and the
distance between two
objects.
Starter: Students are presented with a group of big and small objects.
Teacher asks them to point, sort or talk about them so s/he can take
stock of what they know and proceed from there.
Students are given a grid with a small and a big square drawn on it. The
teacher asks them to count the number of cubes covered by the square
and eventually they will compare them and talk about their sizes.
Similarly, students are given two locations within their immediate
environment and they have to compare the distances.
Students are given a set of objects and they choose the smaller/shorter
and put them in order of size according to their length.
Students will be able to sort objects according to their size. The teachers
use a magnifier or a visualiser to enlarge objects.
2.1 Make and describe
patterns using
construction kits.
Starter: Students are shown a sequence of shapes in a diagram and with
guidance they talk about they see so the teacher can identify whether
they have any idea of sequences.
Students are presented with a model made up of shapes. Then they are
given a copy of the same shape but with missing shapes. They have to
complete the model.
Students are presented with a simple model and an enlarged outline of
that same model. By using construction shapes, they have to fill the
outline to make the model thus giving them the idea that the model can
be represented on a bigger scale.
At a lower level, students will be able to match identical picture patterns
together.
Students will explore a small and a bigger version of the same object.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to use objects to find the
length and width and talk about the size
differences.
(Level 4)
Students will be able to recognise and choose the
smaller/shorter and then the largest/tallest from
a set.
(Level 3)
Students will be able to make sets of objects by
size.
(Level 2)
Students will be able to become aware that
things can be enlarged.
(Level 1)
Students will be able to use the right construction
tools to make an enlarged version of a model.
(Level 4).
Students will be able to decide on the missing
shape and put the correct shape into the pattern.
(Level 3).
Students will be able to match up to 6 familiar
objects.
(Level2)
Students will be able to become aware and
engage in the exploration of objects of different
sizes. (Level 1)
142
Subject:
Unit code and title:
Strand 1:
Strand 2:
MATHEMATICS
MTH 8.9 Directed Numbers and Sequences (Levels 7.1 – 8.1)
Number
Algebra
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach students to:
1. Add/subtract/multiply/divide directed numbers.
2. Solve problems using directed numbers.
3. Recognise arithmetic and geometric patterns; generate terms of a sequence using term to term and position to term rules.
4. Write the nth term expression of linear sequences of the form kn + m where k and m are integers.
Key Words
Number line, positive, negative,
integers, zero, consecutive,
directed numbers, °C (Celsius),
thermometer, below, above,
increase, decrease, greater
than, less than, symbols: ‹, ›.
Number pattern, geometric
pattern , terms , sequence, nth
term, position.
Points to Note
Resources
Three main teaching approaches are being recommended to promote a FOM B2, Students’ Book, Practice Book,
student centred learning environment.
Resource Pack – Chapters 9 & 22
Various number lines: vertical and
horizontal; thermometers.
Exposition: the teacher states the objectives of the lesson and may use ICT
software for students to practise new knowledge. This is consolidated by
From Teachers’ laptop:
setting students tasks that offer students the opportunity to apply
C:\Documents and Settings\teacher\My
mathematics to a variety of real life situations.
Documents\Maths Excel Lessons
Discovery: the teacher can set group tasks in which students discuss and
Internet Links:
construct mathematical knowledge. Students may become active learners
http://www.bbc.co.uk/skillswise/numbers/
while testing hypotheses and/or making generalisations.
http://www.ixl.com/math/practice/
http://skola.gov.mt/maths/resources.htm
Exploration: the teacher integrates an inquiry based learning approach that
http://www.mathsisfun.com/
enhances the students’ understanding of concepts. These tasks might
http://www.mathgoodies.com/
employ the processes of reasoning, problem solving, investigations,
http://www.apples4theteacher.com/
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
143
Teaching Objective
Examples of teaching experiences and activities
Indicators of Learning outcomes
The teacher will teach the
students to:
The students are reminded of the concept of negative numbers through
practical examples such as: walking forward/backwards, going up/down the
stairs, lifts, having a sum of money or owing it, temperature above/below
zero.
Students will be able to
add/subtract/multiply/divide more than
two directed numbers.
(Level 8.1)
The students access the following site to place positive and negative
numbers on a number line.
http://www.bbc.co.uk/skillswise/numbers/wholenumbers/whatarenumbers
/negativenumbers/flash1.shtml
Students will be able to multiply or divide
two directed numbers.
(Level 7.3)
1. Add/subtract/multiply/
divide directed numbers.
Students are shown 2 numbers on the number line marked from −10 to 10.
They are encouraged to make statements involving ‘is greater than’ or ‘ is
less than’ or ‘have a difference of’ etc.
The value of two or more negative numbers may be compared by accessing
the site http://www.ixl.com/math/practice/grade-8-compare-and-orderintegers
The excel worksheet -The Number Line, may be accessed on
http://skola.gov.mt/maths/resources.htm
Students will be able to add/subtract any
two integers without the help of the
calculator.
(Level 7.2)
Students will be able to add +ve/-ve
integers and subtract +ve integers
without the help of the
calculator/number line; subtract a
negative number with the help of the
calculator.
(Level 7.1)
Students may practice addition/subtraction of directed numbers on the site:
http://www.ixl.com/math/grade-8/integer-addition-and-subtraction-rules
The teacher uses the following site for a pictorial explanation of
multiplication of negative numbers.
http://www.mathsisfun.com/multiplying-negatives.html
The students are lead through discussion to establish that (+ve number) 
(−ve number) = (−ve number) and that (−ve number)  (−ve number) = (+ve
number). This is done through pattern recognition i.e. plotting a straight line
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
144
graph passing through the origin taking points on both sides of the y-axis
Further challenging practice on multiplication and division can be done on
the sites http://www.ixl.com/math/practice/grade-8-multiply-and-divideintegers or http://www.ixl.com/math/practice/grade-8-integermultiplication-and-division-rules
or
http://www.mathgoodies.com/lessons/toc_vol5.html
For games challenging speed in working out calculations involving –ve
numbers:
http://www.free-training-tutorial.com/negative-numbers-games.html
2. Solve problems using
directed numbers.
Students may be introduced to simple problems by finding ‘the mystery
number’ involving addition/subtraction and using the number line.
Students get interactive practice on solving word problems involving
negative numbers in real life using the following sites:
http://au.ixl.com/math/year-7
http://www.mathgoodies.com/lessons/vol5/challenge_vol5.html
Students will be able to solve complex
problems involving
addition/subtraction/multiplication/divi
sion of +ve/-ve numbers without the
help of the number line or calculator.
(Level 8.1)
Students will be able to solve simple
problems involving addition
/subtraction/multiplication/division of
+ve/-ve numbers without the help of the
number line or calculator.
(Level 7.3)
Students will be able to solve simple
problems involving addition /subtraction
of +ve/-ve integers without the help of
the number line or calculator.
(Level 7.2)
Students will be able to solve simple
problems involving addition of two +ve/-
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
145
ve integers and subtraction of +ve
integers without the help of the number
line or calculator; subtraction of –ve
integers using a calculator when
necessary.
(Level 7.1)
3. Recognise arithmetic and
geometric patterns;
generate terms of a
sequence using term to term
and position to term rules.
Students working in groups construct their own pictorial or number pattern
and ask another group to expand the sequence.
Students colour patterns on a number chart and discuss the pattern with
the class using the following site:
http://www.apples4theteacher.com/math/games/100-number-chartone.html
Students investigate and identify arithmetic and geometric sequences using
the site;
http://au.ixl.com/math/year-7
Students practice recognising and generating arithmetic and geometric
patterns using term to term and position with the help of interactive site:
http://www.mathsisfun.com/numberpatterns.html
http://www.ixl.com/math/grade-8/identify-arithmetic-and-geometricsequences
4. Write the nth term
expression of linear
sequences of the form
Students can be introduced to describing rules and writing it down in words
using number machines like these shown below:
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to generate terms of
a complex sequence using position to
term rules.
(Level 8.1)
Students will be able to generate terms of
a simple sequence using position to term
rules.
(Level 7.3)
Students will be able to continue
complex arithmetic /geometric patterns
using term to term rule.
(Level 7.2)
Students will be able to continue simple
arithmetic /geometric patterns using
term to term rule.
(Level 7.1)
Students will be able to write the nth
term expression of linear sequences of
the form kn + m where k and m are
146
kn + m where k and m are
integers.
integers.
(Level 8.1)
x
1
2
3
4
5
y
4
5
6
7
8
x
1
2
3
4
5
y
5
10
15
20
25
x
1
2
3
4
5
y
7
12
17
22
27
Through a discussion lesson explain why it might be better to use letters
rather than words.
The next step is to write the nth term expression of the linear sequences
Students will be able to write down the
rule in words of a sequence of the form
kn + m where k and m are integers.
(Level 7.3)
Students will be able to tell that the rule
is a combination of addition/subtraction
and multiplication.
(Level 7.2)
Students will be able to describe the rule
in words of a sequence of the form n ± k
and kn where k is a positive integer.
(Level 7.1)
Students practice writing the rule for the nth term of linear sequences using
interactive sites:
http://www.mathsisfun.com/numberpatterns.html
http://www.ixl.com/math/grade-8/write-variable-expressions-forarithmetic-sequences
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
147
Subject:
MATHEMATICS
Unit code and title: MTH 8.9 Directed Numbers & Sequences (Levels 6.3 – 7.3)
Strand 1:
Number
Strand 2:
Algebra
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Recognise and understand negative numbers through practical examples and represent directed numbers on the number line.
2. Add / subtract / multiply / divide directed numbers.
3. Solve problems using directed numbers.
4. Recognise arithmetic and geometric patterns; generate terms of a sequence using term to term and position to term rules.
5. Write down the rule in words of a sequence of the form kn +m where k and m are integers.
Key Words
Number line, positive,
negative, integers, zero,
consecutive, directed
numbers, °C (Celsius),
thermometer, below, above,
increase, decrease, greater
than, less than, symbols: ‹, ›.
Growing pattern, sequence,
number pattern, arithmetic
pattern, geometric pattern,
terms.
Points to Note
Resources
Three main teaching approaches are being recommended to promote a student FOM B1, Students’ Book, Practice Book,
centred learning environment.
Resource Pack – Chapters 9 & 22
Various number lines: vertical and
Exposition: the teacher states the objectives of the lesson and may use ICT
horizontal; thermometers.
software for students to practise new knowledge. This is consolidated by
setting students tasks that offer students the opportunity to apply mathematics
From Teachers’ laptop:
to a variety of real life situations.
C:\Documents and Settings\teacher\My
Documents\Maths Excel Lessons
Discovery: the teacher can set group tasks in which students discuss and
construct mathematical knowledge. Students may become active learners while
Internet Links:
testing hypotheses and/or making generalisations.
http://www.bbc.co.uk/skillswise/numbers/
http://www.ixl.com/math/practice/
Exploration: the teacher integrates an inquiry based learning approach that
http://skola.gov.mt/maths/resources.htm
enhances the students’ understanding of concepts. These tasks might employ
http://www.mathsisfun.com/
the processes of reasoning, problem solving, investigations, connecting ideas
http://www.mathgoodies.com/
and concepts, and expressing results by using the precise language of
mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
148
Teaching Objective
Examples of teaching experiences and activities
Indicators of Learning Outcomes
The teacher will teach the
students to:
The students are reminded of the concept of negative numbers through
practical examples such as: walking forward/backwards, going up/down the
stairs, lifts, having a sum of money or owing it, temperature above/below zero.
Students will be able to place integers
in order of size without the use of a
number line
(Level 7.3)
The students access the following site to place positive and negative numbers
on a number line.
http://www.bbc.co.uk/skillswise/numbers/wholenumbers/whatarenumbers/n
egativenumbers/flash1.shtml
Students will be able to compare the
value of two or more positive/negative
integers.
(Level 7.2)
Students are shown 2 numbers on the number line marked from −10 to 10.
They are encouraged to make statements involving ‘is greater than’ or ‘is less
than’ or ‘have a difference of’ etc.
Students will distinguish between
positive and negative numbers. They
can also represent both positive and
negative integers on the number line.
(Level 7.1)
1. Recognise and
understand negative
numbers through
practical examples and
represent directed
numbers on the number
line.
.
The value of two or more negative numbers may be compared by accessing the
site http://www.ixl.com/math/practice/grade-8-compare-and-order-integers
The excel worksheet -The Number Line, may be accessed on
http://skola.gov.mt/maths/resources.htm
2. Add/subtract/multiply/
divide directed numbers.
Students may practice addition/subtraction of directed numbers on the site:
http://www.ixl.com/math/grade-8/integer-addition-and-subtraction-rules
The teacher uses the following site for a pictorial explanation of multiplication
of negative numbers. http://www.mathsisfun.com/multiplying-negatives.html
The students are lead through discussion to establish that (+ve number)  (−ve
number) = (−ve number) and that (−ve number)  (−ve number) = (+ve
number). This is done through pattern recognition i.e. plotting a straight line
graph passing through the origin taking points on both sides of the y-axis
Further practice on multiplication and division can be done on the sites
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to compare the
value of two positive integers.
(Level 6.3)
Students will be able to multiply or
divide two directed numbers.
(Level 7.3)
Students will be able to add/subtract
any two integers without the help of
the calculator.
(Level 7.2)
Students will be able to add +ve/-ve
integers and subtract +ve integers
149
http://www.ixl.com/math/practice/grade-8-multiply-and-divide-integers or
http://www.ixl.com/math/practice/grade-8-integer-multiplication-anddivision-rules
without the help of the
calculator/number line; subtract a
negative number with the help of the
calculator.
(Level 7.1)
Students will be able to add/subtract
two positive integers which give a
positive/negative result, using the
number line.
(Level 6.3)
3.
Solve problems using
directed numbers.
Students get interactive practice on solving problems involving negative
numbers in real life using the following sites:
ww.interactiveessentials,co.uk/Number.htm
http://www.mathgoodies.com/lessons/toc_vol5.html
Students will be able to solve simple
problems involving
addition/subtraction/multiplication/di
vision of +ve/-ve numbers without the
help of the number line or calculator.
(Level 7.3)
http://www.ixl.com/math/practice/grade-8-multiply-and-divide-integers
Students will be able to solve simple
problems involving addition
/subtraction of +ve/-ve integers
without the help of the number line or
calculator.
(Level 7.2)
Students will be able to solve simple
problems involving addition of two +ve/ve integers and subtraction of +ve integers
without the help of the number line or
calculator; subtraction of –ve integers
using a calculator when necessary.
(Level 7.1)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
150
Students will be able to solve simple
problems involving addition of two
+ve/-ve integers and subtraction of +ve
integers.
(Level 6.3)
4
Recognise arithmetic and
geometric patterns;
generate terms of a
sequence using term to
term and position to term
rules.
Students working in groups construct their own pictorial or number pattern
and ask another group to expand the sequence, thus explore growing patterns
(sequences)
Students colour patterns on a number chart and discuss the pattern with the
class using the following site:
http://www.apples4theteacher.com/math/games/100-number-chart-one.html
Students investigate and identify arithmetic and geometric sequences using the
site;
http://au.ixl.com/math/year-7
Students practice recognising and generating arithmetic and geometric
patterns using term to term and position to term with the help of interactive
site: http://www.mathsisfun.com/numberpatterns.html
http://www.ixl.com/math/grade-8/identify-arithmetic-and-geometricsequences
5.
Write down the rule in
words of a sequence of the
form kn + m where k and m
are integers.
Students can be introduced gradually to describe rules and write them in words
using number machines like these shown below:
Students will be able to generate terms
of simple sequences using position to
term rules.
(Level 7.3)
Students will be able to continue
complex arithmetic /geometric number
patterns using term to term rule.
(Level 7.2)
Students will be able to continue
simple arithmetic /geometric number
patterns using term to term rule.
(Level 7.1)
Students will be able to fill in a
missing term in arithmetic patterns.
(Level 6.3)
Students will be able to write down the
rule in words of a sequence of the form
kn + m where k and m are integers.
(Level 7.3)
Students will be able to tell that the
rule is a combination of
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
151
x
1
2
3
4
5
y
4
5
6
7
8
x
1
2
3
4
5
y
5
10
15
20
25
x
1
2
3
4
5
y
7
12
17
22
27
Students practice writing the rule in words of linear sequences using the
interactive site: http://www.mathsisfun.com/numberpatterns.html
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
addition/subtraction and
multiplication.
(Level 7.2)
Students will be able to describe the
rule in words of a sequence of the
form n ± k and kn where k is a
positive integer
(Level 7.1)
Students will be able to tell that the
rule involves only multiplication.
(Level 6.3)
152
Subject:
MATHEMATICS
Unit code and title: MTH 8.9 Directed Numbers & Sequences (Levels 5.3 – 7.1)
Strand 1:
Number
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Recognize and understand negative numbers through practical examples and represent directed numbers on the number line.
2. Add and subtract directed numbers; use a calculator to subtract a negative number.
3. Solve problems using directed numbers.
4. Recognise arithmetic and geometric patterns; complete a given sequence using term to term rule.
5. Describe the rule in words of a sequence of the form n ± k and kn where k is a positive integer.
Key Words
Number line, positive,
negative, integers, zero,
directed numbers, °C
(Celsius), thermometer,
below, above, increase,
decrease, greater than, less
than.
Growing pattern, sequence,
number pattern, arithmetic
pattern, geometric pattern,
terms.
Points to Note
Resources
Three main teaching approaches are being recommended to promote a FOM B Gold, Students’ Book, Resource
student centred learning environment.
Pack – Chapters 9 & 21
Various number lines: vertical and
Exposition: the teacher states the objectives of the lesson and may use ICT
horizontal; thermometers.
software for students to practise new knowledge. This is consolidated by
setting students tasks that offer students the opportunity to apply
From Teachers’ laptop:
mathematics to a variety of real life situations.
C:\Documents and Settings\teacher\My
Documents\Maths Excel Lessons
Discovery: the teacher can set group tasks in which students discuss and
construct mathematical knowledge. Students may become active learners
Internet Links:
while testing hypotheses and/or making generalisations.
http://www.bbc.co.uk/skillswise/numb
ers/wholenumbers/
Exploration: the teacher integrates an inquiry based learning approach that
http://www.ixl.com/math/practice/
enhances the students’ understanding of concepts. These tasks might
http://skola.gov.mt/maths/resources.htm
employ the processes of reasoning, problem solving, investigations,
http://www.teacherled.com/resources/
connecting ideas and concepts, and expressing results by using the precise
http://www.mathsisfun.com/
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
153
Teaching Objective
Examples of teaching experiences and activities
Indicators of Learning Outcomes
The teacher will teach students
to:
The students are reminded of the concept of negative numbers through
practical examples such as: walking forward/backwards, going up/down the
stairs, lifts, having a sum of money or owing it, temperature above/below
zero.
Students will distinguish between
positive and negative numbers. They
can also represent both positive and
negative integers on the number line.
(Level 7.1)
1. Recognise and understand
negative numbers through
practical examples and
represent directed numbers
on the number line.
The students access the following site to place positive and negative
numbers on a number line.
http;//www.bbc.co.uk/skillswise/numbers/wholenumbers/whatarenumbers
/negativenumbers/flash1.shtml
The value of two or more negative numbers may be compared by accessing
the site http://www.ixl.com/math/practice/grade-8-compare-and-orderintegers
The excel worksheet -The Number Line, may be accessed on
http://skola.gov.mt/maths/resources.htm
Students compare temperatures on this site:
http://www.teacherled.com/resources/eurotemps/eurotempsload.html
The following presentation about thermometers and sea level can be used
as an exercise for the students to work out.
http://www.whiteboardmaths.com/downloads/cd7c2a230f6bba7574cc9a5e
ebdedce5.zip
2. Add and subtract directed
numbers; use a calculator to
subtract a negative number.
Additionally, this game represents another practical situation (lifts):
http://www.interactiveessentials.co.uk/software/Numeracy/NegativeNumb
ersLoader.swf
Students practice addition and subtraction of directed numbers through
real-life situations involving spending money, making a debt, moving
forward and backwards, change of temperature, etc.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to compare the
value of two positive integers.
(Level 6.3)
Students will be able to put positive
integers in order of size on a number
line.
(Level 6.2)
Students will understand that on a
number line, the positive numbers
are found on the right hand side of
zero while the negative numbers are
found on the left hand side.
(Level 6.1)
Students will understand that
positive numbers carry a “+” sign
while negative numbers carry a “-”
sign and apply this to real life
situations.
(Level 5.3)
Students will be able to add +ve/-ve
integers and subtract +ve integers
without the help of the
154
Students may practice addition/subtraction of directed numbers on the site:
http://www.ixl.com/math/grade-8/integer-addition-and-subtraction-rules
calculator/number line; subtract a
negative number with the help of the
calculator.
(Level 7.1)
Students will be able to subtract two
positive integers which give a
positive/negative result, using the
number line.
(Level 6.3)
Students will be able to add a positive
integer to a negative integer which
gives a positive/negative result,
without the help of the number line.
(Level 6.2)
Students will be able to add a positive
integer to a negative integer which
gives a positive/negative result, using
the number line.
(Level 6.1)
3. Solve problems using
directed numbers.
Students get interactive practice on solving problems involving negative
numbers in real life using the following sites:
ww.interactiveessentials,co.uk/Number.htm
http://www.mathgoodies.com/lessons/toc_vol5.html
http://www.ixl.com/math/practice/grade-8-multiply-and-divide-integers
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to add two or
more positive integers.
(Level 5.3)
Students will be able to solve simple
problems involving addition of two +ve/ve integers and subtraction of +ve
integers without the help of the number
line or calculator; subtraction of –ve
integers using a calculator when
necessary.
(Level 7.1)
155
Students will be able to solve simple
problems involving addition of +ve/-ve
integers and subtraction of +ve
integers.
(Level 6.3)
Students will be able to solve
problems involving addition of more
than two +ve/-ve integers.
(Level 6.2)
Students will be able to solve simple
problems involving addition of two
+ve/-ve integers.
(Level 6.1)
Students will be able to express
actions as +ve/-ve numbers, i.e. go up
3 levels and down 2 expressed as +3
and -2.
(Level 5.3)
4. Recognise arithmetic and
geometric patterns;
complete a given sequence
using term to term rule.
Students working in groups construct their own pictorial or number pattern
Stu Students will be able to continue
and ask another group to expand the sequence, thus exploring growing
simple arithmetic/ geometric patterns
patterns (sequences).
using term to term rule.
(Level 7.1)
Students colour patterns on a number chart and discuss the pattern with
the class using the following site:
7.1 Students will be able to fill in a
http://www.apples4theteacher.com/math/games/100-number-chartmissing term in arithmetic patterns.
one.html
(Level 6.3)
Students investigate and identify arithmetic and geometric sequences using
6.2 Students will be able to recognise
the site:
arithmetic patterns.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
156
http://au.ixl.com/math/year-7
(Level 6.2)
Students practice recognising and generating arithmetic and geometric
patterns with the help of interactive site:
http://www.mathsisfun.com/numberpatterns.html
http://www.ixl.com/math/grade-8/identify-arithmetic-and-geometricsequences
6.1 Students will be able to continue
pictorial patterns.
(Level 6.1)
5.3 Students will be able to recognise
pictorial patterns.
The following site should be helpful for students who need more practice:
(Level 5.3)
http://mathwire.com/algebra/growingpatterns.html
5. Describe the rule in words of
a sequence of the form n ±
k and kn where k is a positive
integer.
Students can be introduced gradually to describe rules and write them in
words using number machines like these shown below:
input
output
1
4
2
5
3
6
4
7
5
8
output = input +3
input
Students will be able to describe the
rule in words of a sequence of the
form n ± k and kn where k is a
positive integer.
(Level 7.1)
output
1
5
2
10
3
15
4
20
5
25
output = input ×5
Students practice writing the rule in words of linear sequences using the
interactive site: http://www.mathsisfun.com/numberpatterns.html
Students will be able to tell that the
rule involves only multiplication.
(Level 6.3)
Students will be able to write the rule
in words in number sequences of the
form n ± k where k is a positive
integer.
(Level 6.2)
Students will be able to write the
rule in words in number sequences of
the form n + k where k is a positive
integer.
(Level 6.1)
Students will be able to tell the
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
157
pattern is increasing /decreasing in
number sequences of the form n + k
where k is an integer.
(Level 5.3)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
158
Subject:
Mathematics
Unit code and title: MTH 8.9 Directed Numbers & Sequences (Levels 1 - 4)
Strand 1:
Number
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives at attainment Level 5 and 6
The teacher will teach the students to:
1. Recognise and understand negative numbers through practical examples and represent directed numbers on the number line.
2. Add and subtract directed numbers; use a calculator to subtract a negative number.
3. Solve problems using directed numbers.
4. Recognise arithmetic and geometric patterns; complete a given sequence using term to term rule.
5. Describe the rule in words of a sequence of the form n ± k and kn where k is a positive integer.
Objectives at attainment levels 1, 2, 3, 4 (Mainstream objective 3 is beyond attainment level 4.)
The teacher will teach the students to:
1.1 Understand the basic idea of negative numbers through practical games.
2.1 Follow instructions to work out sums with simple operations.
4.1 Continue a simple sequence.
5.1 Identify and write the action that is leading to the end result.
Key Words
Number line, numbers less
than zero (negative
numbers), numbers greater
than zero (positive
numbers), more/less, what’s
the next pattern?
Points to Note
In addition to the points to note recommended for students
performing at Level 5 or higher, it is very important for the teacher
to allow time for the students to respond. This response can take
the form of unaided and/or aided means of communication and
the teacher needs to provide adequate scaffolding techniques to
enable the students to respond affectively or intentionally.
Resources
New Maths Frame Working Step Up Workbook.
Oxford Framework Maths 7
For further examples about level 1 refer to the handbook Pg.
Internet Links:
http://www.topmarks.co.uk/Flash.aspx?f=HigherAndL
ower
http://www.topmarks.co.uk/Flash.aspx?f=countingstickv4
http://www.learnalberta.ca/content/mejhm/index.ht
ml?
From Teachers’ laptop:
C:\Documents and Settings\teacher\My
Documents\Maths Excel Lessons
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
159
Teaching Objective
The teacher will teach the
students to:
1.1 Understand the basic
idea of negative
numbers through
practical games.
Examples of teaching experiences and activities
Starter: Students are presented with an empty number line. They
are given positive numbers and they have to sort them out on the
right side of the number line.
The teacher gets two beakers with just boiled water, warm water,
cold water and iced water. She places a thermometer inside each
beaker and the students read the readings. Then they will discuss
the results and begin to understand that the colder the water or
the weather the lower the value of the temperature is.
Students are presented with different temperature readings and
they have to match them with their numbers on the number line.
Students will sort numbers with a symbol in front of them
(negative numbers) and those with positive.
Students are presented with a touch screen or switch activity in
which they experience the effect of disappearance when they
touch the screen or press the mouse. Student looks for an object
that has been removed from direct line of vision.
2.1 Follow instructions to
work out sums with
simple operations.
Starter: Students have a go on a computer game so the teacher
can check whether they can follow instructions or not.
Teacher writes a set of simple sums on the board and they follow
the instructions as to which one they should work out first.
Students are presented with a board game activity. They follow the
teacher as she recites the numbers whilst moving a counter
through it. The teacher can say move one, two and three and show
the three on her fingers. The student is allowed to move the
counter herself.
Using the beebot students suggest the path that the beebot needs
to take to get to the final destination. They have to count the
Indicators of Learning outcomes
Students will discuss and compare different numbers.
They are shown that the colder the weather the less
the temperature is.
(Level 4)
Students will differentiate between the two number
representations by colouring a negative number in red
and a positive number in blue (a model example is
shown).
(Level 3)
Students will be able to match the negative numbers
with the negative numbers and the positive with the
positive.
(Level 2)
Students will follow a slow moving object on the
screen and turn head to look for a disappeared object.
(Level 1)
Students will begin to use the vocabulary involved in
addition and subtraction of number patterns.
(Level 4)
Students will start applying adding and subtracting in
practical situations.
(Level 3)
Students will show an interest in number activities and
join in rote counting and familiar number activities up
to 3.
(Level 2)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
160
4.1 Continue a simple
sequence.
number of steps needed to move up, down, left or right.
Students will follow the above activities by sustaining longer
attention and by showing some kind of reaction to the reciting of
numbers.
Starter: Teacher shows two sequences and the students have to
identify the one which has a specific rule.
Students are shown a sequence of symbols made up of three
different symbols. They have to continue the pattern and talk
about their choice of continuity.
Students will watch their hands when it moves and
maybe laugh at the one two three movements.
(Level 1)
Students will recognise and extend on a given pattern
whilst explaining their choice.
(Level 4)
Students will recognise and continue a given pattern
using two variations.
(Level 3)
The above example will be limited to two symbols.
Students will match a pattern of three items with another pattern
of 3 items.
Students will follow the rhythm of a musical beat.
5.1 Identify and write the
action that is leading to
the end result
Teacher writes four numbers on the board. Students have to guess
and then write (e.g. + 2) how they can get the second number from
the first and the third from the second. Eventually, they will
generate their own numbers for others to guess the action.
Students are presented with a picture of three objects and another
one with two. Students are encouraged to talk about the two
groups and that one has more and one has less.
Using the above activity, students will give one object from a set
thus observing the process of say having 3 objects and taking away
one.
Students are presented with an object which is then taken away.
Students will match sets of patterns together.
(Level 2)
Students will anticipate and be involved in musical
rhythm experiences.
(Level 1)
Students will use addition and subtraction facts to find
the hidden rule.
(Level 4)
Students will understand the differences in quantities
by using more or less.
(Level 3)
Students will recognise the differences in quantities by
using more or less.
(Level 2)
Students will participate in activities involving objects
in the line of vision and out of their sight.
(Level 1)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
161
Subject:
MATHEMATICS
Unit code and title: MTH 8.10 Algebraic Expressions and Formulae (Levels 7.1 – 8.1)
Strand 2:
Algebra
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Simplify algebraic expressions by multiplying a single term over a bracket and/or collecting like terms.
2. Factorise expressions by identifying a numerical common factor.
3. Evaluate simple formulae by substituting letters with positive and negative inputs.
4. Derive and use formulae to solve problems.
Key Words
Simplify, solve, algebraic
expression, single term, like
terms, factorise, common
factor, formula, inputs,
substitution, symbols, values,
evaluate.
Points to Note
Resources
FOM B2, Students’ Book, Practice
Three main teaching approaches are being recommended to promote a
Book, Resource Pack - Chapters 6 &
student centred learning environment.
16
Exposition: the teacher states the objectives of the lesson and may use ICT
software for students to practise new knowledge. This is consolidated by
setting students tasks that offer students the opportunity to apply
mathematics to a variety of real life situations.
From Teachers’ laptop:
C:\Documents and
Settings\teacher\My
Documents\Maths Excel Lessons
Skillsheets CD
Discovery: the teacher can set group tasks in which students discuss and Algebra Tiles
construct mathematical knowledge. Students may become active learners
while testing hypotheses and/or making generalisations.
Internet Links:
http://www.ixl.com/math/
Exploration: the teacher integrates an inquiry based learning approach that http://www.bbc.co.uk/
enhances the students’ understanding of concepts. These tasks might employ http://www.wtamu.edu/academic/
the processes of reasoning, problem solving, investigations, connecting ideas anns/mps/math
and concepts, and expressing results by using the precise language of
mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
162
Teaching Objective
The teacher will teach the
students to:
1. Simplify algebraic
expressions by
multiplying a single
term over a bracket
and/or collecting like
terms.
Examples of teaching experiences and activities
Indicators of Learning Outcomes
The students are encouraged to use the grid method to multiply a single term
over a bracket.
e.g. 4(p + 2q)
p
+2q
4
4p
+8q
Students will be able to simplify
quadratic algebraic expressions by
multiplying a single term over a
bracket and/or collecting like terms.
(Level 8.1)
The students access the following site to practice adding and subtracting like
terms. http://www.ixl.com/math/practice/grade-8-add-and-subtract-like-terms
Students will be able to simplify linear
algebraic expressions by multiplying a
single term over a bracket and/or
collecting like terms.
(Level 7.3)
Students practise expanding and simplifying expressions through the site:
http://www.ixl.com/math/grade-8/simplify-variable-expressions
Students practise multiplying a term over a bracket and simplifying using the
sites:
http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg
_alg_tut11_simp.htm
http://www.bbc.co.uk/scotland/learning/bitesize/standard/maths_i/relationshi
ps/manipulation_rev1.shtml
Students will be able to multiply an
integer over a bracket.
(Level 7.2)
Students will be able to simplify linear
expressions made up of up to two
variables by collecting like terms.
(Level 7.1)
Students can visualize working algebraically through Algebra tiles using the site:
http://mathbits.com/mathbits/AlgebraTiles/AlgebraTilesMathBitsNew07ImpFr
ee.html
Skillsheets CD provides both introduction and practice on expansion and
simplification of algebraic expressions which can also be used on IWB or as
hand outs.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
163
2. Factorise expressions
by identifying a
numerical common
factor.
Students are introduced to factorisation using the site:
http://www.bbc.co.uk/scotland/learning/bitesize/standard/maths_i/relationshi
ps/manipulation_rev4.shtml
Students can visualize factorisation through Algebra tiles using, among others,
the site:
http://mathbits.com/mathbits/AlgebraTiles/AlgebraTilesMathBitsNew07ImpFr
ee.html
Students will be able to factorise fully
linear expressions by identifying a
numerical common factor.
(Level 8.1)
Students will be able to identify a
numerical common factor in linear
expressions.
(Level 7.3)
Students will be able to find the
common factor of two or more
integers.
(Level 7.2)
Students will be able to find the
factors of an integer.
(Level 7.1)
3.
Evaluate simple
formulae by
substituting letters with
positive and negative
inputs.
Students are introduced to/practise substituting a letter/s with +ve/ –ve integer/s
through the sites:
http://www.ixl.com/math/grade-8/evaluate-single-variable-expressions
http://www.ixl.com/math/grade-8/evaluate-multi-variable-expressions
http://www.ixl.com/math/grade-8/evaluate-variable-expressions-for-numbersequences
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to evaluate
quadratic formulae by substituting
letters with positive and negative
inputs.
(Level 8.1)
Students will be able to evaluate
linear formulae involving brackets by
substituting letters with positive and
negative integral or decimal inputs.
(Level 7.3)
164
Students will be able to evaluate
simple linear formulae by substituting
letters with positive and negative
inputs.
(Level 7.2)
Students will be able to evaluate
linear formulae involving brackets by
substituting letters with positive
integral inputs.
(Level 7.1)
4.
Derive and use
formulae to solve
problems.
Students write ordinary language as algebraic expressions and formulae in site:
http://www.themathpage.com/alg/algebraic-expressions.htm#expressions
Students will be able to derive and use
formulae to solve problems involving
positive/negative integers.
(Level 8.1)
Students use the following sites to derive formulae:
http://www.ixl.com/math/grade-8/write-variable-expressions
http://www.ixl.com/math/grade-8/write-variable-expressions-to-representdiagrams
Students will be able to derive and use
formulae to solve problems involving
positive integers only.
(Level 7.3)
Students will be able to choose the
correct variable expression involving
two operations to represent a word
problem.
(Level 7.2)
Students will be able to write variable
expressions to represent diagrams.
(Level 7.1)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
165
Subject:
MATHEMATICS
Unit code and title: MTH 8.10 Algebraic Expressions and Formulae (Levels 6.3 – 7.3)
Strand 2:
Algebra
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Simplify algebraic expressions by multiplying a single term over a bracket and/or collecting like terms.
2. Evaluate simple linear formulae by substituting letters with positive and negative inputs.
3. Derive and use formulae to solve problems.
Key Words
Simplify, solve, algebraic
expression, single term, like
terms, factorise, common
factor, formula, inputs,
substitution, symbols, values
evaluate.
Points to Note
Resources
Three main teaching approaches are being recommended to promote a student FOM B1, Students’ Book, Practice
centred learning environment.
Book, Resource Pack - Chapters 6 & 16
From Teachers’ laptop:
Exposition: the teacher states the objectives of the lesson and may use ICT
C:\Documents and
software for students to practise new knowledge. This is consolidated by
Settings\teacher\My
setting students tasks that offer students the opportunity to apply
Documents\Maths Excel Lessons
mathematics to a variety of real life situations.
Skillsheets CD
Discovery: the teacher can set group tasks in which students discuss and
Algebra tiles
construct mathematical knowledge. Students may become active learners while
testing hypotheses and/or making generalisations.
Internet Links:
http://www.ixl.com/math/
Exploration: the teacher integrates an inquiry based learning approach that
http://www.bbc.co.uk/
enhances the students’ understanding of concepts. These tasks might employ
http://www.wtamu.edu/academic/an
the processes of reasoning, problem solving, investigations, connecting ideas
ns/mps/math
and concepts, and expressing results by using the precise language of
mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
166
Teaching Objective
Examples of teaching experiences and activities
Indicators of Learning Outcomes
The teacher will teach the
students to:
The students are encouraged to use the grid method to multiply a single term
over a bracket.
e.g. 4(p + 2q)
p
+2q
4
4p
+8q
Students will be able to simplify linear
algebraic expressions by multiplying a
single term over a bracket and/or
collecting like terms.
(Level 7.3)
The students access the following site to practise adding and subtracting like
terms. http://www.ixl.com/math/practice/grade-8-add-and-subtract-like-terms
Students will be able to multiply an
integer over a bracket.
(Level 7.2)
1. Simplify algebraic
expressions by
multiplying a single
term over a bracket
and/or collecting like
terms.
Students practise expanding and simplifying expressions through the site:
http://www.ixl.com/math/grade-8/simplify-variable-expressions
Students practise multiplying a term over a bracket and simplifying using the
sites:http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra
/begalg_tut11_simp.htm
http://www.bbc.co.uk/scotland/learning/bitesize/standard/maths_i/relationshi
ps/manipulation_rev1.shtml
Skillsheets CD provides both introduction and practice on expansion and
simplification of algebraic expressions which can also be used on IWB or as
hand outs.
2. Evaluate simple linear
formulae by
substituting letters with
positive and negative
inputs.
Students are introduced to/practise substituting a letter/s with +ve/ –ve
integer/s through the sites:
http://www.ixl.com/math/grade-8/evaluate-single-variable-expressions
http://www.ixl.com/math/grade-8/evaluate-multi-variable-expressions
http://www.ixl.com/math/grade-8/evaluate-variable-expressions-for-numbersequences
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to simplify linear
expressions made up of up to two
variables by collecting like terms.
(Level 7.1)
Students will be able to simplify linear
expressions made up of one variable
by collecting like terms.
(Level 6.3)
Students will be able to evaluate
linear formulae involving brackets by
substituting letters with positive and
negative integral or decimal inputs.
(Level 7.3)
Students will be able to evaluate
simple linear formulae by substituting
letters with positive and negative
167
inputs.
(Level 7.2)
Students will be able to evaluate
linear formulae involving brackets by
substituting letters with positive
integral inputs.
(Level 7.1)
3. Derive and use formulae
to solve problems.
Students write ordinary language as algebraic expressions and formulae in site:
http://www.themathpage.com/alg/algebraic-expressions.htm#expressions
Students use the following sites to derive and use formulae:
http://www.ixl.com/math/grade-8/write-variable-expressions
http://www.ixl.com/math/grade-8/write-variable-expressions-to-representdiagrams
Students will be able to evaluate
simple linear formulae involving more
than two variables by substituting
letters with positive integral inputs.
(Level 6.3)
Students will be able to derive and use
formulae to solve problems involving
positive integers only.
(Level 7.3)
Students will be able to choose the
correct variable expression involving
two operations to represent a word
problem.
(Level 7.2)
Students will be able to write variable
expressions to represent diagrams.
(Level 7.1)
Students will be able to choose the
correct variable expression involving
one operation to represent a word
problem.
(Level 6.3)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
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Subject:
MATHEMATICS
Unit code and title: MTH 8.10 Algebraic Expressions and Formulae (Levels 5.3 – 7.1)
Strand 2:
Algebra
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Use letter symbols to represent unknown numbers.
2. Evaluate simple formulae by substituting letters with positive integral inputs.
3. Work simple formulae backwards.
Key Words
Simplify, solve, like terms,
factorise, formula, inputs,
substitution, symbols,
values, evaluate, backwards.
Points to Note
Resources
Three main teaching approaches are being recommended to promote a FOM B Gold, Students’ Book, Practice Book,
student centred learning environment.
Resource Pack - Chapters 6
From Teachers’ laptop:
Exposition: the teacher states the objectives of the lesson and may use ICT
C:\Documents and Settings\teacher\My
software for students to practise new knowledge. This is consolidated by
Documents\Maths Excel Lessons
setting students tasks that offer students the opportunity to apply
mathematics to a variety of real life situations.
Skillsheet CD
Algebra tiles
Discovery: the teacher can set group tasks in which students discuss and
construct mathematical knowledge. Students may become active learners
Internet Links:
while testing hypotheses and/or making generalisations.
http://www.themathpage.com/alg/algebraicexpressions.htm#expressions
Exploration: the teacher integrates an inquiry based learning approach that
http://www.ixl.com/math
enhances the students’ understanding of concepts. These tasks might
www.mathsisfun.com/
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
169
Teaching Objective
Examples of teaching experiences and activities
Indicators of Learning Outcomes
The teacher will teach the
students to:
Students write ordinary language as algebraic expressions and formulae in
site:
http://www.themathpage.com/alg/algebraic-expressions.htm#expressions
Students will be able to use letters to
represent two or three unknown values in
linear expressions involving up to two
operations of addition, subtraction,
multiplication or division.
(Level 7.1)
1. Use letter symbols to
represent unknown
numbers.
Students use the following sites to derive formulae:
http://www.ixl.com/math/grade-8/write-variable-expressions
http://www.ixl.com/math/grade-8/write-variable-expressions-to-representdiagrams
Skillsheets Algebra 1&2 can be projected and serve as introduction to
substitute numbers for letters especially for the weaker students.
Students will be able to use letters to
represent two or three unknown values in
simple linear expressions.
(Level 6.3)
Students will be able to use a letter to
represent an unknown value in simple linear
expressions.
(Level 6.2)
Students will be able to use a letter symbol
to represent an unknown number.
(Level 6.1)
Students will be able to represent an
unknown value by means of an empty space
or picture in simple expressions.
(Level 5.3)
2. Evaluate simple
formulae by substituting
letters with positive
integral inputs.
Students are introduced to/practise substituting a letter/s with +ve integer/s
through the sites:
http://www.ixl.com/math/grade-8/evaluate-single-variable-expressions
http://www.ixl.com/math/grade-8/evaluate-multi-variable-expressions
http://www.ixl.com/math/grade-8/evaluate-variable-expressions-for-
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to evaluate linear
formulae involving brackets by substituting
letters with positive integral inputs.
(Level 7.1)
170
number-sequences
www.mathsisfun.com/
Students are introduced to the topic through the use of Algebra Tiles
Students will be able to evaluate simple
linear formulae involving more than two
variables by substituting letters with positive
integral inputs.
(Level 6.3)
Students will be able to evaluate simple
linear formulae involving two variables by
substituting letters with positive integral
inputs.
(Level 6.2)
Students will be able to evaluate simple
linear formulae involving one variable by
substituting letters with positive integral
inputs.
(Level 6.1)
Students will be able to evaluate simple
linear formulae involving one variable by
substituting letters with small positive
integral inputs and involving one operation.
(Level 5.3)
3. Work simple formulae
backwards.
Students are given actions and undo actions to match eg. Wake, sleep; open
close; up, down etc.
Students will be able to work simple
formulae backwards.
(Level 7.1)
Students are given number puzzles to solve. Then the students themselves
form number puzzles (starting with one step operation) in pairs and another
pair of students find the mystery number. Both puzzle and solution are
recorded showing all steps. The number of operations is then gradually
increased.
Students will be able to find the input when
given the output in one/two operation
number machines.
(Level 6.3)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
171
Number machines done in previous year can be revised to remind students
how to find the input from the output. Further practice can be found in
Maths Excel lessons: Describe Function machines.
Students will be able to solve one/two
operation number puzzles through inverse
operations.
(Level 6.2)
Students will be able to give the inverse of
simple mathematical operations.
(Level 6.1)
Students will be able to evaluate linear
formulae with one operation by trial and
error given a set of options.
(Level 5.3)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
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Subject:
Mathematics
Unit code and title: MTH 8.10 Algebraic Expressions and Formulae (Level 1-4)
Strand 2:
Algebra
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives at attainment Level 5 and 6
The teacher will teach the students to:
1. Use letter symbols to represent unknown numbers.
2. Evaluate simple formulae by substituting letters with positive inputs.
3. Solve simple formulae by working backwards.
Objectives at attainment levels 1, 2, 3, 4
The teacher will teach the students to:
1.1 Use letters instead of a symbol to represent a missing number.
2.1 Use addition and subtraction to solve equations first pictorially and then in a more formal way.
Key Words
Missing number, value of
the letter or symbol,
equation
Points to Note
In addition to the points to note recommended for students performing
at Level 5 or higher, it is very important for the teacher to allow time for
the students to respond. This response can take the form of unaided
and/or aided means of communication and the teacher needs to provide
adequate scaffolding techniques to enable the students to respond
affectively or intentionally.
Resources
New Maths Frame Working Step Up Workbook.
Oxford Framework Maths 7
For further examples about level 1 refer to the handbook.
Internet Links:
http://www.learnalberta.ca/content/mejhm
From Teachers’ laptop:
C:\Documents and Settings\teacher\My
Documents\Maths Excel Lessons
www.primaryresources.co.uk
http://www.mymaths.co.uk/samples/sampleLesso
nFormulae.swf
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
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Teaching Objective
The teacher will teach
the students to:
Examples of teaching experiences and activities
Starter: The teacher will show a visual representation of an equation and
two formal equations and the students have to choose which one
represents the visual representation.
1.1 Use letters instead of
a symbol to
represent a missing
number.
Students will be shown three groups of objects, with one group being left
empty. Underneath each group the students have to write the numbers
in each and then find the quantity of the empty one.
Students will be involved in a picture exchange system whereby for a
card of a set of objects, the students count the objects and exchange
them with card representing the value of the group.
Students will match same picture groups.
2.1 Use addition and
subtraction to solve
equations first
pictorially and then
in a more formal
way.
Subject:
Students will be shown that a set of jars or anything that can be opened
and be closed. Students observe and possibly follow the rule of open and
closed.
Starter: The teacher says a statement like, I bought 4 waffles but I would
like to have 5, how much more do I need?
Students are given dominoes containing a number of dots on one side
and a blank slot on the other side. For e.g.
4
Students have to fill in the blank side with the number of dots that are
needed to make 4. The more formal way would be 2 + ____ = 4
Students will work with sets of objects; they find the value and match it
to the corresponding number.
Students will match pictures and observe that taking away or adding on
can match the new situation with its equal.
Students will be exposed to an online balance and they observe the
adults putting on and taking away items. If the screen is a touch one,
they can interact with it too.
MATHEMATICS
Indicators of Learning Outcomes
Students will be able to apply their simple
arithmetic knowledge to solve the equation and
find the missing quantity.
(Level 4)
Students will participate in activities involving the
exchange of something for another. They would
show they have understood by giving the correct
value card.
(Level 3)
Students will match same value groups.
(Level 2)
Students will show an interest in the activity by
sustaining attention and possibly by initial
interaction with adults.
(Level 1)
Students will find the missing quantity by using
addition and subtraction skills.
(Level 4)
Students will match a group of pictures to its
number value.
(Level 3)
Students will be able to match pictures.
(Level 2)
Students will be involved in activities involving
changing in quantities.
(Level 1)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Form 2
174
Unit code and title:
Strand 4:
MTH 8.11 Statistics and Probability (Levels 7.1 – 8.1)
Data Handling
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Draw and interpret bar charts and pie charts.
2. Compile and interpret frequency tables for grouped / ungrouped discrete and continuous data.
3. Understand, compute and interpret the mean, mode, median and range of a set of ungrouped data.
4. Use a spreadsheet to construct bar charts and pie charts and compute the mean and range of a set of ungrouped data.
5. Understand and work out the probability of an event.
6. Compile a possibility space and use it to find the probability of two events.
Key Words
Mean, mode, median, range,
data, ungrouped data, grouped
data, frequency table, bar chart,
pie chart, spreadsheet,
questionnaire, tally, average,
between, less than, less than or
equal to, greater than, greater
than or equal to, discreet,
continuous, event, probability,
chance, certain, impossible,
likely, unlikely, occurring,
possibility space
Points to Note
Three main teaching approaches are being recommended to promote a
student centred learning environment.
Resources
FOM B2, Students’ Book, Practice Book,
Resource Pack – Chapters 4, 14 & 21
Exposition: the teacher states the objectives of the lesson and may use ICT
software for students to practise new knowledge. This is consolidated by
setting students tasks that offer students the opportunity to apply
mathematics to a variety of real life situations.
From Teachers’ laptop:
C:\Documents and Settings\teacher\My
Documents\Maths Excel Lessons\
Pie Chart & Mode, Mean, Median, Range
& Coins (probability)
Discovery: the teacher can set group tasks in which students discuss and
construct mathematical knowledge. Students may become active learners Internet Links:
while testing hypotheses and/or making generalisations.
www.solvemymath.com
www.superteacherworksheets.com
Exploration: the teacher integrates an inquiry based learning approach that www.harcourtschool.com
enhances the students’ understanding of concepts. These tasks might www.mathsonline.co.uk
employ the processes of reasoning, problem solving, investigations, www.teachers.guardian.co.uk
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
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Teaching Objective
The teacher will teach
students to:
1. Draw and interpret
bar charts and pie
charts.
Examples of teaching experiences and activities
Students can be divided in teams to compete in any of the appropriate level quiz
found at
http://www.mathsframe.co.uk/resources/fullscreen.aspx?ref=jechpkmojxujwogjfxwf
wntwkieaxqj_51
Practice worksheet, according to the different ability of the students, can be
generated at the link
http://www.superteacherworksheets.com/bar-graphs.html
The worksheet 7-11 Pie Chart Challenge found at
http://www.teachingideas.co.uk/maths/contents_datahandling.htm
can be used to introduce the concept of pie charts and their interpretation.
The games found at
http://www.bbc.co.uk/schools/ks2bitesize/maths/data/frequency_diagrams/play.sht
ml can be used as a recapitulation of drawing bar charts and pie charts.
2. Compile and interpret
frequency tables for
grouped / ungrouped
discrete and
continuous data.
The questions found at the site
http://www.harcourtschool.com/activity/theme_park_favorites/ are set in a real life
context and can be easily used as an interactive whole class activity to help in the
interpretation of data as shown in bar charts and pie charts.
Hoola-Hoop activity
Students compile an information sheet each, including discreet, continuous and nonnumerical data. Start by non-numerical data - students show their answer on the
show-me board. Select a student for each of the different answers and have Hoolahoops prepared at the front of the class, labelled according to the different answers.
Ask chosen students to group students with same answers as theirs standing inside
the hoola-hoop. A frequency table can then be recorded. Do the same for a set of
discreet data, which cannot be grouped due to a small range (such us number of
siblings) and move on to other discreet data question that has a larger range that has
to be grouped (eg. exam mark) Ask students to look around and decide how many
hoops are needed to group students in and guide them to the idea of having hoops
for sets of marks. Then compile, discuss and interpret the grouped frequency table.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Indicators of Learning outcomes
Students will be able to interpret bar
charts and pie charts for grouped data.
(Level 8.1)
Students will be able to compile tally
charts and use them to draw bar
charts/pie charts for grouped data.
(Level 7.3)
Students will be able to draw pie
charts from tally charts / bar charts, by
finding the necessary angle. They will
be able to interpret pie charts.
(Level 7.2)
Students will be able to interpret
simple pie charts, limited to sectors of
180°, 90°, 60° and 30°.
(Level 7.1)
Students will be able to interpret
frequency tables by answering
complex questions about the grouped
continuous data.
(Level 8.1)
Students will be able to interpret
frequency tables of grouped
continuous data by answering simple
questions about the grouped data.
(Level 7.3)
Students will be able to sort and
176
Finally focus on continuous data (height/weight), discussing the difference between
previous discreet data and this data and the difference in their grouping and the
grouping notation used.
Drawing a line
Ask students to draw a 10cm line without using a ruler and swap sheets to accurately
measure the line. Compile a frequency table with the continuous data produced and
then divide the class in 2 groups and ask students to formulate questions about the
data that can be answered from the frequency table. A valid question yields 3 points,
while a correct answer yields 5 points. An invalid question carries 2 points, while an
incorrect answer gets no points.
3. Understand, compute
and interpret the
mean, mode, median
and range of a set of
ungrouped data.
Further practice on frequency tables can be provided through the Worksheets WS26s
in the Formula One Maths Teacher’s Resource B2 and WS26s and WS27e, found the in
the Formula One Maths Teacher’s Resource B1.
The links http://www.kidsmathgamesonline.com/numbers/meanmedianmode.html
and
http://www.bbc.co.uk/schools/ks2bitesize/maths/data/mode_median_mean_range/
play.shtml offer an interactive online game to help students understand, revise and
compute the mean, median and mode.
The link http://www.bbc.co.uk/education/mathsfile/shockwave/games/train.html
offers students the opportunity to practice the computation of mean, median, mode
and range and understand their interpretations.
The link http://www.mathgoodies.com/lessons/toc_vol8.html in the section
Challenge Exercises offers ideas to help high achievers reach learning outcome 8.3.
Other activities found on this page can also be used as reinforcement.
Card Game
Divide Students in groups of 4 and hand each group a deck of 40 number cards made
of 4 groups of cards from 1 to 10 (or using playing cards ace through to 10). Deal out
7 cards to each player. The winner of is the first person who scores 21 points.
Finding the Mean. Each player finds the mean of his/her cards and that is his/her
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
classify numerical data in groups, using
the inequality sign grouping notations
and to compile frequency tables for
grouped data, applying the most
appropriate grouping.
(Level 7.2)
Students will be able to sort and
classify numerical discrete data in
groups. They will be able to compile
and interpret frequency tables of
grouped discrete data.
(Level 7.1)
Students will be able to find missing
entries of data, given their mean,
mode, median and range.
(Level 8.1)
Students will be able to identify the
outliers of a set of data and
understand that such outliers effect
the mean and range of the data.
(Level 7.3)
Students will be able to compare two
sets of data according to their mean,
median, mode and range.
(Level 7.2)
Students will be able to find the mean,
median, mode and range from lists,
bar charts or frequency table of
177
points for that round. Students can use pencil and paper methods or a calculator.
Finding the Median. The median card in their hand is their point value for this round.
Finding the Mode. The mode in their hand of cards is the point value for this round.
No mode scores 0 points, while if two modes the player snags the point values for
both modes!
discrete ungrouped data and decide
which one represents the best data.
(Level 7.1)
Practice worksheet, according to the different ability of the students, can be
generated at the link http://www.mathaids.com/Mean_Mode_Median/Mean_Mode_Median_Range.html
(Before creating the handout, PLS tick  the option found under the button
Check this box if you have Adobe Reader installed and are still having problems
displaying the PDF file.
4. Use a spreadsheet to
construct bar charts
and pie charts and
compute the mean
and range of a set of
ungrouped data.
Provide students with handouts, which they can work through even on their own,
guiding them to use Excel to construct Bar charts and Pie Charts. Worksheets WS5.2
and WS5.3 in Formula One Maths Euro Edition Teacher’s Pack Gold A, and WS4.1 and
WS4.2 in Formula One Maths Euro Edition Teacher’s Pack Gold B can be useful
resources in this respect.
Otherwise data collected in the Information sheet mentioned above can be presented
as a whole to students and they can be asked to construct the relevant charts for
indicated questions.
Further handouts can be given to students to help them understand and use the
required formula to find the mean and range of lists of data.
Student will be able to understand the
meaning of the functions MAX and
MIN and be able to use them to find
the range of a list of data inputted in a
spreadsheet.
(Level 8.1)
Students will be able to use the
AVERAGE function to be able to find
the mean of a list of data inputted in a
spreadsheet.
(Level 7.3)
Students will be able to convert a
given/compiled spreadsheet table into
a Column/Bar chart or Pie chart,
including the category names.
(Level 7.2)
Students will be able to input the data
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
178
in a spreadsheet and use it to
construct simple bar charts.
(Level 7.1)
5. Understand and work
out the probability of
an event.
Meteo
Ask students to keep track of the weather during the fortnight before, marking the
daily weather as sunny, cloudy, rainy, windy on a given chart in class. Use the data to
write the probabilities for the weather on a day chosen at random and to discuss with
students why the events are not equally likely and what would had happened should
the experiment had been conducted in Summer or Winter. The data can also be used
to find the probabilities of an event not occurring, thus helping students realize that
probabilities of an event happening and not happening add up to 1, while adding the
probabilities of the different type of weather will help them understand that the
probabilities of all possible outcomes add up to 1. Finally discuss with students
whether they can decide how many days in the same month next year would they
expect to have with a particular kind of weather.
A Revision game that can be played individually can be found at:
http://www.bbc.co.uk/schools/ks2bitesize/maths/data/probability/play.shtml
A virtual spinner and die can be found and edited according to need at:
http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/ca/common/itools_int_9780153616
334_/probability.html
and
http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/ca/common/itools_int_9780153616
334_/probability.html
Students will be able to use
probabilities to estimate the number
of times an event will occur.
(Level 8.1)
Students will be able to understand
that the probabilities of all possible
outcomes add up to 1.
(Level 7.3)
Students will be able to understand
that the probabilities of an event
happening and not happening add up
to 1.
(Level 7.2)
Students will be able to calculate
probabilities of an event having more
than one possible outcome.
(Level 7.1)
The Level 2 activity at the following link can be suggested to level 8.3 students,
reinforcing their understanding of the probability of an event:
http://www.bbc.co.uk/education/mathsfile/shockwave/games/fish.html
6. Compile a possibility
The link :
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to find the
179
space and use it to
find the probability of
two events.
http://teachers.guardian.co.uk/Guardian_RootRepository/Saras/ContentPackaging/U
ploadRepository/learnpremium/Lesson/learnpremium/maths~00/keysta~04/righth~0
0/probab~00/whiteb~00/wbpopup.htm
Offers a whiteboard tool where teachers can demonstrate how a possibility space
diagram is constructed and how it can be used to help calculate probabilities for two
events. Users can choose from four event types that include a custom event to be
defined by the user. The teacher drags events into Event 1 and Event 2 regions and
after encouraging students to construct their own possibility space diagram, shows
possibility space diagram and its contents. S/he can then encourage students to come
up with questions to be asked about probabilities of events and show the probabilities
by clicking in the possibility space to select the relevant single or multiple cells.
Chase me :
Present students with the game at :
http://www.mathsonline.co.uk/nonmembers/resource/prob/chaseme1.html
Hence encourage students to compile a possibility space diagram showing the total of
the two dice and then discuss whether the game is fair or not, and how the scores
should be distributed between the hare and the tortoise for the game to be fair.
probability of two events occurring at
the same time by multiplying their
probabilities.
(Level 8.1)
Students will be able to use a
possibility space diagram to calculate
harder probabilities, such as the
probability of two normal dice showing
numbers which differ by 3 but add up
to 7.
(Level 7.3)
Students will be able to use a
possibility space diagram to calculate
simple probabilities such as getting a
total of 7 when rolling two normal
dice.
(Level 7.2)
Students will be able to calculate the
number of all possible outcomes given
the two events.
(Level 7.1)
Subject:
MATHEMATICS
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Form 2
180
Unit code and title: MTH 8.11 Statistics and Probability (Levels 6.3 – 7.3)
Strand 4:
Data Handling
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will:
1. Draw and interpret bar charts and pie charts.
2. Compile and interpret frequency tables for grouped / ungrouped discrete and continuous data.
3. Understand, compute and interpret the mean, mode, median and range of a set of ungrouped data.
4. Understand and work out the probability of an event.
5. Compile a possibility space and use it to find the probability of two events.
Key Words
Mean, mode, median, range,
data, ungrouped data, grouped
data, frequency table, bar chart,
pie chart, spreadsheet,
questionnaire, tally, average,
between, less than, less than or
equal to, greater than, greater
than or equal to, discreet,
continuous, event, probability,
chance, certain, impossible,
likely, unlikely, occurring,
possibility space
Teaching Objective
Points to Note
Resources
FOM B1, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to promote a
Resource Pack – Chapters 4, 14 & 21
student centred learning environment.
Exposition: the teacher states the objectives of the lesson and may use ICT
software for students to practice new knowledge. This is consolidated by
setting students tasks that offer students the opportunity to apply
mathematics to a variety of real life situations.
From Teachers’ laptop:
C:\Documents and Settings\teacher\My
Documents\Maths Excel Lessons\
Pie Chart & Mode, Mean, Median, Range
& Coins (probability)
Discovery: the teacher can set group tasks in which students discuss and Internet Links:
construct mathematical knowledge. Students may become active learners http://www.solvemymath.com/math_ga
while testing hypotheses and/or making generalisations.
mes/kids/bar_charts.php
http://www.superteacherworksheets.co
Exploration: the teacher integrates an inquiry based learning approach that m/bar-graphs.html
enhances the students’ understanding of concepts. These tasks might http://www.harcourtschool.com/activity/
employ the processes of reasoning, problem solving, investigations, theme_park_favorites/
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Examples of teaching experiences and activities
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Indicators of Learning outcomes
181
The teacher will teach
students to:
1. Draw and interpret
bar charts and pie
charts.
Students are divided in teams to compete in any of the appropriate level quiz found at
http://www.mathsframe.co.uk/resources/fullscreen.aspx?ref=jechpkmojxujwogjfxwfwnt
wkieaxqj_51
Practice worksheet, according to the different ability of the students, can be generated at
the link http://www.superteacherworksheets.com/bar-graphs.html
The worksheet 7-11 Pie Chart Challenge found at
http://www.teachingideas.co.uk/maths/contents_datahandling.htm
can be used to introduce the concept of pie charts and their interpretation.
The games found at
http://www.bbc.co.uk/schools/ks2bitesize/maths/data/frequency_diagrams/play.shtml
can be used as a recapitulation of drawing bar charts and pie charts.
The questions found at the site
http://www.harcourtschool.com/activity/theme_park_favorites/
are set in a real life context and can be easily used as an interactive whole class activity to
help in the interpretation of data as shown in bar charts and pie charts.
2.Compile and
interpret frequency
tables for grouped /
ungrouped discrete
and continuous
data.
Hoola-Hoop activity - an activity to help reinforce the concept of tallying and drawing
frequency tables as well as introducing the concept of grouping discreet and continuous
data - Refer to syllabus Level 7 – 8 for details.
Drawing a line
Ask students to draw a 10cm line without using a ruler and swap sheets to accurately
measure the line. Compile a frequency table with the continuous data produced and
then divide the class in 2 groups and ask students to formulate questions about the data
that can be answered from the frequency table. A valid question yields 3 points, while a
correct answer yields 5 points. An invalid question carries 2 points, while an incorrect
answer gets no points.
Further practice on frequency tables can be provided through the Worksheets WS26s in
the Formula One Maths Teacher’s Resource B2 and WS26s and WS27e, found the in the
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to compile tally
charts and use them to draw bar
charts/pie charts for grouped data.
(Level 7.3)
Students will be able to draw pie
charts from tally charts / bar charts,
by finding the necessary angle. They
will be able to interpret pie charts.
(Level 7.2)
Students will be able to interpret
simple pie charts, limited to sectors
of 180°, 90°, 60° and 30°.
(Level 7.1)
Students will be able to interpret
simple pie charts, limited to sectors
of 180°, 90° and 45°.
(Level 6.3)
Students will be able to interpret
frequency tables of grouped
continuous data by answering simple
questions about the grouped data.
(Level 7.3)
Students will be able to sort and
classify numerical data in groups,
using the inequality sign grouping
notations and to compile frequency
tables for grouped data, applying the
most appropriate grouping.
(Level 7.2)
Students will be able to sort and
182
Formula One Maths Teacher’s Resource B1.
3. Understand,
compute and
interpret the mean,
mode, median and
range of a set of
ungrouped data.
The links http://www.kidsmathgamesonline.com/numbers/meanmedianmode.html
and
http://www.bbc.co.uk/schools/ks2bitesize/maths/data/mode_median_mean_range/pla
y.shtml Offer an interactive online game to help students understand, revise and
compute the mean, median and mode.
Ask 5 students (preferably of obvious different height) out and ask the rest of the class to
identify the student who has the median height, helping them understand that students
have to stay in the order of their heights. Ask one more student out and guide the
students’ discussion to the fact that the students’ height has to be measured so that
average of the middle two can in fact give the median height. Computation of the
median can be further reinforced for data such as shoe sizes, number of siblings, etc.
This activity can also be used to reinforce the concept of mean and mode (if existing in
the group of students) and deciding upon which average best represents the group of
students.
Card Game Activity can be used to reinforce the computation of mean, median and
mode in a fun way – Refer to syllabus Level 7 – 8 for details.
Board Game - The simple board game on Worksheet WS16.3 in Formula One Maths
Gold Teacher’s Pack A offers good practice for finding the median. The level of practice
can be increased by using more number cards, up to 30 and having repeated numbers.
classify numerical discrete data in
groups. They will be able to compile
and interpret frequency tables of
grouped discrete data.
(Level 7.1)
Students will be able to compile a
frequency table for a set of
ungrouped discrete numerical data.
(Level 6.3)
Students will be able to identify the
outliers of a set of data and
understand that such outliers effect
the mean and range of the data.
(Level 7.3)
Students will be able to compare two
sets of data according to their mean,
median, mode and range.
(Level 7.2)
Students will be able to find the
mean, median, mode and range from
lists, bar charts or frequency table of
discrete ungrouped data and decide
which one represents the best data.
(Level 7.1)
Students will be able to find the
mean, median, mode and range from
a longer list of entries, with an even
number of entries.
(Level 6.3)
The link http://www.bbc.co.uk/education/mathsfile/shockwave/games/train.html offers
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
183
students the opportunity to practice the computation of mean, median, mode and range
and understand their interpretations.
Practice worksheets, according to the different ability of the students, can be generated
at the link http://www.mathaids.com/Mean_Mode_Median/Mean_Mode_Median_Range.html
(Before creating the handout, PLS tick  the option found under the button
Check this box if you have Adobe Reader installed and are still having problems
displaying the PDF file.
4. Understand and
work out the
probability of an
event.
The link http://www.mathgoodies.com/lessons/toc_vol8.html offers other activities
that can be used as further reinforcement.
Meteo
Ask students to keep track of the weather during the fortnight before, marking the daily
weather as sunny, cloudy, rainy, windy on a given chart in class. Use the data to write
the probabilities for the weather on a day chosen at random and to discuss with students
why the events are not equally likely and what would had happened should the
experiment had been conducted in Summer or Winter. The data can also be used to find
the probabilities of an event not occurring, thus helping students realize that
probabilities of an event happening and not happening add up to 1, while adding the
probabilities of the different type of weather will help them understand that the
probabilities of all possible outcomes add up to 1.
A virtual spinner and die can be found and edited according to need at: http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/ca/common/itools_int_978015361633
4_/probability.html
And http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/ca/common/itools_int_978015361633
4_/probability.html
A Revision game that can be played individually can be found at:
http://www.bbc.co.uk/schools/ks2bitesize/maths/data/probability/play.shtml
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to understand
that the probabilities of all possible
outcomes add up to 1.
(Level 7.3)
Students will be able to understand
that the probabilities of an event
happening and not happening add up
to 1.
(Level 7.2)
Students will be able to calculate
probabilities of an event having more
than one possible outcome.
(Level 7.1)
Students will be able to understand
the notion of equally likely events
and find simple probabilities, of
events having just one possible
184
5.Compile a possibility
space and use it to
find the probability of
two events.
A good interactive activity that students can play on their own to practice writing
probabilities as fractions, can be found as Level 1 game at the link:
http://www.bbc.co.uk/education/mathsfile/shockwave/games/fish.html
Grid Bingo :
Divide the class in pairs and give students a grid of a possibility space diagram of rolling
two dice. Each should be given a grid and two coloured dice per pair. Students will take
turns to roll the dice and fill in the corresponding cell in the grid according to what the
dice show. The students who fills the whole grid first wins. This activity helps students
understand the possible outcomes and learn where to represent each in the grid.
Rock, Paper and Scissors :
Explain the game of Rock, paper and scissors, reminding students that paper wraps the
rock, rock blunts the scissors and scissors cut the paper, while if both players show the
same event is considered a draw. Encourage students to compile a possibility space
diagram for two players playing this game and then discuss with students whether there
is any winning move.
The link :
http://teachers.guardian.co.uk/Guardian_RootRepository/Saras/ContentPackaging/Uplo
adRepository/learnpremium/Lesson/learnpremium/maths~00/keysta~04/righth~00/pro
bab~00/whiteb~00/wbpopup.htm
Offers a whiteboard tool where teachers can demonstrate how a possibility space
diagram is constructed and how it can be used to help calculate probabilities for two
events. Users can choose from four event types that include a custom event to be
defined by the user. The teacher drags events into Event 1 and Event 2 regions and after
encouraging students to construct their own possibility space diagram, shows possibility
space diagram and its contents. S/he can then discuss with students questions about
probabilities of events and show the probabilities by clicking in the possibility space to
select the relevant single or multiple cells.
Subject:
MATHEMATICS
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
outcome, such as getting a 5 when
rolling a die.
(Level 6.3)
Students will be able to use a
possibility space diagram to calculate
harder probabilities, such as the
probability of two normal dice
showing numbers which differ by 3
but add up to 7.
(Level 7.2)
Students will be able to use a
possibility space diagram to calculate
simple probabilities such as getting a
total of 7 when rolling two normal
dice.
(Level 7.1)
Students will be able to calculate the
number of all possible outcomes
given the two events.
(Level 6.3)
Form 2
185
Unit code and title:
Strand 4:
MTH 8.11 Statistics and Probability (Levels 5.3 – 7.1)
Data Handling
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Draw and interpret bar charts, pie charts and pictograms
2. Compile and interpret frequency tables for ungrouped discrete data.
3. Understand, compute and interpret the mean, mode, median and range of a set of ungrouped data.
4. Understand and work out the probability of an event.
5. Compile a possibility space.
Key Words
Mean , mode , median , range
, data , ungrouped data ,
grouped data , frequency
table , bar chart , pie chart,
pictogram, tally, average,
questionnaire, event,
probability, chance, certain,
impossible, likely, unlikely,
occurring, possibility space
Points to Note
Resources
FOM B Gold, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to
Resource Pack – Chapters 4 & 14 & 20
promote a student centred learning environment.
Exposition: the teacher states the objectives of the lesson and may
use ICT software for students to practice new knowledge. This is
consolidated by setting students tasks that offer students the
opportunity to apply mathematics to a variety of real life situations.
From Teachers’ laptop:
C:\Documents and Settings\teacher\My
Documents\Maths Excel Lessons\
Pie Chart & Mode, Mean, Median, Range
& Coins (probability)
Discovery: the teacher can set group tasks in which students discuss
and construct mathematical knowledge. Students may become
active learners while testing hypotheses and/or making
generalisations.
Internet Links:
http://www.brainpopjr.com/math/data/tallyc
hartsandbargraphs/
http://www.solvemymath.com/math_games/
kids/bar_charts.php
Exploration: the teacher integrates an inquiry based learning http://www.superteacherworksheets.com/bar
approach that enhances the students’ understanding of concepts. -graphs.html
These tasks might employ the processes of reasoning, problem http://jmathpage.com/JIMSProbabilitypage.html
solving, investigations, connecting ideas and concepts, and
expressing results by using the precise language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
186
Teaching Objective
The teacher will teach
students to:
1. Draw and interpret bar
charts, pie charts and
pictograms
Examples of Teaching Experiences and Activities
Clear a large floor space or if good weather, try this activity outdoors.
Place cards on the floor, with numbers from 0 to 4 and one ‘more
than 4’. These are to represent the number of siblings that students
have. Ask students to sit cross legged behind the card that shows
their respective number of siblings. Ask students to look around
them and describe what they see, discussing the most common
number of siblings etc. Take a photograph of the class and show it on
the interactive whiteboard…discussing with students how they can
show this information on paper. Students can come up with the idea
3
of pictograms and bar charts. With the help of students draw these
graphs, using pictures to represent one student, pictures to represent a group of
students and finally blocks in the bar chart.
Indicators of Learning Outcomes
Students will be able to interpret
simple pie charts, limited to
sectors of 180°, 90°, 60° and 30°.
(Level 7.1)
As an introduction to the use of tallying and bar charts, the teacher can play the
movie at http://www.brainpopjr.com/math/data/tallychartsandbargraphs/
Students will be able to draw and
interpret simple bar charts for
ungrouped data.
(Level 6.2)
Many different sets of data can be generated at the websites
http://www.solvemymath.com/math_games/kids/bar_charts.php
http://www.bbc.co.uk/schools/teachers/ks2_activities/maths/interpreting_data.shtml So
that student can draw different barcharts online after having discussed the frequency
table generated.
Students are divided in teams to compete in an appropriate level quiz found at
http://www.mathsframe.co.uk/resources/fullscreen.aspx?ref=jechpkmojxujwogjfxwfwntwkieaxqj_51
2. Compile and interpret
Ask 8 students to choose from any 4 options (eg. Whether they like scrambled eggs,
boiled eggs, fried eggs or do not like eggs at all). Once all their selections are done
represent the data collected by drawing the 45° sectors according to the selections.
This will be an introduction to pie charts.
To reinforce the use of tallying and recapitulate their understanding and
interpretation of pictorial representation of data in bar and pie charts, students can
try the activity at http://www.bbc.co.uk/education/mathsfile/shockwave/games/datapick.html
Hoola-Hoop activity
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to draw pie
charts (limited to fractions of
1
2
, 14
1
and 8 , using a given table to
guide them find the necessary
angles.
(Level 6.3)
Students will be able to draw and
interpret pictograms where each
picture represents a group of
units.
(Level 6.1)
Students will be able to draw and
interpret pictograms where each
picture represents only one unit.
(Level 5.3)
Students will be able to sort and
187
frequency tables for
ungrouped discrete
data.
Students compile an information sheet each, including discreet, continuous and nonnumerical data. Start by non-numerical data - students show their answer on the
show-me board. Select a student for each of the different answers and have Hoolahoops prepared at the front of the class, labeled according to the different answers.
Ask chosen students to group students with same answers as theirs standing inside
the hoola-hoop. A frequency table can then be recorded. Do the same for a set of
discreet data, which cannot be grouped due to a small range (such us number of
siblings)
Other discreet data can be used to compile another frequency table on the board.
Divide the class in2 groups and ask students to formulate questions about the data
that can be answered from the frequency table. A valid question to be asked to the
other group yields 3 points, while a correct answer yields 5 points. Also an invalid
question carries -2 points, whilst an incorrect answer gets no points at all.
Many different sets of data can be generated at the websites
http://www.solvemymath.com/math_games/kids/bar_charts.php
http://www.bbc.co.uk/schools/teachers/ks2_activities/maths/interpreting_data.shtml
So that, using the interactive whiteboard students can help compile and discuss the
frequency tables generated online.
3. Understand, compute
and interpret the
mean, mode, median
and range of a set of
ungrouped data.
M&M’s Activity - Students are to have a packet of M&M’s each and
start by predicting the number of M&M’s in their bag for each
colour (BEFORE opening bag) and to colour their predictions on a
chart. Then have them actually open the bag and count the
coloured M&M’s separately and compare results to their charts.
Through a class discussion, compare students’s results concluding
that not all packets had the same amount of coloured M&M’s. Suggest that
we have to fill in back the packets so that each student has the same number of each
of the coloured M&M’s in his/her bag. Students should therefore come up with the
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
classify numerical discrete data in
groups. They will be able to
compile and interpret frequency
tables of grouped discrete data.
(Level 7.1)
Students will be able to compile a
frequency table for a set of
ungrouped discreet numerical
data. (Level 6.3)
Students will be able to answer
simple questions about simple
data displayed in frequency table,
with/without the tally column.
(Level 6.2)
Students will be able to compile a
frequency table, with a tally
column, from a set of given
pictures/words. (Level 6.1)
Students will be able to sort and
classify given pictures in a table
with specified categories. (Level 5.3)
Students will be able to find the
mean, median, mode and range
from lists, bar charts or frequency
table of discrete ungrouped data
and decide which one represents
the best data.
(Level 7.1)
Students will be able to find the
188
idea of the mean. Work out the total for each colour by collecting data from the
students and hence ask the students to find the mean for each colour. Students’
individual results or class results can also be used to find the modal colour while the
total number of M&M’s in each bag can be used to find the bag that had the median
number of sweets. At the end of the lessons (not any time before!), students can
enjoy their bag of M&M’s.
Ask 5 students (preferably of obvious different height) out and ask the rest of the
class to identify the student who has the median height, helping them understand
that students have to stay in the order of their heights. Ask one more student out and
guide the students’ discussion to the fact that the students’ height has to be
measured so that average of the middle two can in fact give the median height.
Computation of the median can be further reinforced for data such as shoe sizes,
number of siblings, etc. This activity can also be used to reinforce the concept of
mean and mode (if existing in the group of students) and deciding upon which
average best represents the group of students.
mean, median, mode and range
from a longer lists of entries,
including lists with an even
number of entries.
(Level 6.3)
Students will be able to find the
mean, median, mode and range
from a short list of entries, limited
to lists with odd number of
entries only.
(Level 6.2)
Students will understand the
meaning of range as the spread of
data.
(Level 6.1)
The links http://www.kidsmathgamesonline.com/numbers/meanmedianmode.html and
http://www.bbc.co.uk/schools/ks2bitesize/maths/data/mode_median_mean_range/play.shtml
Offer an interactive online game to help students understand, revise and compute the
mean, median and mode.
Card Game Activity can be used to reinforce the computation of mean, median and
mode in a fun way – Refer to syllabus Level 7 – 8 for details.
Board Game - The simple board game found as Worksheet WS16.3 in Formula One
Maths Gold Teacher’s Pack A offers good practice for finding the median. The level of
practice can be increased by using more number cards, so up to 30 and having
repeated numbers. Practice worksheet, according to the different ability of the
students, can be generated at the link
Students will know the meaning
of average and understand the
difference between mean,
median and mode.
(Level 5.3)
http://www.math-aids.com/Mean_Mode_Median/Mean_Mode_Median_Range.html
(Before creating the handout, PLS tick  the option found under the button)
4. Understand and work
Check this box if you have Adobe Reader installed and are still having
problems displaying the PDF file.
Students can try the activity at the following link to get more fluent with the
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to calculate
189
out the probability of
an event.
vocabulary, certain, impossible, likely, etc…
http://www.ixl.com/math/grade-3/certain-probable-unlikely-impossible
And
http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/ca/common/itools_int_9780153616
334_/probability.html
An interactive activity to practice the meaning of fractions as probabilities :
http://www.hbschool.com/activity/probability_circus/
A good interactive activity that students can play on their own to practice writing
probabilities as fractions, can be found as the Level 1 game at the link:
http://www.bbc.co.uk/education/mathsfile/shockwave/games/fish.html
A virtual spinner and die can be found and edited according to need at:
http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/ca/common/itools_int_9780153616
334_/probability.html
And
http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/ca/common/itools_int_9780153616
334_/probability.html
probabilities of an event having
more than one possible outcome.
(Level 7.1)
Students will be able to
understand what it means for
events to be equally likely to
happen and find simple
probabilities, such as getting a 5
when rolling a die. (Level 6.3)
Students will be able to
understand that probabilities for
unlikely and likely events fall in
1
1
the ranges 0 to 2 and 2 to 1
respectively. They will be able to
mark such probabilities on a
numerical scale.
(Level 6.2)
Students will be able to relate the
basic language use for
probabilities to their numerical
value, i.e impossible = 0, evens =
1
2
and certain = 1.
(Level 6.1)
Students will be able to describe
events as being impossible,
unlikely, evens, likely and certain,
and mark the probabilities on a
scale marked with a range from
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
190
5. Compile a possibility
space.
Grid Bingo : Divide the class in pairs and present students with the grid of a possibility
space diagram of rolling two dice. Each should be given a grid and two coloured dice
per pair. Students will take turns to roll the dice and colour the corresponding cell in
the grid according to what the dice show. Who manages to fill the whole grid first
wins. This activity helps students understand the possible outcomes and learn where
to represent each in the grid.
Rock, Paper and Scissors : Explain the game of Rock, paper and scissors, reminding
students that paper wraps the rock, rock blunts the scissors and scissors cut the
paper, while if both players show the same that is considered a draw. After giving
some students the opportunity to try the game, encourage students to compile a
possibility space diagram for two players playing this game and then discuss with
students whether there is any winning move.
Chase me : Present students with the game at :
http://www.mathsonline.co.uk/nonmembers/resource/prob/chaseme1.html
And give them the opportunity to try it out a number of times. Then together with
the students compile a possibility space diagram showing the total of the two dice.
Discuss with students who has the greater chance to make a move. Hence with
suggestions from the class change the scores for the tortoise and the hare so that
both have the same chance of getting a move according to the scores on the dice.
The link :
http://teachers.guardian.co.uk/Guardian_RootRepository/Saras/ContentPackaging/U
ploadRepository/learnpremium/Lesson/learnpremium/maths~00/keysta~04/righth~0
0/probab~00/whiteb~00/wbpopup.htm
Offers a whiteboard tool where teachers can demonstrate how a possibility space
diagram is constructed and how it can be used to help calculate probabilities for two
events. Users can choose from four event types that include a custom event to be
defined by the user. The teacher drags events into Event 1 and Event 2 regions and
after encouraging students to construct their own possibility space diagram, shows
possibility space diagram and its contents. Probabilities of simple events can be found
by clicking in the possibility space to select the relevant single or multiple cells.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
impossible to certain. (Level 5.3)
Students will be able to use a
possibility space diagram to
calculate simple probabilities
such as getting a total of 7 when
rolling two normal dice.
(Level 7.1)
Students will be able to compile
the possibility space diagram by
inserting all the possible
outcomes in cells of the grid.
(Level 6.3)
Students will be able to construct
the grid for a possibility space
diagram according to the two
simple events.
(Level 6.2)
Students will be able to list all the
possible outcome of 2 simple
events happening together, such
as two coins. (Level 6.1)
Students will be able to
understand that when having two
events happening together, the
number of all possible outcomes
is given by all the possible
combinations of both events.
(Level 5.3)
191
Subject:
MATHEMATICS
Unit code and title: MTH 8.11 Statistics & Probability (Levels 1-4)
Strand 4:
Data Handling
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Draw and interpret bar charts, pie charts and pictograms.
2. Understand, compute and interpret the mean, mode, median and range of a set of ungrouped data.
3. Compile and interpret frequency tables for ungrouped discrete data.
4. Understand and work out the probability of an event.
5. Compile a possibility space.
The objectives at attainment levels 1,2,3,4. (Mainstream objective 2 is beyond attainment level 4.)
The teacher will teach the students to:
1.1 Put data in a table, read data from a table and draw bar charts on a grid and picture charts .
2.1 Recognise the most frequent number, the range and the median in a set of ungrouped data.
4.1 Find the chances of occurrence and non-occurrences and fill in the results in a grid.
Key Words
mode, range, median,
middle, oder, chances
of occurrence, nonoccurrence, never,
always.
Points to Note
In addition to the points to note recommended for students
performing at Level 5 or higher, it is very important for the
teacher to allow time for the students to respond. This response
can take the form of unaided and/or aided means of
communication and the teacher needs to provide adequate
scaffolding techniques to enable the students to respond
affectively or intentionally.
For further material at level 1, refer to handbook.
Resources
New Maths Frame Working Step Up Workbook.
Oxford Framework Maths 7
From Teachers’ laptop:
C:\Documents and Settings\teacher\My
Documents\Maths Excel Lessons
http://www.bbc.co.uk/schools/ks3bitesize/maths/
handling_data/
http://elearningforkids.org/Courses/EN/M1001/launch.html
http://www.mathsisfun.com/data/
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
192
Teaching Objective
The teacher will teach
the students to:
1.1 Put data in a table,
read data from a
table and draw bar
charts on a grid and
picture charts.
2.1 Recognise the most
frequent number,
the range and the
median in a set of
ungrouped data.
Examples of Teaching Experiences and Activities
Starter: Students are shown pictorial representations of different
groups and they are left to point and talk about the information they
are shown.
Students sort objects bought from a supermarket, such as tin food,
frozen food, toiletry into their appropriate places and explain why.
Students reinforce tallying on the computer using this site:
http://www.bbc.co.uk/schools/ks3bitesize/maths/handling_data/
collecting_recording/activity.shtml
Indicators of Learning Outcomes
Students will be able to put the sorted data
into a table and answer questions related to
what is in the table. Then they apply it to
build a bar chart or a picture chart.
(Level 4)
Students are shown a selection of pictures of video games like PSP,
Nintendo, and WII. They sort the categories into a table.
Students will be able to classify objects into
particular categories and start finding
information from the table by counting.
Eventually, they will represent this onto a
grid.
(Level 3)
The above activities can be extended to bar charts and picture charts as
the students will colour the boxes of the bar chart according to the
information in the table.
Students will be able to sort objects and
materials according to given criteria. They
can use colours to fill a grid. (Level 2)
Starter: Students are presented with a set of numbers. They observe
the repetitions of some numbers.
Students will be able to show interest in
activities presented by moving their hands.
(Level 1)
Students will be able to identify and talk
about the data at hand e.g. most number
shown, the difference between the largest
and the smallest number, and the median.
(Level 4)
Students are invited to a party and they have to pre-order the food. By
the end of this activity the students will be in a position to discuss and
comment on the most popular choice. Then they can use simple
subtraction facts to find the difference between the largest and
smallest number of items ordered. Eventually, they can put the
quantities in ascending order and through cancelling numbers from
both ends they will find the median.
Students will use the above data to identify the most frequent item,
the difference between two numbers by counting on (numbers will be
Students will be able to identify the largest
group.
(Level 3)
Students will be able to give consistently the
same requested object to an adult.
(Level 2)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
193
limited to 5) and to point to the number that lies between two
numbers.
4.1 Find the chances of
occurrence and
non-occurrence
and fill-in the
results in a grid.
Starter: Students will have the opportunity to show if and how they
react to the presence and absence of objects.
Students are shown a coloured spinner with four coloured sections like
red, yellow, green and blue. Students respond to questions like, can the
spinner stop on a black colour or can the spinner stop on a red colour?
Students are shown an object and then it is taken out of their vision.
Sometime later the students are shown the object again so they
experience the occurrence and absence of an object. Eventually the
students will start looking for it even when out of sight.
Students are presented with a TV remote control or a cassette player. If
they want to switch on the player or the TV they have to press the
button. They will experience that unless they press the button, the
effect will not happen.
Students will respond to sounds and try to
activate the object.
(Level 1)
Students will be able to answer questions
about the probable outcome of an event.
E.g. it is impossible to find an elephant at
home as it is neither a domestic animal nor
an animal found in our country.
(Level 4)
Students will be able to start to respond
appropriately to simple questions.
(Level 3)
Students will be aware of cause and effect.
(Level 2)
Students will be able to develop the concept
of object permanence.
(Level 1)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
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Subject:
Unit code and title:
Strand 1:
MATHEMATICS
MTH 8.12 Ratio and Proportion (Levels 7.1 – 8.1)
Number
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Solve problems involving direct proportion using the unitary method.
2. Use the ratio notation to compare two or more quantities and write ratios in their simplest form.
3. Divide a quantity in a given ratio.
Key Words
Directly proportional
Ratio, quantity
Points to Note
Resources
FOM B2, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to promote a
Resource Pack - Chapters 15
student centred learning environment.
From Teachers’ laptop:
Exposition: the teacher states the objectives of the lesson and may use ICT C:\Documents and Settings\teacher\My
software for students to practice new knowledge. This is consolidated by Documents\Maths Excel Lessons
setting students tasks that offer students the opportunity to apply
- Ratio.XLS
mathematics to a variety of real life situations.
Internet Links:
Discovery: the teacher can set group tasks in which students discuss and http://nrich.maths.org
construct mathematical knowledge. Students may become active learners http://www.arcademicskillbuilders.com/ga
while testing hypotheses and/or making generalisations.
mes/
http://www.bbc.co.uk/schools/ks3bitesize/
Exploration: the teacher integrates an inquiry based learning approach maths/number/ratio/activity.shtml
that enhances the students’ understanding of concepts. These tasks might
employ the processes of reasoning, problem solving, investigations, Other Resources:
connecting ideas and concepts, and expressing results by using the precise
 Empty Containers of Products
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
195
Teaching Objective
The teacher will teach the
students to:
1. Solve problems
involving direct
proportion using the
unitary method.
Examples of teaching experiences and activities
The teacher presents students with empty containers of products (in
different sizes) bought from a local supermarket, including the selling price
as marked at the store – ideally the teacher asks students to collect the
containers weeks before this lesson in order to have enough containers for
the whole class.
The teacher could then set different groups of students to work on finding
the ‘best buy’ of products of the same brand but having different sizes
(e.g.: cereal boxes, coffee jars/tins, tomato paste cans etc.).
Indicators of Learning outcomes
Students will be able to solve complex
problems involving direct proportion with
and without the use of the unitary method
(e.g.: including exchange rates, recipes
etc.).
(Level 8.1)
Students will be able to solve complex
problems involving direct proportion using
the unitary method (e.g.: finding rates).
(Level 7.3)
Students will be able to solve simple
problems involving direct proportion using
the unitary method (that is, finding a unit
measure including the price, distance,
time, weight and capacity).
(Level 7.2)
The task involves students in working out the ‘best buy’ using the unitary
method and/or direct proportion (for example: the cost by mass or by
volume of say 1 g or 100 g; or 1 ml or 50 ml) based on the information
indicated on the different container sizes.
The final part of the lesson involves students in presenting their methods
and findings.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to solve simple
problems involving finding the unit price.
(Level 7.1)
196
2. Use the ratio notation
to compare two or
more quantities and
write ratios in their
simplest form.
The teacher can use the following two links below for students to practice
using and simplifying equivalent ratios.
http://www.arcademicskillbuilders.com/games/ratio-blaster/ratioblaster.html
http://www.arcademicskillbuilders.com/games/ratio-stadium/ratiostadium.html
Both games teach students in recognising and finding equal ratios.
These games are ideally used as consolidation activities.
Similar to the game available on http://nrich.maths.org/4824, the teacher
can prepare a set of card which students can use to match in representing
equivalent fractions.
As practice exercises, the teacher can use the Maths Excel Lesson
‘Ratio.XLS’ available on the teacher’s laptop for students to simplify given
fractions and to write fractions in the form 1: n.
3. Divide a quantity in a
given ratio.
The teacher initiates a whole class discussion using the situation presented
in the FOM Students’ Book on page 130. The teacher can select three
students to perform a role play for this situation described below.
Situation:
Tony, Joe and Sophie buy a set of 60 old football programmes between
them. The set costs €180. Tony pays €30, Joe pays €60 and Sophie pays
€90.
Tony:
That is 20 programmes each.
Sophie: Not fair!
Question:
Why does Sophie say ‘Not fair!’?
The discussion can lead students to discover, communicate and present a
‘fair’ way/method of sharing the football programmes.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to apply the ratio
notation to compare two or more
quantities within real-life situations.
(Level 8.1)
Students will be able to use the ratio
notation to compare and simplify two or
more quantities involving different units.
(Level 7.3)
Students will be able to compare and
simplify the ratio of two quantities
involving different units.
(Level 7.2)
Students will be able to compare and
simplify the ratio of two quantities
involving common units.
(Level 7.1)
Students will be able to divide a quantity in
a given ratio of three or more unequal
parts. (Level 8.1)
Students will be able to divide a quantity in
a given ratio of up to three parts.(Level 7.3)
Students will be able to divide a quantity
into two unequal parts. (Level 7.2)
Students will be able to divide a quantity
into unequal parts indicated by the given
ratio. (Level 7.1)
197
Subject:
Unit code and title:
Strand 1:
MATHEMATICS
MTH 8.12 Ratio and Proportion (Levels 6.3 – 7.3)
Number
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Solve problems involving direct proportion using the unitary method.
2. Use the ratio notation to compare two or more quantities and write ratios in their simplest form.
3. Divide a quantity in a given ratio.
Key Words
Directly proportional
Ratio, quantity
Points to Note
Three main teaching approaches are being recommended.
Resources
FOM B1, Students’ Book, Practice Book,
Resource Pack – Chapter 15
Exposition: the teacher states the objectives of the lesson and may use ICT
software for students to practice new knowledge. This is consolidated by From Teachers’ laptop:
setting students tasks that offer students the opportunity to apply C:\Documents and Settings\teacher\My
mathematics to a variety of real life situations.
Documents\Maths Excel Lessons
- Ratio.XLS
Discovery: the teacher can set group tasks in which students discuss and
construct mathematical knowledge. Students may become active learners Internet Links:
while testing hypotheses and/or making generalisations.
http://www.arcademicskillbuilders.com/ga
mes/
Exploration: the teacher integrates an inquiry based learning approach http://nrich.maths.org
that enhances the students’ understanding of concepts. These tasks might http://www.bbc.co.uk/schools/ks3bitesize/
employ the processes of reasoning, problem solving, investigations, maths/number/ratio/activity.shtml
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Other Resources:
 Fraction Magnets
 Empty Containers of Products
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
198
Teaching Objective
The teacher will teach the
students to:
1. Solve problems
involving direct
proportion using the
unitary method.
Examples of teaching experiences and activities
The teacher presents students with empty containers of products (in
different sizes) bought from a local supermarket, including the selling price
as marked at the store – ideally the teacher asks students to collect the
containers weeks before this lesson in order to have enough containers for
the whole class.
The teacher could then set different groups of students to work on finding
the ‘best buy’ of products of the same brand but having different sizes
(e.g.: cereal boxes, coffee jars/tins, tomato paste cans etc.).
Indicators of Learning outcomes
Students will be able to solve complex
problems involving direct proportion using
the unitary method (e.g.: finding rates).
(Level 7.3)
Students will be able to solve simple
problems involving direct proportion using
the unitary method (that is, finding a unit
measure including the price, distance,
time, weight and capacity).
(Level 7.2)
Students will be able to solve simple
problems involving finding the unit price.
(Level 7.1)
Students will be able to solve simple
problems when given the unit measure.
(Level 6.3)
The task involves students in working out the ‘best buy’ using the unitary
method and/or direct proportion (for example: the cost by mass or b
volume of say 1 g or 100 g; or 1 ml or 50 ml) based on the information
indicated on the different container sizes.
The final part of the lesson involves students in presenting their methods
and findings.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
199
2. Use the ratio notation
to compare two or
more quantities and
write ratios in their
simplest form.
The teacher can use the following two links below for students to practice
using and simplifying equivalent ratios.
http://www.arcademicskillbuilders.com/games/ratio-blaster/ratioblaster.html
http://www.arcademicskillbuilders.com/games/ratio-stadium/ratiostadium.html
Both games teach students in recognising and finding equal ratios.
These games are ideally used as consolidation activities.
Similar to the game available on http://nrich.maths.org/4824, the teacher
can prepare a set of card which students can use to match in representing
equivalent fractions.
As practice exercises, the teacher can use the Maths Excel Lesson
‘Ratio.XLS’ available on the teacher’s laptop for students to simplify given
fractions and to write fractions in the form 1: n.
The teacher can also use ‘Fraction Magnets’ for pictorial representations
of ratios.
⅙
⅙
⅙
⅙
⅙
2
1
:
:
⅙
⅙
⅙
⅙
⅙
⅙
Students will be able to use the ratio
notation to compare and simplify two or
more quantities involving different units.
(Level 7.3)
Students will be able to compare and
simplify the ratio of two quantities
involving different units.
(Level 7.2)
Students will be able to compare and
simplify the ratio of two quantities
involving common units.
(Level 7.1)
Students will be able to understand the
concept of ratio through pictorial
representations.
(Level 6.3)
⅙
4
2
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
200
3. Divide a quantity in a
given ratio.
The teacher initiates a whole class discussion using the situation presented
by the following:
Students will be able to divide a quantity in
a given ratio of up to three parts.
(Level 7.3)
Situation:
John and Martha buy 40 packets of football cards between them. The set
costs €80. John pays €30 and Martha pays €50.
John:
That is 20 packets each.
Martha: Not fair!
Students will be able to divide a quantity
into two unequal parts.
(Level 7.2)
Question:
Why does Martha say ‘Not fair!’?
Students will be able to divide a quantity
into unequal parts indicated by the given
ratio.
(Level 7.1)
The discussion can lead students to discover, communicate and present a
‘fair’ way/method of sharing the football cards.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will understand order of ratio. Eg:
the ratio 2:3 is not the same as the ratio
3:2.
(Level 6.3)
201
Subject:
Unit code and title:
Strand 1:
MATHEMATICS
MTH 8.12 Ratio and Proportion (Levels 5.3 – 7.1)
Number
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Solve problems involving direct proportion using the unitary method.
2. Use the ratio notation to compare two or more quantities and write ratios in their simplest form.
3. Divide a quantity in a given ratio.
Key Words
Directly proportional
Ratio
Points to Note
Resources
FOM B Gold, Students’ Book, Practice
Three main teaching approaches are being recommended to promote a
Book, Resource Pack – Chapter 15
student centred learning environment.
From Teachers’ laptop:
Exposition: the teacher states the objectives of the lesson and may use ICT C:\Documents and Settings\teacher\My
software for students to practice new knowledge. This is consolidated by Documents\Maths Excel Lessons
setting students tasks that offer students the opportunity to apply
- Ratio.XLS
mathematics to a variety of real life situations.
Internet Links:
Discovery: the teacher can set group tasks in which students discuss and http://www.arcademicskillbuilders.com/ga
construct mathematical knowledge. Students may become active learners mes/
while testing hypotheses and/or making generalisations.
http://nrich.maths.org
http://www.softschools.com/math/ratios/
Exploration: the teacher integrates an inquiry based learning approach
that enhances the students’ understanding of concepts. These tasks might Other Resources:
employ the processes of reasoning, problem solving, investigations,
 Fraction Magnets
connecting ideas and concepts, and expressing results by using the precise
 Empty Containers of Products
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
202
Teaching Objective
The teacher will teach the
students to:
1. Solve problems
involving direct
proportion using the
unitary method.
Examples of teaching experiences and activities
The teacher presents students with different challenging situations
involving direct proportion including:
 Best buys – between the small, medium and large containers
 Special offers – buy one get one free; two for the price of three,
etc.
 Recipes – working out the quantities needed for 4 people from a
recipe for 2 people or vice-versa
 Rate of pay – weekly pay or monthly pay to find the payment rate
per hour or vice-versa
Each group of students will engage in solving the presented problems and
then the teacher can ask each group of students to present their work and
explanations.
The teacher might choose to focus on one situation per lesson depending
on the students’ ability.
Indicators of Learning outcomes
Students will be able to solve simple
problems involving finding the unit price.
(Level 7.1)
Students will be able to solve simple
problems involving direct proportion when
they are given the unit measure.
(Level 6.3)
Students will be able to understand that
solving problems involving direct
proportion requires using multiplication or
division.
(Level 6.2)
Students will be able to understand that by
direct proportion the value of a larger
quantity is represented by a greater
amount.
(Level 6.1)
Students will be able to understand that
the price indicated on an item at a store is
its unit price.
(Level 5.3)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
203
2. Use the ratio notation
to compare two or
more quantities and
write ratios in their
simplest form.
The teacher can use the following two links below for students to practice
using and simplifying equivalent ratios.
http://www.arcademicskillbuilders.com/games/ratio-blaster/ratioblaster.html
http://www.arcademicskillbuilders.com/games/ratio-stadium/ratiostadium.html
Both games teach students in recognising and finding equal ratios.
These games are ideally used as consolidation activities.
Similar to the game available on http://nrich.maths.org/4824, the teacher
can prepare a set of card which students can use to match in representing
equivalent fractions.
As practice exercises, the teacher can use the Maths Excel Lesson
‘Ratio.XLS’ available on the teacher’s laptop for students to simplify given
fractions.
The teacher can also use ‘Fraction Magnets’ for pictorial representations
of ratios.
⅙
⅙
⅙
⅙
⅙
2
1
:
:
⅙
⅙
⅙
⅙
⅙
⅙
⅙
4
2
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to compare and
simplify the ratio of two quantities
involving common units.
(Level 7.1)
Students will be able to compare two
quantities identifying a simple scale factor.
(Level 6.3)
Students will be able to recognise the use
of simple ratios in real life situations. Eg:
doubling or halving a recipe.
(Level 6.2)
Students will be able to understand the
concept of ratio through pictorial
representations which compare one part
with another part or several parts.
(Level 6.1)
Students will know that a fraction
compares a part with the whole.
(Level 5.3)
204
3. Divide a quantity in a
given ratio.
The teacher initiates a whole class discussion using the situation presented
by the following:
Situation:
John and Martha buy 40 packets of football cards between them. The set
costs €80. John pays €30 and Martha pays €50.
John:
That is 20 packets each.
Martha: Not fair!
Question:
Why does Martha say ‘Not fair!’?
The discussion can lead students to discover, communicate and present a
‘fair’ way/method of sharing the football cards.
Using the interactive whiteboard, the teacher can also make use of the
following site for students to practice dividing the given quantity in the
indicated ratio.
http://www.softschools.com/math/ratios/ratio_coloring_game/
Students will be able to divide a quantity
into unequal parts indicated by the given
ratio.
(Level 7.1)
Students will understand order of ratio. Eg:
the ratio 2:3 is not the same as the ratio
3:2.
(Level 6.3)
Students will understand that equal
division is not always appropriate.
(Level 6.2)
Students will be able to use the ratio 1:1 to
divide a given quantity into two equal
parts.
(Level 6.1)
Students will understand that the ratio
indicates the number of parts in a whole.
Eg: a ratio of 1:5 means “1 for every 5” (a
total of 6)
(Level 5.3)
Subject:
MATHEMATICS
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Form 2
205
Unit code and title: MTH 8.12 Ratio & Proportion (Level 1-4)
Strand 1:
Number
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives at attainment Levels 5,6.
The teacher will teach the students to:
1. Solve problems involving direct proportion using the unitary method.
2. Use the ratio notation to compare two or more quantities and write ratios in their simplest form.
3. Divide a quantity in a given ratio.
Objectives at attainment levels 1 - 4.
The teacher will teach the students to:
1.1 Develop the basic idea of ratios.
2.1 Read, understand and talk about the basic idea of ratio.
3.1 Share two quantities in a given amount.
Key Words
Number of, is to, there are so
much, for every, share.
Points to Note
In addition to the points to note recommended for students
performing at Level 5 or higher, it is very important for the
teacher to allow time for the students to respond. This response
can take the form of unaided and/or aided means of
communication and the teacher needs to provide adequate
scaffolding techniques to enable the students to respond
affectively or intentionally.
For further material at level 1 refer to the handbook.
Resources
New Maths Frame Working-Step Up
Workbook.
Oxford Framework Maths 7
Software: Ilearn Maths, Calculator, Excel
Worksheets
From Teachers’ laptop:
C:\Documents and Settings\teacher\My
Documents\Maths Excel Lessons
Internet Links: in examples below.
Teaching Objective
Examples of Teaching Experiences and Activities
Indicators of Learning Outcomes
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
206
The teacher will teach the
students to:
1.1 Develop the basic idea of
ratios.
Starter: Students are given two PlayStation games titles and
they have to indicate their preference. They are encouraged to
put their preference in writing.
Students will be able to ask, write the
information and compare the choices.
(Level 4)
Teacher shows age appropriate real pictures of objects of
interest to this age group. E.g. a sports car and a jeep. Teacher
asks, which one would you prefer? Then students fill in the data
(Number of sports car = ; Number of jeep= ). In our class, the
number of sports car to the number of jeep is ______.
http://www.softschools.com/math/ratios/ratio_coloring_game/
Students will choose the named object,
group it by category, count and match the
set to its value.
(Level 3)
Same activity can be repeated but this time the students select
and group the responses and eventually match the set of data
with its number.
Students will simply match an object with its set.
2.1 Read, understand and talk
about the basic idea of
ratio.
Students will observe the difference when an object is seen
under a magnifying glass.
The examples for this objective can be the same as those for
objective 1.1 but in reverse order.
Teacher writes or shares a statement orally with the students.
They have to represent the statements visually. Then, they can
be given a mixed set of pictures and simply asked to talk about
the visual representations.
At a lower level, the students can be read to the statements and
they draw accordingly e.g. mobiles to ipads.
Students will use their matching skills to sort data.
Students will look at the reflection of their face in a mirror and
respond to named parts by touching them.
Students will match same objects by
categories.
(Level 2)
Students will observe the differences in
size of the same object.
(Level 1)
Students will be able to read, draw, talk
about and interpret visual representations
to come up with the correct mathematical
ratio.
(Level 4)
Students will use their basic knowledge of
number value to represent the ratios
pictorially.
(Level 3)
Students will be able to sort a pre-selected
set of data.
(Level 2)
Students will be involved and participate in
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
207
sensory experiences of different sizes of
objects.
(Level 1)
3.1 Share two quantities in a
given amount.
Starter: Students are going to play monopoly and they are asked
to share the initial bank money to start the game.
In a school, the secretary needs to pass on a number of circulars
to the students. Each students needs to have 3 circulars. Write
this as a ratio.
Students are given a number grid with repeated numbers and
colour coded instructions. They will colour the boxes according
to the code and talk about it. E.g. 2 yellow and 1 red.
Level 3 activity can be adapted for level 2 by having the
students matching the numbers or the colour according to the
code.
Students will observe and experience the other activities.
Students will be able to translate (change)
simple communication into mathematical
representations.
(Level 4)
Students will be able to talk about the
visual ratio representations.
(Level 3)
Students will participate in the ideas of
sharing through their matching skills.
(Level 2)
Students will focus for a longer period of
time to observe the activities.
(Level 1)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
208
Subject:
MATHEMATICS
Unit code and title: MTH 8.13 Transformations (Levels 7.1 – 8.1)
Strand 3:
Shape, Space and Measures
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Identify shapes having reflection and/or rotational symmetry in 2D; determine the order of rotational symmetry in 2D; determine the symmetrical
properties of a polygon.
2. Reflect a shape in the x axis, y axis, x = c, y = c and y =  x; describe a reflection.
3. Translate a shape horizontally and/or vertically given a column vector; describe a translation by a column vector.
4. Rotate a shape about the origin or one of the vertices, using angles of 90° and 180°; describe a rotation.
5. Enlarge a shape by a positive integral scale factor using a centre of enlargement; describe an enlargement.
Key Words
symmetry, reflection symmetry,
line of symmetry, rotational
symmetry, centre of rotation,
order of rotation, polygon
axes, coordinates, object,
image, transformation,
mapping, shape, size,
congruent
translation, right, left, up,
down, column vector
reflection
rotation, clockwise,
anticlockwise, origin
enlargement, centre of
enlargement, scale factor,
similar shapes
Points to Note
Resources
FOM B2, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to promote a
Resource Pack - Chapters 19 and 24.
student centred learning environment.
Teaching Objective
Examples of teaching experiences and activities
Exposition: the teacher states the objectives of the lesson and may use ICT
software for students to practise new knowledge. This is consolidated by
setting students tasks that offer students the opportunity to apply
mathematics to a variety of real life situations.
From Teachers’ laptop:
C:\Documents and settings\teacher\My
Documents\Maths Excel Lessons
Translations
Discovery: the teacher can set group tasks in which students discuss and Dynamic Geometry Software
construct mathematical knowledge. Students may become active learners rotational symmetry board
while testing hypotheses and/or making generalisations.
Internet Links:
Exploration: the teacher integrates an inquiry based learning approach that http://www.mathsisfun.com
enhances the students’ understanding of concepts. These tasks might http://www.innovationslearning.co.uk
employ the processes of reasoning, problem solving, investigations, http://www.gcsemathstutor.com
connecting ideas and concepts, and expressing results by using the precise http://www.ngfl-cymru.org.uk
language of mathematics.
http://www.ixl.com/math/grade-8
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Indicators of Learning outcomes
209
The teacher will teach the
students to:
1. Identify shapes having
reflection and/or rotational
symmetry in 2D; determine
the order of rotational
symmetry in 2D; determine
the symmetrical properties
of a polygon.
The following activities can be carried out either as a single activity or in the
form of different workstations. The students in groups rotate from one
station to another.
Students, in groups, are given a set of laminated cards showing different
shapes. They are asked to identify which shapes have reflection symmetry.
The students then draw the line of symmetry of these shapes on the card.
The students access the site
http://www.mathsisfun.com/geometry/symmetry-rotational.html to
understand the meaning of rotational symmetry and order of rotational
symmetry.
Students, in groups, are given a rotational symmetry board made up of
shapes and symbols such as club, diamond, star, etc. They have to identify
which shapes have a rotational symmetry. The students then determine the
order of rotational symmetry of these shapes.
The students, in groups, investigate reflection symmetry of different
quadrilaterals illustrated on a handout. They then investigate the rotational
symmetry of these quadrilaterals with the help of a rotational symmetry
board. This activity may be repeated with triangles and other polygons.
At the end of the activity students compare their results with the whole
class.
Students will be able to determine the
symmetrical properties of any 2D shape.
(Level 8.1)
Students will be able to determine the
symmetrical properties of triangles and
special quadrilaterals.
(Level 7.3)
Students will be able to determine the
symmetrical properties of regular
polygons.
(Level 7.2)
Students will be able to identify shapes
having reflection and/or rotational
symmetry, determine the order of
rotational symmetry and be able to
complete part shapes using two lines of
symmetry.
(Level 7.1)
The students access the site
http://www.innovationslearning.co.uk/subjects/maths/activities/year3/sym
metry/shape_game.asp
to understand the geometric properties of polygons.
2. Reflect a shape in the x axis,
y axis, x = c, y = c and
y =  x; describe a reflection.
The students observe the reflection of shapes and letters in a mirror.
Through this activity the students appreciate that reflection causes an object
to change its orientation from left to right and up to down depending on the
position of the reflecting surface. The students suggest real life situations
where this effect may be observed, such as the inversion of the word
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to label correctly the
vertices of the object and image in a
reflection.
(Level 8.1)
Students will be able to reflect a shape in
210
‘Ambulance’ and reflection in water.
The students access these interactive sites to draw the image of points and
objects in the x and y axes.
http://www.ixl.com/math/grade-8/reflections-find-the-coordinates
http://www.ixl.com/math/grade-8/reflections-graph-the-image
The teacher uses Dynamic Geometry Software on the IWB to illustrate
different reflections in the x axis, y axis, x = c, y = c and y =  x. Students
predict the position and shape of the image and check their result using this
software. The students are asked questions such as ‘What happened to the
shape after reflection in the mirror?’ and ‘Are the two shapes equal in all
respects (congruent)?’
On the following interactive site the students may predict and hence
observe the reflection of objects in different mirror lines. The teacher may
present the students with an example of a reflection and ask the students to
describe it.
http://www.ngflcymru.org.uk/vtc/ngfl/maths/echalk/reflection/reflection.html
3. Translate a shape
horizontally and/or vertically
given a column vector;
describe a translation by a
column vector.
The students are given a grid with a shape, A, drawn on it. They are asked to
reflect shape A in the x axis and label it B. Shape B is reflected in the y axis
and labelled C and shape C is in turn reflected in the x axis and labelled D.
Finally the students have to describe the transformation from A to D.
Different students may be given different shapes and their observations
discussed. The students may view these multiple reflections with the aid of
Dynamic Geometry Software.
The teacher may use Dynamic Geometry Software on the IWB to illustrate
horizontal and/or vertical translations. Students predict the position and
shape of the image and check their result using this software. The students
are asked questions such as ‘What happened to the shape after the
translation?’ and ‘Are the two shapes equal in all respects (congruent)?
The students are given a puzzle consisting of shapes drawn on a grid,
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
y =  x and describe the reflection in
words.
(Level 7.3)
Students will be able to reflect a shape in
x = c or y = c and describe the
reflection in words.
(Level 7.2)
Students will be able to reflect a shape in
the x axis and/or y axis, describe the
reflection in words and understand that
in a reflection the object and image are
congruent and inverted.
(Level 7.1)
Students will be able to apply multiple
translations to a shape.
(Level 8.1)
Students will be able to translate shapes
given a column vector and describe
211
together with a set of instructions to translate each shape. When all the
shapes have been translated the image of a bigger shape is formed.
translations by a column vector.
(Level 7.3)
The students work in pairs. They are asked to prepare the above activity for
their partner. While creating instructions the students practise describing
translations. The students may then solve each other’s puzzle thus checking
whether the instructions given were correct.
Students will be able to translate a shape
given a column vector.
(Level 7.2)
The teacher may use the Maths Excel Lessons - Translations, to explain the
effect of translation.
On the following site the students mark on a graph the image of a point that
has undergone a translation. http://www.ixl.com/math/practice/grade-8translations-graph-the-image
Students will be able to translate a shape
horizontally and/or vertically through
descriptions: right, left, up and down and
understand that in a translation the
object and image are congruent.
(Level 7.1)
On the following site the students find the coordinates of the image of a
point that has undergone a translation.
http://www.ixl.com/math/practice/grade-8-translations-find-thecoordinates
4. Rotate a shape about the
origin or one of the vertices,
using angles of 90° and 180°;
describe a rotation.
The students are shown a number of cards representing an object and its
transformed image. They have to classify the transformations in reflection,
translation and rotation.
The teacher may use Dynamic Geometry Software on the IWB to illustrate
clockwise and anticlockwise rotations through an angle of 90°. Students
predict the position and shape of the image and check their result using this
software. The students are asked questions such as ‘What happened to the
shape after the rotation?’ and ‘Are the two shapes equal in all respects
(congruent)?’
On the following site the students mark on a graph the image of a point that
has undergone a rotation.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to rotate a shape
when the centre of rotation is outside the
shape and describe the transformation in
words.
(Level 8.1)
Students will be able to rotate a shape
about one of the vertices using angles of
90° and 180° and describe the
transformation in words.
(Level 7.3)
Students will be able to rotate a shape
212
http://www.ixl.com/math/grade-8/rotations-graph-the-image
On the following site the students find the coordinates of the image of a
point that has undergone a rotation.
http://www.ixl.com/math/grade-8/rotations-find-the-coordinates
On the following interactive site the students predict and hence observe the
rotation of objects about the origin. The teacher may present the students
with an example of a rotation and ask the students to describe it.
http://www.ngflcymru.org.uk/vtc/ngfl/maths/echalk/rotation/rotation.html
about one of the vertices through an
angle of 90°.
(Level 7.2)
Students will be able to rotate squares,
rectangles and right-angled triangles
about one of the vertices using angles of
90° and 180° and understand that in a
rotation the object and image are
congruent.
(Level 7.1)
The students are given a puzzle consisting of shapes drawn on a grid,
together with a set of instructions to rotate each shape. When all the shapes
have been rotated the image of a bigger shape is formed.
Students are given a set of cards representing an object and its rotated
image and they have to describe the rotations.
Students can play a matching game involving diagrams representing an
object and its rotated image and descriptions of various rotations, e.g.
anticlockwise rotation of 90° about vertex A, clockwise rotation of 90° about
the origin, etc.
5. Enlarge a shape by a positive
integral scale factor using a
centre of enlargement;
describe an enlargement.
The teacher uses Dynamic Geometry Software on the IWB to illustrate the
enlargement of an object by a positive integral scale factor. Students predict
the position and shape of the image and check their result using this
software. The students are asked questions such as ‘What happened to the
shape after the enlargement?’ and ‘Are the two shapes congruent?’
The students observe the effect of enlarging objects by a scale factor of 1, 2,
3 and 4 on the following interactive site:
http://www.ngflcymru.org.uk/vtc/ngfl/maths/echalk/enlargement/intro/enlargementIntro.html
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to understand that
in an enlargement the object and image
are similar.
(Level 8.1)
Students will be able to find the centre of
enlargement and the scale factor (limited
to positive integers) and describe an
enlargement in words.
(Level 7.3)
213
The students draw the enlargement of objects on the following interactive
site. They can then check whether the image drawn is correct.
http://www.ngflcymru.org.uk/vtc/ngfl/maths/echalk/enlargement/drawing/drawingEnlarge
ments.html
The students use this interactive tool to observe how an enlargement is
constructed with the help of construction lines drawn from the centre of
enlargement.
http://www.ngflcymru.org.uk/vtc/ngfl/maths/echalk/enlargement/teachingTool/enlargeme
ntTool.html
Students will be able to enlarge a shape
by a positive integral scale factor, using
the origin as the centre of enlargement.
(Level 7.2)
Students will be able to enlarge squares,
rectangles and right-angled triangles by a
positive integral scale factor.
(Level 7.1)
The students are shown a number of cards representing an object and its
transformed image. They have to classify the transformations as reflections,
translations, rotations and enlargements.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
214
Subject:
MATHEMATICS
Unit code and title: MTH 8.13 Transformations (Levels 6.3 – 7.3)
Strand 3:
Shape, Space and Measures
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Identify shapes having reflection and/or rotational symmetry in 2D; determine the order of rotational symmetry in 2D; determine the symmetrical
properties of a polygon.
2. Reflect a shape in the x axis, y axis, x = c, y = c and y =  x; describe a reflection.
3. Translate a shape horizontally and/or vertically given a column vector; describe a translation by a column vector.
4. Rotate a shape about the origin or one of the vertices, using angles of 90° and 180°; describe a rotation.
5. Enlarge a shape by a positive integral scale factor using a centre of enlargement; describe an enlargement.
Key Words
symmetry, reflection symmetry,
line of symmetry, vertical,
horizontal, rotational
symmetry, centre of rotation,
order of rotation, polygon
axes, coordinates, object,
image, transformation,
mapping, shape, size,
congruent
translation, right, left, up,
down, column vector
reflection
rotation, clockwise,
anticlockwise, origin
Points to Note
Resources
FOM B1, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to promote a
Resource Pack - Chapters 19 and 24.
student centred learning environment.
From Teachers’ laptop:
Exposition: the teacher states the objectives of the lesson and may use ICT C:\Documents and settings\teacher\My
software for students to practise new knowledge. This is consolidated by Documents\Maths Excel Lessons
setting students tasks that offer students the opportunity to apply Translations
mathematics to a variety of real life situations.
Dynamic Geometry Software
Discovery: the teacher can set group tasks in which students discuss and rotational symmetry board
construct mathematical knowledge. Students may become active learners
while testing hypotheses and/or making generalisations.
Internet Links:
http://www.mathsisfun.com
Exploration: the teacher integrates an inquiry based learning approach that http://www.innovationslearning.co.uk
enhances the students’ understanding of concepts. These tasks might http://www.gcsemathstutor.com
employ the processes of reasoning, problem solving, investigations, http://www.ngfl-cymru.org.uk
connecting ideas and concepts, and expressing results by using the precise http://www.ixl.com/math/grade-8
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
215
Teaching Objective
The teacher will teach the
students to:
1. Identify shapes having
reflection and/or rotational
symmetry in 2D; determine
the order of rotational
symmetry in 2D; determine
the symmetrical properties
of a polygon.
Examples of teaching experiences and activities
Students, in groups, are given a set of laminated cards showing different
shapes. They are asked to identify which shapes have reflection symmetry.
The students then draw the line of symmetry of these shapes on the card.
The students access the following site to understand the meaning of
rotational symmetry and order of rotational symmetry:
http://www.mathsisfun.com/geometry/symmetry-rotational.html
Students, in groups, are given a rotational symmetry board made up of
shapes and symbols such as club, diamond, star, etc. They have to identify
which shapes have a rotational symmetry. The students then determine the
order of rotational symmetry of these shapes.
The students, in groups, investigate reflection symmetry of different
quadrilaterals illustrated on a handout. They then investigate the rotational
symmetry of these quadrilaterals with the help of a rotational symmetry
board. This activity may be repeated with triangles and other polygons.
At the end of the activity students compare their results with the whole
class.
2. Reflect a shape in the x axis,
y axis, x = c, y = c and y
=  x; describe a reflection.
The students access the following site to understand the geometric
properties of polygons:
http://www.innovationslearning.co.uk/subjects/maths/activities/year3/sym
metry/shape_game.asp
The students observe the reflection of shapes and letters in a mirror.
Through this activity the students appreciate that reflection causes an object
to change its orientation from left to right and up to down depending on the
position of the reflecting surface. The students suggest real life situations
where this effect may be observed, such as the inversion of the word
‘Ambulance’ and reflection in water.
The students access these interactive sites to draw the image of points and
objects in the x and y axes.
http://www.ixl.com/math/grade-8/reflections-find-the-coordinates
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Indicators of Learning outcomes
Students will be able to determine the
symmetrical properties of triangles and
special quadrilaterals.
(Level 7.3)
Students will be able to determine the
symmetrical properties of regular
polygons.
(Level 7.2)
Students will be able to identify shapes
having reflection and/or rotational
symmetry, determine the order of
rotational symmetry and be able to
complete part shapes using two lines of
symmetry.
(Level 7.1)
Students will be able to identify shapes
having reflection and/or rotational
symmetry.
(Level 6.3)
Students will be able to reflect a shape
in y =  x and describe the reflection in
words.
(Level 7.3)
Students will be able to reflect a shape in
x = c or y = c and describe the
reflection in words.
(Level 7.2)
216
http://www.ixl.com/math/grade-8/reflections-graph-the-image
The teacher uses Dynamic Geometry Software on the IWB to illustrate
different reflections in the x axis, y axis, x = c, y = c and y =  x. Students
predict the position and shape of the image and check their result using this
software. The students are asked questions such as ‘What happened to the
shape after reflection in the mirror?’ and ‘Are the two shapes equal in all
respects (congruent)?’
On the following interactive site the students may predict and hence
observe the reflection of objects in different mirror lines. The teacher may
use the site to represent a reflection and ask the students to describe it.
http://www.ngflcymru.org.uk/vtc/ngfl/maths/echalk/reflection/reflection.html
Students will be able to reflect a shape in
the x axis and/or y axis, describe the
reflection in words and understand that
in a reflection the object and image are
congruent and inverted.
(Level 7.1)
Students will be able to reflect a shape in
the x axis and/or y axis and describe the
reflection in words.
(Level 6.3)
The students are given a grid with a shape, A, drawn on it. They are asked to
reflect shape A in the x axis and label it B. Shape B is reflected in the y axis
and labelled C and shape C is in turn reflected in the x axis and labelled D.
Finally the students have to describe the transformation from A to D.
Different students may be given different shapes and their observations
discussed.
3. Translate a shape
horizontally and/or vertically
given a column vector;
describe a translation by a
column vector.
The teacher uses Dynamic Geometry Software on the IWB to illustrate
horizontal and/or vertical translations. Students predict the position and
shape of the image and check their result using this software. The students
are asked questions such as ‘What happened to the shape after the
translation?’ and ‘Are the two shapes equal in all respects (congruent)?’
The students are given a puzzle consisting of shapes drawn on a grid,
together with a set of instructions to translate each shape. When all the
shapes have been translated the image of a bigger shape is formed.
The students work in pairs. They have to prepare the above activity for their
partner. While creating instructions the students practise describing
translations. The students may then solve each other’s puzzle thus checking
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to translate shapes
given a column vector and describe
translations by a column vector.
(Level 7.3)
Students will be able to translate a shape
given a column vector.
(Level 7.2)
Students will be able to translate a shape
horizontally and/or vertically through
descriptions: right, left, up and down and
217
whether the instructions given were correct.
The teacher uses the Maths Excel Lessons - Translations, to explain the
effect of translation.
On the following site the students mark on a graph the image of a point that
has undergone a translation. http://www.ixl.com/math/practice/grade-8translations-graph-the-image
understand that in a translation the
object and image are congruent.
(Level 7.1)
Students will be able to translate shapes
right, left, up and down.
(Level 6.3)
On the following site the students find the coordinates of the image of a
point that has undergone a translation.
http://www.ixl.com/math/practice/grade-8-translations-find-thecoordinates
4. Rotate a shape about the
origin or one of the vertices,
using angles of 90° and 180°;
describe a rotation.
The students are shown a number of cards representing an object and its
transformed image. They have to classify the transformations in reflection,
translation and rotation.
The teacher uses Dynamic Geometry Software on the IWB to illustrate
clockwise and anticlockwise rotations through an angle of 90°. Students
predict the position and shape of the image and check their result using this
software. The students are asked questions such as ‘What happened to the
shape after the rotation?’ and ‘Are the two shapes equal in all respects
(congruent)?’
On the following interactive site the students may predict and hence
observe the rotation of objects about one of the vertices. The teacher may
present the students with an example of a rotation and ask the students to
describe it.
http://www.ngflcymru.org.uk/vtc/ngfl/maths/echalk/rotation/rotation.html
The students are given a puzzle consisting of shapes drawn on a grid,
together with a set of instructions to rotate each shape. When all the shapes
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to rotate a shape
about one of the vertices using angles of
90° and 180° and describe the
transformation in words.
(Level 7.3)
Students will be able to rotate a shape
about one of the vertices through an
angle of 90°.
(Level 7.2)
Students will be able to rotate squares,
rectangles and right-angled triangles
about one of the vertices using angles of
90° and 180° and understand that in a
rotation the object and image are
congruent.
(Level 7.1)
Students will be able to rotate squares
218
have been rotated the image of a bigger shape is formed.
Students are given a set of cards representing an object and its rotated
image and they have to describe the rotations.
5. Enlarge a shape by a positive
integral scale factor using a
centre of enlargement;
describe an enlargement.
Students can play a matching game involving diagrams representing an
object and its rotated image and descriptions of various rotations, e.g.
anticlockwise rotation of 90° about vertex A, clockwise rotation of 90° about
the origin, etc.
The teacher uses Dynamic Geometry Software on the IWB to illustrate the
enlargement of an object by a positive integral scale factor. Students predict
the position and shape of the image and check their result using this
software. The students are asked questions such as ‘What happened to the
shape after the enlargement?’ and ‘Are the two shapes congruent?’
The students observe the effect of enlarging objects by a scale factor of 1, 2,
3 and 4 on the following interactive site:
http://www.ngflcymru.org.uk/vtc/ngfl/maths/echalk/enlargement/intro/enlargementIntro.html
The students may draw the enlargement of objects on the following
interactive site. They can then check whether the image drawn is correct.
http://www.ngflymru.org.uk/vtc/ngfl/maths/echalk/enlargement/drawing/drawingEnlargements.html
and rectangles about one of the vertices
through an angle of 90° and 180°.
(Level 6.3)
Students will be able to find the centre of
enlargement and the scale factor (limited
to positive integers) and describe an
enlargement in words.
(Level 7.3)
Students will be able to enlarge a shape
by a positive integral scale factor, using
the origin as the centre of enlargement.
(Level 7.2)
Students will be able to enlarge squares,
rectangles and right-angled triangles by a
positive integral scale factor.
(Level 7.1)
The students use this interactive tool to observe how an enlargement is
constructed with the help of construction lines drawn from the centre of
enlargement.
Students will be able to recognise an
http://www.ngflenlargement.
cymru.org.uk/vtc/ngfl/maths/echalk/enlargement/teachingTool/enlargementTool.html (Level 6.3)
The students are shown a number of cards representing an object and its
transformed image. They have to classify the transformations as reflections,
translations, rotations and enlargements.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
219
Subject:
MATHEMATICS
Unit code and title: MTH 8.13 Transformations (Levels 5.3 – 7.1)
Strand 3:
Shape, Space & Measures
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Identify shapes having reflection and/or rotational symmetry in 2D; determine the order of rotational symmetry in 2D.
2. Reflect a shape in the x axis and y axis; describe a reflection.
3. Translate a shape horizontally and/or vertically through descriptions: right, left, up and down.
4. Rotate a shape about one of the vertices using angles of 90° and 180°.
Key Words
symmetry, reflection symmetry,
line of symmetry, vertical,
horizontal, rotational
symmetry, centre of rotation,
order of rotation
axes, coordinates, object,
image, transformation, shape,
size
translation, right, left, up, down
reflection
rotation, clockwise,
anticlockwise
Points to Note
Resources
FOM B Gold, Students’ Book and
Three main teaching approaches are being recommended to promote a
Resource Pack - Chapters 19 and 23.
student centred learning environment.
From Teachers’ laptop:
Exposition: the teacher states the objectives of the lesson and may use ICT C:\Documents and settings\teacher\My
software for students to practise new knowledge. This is consolidated by Documents\Maths Excel Lessons
setting students tasks that offer students the opportunity to apply Translations
mathematics to a variety of real life situations.
Dynamic Geometry Software
Discovery: the teacher can set group tasks in which students discuss and rotational symmetry board; mirror
construct mathematical knowledge. Students may become active learners
while testing hypotheses and/or making generalisations.
Internet Links:
http://www.mathsisfun.com
Exploration: the teacher integrates an inquiry based learning approach that http://www.innovationslearning.co.uk
enhances the students’ understanding of concepts. These tasks might http://www.gcsemathstutor.com
employ the processes of reasoning, problem solving, investigations, http://www.ngfl-cymru.org.uk
connecting ideas and concepts, and expressing results by using the precise http://www.ixl.com/math/grade-8
language of mathematics.
http://www.bbc.co.uk/schools/gcsebitesi
ze/maths
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
220
Teaching Objective
The teacher will teach the
students to:
1. Identify shapes having
reflection and/or rotational
symmetry in 2D; determine
the order of rotational
symmetry in 2D.
Examples of teaching experiences and activities
The students are given a set of cards with part shapes drawn on them. They
may use a mirror to identify the position and shape of the image. Hence
they draw the image.
Students, in groups, are given a set of laminated cards showing different
shapes. They are asked to identify which shapes have reflection symmetry.
The students then draw the line of symmetry of these shapes on the card.
Student access this site to understand the reflection symmetry of shapes.
http://www.ngflcymru.org.uk/vtc/ngfl/maths/greg_morgan_symmetry/symmetry.swf
The students access the following sites to understand the meaning of
rotational symmetry and order of rotational symmetry.
http://www.mathsisfun.com/geometry/symmetry-rotational.html
http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/symmetryact.
shtml
Students, in groups, are given a rotational symmetry board made up of
shapes and symbols such as club, diamond, star, etc. They have to identify
which shapes have a rotational symmetry. The students then determine the
order of rotational symmetry of these shapes.
2. Reflect a shape in the x axis
and y axis; describe a
reflection.
The students observe the reflection of shapes and letters in a mirror. The
students are asked questions such as ‘What happened to the shape after
reflection in the mirror?’ and ‘Are the two shapes equal in all respects?’
Through this activity the students appreciate that reflection causes an object
to change its orientation from left to right and up to down depending on the
position of the reflecting surface. The students suggest real life situations
where this effect may be observed, such as the inversion of the word
‘Ambulance’ and reflection in water.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Indicators of Learning outcomes
Students will be able to identify shapes
having reflection and/or rotational
symmetry, determine the order of
rotational symmetry and be able to
complete part shapes using two lines of
symmetry.
(Level 7.1)
Students will be able to identify shapes
having reflection and/or rotational
symmetry.
(Level 6.3)
Students will be able to complete part
shapes using two lines of symmetry.
(Level 6.2)
Students will be able to complete part
shapes using one line of symmetry.
(Level 6.1)
Students will be able to identify shapes
having reflection symmetry.
(Level 5.3)
Students will be able to reflect a shape in
the x axis and/or y axis, describe the
reflection in words and understand that
in a reflection the object and image are
inverted and have the same shape and
size.
(Level 7.1)
221
The students may access these interactive sites to draw the image of points
and objects in the x and y axes.
http://www.ixl.com/math/grade-8/reflections-find-the-coordinates
http://www.ixl.com/math/grade-8/reflections-graph-the-image
Students will be able to reflect a shape in
the x axis and/or y axis and describe the
reflection in words.
(Level 6.3)
The teacher may use Dynamic Geometry Software on the IWB to illustrate
different reflections in the x axis, y axis. Students may be asked to predict
the position and shape of the image and check their result using this
software. The students are asked questions such as ‘What happened to the
shape after reflection in the mirror?’ and ‘Are the two shapes equal in all
respects?’
Students will be able to reflect a shape in
the x axis or y axis.
(Level 6.2)
On the following interactive site the students may predict and hence
observe the reflection of objects in different mirror lines. The teacher may
use the site to represent a reflection and ask the students to describe it.
http://www.ngfl-cymru.org.uk/vtc/ngfl/maths/echalk/reflection/reflection.html
3. Translate a shape
horizontally and/or vertically
through descriptions: right,
left, up and down.
The students are given a grid with a shape, A, drawn on it. They are asked to
reflect shape A in the x axis and label it B. Shape B is reflected in the y axis
and labelled C and shape C is in turn reflected in the x axis and labelled D.
Finally the students have to describe the transformation from D to A.
Different students may be given different shapes and their observations
discussed.
The teacher may use Dynamic Geometry Software on the IWB to illustrate
horizontal and/or vertical translations. Students may be asked to predict the
position and shape of the image and check their result using this software.
The students are asked questions such as ‘What happened to the shape
after the translation?’ and ‘Are the two shapes equal in all respects?’
The students are given a puzzle consisting of a letters written on a squared
paper together with a set of instructions to translate each letter. When all
the letters are translated a word is formed. This activity may be repeated
with shapes. When all the shapes are translated a new shape is formed.
On the following site the students mark on a graph the image of a point that
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to reflect a shape in
one line of symmetry.
(Level 6.1)
Students will be able to recognise a
reflection.
(Level 5.3)
Students will be able to translate a shape
horizontally and/or vertically and
understand that in a translation the
object and image have the same shape
and size.
(Level 7.1)
Students will be able to translate shapes
right, left, up and down.
(Level 6.3)
222
has undergone a translation.
http://www.ixl.com/math/practice/grade-8-translations-graph-the-image
On the following site the students find the coordinates of the image of a
point that has undergone a translation.
http://www.ixl.com/math/practice/grade-8-translations-find-thecoordinates
4. Rotate a shape about one of
the vertices using angles of
90° and 180°.
The students are shown a number of cards representing an object and its
transformed image. They have to classify the transformations in reflection,
translation and rotation.
Students are given a set of cards representing an object and its rotated
image. They have to classify the rotations in clockwise or anticlockwise
rotations.
The teacher may use Dynamic Geometry Software on the IWB to illustrate
clockwise and anticlockwise rotations through an angle of 90°. Students may
be asked to predict the position and shape of the image and check their
result using this software. The students are asked questions such as ‘What
happened to the shape after the translation?’ and ‘Are the two shapes equal
in all respects?’
On the following interactive site the students may predict and hence
observe the rotation of objects about one of the vertices.
http://www.ngfl-cymru.org.uk/vtc/ngfl/maths/echalk/rotation/rotation.html
Students can play a matching game involving diagrams representing an
object and its rotated image and descriptions of various rotations, e.g.
anticlockwise rotation of 90° about vertex A, clockwise rotation of 90° about
vertex B, etc.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to translate simple
shapes to the right/left only or up/down
only. (Level 6.2)
Students will be able to recognise a
translation. (Level 6.1)
Students understand the meaning of the
vocabulary: right, left, up and down.
(Level 5.3)
Students will be able to rotate squares,
rectangles and right-angled triangles
about one of the vertices using angles of
90° and 180° and understand that in a
rotation the object and image have the
same shape and size.
(Level 7.1)
Students will be able to rotate squares
and rectangles about one of the vertices
through an angle of 90° and 180°.
(Level 6.3)
Students will be able to recognise a
rotation.
(Level 6.2)
Students will be able to understand the
meaning of clockwise and anticlockwise.
(Level 6.1)
Students will be able to recognise the size
of a 90° angle and multiple angles of 90°.
(Level 5.3)
223
Subject:
Unit code and title:
Strand 3:
MATHEMATICS
MTH 8.13 Transformations (Levels 1 – 4)
Shape, Space & Measures
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Identify shapes having reflection and/or rotational symmetry in 2D; determine the order of rotational symmetry in 2D.
2. Reflect a shape in the x axis and y axis; describe a reflection.
3. Translate a shape horizontally and/or vertically through descriptions: right, left, up and down.
4. Rotate a shape about one of the vertices using angles of 90° and 180°.
Objectives at attainment levels 1- 4.
The teacher will teach the students to:
1.1 Recognise and count the rotational symmetry of a shape.
1.2 Identify the reflection of a shape; draw the reflection of a shape by imitation.
1.3 Recognise and draw the new position of a shape after they have moved it sideways, upward and downward.
1.4 Rotate a shape by a quarter and half a turn.
Key Words
symmetry , rotational
symmetry , order of
rotational symmetry ,
pattern, half turn,
reflection , quarter of
a turn, up, down, left
and right movement.
Points to Note
In addition to the points to note recommended for students performing at Level 5
or higher, it is very important for the teacher to allow time for the students to
respond. This response can take the form of unaided and/or aided means of
communication and the teacher needs to provide adequate scaffolding
techniques to enable the students to respond affectively or intentionally.
Resources
New Maths Frame Working-Step Up
Workbook.
Oxford Framework Maths 7
Software: Ilearn Maths, Calculator, Excel
Worksheets
For further material at level 1 refer to handbook pg.
From Teachers’ laptop:
C:\Documents and Settings\teacher\My
Documents\Maths Excel Lessons
Internet Links: see below in examples.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
224
Teaching Objective
The teacher will teach
the students to:
Examples of Teaching Experiences and Activities
Starter: Students are given different shapes having rotational symmetry. They are
left to explore them and talk about them.
1.1 Recognise and
count the
rotational
symmetry of a
shape
Students, in groups, are given a square, triangle, oval, rectangle and a diamond.
They are asked to mark one corner with a marker or a blu tac. They turn the
shape and count many times the shape will land on itself as if it was not rotated.
http://www.mathsisfun.com/geometry/symmetry-rotational.html
http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/symmetryact.shtml
Students are given a shape and its different positions for a whole turn. They
count how many times it looks like the original position. Also, they can be given a
pattern of turns and indicate which is the next pattern from a choice of two. E.g.
What’s next?
Or
The previous activity can be lowered down to just matching the shapes. The
students have the different positions and they match and count their matches
with an adult.
1.2 Identify the
reflection of a
shape; draw the
reflection of a
shape by
imitation.
Students are given a shape and they focus and sustain their attention on the
object being rotated.
Starter: Students are given a mirror to explore the reflection of a shape.
As a continuation to the above starter activity, the students are asked questions
like, ‘Are there any differences between the object and the one seen in the
mirror?’ Students will talk about it and draw the reflection of an object in
imitation. Also, students can be given half the shape and they complete it by
drawing the other half.
http://www.ngfl-cymru.org.uk/vtc/ngfl/maths/echalk/reflection/reflection.html
Students are given half the shape and they match it with the other half.
Students are given an object and its reflection and they have to match them with
a similar shadowing pattern.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Indicators of Learning Outcomes
Students will be able to rotate a shape
and state the number of times they
rotated it.
(Level 4)
Students will be able to count the
number of times the shape looks like
the original shape.
(Level 3)
Students will be able to match the
shapes and count by rote with adult
support.
(Level 2)
Students will be able to focus on an
object being rotated with sustained
attention.
(Level 1)
Students will be able to recognize the
reflection of a shape and draw the
reflection of an object.
(Level 4)
Students will be able to choose the
shape that is the odd one out.
(Level 3)
Students will be able to match the
225
Students look at their face in a mirror and point to named body parts or objects.
1.3 Recognise and
draw the new
position of a shape
after they have
moved it sideways,
upward and
downward.
Starter: Students are given a shape and some instructions like move two boxes
left, one up, one right and one down. Teacher will observe whether the students
have an idea of this vocabulary.
Students are given the original and the new position of a shape. They describe
the moves that the shape has made. On the other hand, they have the original
shape, someone says the moves and someone else has to find and draw the new
position.
The above activity can be limited to two instructions including up and down
movements.
The above activity can be limited to one movement instruction, say up.
On the computer, the students are involved in click, drag and click activities to
experience the movement of an object from one place to another.
1.4 Rotate a shape by
a quarter and
half a turn.
Starter: Students are presented with a circle divided into four equal parts and
each point marked as ABCD and a moveable arrow. At first, the arrow points to A.
The teacher gives them some instruction cards to follow like turn ¼ , ½, one half,
one quarter etc.
shape and its reflection with an equal
shape and its reflection.
(Level 2)
Students will be able to focus their
attention on named objects being seen
in a mirror.
(Level 1)
Students will be able to describe the
movement of a shape, describe the
movement and have to draw/mark the
final position.
(Level 4)
Students will be able to recognise and
reinforce up and down movement in
translations.
(Level 3)
Students will be able to recognise the
upward movement in translations.
(Level 2)
Students will be able to participate in
click and drag or drag and drop activities
on the computer.
(Level 1)
Students will be able to apply the
rotational instruction in practice as well
as describe the rotation that a shape
has gone through.
(Level 4)
Eventually, students are given shapes and they rotate them according to the
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
226
instruction card as well as they can be given the end product on the card and
they describe the movement.
Students will continue a pattern of ¼ or ½ movements. For example,
Students will be able to continue a
pattern of quarter and half turns
without any example prompt.
(Level 3)
Students will be able to choose the odd
one out from a category of shapes.
(Level 2)
Students will be able to focus their
attention on click and drop techniques
to continue a pattern of half turns.
(Level 1)
Students will choose the odd one out pattern from a sequence of patterns.
Using the click and drag, or the drag and drop techniques students will be helped
to move the shapes on the screen to fit their outer border.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
227
Subject:
MATHEMATICS
Unit code and title: MTH 8.14 Solving Equations (Levels 7.1 – 8.1)
Strand 2:
Algebra
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Solve linear equations in one unknown.
2. Solve linear equations involving brackets.
3. Use equations to solve problems.
Key Words
solve, equation, unknown, like
terms, tidy up, simplify, scales,
balance, operation, addition,
subtraction, multiplication,
division, inverse operation,
brackets, expand
Points to Note
Resources
FOM B2, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to promote a
Resource Pack - Chapter 20.
student centred learning environment.
IWB
Exposition: the teacher states the objectives of the lesson and may use ICT Algebra tiles
software for students to practise new knowledge. This is consolidated by
setting students tasks that offer students the opportunity to apply
mathematics to a variety of real life situations.
Internet Links:
http://nlvm.usu.edu/
Discovery: the teacher can set group tasks in which students discuss and http://www.mathsisfun.com
construct mathematical knowledge. Students may become active learners http://mathsnet.net/
while testing hypotheses and/or making generalisations.
http://www.waldomaths.com
http://www.ixl.com/math/
Exploration: the teacher integrates an inquiry based learning approach that
enhances the students’ understanding of concepts. These tasks might
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
228
Teaching Objective
The teacher will teach the
students to:
1. Solve linear equations in one
unknown.
Examples of teaching experiences and activities
Students use the Math tool: Algebra Balance Scales, to click and drag
quantities to balance beam pans representing an equation.
http://nlvm.usu.edu/en/nav/frames_asid_201_g_4_t_2.html
Students access the following sites to practise balancing equations
pictorially http://www.mathsisfun.com/algebra/add-subtract-balance.html
Indicators of Learning outcomes
Students will be able to solve linear
equations with one unknown on both
sides.
(Level 8.1)
Students practise solving equations on the following interactive site
http://mathsnet.net/algebra/l4_equation.html
Students will be able to solve linear
equations with one unknown on both
sides involving up to two operations.
(Level 7.3)
The students use the following site to solve equations by
adding/subtracting/dividing both sides by a quantity. Levels 1 to 4 provide
examples related to this teaching objective.
http://www.waldomaths.com/Equation2NL.jsp
Students will be able to solve linear
equations with one unknown on one side
involving up to two operations.
(Level 7.2)
The students, in groups, play a card matching game. They have to match
cards showing an equation to cards showing a solution. This game may be
applied to equations involving either one or two operations, depending on
the students’ ability.
Students will be able to solve linear
equations involving one operation.
(Level 7.1)
Algebra Tiles may be used to solve equations in one unknown.
 The Algebra Tiles template is available on the site:
http://mathbits.com/MathBits/AlgebraTiles/AlgebraTiles.htm
to produce their own tiles;
 The students can access the site:
http://go.hrw.com/math/midma/gradecontent/manipulatives/A
lgebra_Tiles/Algebra_Tiles.html
and manipulate the tiles on the IWB.
2. Solve linear equations
involving brackets.
Students access the following site to practise adding and subtracting like
terms.
http://www.ixl.com/math/practice/grade-8-add-and-subtract-like-terms
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to solve linear
equations involving brackets.
(Level 8.1)
229
Students practise solving equations involving brackets by accessing the
following site on Levels 1 to 4.
http://www.waldomaths.com/Equation3NL.jsp
Students play a game of Equation Bingo which involves solving equations
with brackets. The students have a Bingo card each. An equation card is
drawn from a pile, the students work out the equation and cross off the
solution on their bingo card. The winner is the first one to cross off a
complete row or column from their card. The bingo cards and equation
cards are available on worksheets SU10 ad SU11 of the Teachers’ Resource
Pack B2.
Students are given examples, such as the following, and they have to spot
the error. Example:
5(x − 4) + 3 =3(x − 3)
5x − 20 + 15 = 3x − 9
5x − 5 = 3x − 9
5x − 5 + 5 = 3x − 9 + 5
5x = 3x − 4
5x − 3x = 3x − 3x − 4
2x = − 4
x=2
3. Use equations to solve
problems.
Students will be able to solve linear
equations involving one pair of brackets
on one side only.
(Level 7.3)
Students will be able to collect like terms
in an expression and will be able to
multiply a single term over a bracket.
(Level 7.2)
Students will be able to collect terms in
an expression involving like terms.
(Level 7.1)
Students are given a problem and three equations. They have to identify the
equation that represents the information given in the problem. This
exercise encourages the students to examine their work when they form an
equation from given information.
Students will be able to form and solve
linear equations with one unknown on
both sides.
(Level 8.1)
Students access the following site to practise writing an equation from
words.
http://www.ixl.com/math/algebra-1/write-variable-equations
Students are given cards showing a triangle or quadrilateral. Some cards
show the size of the angles given in terms of x. Other cards show the length
Students will be able to form and solve
linear equations with one unknown on
both sides involving up to two operations.
(Level 7.3)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
230
of the sides given in terms of x. In each case the students are asked to form
an equation and solve it to find the size of each angle or side.
As a conclusion the students identify whether
 the triangle is equilateral, isosceles or scalene;
 the quadrilateral is a square, a rectangle, a kite or neither
Students will be able to form and solve
linear equations with one unknown on
one side involving up to two operations.
(Level 7.2)
Students will be able to form and solve
linear equations involving one operation.
(Level 7.1)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
231
Subject:
Unit code and title:
Strand 2:
MATHEMATICS
MTH 8.14 Solving Equations Levels 6.3 – 7.3
Algebra
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will each the students to:
1. Solve linear equations in one unknown involving up to two operations.
2. Solve linear equations involving one pair of brackets on one side only.
3. Use equations to solve problems.
Key Words
solve, equation, unknown, like
terms, tidy up, simplify, scales,
balance, operation, addition,
subtraction, multiplication,
division, inverse operation,
brackets, expand
Points to Note
Resources
FOM B1, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to promote a
Resource Pack - Chapter 20.
student centred learning environment.
IWB
Exposition: the teacher states the objectives of the lesson and may use ICT Algebra tiles
software for students to practise new knowledge. This is consolidated by
setting students tasks that offer students the opportunity to apply
mathematics to a variety of real life situations.
Internet Links:
http://nlvm.usu.edu/
Discovery: the teacher can set group tasks in which students discuss and http://www.mathsisfun.com
construct mathematical knowledge. Students may become active learners http://mathsnet.net/
while testing hypotheses and/or making generalisations.
http://www.waldomaths.com
http://www.ixl.com/math/
Exploration: the teacher integrates an inquiry based learning approach that
enhances the students’ understanding of concepts. These tasks might
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
232
Teaching Objective
Examples of teaching experiences and activities
Indicators of Learning outcomes
The teacher will teach the
students to:
Students use the Math tool: Algebra Balance Scales, to click and drag
quantities to balance beam pans representing an equation.
http://nlvm.usu.edu/en/nav/frames_asid_201_g_4_t_2.html
Students will be able to solve linear
equations with one unknown on both
sides involving up to two operations.
(Level 7.3)
1. Solve linear equations in one
unknown involving up to two
operations.
Students access the following sites to practise balancing equations
pictorially http://www.mathsisfun.com/algebra/add-subtract-balance.html
The students practise solving equations on the following interactive site.
Levels 1 to 3 provide examples related to this teaching objective.
http://mathsnet.net/algebra/l4_equation.html
The students use the following site to solve equations by
adding/subtracting/dividing both sides by a quantity. Levels 1 to 3 provide
examples related to this teaching objective.
http://www.waldomaths.com/Equation2NL.jsp
The students, in groups, play a card matching game. They have to match
cards showing an equation to cards showing a solution. This game may be
applied to equations involving either one or two operations, depending on
the students’ ability.
Students will be able to solve linear
equations with one unknown on one side
involving up to two operations.
(Level 7.2)
Students will be able to solve linear
equations involving one operation.
(Level 7.1)
Students will be able to solve equations
by drawing scales, given unknown on one
side and involving up to two operations.
(Level 6.3)
Algebra Tiles may be used to solve equations in one unknown.
 The Algebra Tiles template is available on the site:
http://mathbits.com/MathBits/AlgebraTiles/AlgebraTiles.htm
to produce their own tiles;

The students can access the site:
http://go.hrw.com/math/midma/gradecontent/manipulatives/A
lgebra_Tiles/Algebra_Tiles.html
and manipulate the tiles on the IWB.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
233
2. Solve linear equations
involving one pair of brackets
on one side only.
Students access the following site to practise adding and subtracting like
terms.
http://www.ixl.com/math/practice/grade-8-add-and-subtract-like-terms
Students practise solving equations involving one pair of brackets on one
side by accessing the following site on Level 1.
http://www.waldomaths.com/Equation3NL.jsp
Students play a game of Equation Bingo which involves solving equations
with brackets. The students have a Bingo card each. An equation card is
drawn from a pile, the students work out the equation and cross off the
solution on their bingo card. The winner is the first one to cross off a
complete row or column from their card. The bingo cards and equation
cards are available on worksheets SU18 ad SU19 (solutions A and B only) of
the Teachers’ Resource Pack B1.
Students are given examples, such as the following, and they have to spot
the error. Example:
6x = 2(4 − x)
6x = 8 − 2x
6x − 2x = 8 − 2x + 2x
4x = 8
x=2
3. Use equations to solve
problems.
Students will be able to solve linear
equations involving one pair of brackets
on one side only.
(Level 7.3)
Students will be able to collect like terms
in an expression and will be able to
multiply a single term over a bracket.
(Level 7.2)
Students will be able to collect terms in
an expression involving like terms.
(Level 7.1)
Students will be able to carry out
operations in the correct order (BIDMAS).
(Level 6.3)
Students are given a problem and three equations. They have to identify the
equation that represents the information given in the problem. This
exercise encourages the students to examine their work when they form an
equation from given information.
Students will be able to form and solve
linear equations with one unknown on
both sides involving up to two operations.
(Level 7.3)
Students access the following site to practise writing an equation from
words. http://www.ixl.com/math/algebra-1/write-variable-equations
Students will be able to form and solve
linear equations with one unknown on
one side involving up to two operations.
(Level 7.2)
Students are given cards showing a triangle or quadrilateral. Some cards
show the size of the angles given in terms of x. Other cards show the length
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
234
of the sides given in terms of x. In each case the students are asked to form
an equation and solve it to find the size of each angle or side.
As a conclusion the students identify whether
 the triangle is equilateral, isosceles or scalene;
 the quadrilateral is a square, a rectangle, a kite or neither
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to form and solve
linear equations involving one operation.
(Level 7.1)
Students will be able to form and solve
equations by drawing pictorial
representations, given unknown on one
side and involving up to two operations.
(Level 6.3)
235
Subject:
Unit code and title:
Strand 2:
MATHEMATICS
MTH 8.14 Solving Equations Levels 5.3 – 7.1
Algebra
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Work out the output/input of a number machine.
2. Solve linear equations involving one operation; balance and solve equations pictorially.
Key Words
number machine, input, output,
reverse , addition, subtraction,
multiplication, division,
equation, solve, scales, balance
Points to Note
Resources
FOM B Gold, Students’ Book, Resource
Three main teaching approaches are being recommended to promote a
Pack - Chapter 16.
student centred learning environment.
From Teachers’ laptop:
Exposition: the teacher states the objectives of the lesson and may use ICT C:\Documents and settings\teacher\My
software for students to practise new knowledge. This is consolidated by Documents\Maths Excel Lessons
setting students tasks that offer students the opportunity to apply Function Machines
mathematics to a variety of real life situations.
IWB
Discovery: the teacher can set group tasks in which students discuss and ilearn maths toolbox (the Number
construct mathematical knowledge. Students may become active learners Machine in the Numbers toolbox)
while testing hypotheses and/or making generalisations.
Algebra tiles
Exploration: the teacher integrates an inquiry based learning approach that
enhances the students’ understanding of concepts. These tasks might
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Internet Links:
http://www.teacherled.com
http://teams.lacoe.edu
http://nrich.maths.org
http://nlvm.usu.edu/
http://mathbits.com
http://mathsnet.net/
236
Teaching Objective
The teacher will teach the
students to:
1. Work out the output/input
of a number machine.
Examples of teaching experiences and activities
Students use Excel Lessons Function Machines (lessons 1 to 3) to practise
finding the output of number machines.
Students work out the input/output of a number machine on the IWB using
ilearn maths toolbox (Numbers toolbox - Function Machines)
Students identify the rule and predict the input/output of the number
machine illustrated on the site
http://www.teacherled.com/resources/functionmachine/functionmachinelo
ad.html
Students work out the input/output of a number machine on the following
sites (levels 3-4 and 5-6):
http://teams.lacoe.edu/documentation/classrooms/amy/algebra/34/activities/functionmachine/functionmachine3_4.html
http://teams.lacoe.edu/documentation/classrooms/amy/algebra/56/activities/functionmachine/functionmachine5_6.html
Indicators of Learning outcomes
Students will be able to work out the
output/input of number machines
involving up to two operations.
(Level 7.1)
Students will be able to work out the
output/input of number machines
involving one operation.
(Level 6.3)
Students will be able to work out the
output of number machines involving one
operation.
(Level 6.2)
Students will be able to work out the
output of number machines involving one
operation from addition or subtraction.
(Level 6.1)
Students will be able to understand the
terms input, output and reverse
More able students may attempt working the output of a number machine
operation.
involving multiple operations on “The Number Crunching Machine” available (Level 5.3)
on the site http://nrich.maths.org/1870
2. Solve linear equations
involving one operation;
balance and solve equations
pictorially.
Students use the Math tool: Algebra Balance Scales, to click and drag
quantities to balance beam pans representing an equation.
http://nlvm.usu.edu/en/nav/frames_asid_201_g_4_t_2.html
The students may use this Math tool to create a balance representing their
own equation.
Students access the following sites to practise balancing equations
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to solve linear
equations involving one operation.
(Level 7.1)
Students will be able to solve equations
by drawing scales, given unknown on one
side and involving up to two operations.
237
pictorially. http://www.mathsisfun.com/algebra/add-subtract-balance.html
Algebra Tiles may be used to solve equations in one unknown.
 The Algebra Tiles template is available on the site:
http://mathbits.com/MathBits/AlgebraTiles/AlgebraTiles.htm
to produce their own tiles;
 The students can access the site:
http://go.hrw.com/math/midma/gradecontent/manipulatives/A
lgebra_Tiles/Algebra_Tiles.html
and manipulate the tiles on the IWB.
Students practise solving equations on the following interactive site. Level
1 provides examples related to this teaching objective.
http://mathsnet.net/algebra/l4_equation.html
The students play a domino game in groups. Each domino consists of an
equation on one side and a solution of another equation on the other side.
The students have to match the equation on one domino to its solution on
another domino.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
(Level 6.3)
Students will be able to solve equations
by drawing scales, given unknown on one
side and involving one operation.
(Level 6.2)
Students will be able to solve equations
by drawing scales, given unknown on one
side and involving one operation
(addition or subtraction).
(Level 6.1)
Students will be able to understand that
the left side and the right side of a
balanced scale represent equal amounts.
(Level 5.3)
238
Subject:
Unit code and title:
Strand 2:
MATHEMATICS
MTH 8.14 Solving Equations (Levels 1 – 4)
Algebra
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Work out the output/input of a number machine.
2. Solve linear equations involving one operation; balance and solve equations pictorially.
Objectives at levels of attainment 1,2,3,4.
The teacher will teach the students to:
1.1 Work out the end result and the pattern rule that is leading to that result.
1.2 Work out the value of the missing letter in simple equations both in writing and pictorially.
Key Words
Points to Note
Resources
number machine, input, output,
reverse , addition, subtraction,
multiplication, division,
equation, solve, scales, balance
In addition to the points to note recommended for students performing at
Level 5 or higher, it is very important for the teacher to allow time for the
students to respond. This response can take the form of unaided and/or
aided means of communication and the teacher needs to provide adequate
scaffolding techniques to enable the students to respond affectively or
intentionally.
New Maths Frame Working Step Up
Workbook.
Oxford Framework Maths 7
For further examples about level 1 refer to the handbook.
From Teachers’ laptop:
C:\Documents and settings\teacher\My
Documents\Maths Excel Lessons
Function Machines
IWB
ilearn maths toolbox (the Number
Machine in the Numbers toolbox)
Internet Links:
See below in examples.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
239
Teaching Objective
Examples of teaching experiences and activities
Indicators of Learning outcomes
The teacher will teach the
students to:
Starter: The teacher will put a statement for exploration, e.g. I think of a
number, multiply it by 2, what is this number?
1. Work out the end result and
the pattern rule that is
leading to that result.
Students will work with the function machine on the ilearn software. They
decide the input number and the rule and work out the answer.
Students will be able to work out the
output of number machine involving the
four rules up to one operation.
(Level 4)
Students will follow short instructions like take one, add one, give one.
Students will match the same number machines together, e.g. 1+1=2 with
the same equation.
Students will respond to adult instructions:
http://www.teacherled.com/resources/functionmachine/functionmachinelo
ad.html
Students work out the input/output of a number machine on the following
sites
http://teams.lacoe.edu/documentation/classrooms/amy/algebra/34/activities/functionmachine/functionmachine3_4.html
http://teams.lacoe.edu/documentation/classrooms/amy/algebra/56/activities/functionmachine/functionmachine5_6.html
2.1 Work out the value of the
missing letter in simple
equations both in writing
and pictorially.
Starter: Students are given simple statements and they have to discuss them
in pairs.
The students play a domino game in groups. Each domino consists of an
equation on one side and a solution of another equation on the other side.
The students have to match the equation on one domino to its solution on
another domino.
The above activity will be adapted to be used on a balance scale and the
students have to use counting on to find the missing quantity.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to work out the
output of number machine involving one
operation from addition or subtraction.
(Level 3)
Students will be able to match the same
equations together.
(Level 2)
Students will be able to produce
something following an action e.g. smile.
(Level 1)
Students will be able to solve linear
equations involving one operation.
(Level 4)
Students will be able to solve equations
by drawing scales, given unknown on one
side and involving counting on to find the
unknown quantity.
(Level 3)
240
The above activity will be further adapted to the level that students need
only match the missing quantity on the scale so it balances.
Students will put and remove objects on and from a scale.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to solve equations
by matching quantities on scales.
(Level 2)
Students will be able to observe their
hand whilst grabbing and removing or
putting objects on a scale. (Level 1)
241
Subject:
Unit code and title:
Strand 2:
MATHEMATICS
MTH 8.15 Coordinates and straight line graphs (Levels 7.1 – 8.1)
Algebra
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Understand that the equation of a straight-line describes the relationship between the x and y coordinates, given the line-graph or the
coordinates.
2. Use the equation of a straight-line to generate a sequence of ordered pairs and plot them to produce its graph.
3. Understand what is meant by ‘the gradient of a line’ and find the gradient from the graph. (Restrict to positive gradients)
4. Interpret information presented in a variety of linear graphs; use and draw conversion graphs.
Key Words
Graph, co-ordinates, x
coordinate and y coordinate,
quadrant, ordered pairs, grid,
negative, positive, straight line,
linear, axes, scale, equation,
gradient, steepness, table of
values, y-intercept, conversion
graph, speed, distance, time,
distance-time graph, travel
graph.
Points to Note
Resources
FOM B2, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to promote a
Resource Pack – Chapters 1, 8 and 11.
student centred learning environment.
From Teachers’ laptop:
Exposition: the teacher states the objectives of the lesson and may use ICT C:\Documents and Settings\teacher\My
software for students to practise new knowledge. This is consolidated by Documents\Maths Excel Lessons
setting students tasks that offer students the opportunity to apply
mathematics to a variety of real life situations.
Internet Links:
http://www.cimt.plymouth.ac.uk
Discovery: the teacher can set group tasks in which students discuss and http://www.mathsisfun.com
construct mathematical knowledge. Students may become active learners http://graphs.mathwarehouse.com
while testing hypotheses and/or making generalisations.
Exploration: the teacher integrates an inquiry based learning approach that
enhances the students’ understanding of concepts. These tasks might
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
242
Teaching Objective
Examples of teaching experiences and activities
Indicators of Learning outcomes
The teacher will teach the
students to:
Teacher to start off by showing just the graph of y = 2x on the interactive
white board. Students to write down the coordinates of as many points as
possible that lie on the line - say (1,2); (0,0); (-4,-8). Teacher to ask students
whether they can notice a pattern, that is that the y co-ordinate is twice the
x co-ordinate. Other tasks can include filling a missing co-ordinate in an
ordered pair or giving the value of y when x = 6 and finding the value of x
when y = 0.5. Finally teacher leads students to convert the relationship
between the x and y coordinates into the equation y = 2x. Repeat with other
examples of graphs of the type y = x + c, y = mx + c, y = c and x = c.
Worksheets ws3S and ws 4E from the resource pack may be useful.
Students will be able to find the equation
of a straight line graph given the coordinates of any two points on the line.
(Level 8.1)
1. Understand that the
equation of a straight-line
describes the relationship
between the x and y
coordinates, given the linegraph or the coordinates,
For revision purposes or as an exercise, the teacher may access:
http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i14/bk8_14i2.
htm
2. Use the equation of a
straight-line to generate a
sequence of ordered pairs
and plot them to produce its
graph.
The equation of a line (e.g. y = 2x + 1) tells us how to find a y-coordinate
using an x-coordinate. We can find the coordinates of several points on a
line by picking x values and working out the corresponding y values.
Example Question: A line has equation y = 2x + 1.
Using x values from –2 to +3, plot the graph of this equation.
The first stage is to draw up a table of x values and work
out the y values using the equation:
x
–2 –1 0 1 2 3
y = 2x + 1
–3 –1 1 3 5 7
Next, each pair of x and y values can be plotted on the graph
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to find the equation
of a straight line graph given the coordinates of many points on the line.
(Level 7.3)
Students will be able to find the equation
of the form y = mx + c given a simple linegraph.
(Level 7.2)
Students will be able to find the equation
of a straight line graph of the form y = mx
given a simple line-graph.
(Level 7.1)
Students will be able to draw the graph of
a linear equation given in the form
y = mx+ c
(Level 8.1)
Students will be able to draw the graph of
a linear equation given in the form y = mx
(Level 7.3)
Students will be able to draw the graph of
a linear equation given in the form
y=x+c
(Level 7.2)
243
as coordinates. In this case the coordinates are: ( –2 , –3 ) ,
( –1 , –1 ) , ( 0 , 1 ) , ( 1 , 3 ) , ( 2, 5 ) and ( 3 , 7 ).
Finally the points are joined with a straight line running all the way across
the graph. Other examples to follow.
Students will be able to understand that a
linear equation can be represented as a
straight line on a coordinate grid.
(Level 7.1)
Use Maths excel lessons: “Straight line” as an interactive exercise as well as
a Computer Algebra Software (CAS) such as Derive to plot the graphs of any
given linear equations.
http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i14/bk8_14i3.htm
3. Understand what is meant by
‘the gradient of a line’ and
find the gradient from the
graph. (Restrict to positive
gradients)
Teacher to show Maths excel lessons: “Dynamic gradient” on the Interactive
white board. The teacher asks students to move the ‘gradient’ slider and
investigate how the steepness of the graph changes as m (when in the form
y = m x + c) increases/decreases and by moving the ‘y-intercept’ slider while
keeping the gradient constant will produce graphs which are equally
inclined.
Teacher to point out that in mathematics we use the word gradient to mean
the steepness of a line.
Students are encouraged to investigate what a gradient of 3 means, that is
there is a vertical rise of 3 units for every unit change in the horizontal.
Teacher to plot he graphs of y = 2x and y = 2x + 3 on the interactive white
board.
With a number of triangles drawn under each line, students to calculate the
gradient as the opposite side divided by the adjacent side and to see that
the resulting gradient is always 2. Students to practice with other lines.
Teacher may make use of worksheet ws6S from the teacher’s resource pack.
Through a whole class discussion the following facts are brought up:
Given that the x and y axis are drawn using the same scale:
 A line with an angle of 45 to the horizontal, gradient = 1
 A line with an angle > 45 to the horizontal, gradient >1
 A line with an angle < 45 to the horizontal, gradient <1
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to find the gradient
of a line from any two points on the line
and sketch a line given the gradient.
(Level 8.1)
Students will be able to identify whether
a line has a gradient equal to 1, less than
1 or equal to 1.
(Level 7.3)
Students will be able to calculate the
gradient of a line using the triangle
method.
(Level 7.2)
Students will be able to understand the
meaning of ‘the gradient of a line’.
(Level 7.1)
244
Teacher can also make use of a CAS to help reinforce the concept of the
gradient of a line.
Use the following site to explore the properties of a straight line graph
http://www.mathsisfun.com/data/straight_line_graph.html
4. Interpret information
presented in a variety of
linear graphs; use and draw
conversion graphs.
This lesson is based around an interactive web page that creates distance vs.
time graphs in real time – available at:
http://graphs.mathwarehouse.com/lab/distance-time-interactive-parntersactivity.php
The web page works by having a person move a ship across the screen and
the page creates the distance time graph in real time. The second person in
the activity is supposed to try to emulate the same graph with a second ship
that he or she must move across the screen.
This lesson is all done by the students online in the computer lab. Divide the
students into pairs.
Students will be able to interpret the
relationship between two journeys
represented on one travel graph.
(Level 8.1)
Students will be able to interpret the
gradient of real-life linear graphs.
(Level 7.3)
Students will be able to read distance
travelled and time taken from a travel
graph.
(Level 7.2)
Students will be able to draw and
interpret a conversion graph.
(Level 7.1)
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
245
Subject:
MATHEMATICS
Unit code and title: MTH 8.15 Coordinates and straight line graphs (Levels 6.3 – 7.3)
Strand 2:
Algebra
Form 2
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Read and plot co-ordinates using ordered pairs in all four quadrants.
2.
Understand that the equation of a straight-line describes the relationship between the x and y coordinates, given the line-graph or the
coordinates.
3. Use the equation of a straight-line to generate a sequence of ordered pairs and plot them to produce its graph.
4. Interpret information presented in a variety of linear graphs; use and draw conversion graphs.
Key Words
Graph, co-ordinates, x
coordinate and y coordinate,
quadrant, ordered pairs, grid,
negative, positive, straight line,
linear, axes, scale, equation,
gradient, steepness, table of
values, y-intercept, conversion
graph, speed, distance, time,
distance-time graph, travel
graph.
Points to Note
Resources
FOM B1, Students’ Book, Practice Book,
Three main teaching approaches are being recommended to promote a
Resource Pack – Chapters 1, 8 and 11.
student centred learning environment.
Exposition: the teacher states the objectives of the lesson and may use ICT From Teachers’ laptop:
software for students to practise new knowledge. This is consolidated by C:\Documents and Settings\teacher\My
setting students tasks that offer students the opportunity to apply Documents\Maths Excel Lessons
mathematics to a variety of real life situations.
Internet Links:
Discovery: the teacher can set group tasks in which students discuss and http://www.cimt.plymouth.ac.uk
construct mathematical knowledge. Students may become active learners http://www.studyzone.org
while testing hypotheses and/or making generalisations.
Exploration: the teacher integrates an inquiry based learning approach that
enhances the students’ understanding of concepts. These tasks might
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
246
Teaching Objective
The teacher will teach the
students to:
1. Read and plot co-ordinates
using ordered pairs in all
four quadrants.
Examples of teaching experiences and activities
The teacher should first revise the idea behind coordinates as a
mathematical way of showing the position of an object or a point in a plane
in relation to a fixed point, which we call the origin. The first quadrant (form
1) will now be extended to include all the four quadrants which should bring
to mind the number line with both the negative and positive values.
Indicators of Learning outcomes
Students will be able to draw both axes;
use ordered pairs to identify and plot
points in all four quadrants including
decimal values.
(Level 7.3)
Students are shown a grid for values of x and y between -10 and 10 on the
IWB which can be accessed from the Gallery/Mathematics/Mathematical
papers. Some students will be asked to plot the following points: (-8,-3), (-4,1), (-2,0), (0,1), (2,2), (10,6). The students should notice that these points are
on a straight line. The teacher to draw this line using a different colour and
the students to mark and write down the coordinates of other points which
lie on the line.
Students will be able to use ordered pairs
to identify and plot points in all four
quadrants including decimal values.
(Level 7.2)
Use these sites to practice plotting in all four quadrants
http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i3/bk7_3i4.htm
http://www.studyzone.org/mtestprep/topic6.cfm?TopicID=239
2. Understand that the
equation of a straight-line
describes the relationship
between the x and y
coordinates, given the linegraph or the coordinates.
Teacher to start off by showing just the graph of y = 2x on the interactive
white board. Students to write down the coordinates of as many points as
possible that lie on the line - say (1,2); (0,0); (-4,-8). Teacher to ask students
whether they can notice a pattern, that is that the y co-ordinate is twice the
x co-ordinate. Other tasks can include filling a missing co-ordinate in an
ordered pair or giving the value of y when x = 6 and finding the value of x
when y = 0.5. Finally teacher leads students to convert the relationship
between the x and y coordinates into the equation y = 2x. Repeat with other
examples of graphs of the type y = x + c, y = mx + c, y = c and x = c.
Worksheets ws3S and ws 4E from the resource pack may be useful.
For revision purposes or as an exercise, the teacher may access:
http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i14/bk8_14i2.
htm
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to plot points in all
four quadrants excluding decimal values.
(Level 7.1)
Students will be able to identify points in
all four quadrants.
(Level 6.3)
Students will be able to find the equation
of a straight line graph given the coordinates of many points on the line.
(Level 7.3)
Students will be able to find the equation
of the form y = mx + c given a simple linegraph.
(Level 7.2)
Students will be able to find the equation
of a straight line graph of the form y = mx
given a simple line-graph.
(Level 7.1)
Students will be able to understand that a
247
3. Use the equation of a
straight-line to generate a
sequence of ordered pairs
and plot them to produce its
graph.
The equation of a line (e.g. y = 2x + 1) tells us how to find a y-coordinate
using an x-coordinate. We can find the coordinates of several points on a
line by picking x values and working out the corresponding y values.
linear relationship between the x and y
coordinates can be represented as a
graph on a coordinate grid.
(Level 6.3)
Students will be able to draw the graph of
a linear equation given in the form y = mx
(Level 7.3)
Example Question: A line has equation y = 2x + 1.
Using x values from –2 to +3, plot the graph of this equation.
The first stage is to draw up a table of x values and work
out the y values using the equation:
Students will be able to draw the graph of
a linear equation given in the form
y=x+c
(Level 7.2)
x
–2 –1 0 1 2 3
y = 2x + 1
–3 –1 1 3 5 7
Next, each pair of x and y values can be plotted on the graph
as coordinates. In this case the coordinates are: ( –2 , –3 ) ,
( –1 , –1 ) , ( 0 , 1 ) , ( 1 , 3 ) , ( 2, 5 ) and ( 3 , 7 ).
Finally the points are joined with a straight line running all the way across
the graph. Other examples to follow.
Students will be able to understand that a
linear equation can be represented as a
straight line on a coordinate grid.
(Level 7.1)
Students will be able to use the equation
of a straight-line to generate a sequence
of ordered pairs.
(Level 6.3)
Use Maths Excel lessons: “Straight line” as an interactive exercise as well as
a Computer Algebra Software (CAS) such as Derive to plot the graphs of any
given linear equations.
http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i14/bk8_14i3.htm
4. Interpret information
presented in a variety of
linear graphs; use and draw
conversion graphs.
Teacher to present an example of a shop which accepts both euro and
sterling. A sign outside a shop reads - Sterling accepted: £1 = €1.5. Using a
calculator or otherwise, students will then complete a table of values for £0,
£10, £20,…,£100 into euro which will be used to plot and draw a graph.
Students will be then shown how to use the graph to convert between euro
and sterling for intermediate values like £24 into euro and €128 into
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to interpret the
gradient of real-life linear graphs.
(Level 7.3)
Students will be able to read distance
travelled and time taken from a travel
248
sterling. More challenging questions can include converting values greater
than £100 and €150, and what would happen to the graph when the
exchange rate changes.
Use this site as an interactive exercise using conversion graphs
http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i3/bk7_3i6.htm
graph.
(Level 7.2)
Students will be able to draw and
interpret a conversion graph.
(Level 7.1)
Students will be able to convert values,
including decimal values beyond the
ranges in the conversion graph.
(Level 6.3)
Subject:
MATHEMATICS
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Form 2
249
Unit code and title: MTH 8.15 Coordinates and straight line graphs (Levels 5.3 – 7.1)
Strand 2:
Algebra
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Read and plot co-ordinates using ordered pairs in all four quadrants; draw lines and shapes given the coordinates of their endpoints/vertices.
2. Generate and plot ordered pairs that satisfy a simple linear rule; generate a sequence of ordered pairs and plot them to produce straight line graphs.
3. Plot and interpret information presented in a variety of linear graphs.
Key Words
Graph, co-ordinates, x
coordinate and y coordinate,
quadrant, ordered pairs, grid,
negative, positive, straight line,
axes, scale, equation, table of
values, conversion graph,
vertex.
Points to Note
Resources
FOM B Gold, Students’ Book, Practice
Three main teaching approaches are being recommended to promote a
Book, Resource Pack – Chapters 1 and 8.
student centred learning environment.
From Teachers’ laptop:
Exposition: the teacher states the objectives of the lesson and may use ICT C:\Documents and Settings\teacher\My
software for students to practise new knowledge. This is consolidated by Documents\Maths Excel Lessons
setting students tasks that offer students the opportunity to apply
mathematics to a variety of real life situations.
Internet Links:
http://www.cimt.plymouth.ac.uk
Discovery: the teacher can set group tasks in which students discuss and http://www.studyzone.org
construct mathematical knowledge. Students may become active learners http://www.woodlandswhile testing hypotheses and/or making generalisations.
junior.kent.sch.uk
Exploration: the teacher integrates an inquiry based learning approach that
enhances the students’ understanding of concepts. These tasks might
employ the processes of reasoning, problem solving, investigations,
connecting ideas and concepts, and expressing results by using the precise
language of mathematics.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
250
Teaching Objective
The teacher will teach the
students to:
1. Read and plot co-ordinates
using ordered pairs in all
four quadrants; draw lines
and shapes given the
coordinates of their
endpoints/vertices.
Examples of teaching experiences and activities
The teacher should first revise the idea behind coordinates as a
mathematical way of showing the position of an object or a point in a plane
in relation to a fixed point, which we call the origin. The first quadrant (form
1) will now be extended to include all the four quadrants which should bring
to mind the number line with both the negative and positive values.
Use these sites to practice plotting in all four quadrants
Indicators of Learning outcomes
Students will be able to plot points in all
four quadrants.
(Level 7.1)
Students will be able to identify points in
all four quadrants.
(Level 6.3)
http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i3/bk7_3i4.htm
http://www.studyzone.org/mtestprep/topic6.cfm?TopicID=239
http://www.woodlands-junior.kent.sch.uk/maths/shapes/coordinates.html
Students will be able to plot points in the
first quadrant including points on the
lines x = 0 and y = 0.
(Level 6.2)
Students will be able to identify points in
the first quadrant excluding those on the
lines x = 0 and y = 0.
(Level 6.1)
2. Generate and plot ordered
pairs that satisfy a simple
linear rule; generate a
sequence of ordered pairs
and plot them to produce
straight line graphs.
The teacher will show a grid for values of x and y between -10 and 10 on the
IWB which can be accessed from the Gallery/Mathematics/Mathematical
papers. Some students will be asked to plot the following points:
coordinates x
y
(-3,-6)
-3
-6
(-2,-4)
-2
-4
(0,0)
0
0
(4,8)
4
8
(5,10)
5
10
The students should notice that when joined these points form a straight
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to identify objects in
the first quadrant excluding those on the
lines x = 0 and y = 0.
(Level 5.3)
Students will be able to understand that a
linear equation can be represented as a
straight line on a coordinate grid.
(Level 7.1)
Students will be able to use the equation
of a straight-line to generate a sequence
of ordered pairs.
(Level 6.3)
Students will be able to draw a straight
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line. The teacher to draw this line using a different colour and the students
to mark and write down the coordinates of other points which lie on the
line.
Teacher to help students identify the relationship between the y and the x
value in each ordered pair. In this case, the y value is twice the x value.
Therefore we can say that y = 2x.
So the line drawn represents the equation y = 2x
line given a number of ordered pairs.
(Level 6.2)
Students will be able to generate a
sequence of ordered pairs given a simple
linear rule.
(Level 6.1)
More similar examples of the form y = mx and y = x + c to follow.
3. Plot and interpret
information presented in a
variety of linear graphs.
Students will be able to complete a
simple linear sequence of ordered pairs.
(Level 5.3)
Teacher to present an example of a shop which accepts both euro and
Students will be able to draw and
sterling. A sign outside a shop reads - Sterling accepted: £1 = €1.5. Using a
interpret a conversion graph.
calculator or otherwise, students will then complete a table of values for £0, (Level 7.1)
£10, £20,…,£100 into euro which will be used to plot and draw a graph.
Students will be then shown how to use the graph to convert between euro Students will be able to convert values,
and sterling for intermediate values like £24 into euro and €128 into
including decimal values beyond the
sterling. More challenging questions can include converting values greater
ranges in the conversion graph.
than £100 and €150.
(Level 6.3)
Use this site as an interactive exercise using conversion graphs:
http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i3/bk7_3i6.htm
Students will be able to convert values,
including decimal values but restricted to
the ranges in the conversion graph.
(Level 6.2)
Students will be able to convert values,
excluding decimal values and restricted to
the ranges in the conversion graph.
(Level 6.1)
Subject:
MATHEMATICS
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Students will be able to read the distance
travelled and time taken from a ‘one line’ travel graph. (Level 5.3)
Form 2
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Unit code and title: MTH 8.15 Coordinates & Graphs (Levels 1 – 4)
Strand 2:
Algebra
Unit Duration: 9 sessions of 40 minutes (6 hours)
Objectives
The teacher will teach the students to:
1. Read and plot co-ordinates using ordered pairs in all four quadrants; draw lines and shapes given the co-ordinates of their
endpoints/vertices.
2. Generate and plot ordered pairs that satisfy a simple linear rule; generate a sequence of ordered pairs and plot them to produce straight-line
graphs.
3. Plot and interpret information presented in a variety of linear and non-linear graphs.
Objectives at attainment levels 1, 2, 3 and 4.
The teacher will teach the students to:
1.1 Find and place objects according to their coordinates and join the points to form a shape.
2.1 use their mathematical knowledge of doubling or halving or counting to generate points and plot them.
3.1 get information from a given grid.
Key Words
Points, place, join, find, mark.
Teaching Objective
Points to Note
In addition to the points to note recommended for students
performing at Level 5 or higher, it is very important for the teacher
to allow time for the students to respond. This response can take
the form of unaided and/or aided means of communication and the
teacher needs to provide adequate scaffolding techniques to enable
the students to respond effectively or intentionally.
Resources
New Maths Frame Working-Step
Up Workbook.
Oxford Framework Maths 7
For further material at level 1 please refer to handbook.
From Teachers’ laptop:
C:\Documents and
Settings\teacher\My
Documents\Maths Excel Lessons
Examples of Teaching Experiences and Activities
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
Software: Ilearn Maths
Calculator
Indicators of Learning Outcomes
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The teacher will teach the
students to:
1.1 Find and place objects
according to their coordinates
and join the points to form a
shape.
Starter: Teacher shows a grid (battleship style) and she asks
particular questions to test whether the students have the prerequisite knowledge needed for the lesson.
Students are shown a grid with pictures in particular squares
and the students have to answer the question….’what is in each
square? An add on would be that the students have to put in
something in the location they are given. Furthermore, they
have to find the location of the object given.
At level 3, the above activity can be adapted in such a way that
the students point to the named object, say the box number
and if they have letter recognition they might say the letter too.
At level 2, the students will simply point to the requested object
and given the same pictures they find their position on the grid
through matching. In addition, students are given a grid with
the shapes in shadow form. They have to follow draw the
outline and count how many boxes they have moved from one
point to the next.
2.1 Use their mathematical
knowledge of doubling or halving
or counting to generate points
and plot them.
Students will be able to locate and read
the position, of an object and name it.
Or else they are given the position and
have to place an object on the grid.
(Level 4)
Students will be able to follow a given
path, count how many steps they have
moved and locate the position of the
named object and read the box
number.
(Level 3)
Students will find the position of a
requested object by pointing and then,
through matching, find same shapes or
objects on a given grid.
(Level 2)
Students will be able to focus on a
particular picture for a short period of
time and confirm this by selecting it
through sensory experiences.
(Level 1)
At level 1, the students can use the ilearn software on a touch
screen and they will touch on particular boxes as instructed and
guided by the teacher/LSA.
http://www.woodlandsjunior.kent.sch.uk/maths/shapes/coordinates.html#Coordinates
Starter: Teacher will test knowledge of halving, doubling, and
Students will to able to use and apply
sequences.
previous mathematical knowledge like
doubling, halving and counting on in
Teacher and students are involved in different games like,
the same rule to form points.
doubling whereby the teacher gives a number and the students (Level 4)
double it. They find and mark the point on the graph. After a
series of points, they join the points to form a line.
Students will be able to press the arrow
Students are given the points and they can programme objects
buttons on the beebot or any similar
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
254
like the beebot to move accordingly.
Students will draw the points indicated by the teacher/LSA
through one finger painting and then finger paint movement to
join the dots and form a line.
Students will observe and join in activities at Level 2 through
hand holding and guidance by the adult.
3.1 Get information from a given
grid.
Starter: Teacher tells out some instructions for the students to
follow. She can assess whether they can carry them out or not.
Students are given a room design with furnishing on a grid. They
have to locate which item is in a particular point. On the other
hand, they are given the object and they have to tell its location
point.
Students will locate the object by drawing a circle around it or
else colour it.
Students will be using the same grid to find the objects shown
on a card through matching.
Students are shown three pictures at each point of a Perspex
rectangle and the students get information through scanning
and eye gaze.
Directorate for Quality and Standards in Education - Curriculum Management and eLearning Department – MATHEMATICS – 2012
tool so it moves accordingly.
(Level 3)
Students will be able to paint on the
indicated point and then follow a path
of points to form a line. (Level 2)
Students will be able to follow their
hand movement to perform an action.
(Level 1)
Students will be able to read and share
information from a grid.
(Level 4)
Students will be able to find the
requested object from a group of
objects.
(Level 3)
Students will be able to find the
requested information through
matching.
(Level 2)
Students will scan a number of objects
and focus momentarily on the
requested object.
(Level 1)
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