Maths K–6
Stage 3B
Stage 3B – Unit 17
Number
Fractions and Decimals
Entry 1: Equivalent Fractions
This booklet includes:
• Teacher notes
(to be detached before sending to the student and supervisor)
• Supervisor notes
• Student and supervisor guide
P/M 3B 43862
Centre for Learning Innovation
Number: 43682
Title: Using Maths Tracks Stage 3B Unit 17
This publication is copyright New South Wales Department of Education and Training (DET), however it may contain
material from other sources which is not owned by DET. We would like to acknowledge the following people and
organisations whose material has been used:
Extracts from Mathematics Syllabus Years K-6 © Board of Studies, NSW 2002
Teacher notes p 5,
Supervisor notes p 5
Screenshots of Word used by permission from Microsoft Corporation
Student and
supervisor guide
pp 7-9
Maths Tracks Teacher’s Resource Book, Harcourt Education, 1st ed., 2004, by Trish
Leigh and Jennifer Vincent.
Maths Tracks Student Book, Harcourt Education, 1st ed., 2004, by Trish Leigh and
Jennifer Vincent.
The copyright in the Maths Tracks material is vested in the publisher, Reed
International Books Australia Pty Ltd, trading as Harcourt Education Australia.
Maths Tracks for NSW has been published under the Rigby imprint and the series
covers seven stages from Early Stage 1 to Stage 3B. Each stage has a Teacher’s
Resource Book, Student Book and Homework Book.
For professional development and support, view online at
www.rigby.com.au/pd/event.asp
COMMONWEALTH OF AUSTRALIA
Copyright Regulations 1969
WARNING
This material has been reproduced and communicated to you on behalf of
the
New South Wales Department of Education and Training
(Centre for Learning Innovation)
pursuant to Part VB of the Copyright Act 1968 (the Act).
The material in this communication may be subject to copyright under
the Act. Any further reproduction or communication of this material by
you may be the subject of copyright protection under the Act.
CLI Project Team acknowledgement:
Writer:
Editors:
Illustrator:
Desktop publishing:
Jillian James
Maree Camilleri, Alan Barnes, Rae Lister
David Stanley
Esta Tserpes
All reasonable efforts have been made to obtain copyright permissions. All claims will be settled in good faith.
Published by
Centre for Learning Innovation (CLI)
51 Wentworth Rd
Strathfield NSW 2135
________________________________________________________________________________________________
Copyright of this material is reserved to the Crown in the right of the State of New South Wales. Reproduction or
transmittal in whole, or in part, other than in accordance with provisions of the Copyright Act, is prohibited without
the written authority of the Centre for Learning Innovation (CLI).
© State of New South Wales, Department of Education and Training 2005.
Stage 3B – Unit 17
These Teacher notes support ‘Using Maths Tracks’. The teacher should detach them
before sending the Supervisor notes and the Student and supervisor guide to the
supervisor and student. They contain:
•
•
•
•
•
•
•
•
•
•
Student outcomes
Prior knowledge
Language
What is needed
Preparation
Interactivity
Resources (including websites)
Returns
Checking up answers
Assessment record
Student outcomes
Outcomes from the Mathematics K–6 Syllabus, © Board of Studies NSW 2002
Number
NS3.4
Fractions and Decimals
Compares, orders and calculates with decimals, simple fractions and
simple percentages
Working Mathematically
WMS3.2
Applying Strategies
Selects and applies appropriate problem-solving strategies, including
technological applications, in undertaking investigations
WMS3.3
Communicating
Describes and represents a mathematical situation in a variety of ways
using mathematical terminology and some conventions
WMS3.4
Reasoning
Gives a valid reason for supporting one possible solution over another
Students will learn about:
•
finding equivalent fractions using diagrams and number lines by re-dividing the unit
Prior knowledge
•
•
Modelling thirds, sixths and twelfths of a whole object or collection of objects
Placing thirds, sixths or twelfths on a number line between 0 and 1 to develop
equivalence
Language
equivalent, fraction, denominator, numerator, vertically, horizontally
Using Maths Tracks, Stage 3B, Unit 17
1
Teacher notes
What is needed
Activity 2
•
Microsoft Word, if available
Activity 3
•
Maths Tracks Student Book Stage 3B, pages 55
Activity 4
•
Maths Tracks Student Book Stage 3B, page 56
Activity 5
•
Working backwards problem-solving poster
•
counters (optional)
•
computer (optional)
Activity 6
•
calculator (optional)
Maths Tracks Homework Book Book Stage 3B, page 17 (if you are using it)
Preparation
Select the activities you think suitable for the student by ticking the boxes beside the
activity numbers in the Student and supervisor guide.
Introduction (explicit teaching) – for all students
Activity 1 (beginning) – can provide extra support
Activity 2 (additional assistance) – can provide extra support
Activity 3 (consolidating) – for all students
Activity 4 (establishing) – for all students
Activity 5 (problem solving) – can provide extra challenge
Activity 6 (extension) – can provide extra challenge
Reflection – for all students
Checking up – for all students
Introduction: Look at the online dictionary A Maths Dictionary for Kids
<www.teachers.ash.org.au/jeather/maths/dictionary.html>
and decide if you would direct your students or supervisors to terms such as fraction,
numerator and denominator for this unit. Go to ‘Ee’ for ‘equivalent fraction’ to see
‘equivalent’ defined as ‘having the same value or amount’. Direct students to the
equivalent fraction matching game where they can click and drag to make equivalent
fractions on a fraction wall.
Activity 2: For students without a computer, Student sheet 3 has been provided as an
alternative.
Reflection: Students are asked to halve a recipe for anzac biscuits. They can make the
biscuits if their supervisor allows them, but this is not required to be able to complete the
activity.
Using Maths Tracks, Stage 3B, Unit 17
2
Teacher notes
Interactivity
Introduction: You could use satellite lessons or teleconferences to:
•
revise with students the meaning of the terms fraction, numerator and
denominator.
•
discuss with your students the fact that when fractions are shown in diagrams, the
equal parts are not always drawn but assumed to be there. For example, these two
diagrams show a quarter.
•
•
ask students to explain what an equivalent fraction is and ask them to show why
different examples are or are not equivalent.
demonstrate how they re-divide shapes or the number line to find sixths and
twelfths.
Activity 5: Your students could use telephone or email to discuss the problem with
another student. Have students talk about the different strategies they can use to solve
the problem and their advantages and disadvantages. Discuss why the problem needs to
be worked backwards to find the solution.
Activity 6: Students could discuss the strategies they used to solve the puzzle and
check it.
Reflection: Ask students to talk about the ways equivalent fractions are used in
everyday situations and why.
Resources
Add any you find suitable.
Websites
Check all websites before recommending them to students.
Add any others you find suitable.
Using Maths Tracks, Stage 3B, Unit 17
3
Teacher notes
Returns
Student sheet 1b – Equivalent fractions – Introduction
Student sheet 2b – More equivalent fractions – Activity 1
Student sheet 3 or printed Word document – Activity 2
Student sheet 4 – Swap card fractions – Activity 5
Checking up sheet
personal tape or recording – Introduction, Activities 5, 6, Reflection, Checking up
Supervisor and Student Feedback sheets
the guide (if you ask for it)
Checking up answers
Students should write six fraction sentences using the symbols =, < or >.
Under each fraction sentence they should draw a diagram or a number line to illustrate
the sentence.
Using Maths Tracks, Stage 3B, Unit 17
4
Teacher notes
Student's name:
Assessment record
Using Maths Tracks, Stage 3B – Unit 17
Number: Fractions and Decimals
Entry 1: Equivalent Fractions
Circle the numbers of the activities the student was asked to complete.
1
2
3
4
5
6
The student:
Activity
Comment
•
finds equivalent fractions using
diagrams and number lines by
re-dividing the unit
(NS3.4)
All
•
calculates unit fractions of a
1
collection e.g. calculate of 30
5
(NS3.4)
5, Reflection
•
explains or demonstrates why
two fractions are or are not
equivalent
(WMS3.4)
Introduction,
Checking up
•
uses problem-solving strategies
including those based on
selecting and organising key
information in a systematic way
(WMS3.2)
5, 6
•
solves problems using strategies
like working backwards
(WMS3.2)
5
•
uses mathematical language to Introduction,
explain mathematical situations
5, 6,
(WMS3.3)
Checking up
Using Maths Tracks, Stage 3B, Unit 17
5
Adapted from: Mathematics K–6 Syllabus, © Board of Studies NSW 2002.
Indicator
Teacher notes
Using Maths Tracks, Stage 3B, Unit 17
6
Teacher notes
Maths K–6
Stage 3B – Unit 17
Number
Fractions and Decimals
Entry 1: Equivalent Fractions
Supervisor notes
and
Student and supervisor guide
P/M 3B 43862
Centre for Learning Innovation
Number: 43682
Title: Using Maths Tracks Stage 3B Unit 17
This publication is copyright New South Wales Department of Education and Training (DET), however it may contain
material from other sources which is not owned by DET. We would like to acknowledge the following people and
organisations whose material has been used:
Extracts from Mathematics Syllabus Years K-6 © Board of Studies, NSW 2002
Teacher notes p 5,
Supervisor notes p 5
Screenshots of Word used by permission from Microsoft Corporation
Student and
supervisor guide
pp 7-9
Maths Tracks Teacher’s Resource Book, Harcourt Education, 1st ed., 2004, by Trish
Leigh and Jennifer Vincent.
Maths Tracks Student Book, Harcourt Education, 1st ed., 2004, by Trish Leigh and
Jennifer Vincent.
The copyright in the Maths Tracks material is vested in the publisher, Reed
International Books Australia Pty Ltd, trading as Harcourt Education Australia.
Maths Tracks for NSW has been published under the Rigby imprint and the series
covers seven stages from Early Stage 1 to Stage 3B. Each stage has a Teacher’s
Resource Book, Student Book and Homework Book.
For professional development and support, view online at
www.rigby.com.au/pd/event.asp
COMMONWEALTH OF AUSTRALIA
Copyright Regulations 1969
WARNING
This material has been reproduced and communicated to you on behalf of
the
New South Wales Department of Education and Training
(Centre for Learning Innovation)
pursuant to Part VB of the Copyright Act 1968 (the Act).
The material in this communication may be subject to copyright under
the Act. Any further reproduction or communication of this material by
you may be the subject of copyright protection under the Act.
CLI Project Team acknowledgement:
Writer:
Editors:
Illustrator:
Desktop publishing:
Jillian James
Maree Camilleri, Alan Barnes, Rae Lister
David Stanley
Esta Tserpes
All reasonable efforts have been made to obtain copyright permissions. All claims will be settled in good faith.
Published by
Centre for Learning Innovation (CLI)
51 Wentworth Rd
Strathfield NSW 2135
________________________________________________________________________________________________
Copyright of this material is reserved to the Crown in the right of the State of New South Wales. Reproduction or
transmittal in whole, or in part, other than in accordance with provisions of the Copyright Act, is prohibited without
the written authority of the Centre for Learning Innovation (CLI).
© State of New South Wales, Department of Education and Training 2005.
Stage 3B – Unit 17
These Supervisor notes support the Student and supervisor guide for ‘Using Maths
Tracks’. The supervisor should detach them before giving the guide to the student.
They contain information on:
•
•
•
•
•
How to use this unit
Support and extension
Answer guide
Feedback
Checking up
How to use this unit
Read
•
•
•
•
with your student:
What you’ll do
What you need
Preparation
Words you need to know.
Your student’s teacher may have selected the appropriate activities from 1 to 6 by ticking
them in the list of What you’ll do. See also Support and extension.
The boxes on the right-hand side of the pages in the Student and supervisor guide
contain information and suggestions to help you support your student.
There is also space for you to make notes about how your student managed.
You can use your notes to help you fill in the Feedback sheet at the end of the unit.
An icon
shows when to refer to the Maths Tracks Student Book pages.
page x
After completing the unit, ask your student to complete the Checking up sheet
independently and return it to the teacher. Complete the supervisor side of
the Feedback sheet. Discuss the student side of the Feedback sheet and help
your student complete it.
Support and extension
The activities following the Introduction are at different levels. Your student’s teacher
should have selected the activities for your student. If activities have not been selected
in the guide, choose activities as below:
Introduction – for all students
Activities 1 and 2 – can provide extra support
Activities 3 and 4 – for all students
Activities 5 and 6 - can provide extra challenge
Reflection – for all students
Checking up - for all students
Using Maths Tracks, Stage 3B, Unit 17
1
Supervisor notes
Answer guide
This guide helps you give your student feedback on questions and tasks in the unit or the
Maths Tracks Student Book, especially where answers will vary.
Activity 3
1
d
alternative to answer in back of book
2
Number line:
a
divided into
b
divided into
c
divided into
d
divided into
3
Possible answers
a
circle divided into sixths
b
hexagon divided into twelfths
c
rectangle divided into sixths
d
rectangle divided into tenths
4
number line 0-1 divided into :
a
sixths above and thirds below
b
quarters below and eighths above
quarters
tenths
sixths
twelfths
Activity 4
1
a
1
6
0
2
6
3
6
4
6
1
3
b
1
8
0
2
8
c
0
2
10
3
8
4
8
4
10
d
0
2
12
1
6
3
12
6
8
4
12
2
6
1
3
Using Maths Tracks, Stage 3B, Unit 17
5
12
7
8
1
3
4
5
10
6
10
2
5
1
5
1
12
5
8
2
4
3
10
1
2
3
1
4
1
10
5
6
7
10
8
10
3
5
6
12
7
12
3
6
1
4
5
8
12
4
6
2
3
2
9
10
9
12
10
12
11
12
1
5
6
Supervisor notes
2
a whole circle halved and one half halved
rectangle halved, and one half halved again
hexagon halved, and one half halved again
cross halved, and one half halved again.
3
Number line
a
1
1
of
2
2
0
1
2
1
1
4
b
c
0
1
1
of
2
4
1
2
1
4
1
1
8
0
1
1
of
2
3
1
3
2
3
1
1
6
Activity 5
Your student needs to work backwards to solve this problem because the problem gives
the final outcome, ‘Shelley had four cards’ and asks about something that happened
before, ‘How many cards did Bonnie have?’
They can use counters, number lines, calculation or diagrams to help them.
In the following example, the solution is calculated.
Each girl gives the next girl half her cards.
The opposite of halving is multiplying by 2 (or doubling).
Shelley had four cards.
Lisa’s cards: 4 x 2 = 8
Shara’s cards: 8 x 2 = 16
Bonnie’s cards: 16 x 2 = 32
What fraction of the total number of cards does Shelley have?
4
4 cards out of 32 ( )
32
Divide the numerator and denominator by four.
1
4÷4
=
8
32 ÷ 4
Using Maths Tracks, Stage 3B, Unit 17
3
Supervisor notes
Checking:
How many cards does Shelley have?
32 cards ÷ 8 = 4 cards
Activity 6
Ask your student to predict the number first.
Do they realise the denominator must be even because it is twice the numerator?
7329
14658
6729
13458
Possible ways to check your answer:
Use your calculator to divide the numerator by the denominator. The answer should be
0.5
Multiply the numerator by two. The answer should be the denominator.
Reflection
Ingredients:
1
cup of rolled oats
2
1 cup of flour
2
60 (62.5) grams of butter or margarine
1 cup of coconut
2
1 cup of sugar
4
2 dessertspoons of golden syrup
1
tablespoon of boiling water
2
1
teaspoon of baking soda
2
Recording:
All the ingredients need to be halved because the amounts need to be in the same
relationship or proportion.
We use equivalent fractions when we need to keep the same proportions, for example
halving or doubling the size of an object or recipe.
Using Maths Tracks, Stage 3B, Unit 17
4
Supervisor notes
Feedback
Supervisor
The feedback you provide will help teachers assess your student’s progress and plan
future learning experiences. Please mark the scale and comment on the activities that
your student completed.
Student’s name
Date
Did your student:
divide the shapes and then re-divide
them into equal parts to find the
equivalent fractions
(NS3.4)
•
understand that an equivalent
fraction is the same size as the
original fraction
(NS3.4)
with
difficulty
(Tick along line)
with
independently
help
Introduction,
1
1
Adapted from: Mathematics K–6 Syllabus, © Board of Studies NSW 2002.
•
Activity
Using Maths Tracks, Stage 3B, Unit 17
5
Supervisor notes
Feedback
Student
Help your student
to give feedback
on their learning
for completed
activities.
My favourite activity for this unit was ________________________________________
because _______________________________________________________________.
I had to work hard at ____________________________________________________.
When I halve fractions, ___________________________________________________.
Equivalent fractions ______________________________________________________.
When I check a problem, I ________________________________________________.
Using Maths Tracks, Stage 3B, Unit 17
6
Supervisor notes
Student's name:
Checking up
Make sure your
student completes
this work
independently
for return to the
teacher.
Using Maths Tracks, Stage 3B – Unit 17
Number: Fractions and Decimals
Entry 1: Equivalent Fractions
Look at these examples of fraction sentences.
1
2
=
2
4
3
1
<
4
2
1
1
>
4
2
Write six fraction sentences using the symbols =, < and >.
Each fraction must have a different denominator.
Below each fraction sentence, draw a diagram or a number line to illustrate the sentence.
Using Maths Tracks, Stage 3B, Unit 17
7
Supervisor notes
Using Maths Tracks, Stage 3B, Unit 17
8
Supervisor notes
Stage 3B – Unit 17
Student and supervisor guide
Unit contents
About this unit
ii
What you’ll do ................................................................................ ii
What you need ............................................................................... ii
Preparation .................................................................................... iii
Words you need to know .......................................................... iii
Icons .................................................................................................. iv
Using this guide ............................................................................ iv
Returns ............................................................................................. iv
Introduction
....................................................................................
..........................................................................................
1
Activity 1
.................................................................................................
4
Activity 2
.................................................................................................
7
Activity 3
..............................................................................................
11
Activity 4
..............................................................................................
12
Activity 5
..............................................................................................
14
Activity 6
..............................................................................................
16
Reflection
.............................................................................................
17
Checking up
.......................................................................................
Student sheets
................................................................................
Using Maths Tracks, Stage 3B, Unit 17
i
19
21
Student and supervisor guide
About this unit
What you’ll do
√
Introduction
•
divide a number line into thirds, sixths and twelfths to find the
equivalent fractions
Activity 1
•
divide a rectangle into two, four and eight equal parts to find the
equivalent fractions
•
draw the equivalent fractions on a number line
Activity 2
•
create equivalent fractions using the computer or
•
divide rectangles into equivalent fractions
Activity 3
•
re-divide number lines and diagrams to make fractions
Activity 4
•
halve fractions using diagrams and number lines
Activity 5
•
solve a fraction problem working backwards
Activity 6
•
find the missing numbers in two fractions equivalent to a half
•
tell how you found the missing numbers
√
√
Reflection
•
halve a recipe for anzac biscuits
Checking up
•
write six fraction sentences using equals, greater than and less
than symbols
What you need
Activity 2
•
Microsoft Word
Activity 3
•
Maths Tracks Student Book Stage 3B, pages 55
Activity 4
•
Maths Tracks Student Book Stage 3B, page 56
Activity 5
•
counters (optional)
•
computer (optional)
•
Working backwards problem-solving poster
Activity 6
•
a calculator
Using Maths Tracks, Stage 3B, Unit 17
ii
Student and supervisor guide
Reflection
•
ingredients for anzac biscuits, if you decide to make them:
rolled oats
plain flour
butter or margarine
coconut
sugar
golden syrup
boiling water
baking soda
a mixing bowl
a saucepan
a baking tray
an oven
Maths Tracks Homework Book Stage 3B page 17 (if you are using it)
Preparation
Activity 2: If your student does not have a computer, ask them to
complete Student sheet 3 instead.
Reflection: Your student needs to halve a recipe for anzac biscuits and
make them. If you don’t want to make the biscuits, just ask them to
read the activity and answer the questions on audio.
Words you need to know
equivalent
fraction
denominator
numerator
vertically
horizontally
Using Maths Tracks, Stage 3B, Unit 17
iii
Student and supervisor guide
Icons
Record this for the teacher.
Return this to the teacher.
Use the page in the Maths Tracks Student Book.
Page x
Use a computer for this activity.
Using this guide
The boxes on the right-hand side of pages in the Student and supervisor
guide contain information and suggestions for the supervisor.
After each activity, circle the face that shows how you feel about your
work and talk about it with your supervisor.
Returns
Student sheet 1b – Equivalent fractions – Introduction
Student sheet 2b – More equivalent fractions – Activity 1
your printed Word document or Student sheet 3 – Activity 2
Student sheet 4 – Swap card fractions – Activity 5
Checking up sheet
personal tape or recording – Introduction, Activities 5, 6,
Reflection and Checking up
Supervisor and Student Feedback sheets
this guide (if the teacher asks for it)
Using Maths Tracks, Stage 3B, Unit 17
iv
Student and supervisor guide
Introduction
We say that two halves are equivalent to a
whole.
What are equivalent fractions?
Provide feedback for this
activity on the Feedback
sheet.
If your student has difficulty
answering this question,
you could find ‘equivalent
fractions’ in the online of
CD-ROM Maths Dictionary
for Kids.
at
say th ions
u
o
y
Did
ract
lent f e
a
v
i
u
eq
m
the sa e or size?
e
v
a
h
lu
nt, va
amou
Find Student sheet 1a, Equivalent fractions.
Find coloured pencils.
Cut out one of the strips from Student sheet 1a.
(Keep the other two strips for further activities.)
You can see that 0 has been written at one end
and 1 has been written at the other end to show
a number line.
Fold it into three equal parts.
Each part is a third.
Draw a green line around each third.
1
3
Using Maths Tracks, Stage 3B, Unit 17
1
3
Remind your student:
• the denominator shows
the number of parts a
whole is divided into (‘D’
for ‘down’ could help
them remember the
denominator is down or
below the line)
• the numerator (the top
number of a fraction)
shows the number of
parts you are considering
or talking about.
1
3
1
Student and supervisor guide
What would you do to the number
line to divide it into sixths?
divide
ou’d rey
y
a
s
e
to divid
Did you
lf
a
h
in
ird
each th to sixths?
in
the line
Does your student show
the whole of the sixth part,
not just the line separating
each part?
Is each part equal or the
same size?
Fold the number line into sixths.
Draw a red line around each sixth.
Now divide the line into twelfths.
Trace around each twelfth with a blue pencil.
Did your student re-divide
each sixth in half to divide
the line into twelfths?
How many red shapes fit into a green shape?
Did you find one-third is
equivalent to two-sixths
2
1
( = )?
6
3
How many blue shapes fit
into a red shape?
Did you find two-twelfths
is equivalent to one-sixth
2
1
( 12 = )?
6
Find the places where your lines match to find
the equivalent fractions.
Find Student sheet 1b. Paste one end of
your number line and write underneath any
equivalent fractions.
2
4
For example, = .
3
6
Using Maths Tracks, Stage 3B, Unit 17
2
Did your student organise
their equivalent fractions
in something like a table to
show how one fraction may
have several equivalents?
See the table at the end of
the activity.
If your student wants an
extra challenge, they can
divide the line further into
twenty-fourths.
Student and supervisor guide
Record the following for your teacher.
Use mathematical words such as divide, equal
parts, equivalent fractions, half, halve, thirds,
sixths and twelfths.
Your student could use the
other number lines from
Student sheet 1a to find
other equivalent fractions,
such as halves, quarters
and eighths.
What is an equivalent fraction?
How did you divide your number line into
twelfths?
Is four-sixths equivalent to two-thirds?
How do you know?
Is three-sixths not equivalent to one third?
3
Name two fractions equivalent to 6 .
Name another fraction you made on the number
line. Explain how you made it.
Stop recording.
Do you know these facts?
Fraction
is equivalent to
is equivalent to
1
2
3
6
6
12
1
3
2
6
4
12
2
3
4
6
8
12
1
6
2
12
5
6
10
12
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 17
3
some
help
no
help
Student and supervisor guide
Activity 1
Find Student sheet 2a, More equivalent fractions.
Cut out one rectangle from Student sheet 2a.
Fold your rectangle in half like this.
Halve each half to make four equal parts.
What fraction of the whole is each equal part?
Did you say quarters?
Halve each quarter to make eighths.
Using Maths Tracks, Stage 3B, Unit 17
4
Student and supervisor guide
1
one eighth ( ) green
8
1
one quarter (4) red
1
one half ( ) blue.
2
Colour:
How many green parts fit into a red part?
2
1
=
8
4
Did your student say,
‘Two green parts fit into a
red part’?
On the number line it would look like this.
1
4
1
8
2
8
2
4
3
8
4
8
3
4
5
8
6
8
4
4
7
8
0
How many red parts fit into the blue part?
8
8
1
1
2
=
2
4
Did your student say,
‘Two red parts fit into a
blue part’?
Can you show these equivalent fractions on this
number line?
0
1
Does your number line look like this?
1
2
1
4
2
4
3
4
0
Using Maths Tracks, Stage 3B, Unit 17
5
4
4
1
Student and supervisor guide
Glue your fraction rectangle that you cut
from Sheet 2a onto Student sheet 2b.
Underneath it, draw a number line showing
all the equivalent fractions you can find.
Label your number line clearly so the reader
can follow it easily.
Cut out the second rectangle on Sheet 2a.
Divide this rectangle into five equal parts to
show other equivalent fractions.
Paste it on Student sheet 2b.
Below the rectangle, draw a number line to
show the equivalent fractions you find.
Can you see any patterns in the equivalent
fractions?
As an extra challenge,
your student could find
how many quarters are
equivalent to twelfths.
They first divide the
rectangle into quarters and
then divide each quarter
into thirds.
Provide feedback for this
activity on the Feedback
sheet.
Do you know these facts?
Fraction
is equivalent to
1
2
2
4
is equivalent to is equivalent to
4
8
1
4
2
8
3
4
6
8
5
10
1
5
2
10
2
5
4
10
3
5
6
10
4
5
8
10
5
5
4
4
8
8
10
10
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 17
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some
help
no
help
Student and supervisor guide
Activity 2
If you do not have a computer, read the activity
and then complete the task on Student sheet 3.
If you have Word on a computer, and a printer,
follow the instructions to make equivalent
fractions using rectangles.
Reprinted by permission from Microsoft Corporation.
Open a Word document.
Type your name and Unit 17, Activity 2.
Click Autoshapes on the Drawing toolbar.
Select Basic Shapes and click on Rectangle.
Using Maths Tracks, Stage 3B, Unit 17
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Student and supervisor guide
Place the rectangle at the top of your page.
Click and drag the bottom right corner to make the
rectangle about 12 cm long.
Reprinted by permission from Microsoft Corporation.
Select Line on the Drawing toolbar.
Draw and place two lines to divide the rectangle into thirds.
Reprinted by permission from Microsoft Corporation.
Hold down the Shift key and click to select the
rectangle and both lines. Click Draw and select Group.
Using Maths Tracks, Stage 3B, Unit 17
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Student and supervisor guide
Reprinted by permission from Microsoft Corporation.
Copy and Paste to make a second rectangle.
Use Line on the Drawing toolbar and place three more
lines to divide the thirds to make sixths on the second
rectangle.
Reprinted by permission from Microsoft Corporation.
Group then Copy and Paste to make another rectangle.
Select Line to divide the sixths into twelfths.
Using Maths Tracks, Stage 3B, Unit 17
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Student and supervisor guide
Print your document.
Find coloured pencils.
Colour one third of each rectangle.
For rectangle 2, that will be the equivalent of
one third in sixths.
For rectangle 3 it will be the equivalent of one
third in twelfths.
Write the fraction you have coloured, beside
each rectangle.
If you do not have a computer, find and
complete Student sheet 3.
Your student should write
1
for rectangle 1,
3
2
1
=
for rectangle 2 and
6
3
4
1
=
for rectangle 3.
12
3
For extra challenge your
student could use Word to
draw three more rectangles,
one showing halves, one
showing quarters and
one showing eighths.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 17
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some
help
no
help
Student and supervisor guide
Activity 3
Here is a square divided into two halves.
If you re-divide the square to halve the halves,
it will look like this.
Now the square is divided into four quarters.
You can see the re-division on a number line
below.
1
2
0
1
Find page 55 in the Maths Tracks Student Book.
Do Task 1.
Page 55
If you have difficulty with re-dividing a number
line, read the Introduction again.
In Task 2, write the new fractions above the
lines like the example below.
1
2
0
1
4
Help your student read and
interpret the instructions.
1
2
4
3
4
4
4
Now complete Tasks 3 and 4.
Discuss possible reasons for
different answers and praise
successes.
Mark your answers for this page at the back of
the Maths Tracks Student Book. Have another
try if you went off the track.
Refer to the Answer guide
in the Supervisor notes for
possible diagrams for Tasks
1d, 2, 3 and 4.
Feedback:
lots of
help
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some
help
no
help
Student and supervisor guide
Activity 4
This rectangle has been divided in half.
Colour half of one of the halves.
Your diagram should look similar to the one
below.
You now have half of a half, which is a quarter of
the whole rectangle.
You may need to draw in
the ‘hidden’ parts to show
all the quarters.
What does the following diagram show us?
Can you see that each quarter of the shaded half
4
1
is one-eighth of the whole rectangle? ( =
8
2
1
4
You may need to draw in
the ‘hidden’ parts to show
all the eighths.
Find page 56 in the Maths Tracks Student Book.
Help your student read and
interpret the instructions.
and 8 + 2 = 1).
Page 56
1
a
b
c
d
2
Write the thirds below the number line
and the sixths above.
Write the quarters below the number
line and the eighths above.
Write the fifths below the number
line and the tenths above.
Write the thirds and sixths below the
number line and the twelfths above.
Re-read the beginning of this activity if you
have difficulty re-dividing the shapes.
Using Maths Tracks, Stage 3B, Unit 17
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Student and supervisor guide
3
a
b
c
Write the halves above the number
line and the quarters below.
Show the halves and quarters above
the number line and the eighths below
the line. Take this task one step at a
time.
Show the thirds above the number line
and the sixths below.
Refer to the Answer guide
in the Supervisor notes for
suggested answers.
Mark your answers for this page at the back of
the Maths Tracks Student Book. Have another
try if you went off the track.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 17
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some
help
no
help
Student and supervisor guide
Activity 5
Find Student sheet 4, Swap card fractions.
Use it to show how you solve this problem.
Use the Answer guide in
the Supervisor notes to
help guide your student if
they have difficulties.
Bonnie had some swap cards.
She gave half of them to Shara.
Shara gave half her share of cards to Lisa.
Lisa gave half her share to Shelley.
Shelley had four cards.
How many swap cards did Bonnie start with?
What fraction of the cards does Shelley have?
You could decide to use counters or draw
diagrams using a computer to help.
Follow the steps on the student sheet:
Find out
Re-write the problem in your own words.
Ask questions to help you think through the
problem.
You could ask questions about:
•
working backwards
•
Shelley’s cards.
Select a strategy
What could help you solve the problem?
•
the Working backwards problem-solving
poster
•
diagrams
•
counters
•
talking to another student
•
colour-coding each girl’s share?
Investigate
Show how you solve the problem.
Reflect
Look at your answer to see if it tells you what
the problem asked you to find out.
Does your answer make sense?
Should Bonnie have more or less cards than
Shelley?
Show how you can check your solution.
Using Maths Tracks, Stage 3B, Unit 17
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Student and supervisor guide
Record the answers to these questions.
Use words such as halve, multiply, twice, and
working backwards.
Why did you need to work backwards to solve
this problem?
How did you solve the problem?
How could you make the problem more
challenging?
Stop recording now.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 17
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some
help
no
help
Student and supervisor guide
Activity 6
Find Student sheet 5, Fraction puzzle.
Refer to the Answer guide
in the Supervisor notes.
Find a calculator.
Cut out the numeral cards 1–9 from
Student sheet 5.
Lay them out on the table to make the following
fraction.
73 9
14 5
Can you find the three missing digits?
Each digit is used only once and the fraction
7293
must be equivalent to 1 ; for example 14586 = 1
2
2
When you have worked out the answer, do the
same thing with the following fraction.
It must be equivalent to 1 .
2
6
1
2
458
You could use your calculator to
check your answer.
Record the answers to these questions.
Use mathematical words such as numerator,
denominator, half, even and divide.
What was your solution to the problem?
What strategy did you use to find it?
Why does the last number of the denominator
have to be even?
How did you check your answer?
Stop the recording.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 17
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some
help
no
help
Student and supervisor guide
Reflection
Let’s see how a cook uses equivalent fractions.
This recipe is for twelve anzac biscuits.
You need to change the recipe so you make six.
Your student needs to halve
all the amounts given in this
recipe.
You will find the exact
amounts they need in the
Answer guide.
What will you need to do?
Anzac Biscuits
Traditional recipe for twelve biscuits
You will need
________
1 cup of rolled oats
________
1 cup of flour
________
125 grams of butter or margarine
________
1 cup of coconut
________
1
2
________
4 dessertspoons of golden syrup
________
1 tablespoon of boiling water
________
1 teaspoon of baking soda
________
a mixing bowl
________
a saucepan
________
a baking tray
________
a moderate oven (175°).
cup of sugar
Next to the ingredients above, write what you
would need if you were going to make only
six biscuits. For example, instead of 1 cup of
coconut, you would need 1 cup.
2
Using Maths Tracks, Stage 3B, Unit 17
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Student and supervisor guide
Method
Heat your oven to 175°.
Grease a baking tray or cover it with baking
paper.
Measure out all the ingredients.
Mix the oats, coconut, flour and sugar together
in a mixing bowl.
Melt the butter gently with the golden syrup in a
saucepan.
Put the baking powder in a cup and then pour
boiling water on it.
Pour the foaming mixture into the saucepan with
the melted butter and mix them together.
Add the mixture in the saucepan to the dry
ingredients in the mixing bowl. Mix well.
Roll dessertspoons of biscuit dough into balls
and place them on the tray in rows.
Press them down with a fork to flatten them.
Put the biscuits in a moderate oven for around
ten to fifteen minutes.
Record your answers to the following questions
for your teacher using words like halve and
proportion.
Why do all the ingredients need to be halved and
not just one?
At what other times might you need to halve
amounts or numbers?
Stop the recording now.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 17
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some
help
no
help
Student and supervisor guide
Checking up
Record the answers to these questions for
your teacher using mathematical words such
as numerator and denominator, equivalent,
fractions and size.
What is an equivalent fraction?
Explain why
Explain why
6
12
2
6
1
is equivalent to 2 .
2
is not equivalent to 3 .
When do you use equivalent fractions in the
everyday world?
Stop the recording now.
Complete the Checking up sheet without any
help from your supervisor.
After you have finished the Checking up sheet,
fill in the student side of the Feedback sheet.
You may need to look back at the smiley faces
you circled, to remind you how you felt about
each activity.
The Checking up sheet and
Feedback sheet are near the
back of the Supervisor notes
for this unit.
Make sure your student
works on this assessment
task independently with
your assistance to read and
interpret the instructions.
Return the Checking up sheet
to the teacher unmarked.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 17
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some
help
no
help
Student and supervisor guide
Using Maths Tracks, Stage 3B, Unit 17
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Student and supervisor guide
Equivalent fractions
Introduction
Number lines
1
1
0
1
21
0
0
Using Maths Tracks, Stage 3B, Unit 17
Student sheet 1a
Using Maths Tracks, Stage 3B, Unit 17
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Student sheet 1a
Name:
Equivalent fractions
Introduction
Paste one end of the number line showing thirds, sixths and twelfths below.
Write the equivalent fractions you showed on your number line.
Using Maths Tracks, Stage 3B, Unit 17
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Student sheet 1b
Using Maths Tracks, Stage 3B, Unit 17
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Student sheet 1b
More equivalent fractions
Activity 1
Fraction rectangles
Using Maths Tracks, Stage 3B, Unit 17
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Student sheet 2a
Using Maths Tracks, Stage 3B, Unit 17
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Student sheet 2a
Name:
More equivalent fractions
Activity 1
Paste your fraction rectangles onto this sheet.
Underneath each rectangle, draw a number line of the equivalent fractions
you find. Label them clearly.
Using Maths Tracks, Stage 3B, Unit 17
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Student sheet 2b
Using Maths Tracks, Stage 3B, Unit 17
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Student sheet 2b
Name:
Rectangle fractions
Activity 2
Complete this sheet if you do not have a computer.
1
Divide rectangles a, b and c into three equal parts (thirds).
Re-divide the thirds in rectangles b and c to make six equal parts
(sixths).
Re-divide the sixths in rectangle c to make twelfths.
a
b
c
2
Divide rectangles d, e and f into halves.
Re-divide rectangles e and f to make quarters.
Re-divide rectangle f to make eighths.
d
e
f
Using Maths Tracks, Stage 3B, Unit 17
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Student sheet 3
Using Maths Tracks, Stage 3B, Unit 17
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Student sheet 3
Name:
Swap card fractions
Activity 5
Show how you solve the problem. If you use a computer, attach your
printed document or email it to your teacher.
Find out
Re-write the problem in your own words.
Ask questions to help you think through the problem.
Select a strategy
What strategy are you going to use?
Using Maths Tracks, Stage 3B, Unit 17
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Student sheet 4
Investigate
Show how you solve the problem.
Reflect
Show how you check your solution.
Using Maths Tracks, Stage 3B, Unit 17
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Student sheet 4
Fraction puzzle
Activity 6
Cut out the numeral cards.
1
2
3
4
5
6
7
8
9
Using Maths Tracks, Stage 3B, Unit 17
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Student sheet 5
Using Maths Tracks, Stage 3B, Unit 17
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Student sheet 5
Centre for Learning Innovation
NSW Department of Education and Training
51 Wentworth Road
Strathfield NSW 2135