Maths K–6
Stage 3B
Stage 3B – Unit 40
Patterns and Algebra
Entry 3: Writing Number Sentences
This booklet includes:
• Teacher notes
(to be detached before sending to the student and supervisor)
• Supervisor notes
• Student and supervisor guide
P/M 3B 43885
Centre for Learning Innovation
Number: 43885
Title: Using Maths Tracks Stage 3B Unit 40
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 pp 1,
5, Supervisor notes
p5
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
Supervisor notes p
7, Student sheet 2b,
p 17
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:
Illustrators/Photographers
Desktop Publishing:
Averil Griffith
Maree Camilleri, Nicholas Perkins
Tom Brown, 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 2006.
Stage 3B – Unit 40
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
Patterns and Algebra
PAS3.1b
Constructs, verifies and completes number sentences involving the four
operations with a variety of numbers
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.
Students will learn about:
•
completing number sentences that involve more than one operation by calculating
missing values
•
constructing a number sentence to match a problem that is presented in words and
requires finding an unknown.
Prior knowledge
•
Completing number sentences involving fractions and decimals.
Language
number sentence, problem, missing value, operations, difference, greatest, least
What is needed
Activity 2
•
counters in two different colours
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
1
Teacher notes
Activity 3
•
Maths Tracks Student Book Stage 3B, page 94
Activity 4
•
Maths Tracks Student Book Stage 3B, page 95
Activity 5
•
Work backwards problem-solving poster
Maths Tracks Homework Book Stage 3B, page 26 (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
Interactivity
Reflection: Your students could do the following activity at a mini school or classroom
experience. Provide sheets of paper. Have students work in pairs to write a number
sentence with a missing value; for example, 4 + 6 = 20 ÷ ?. Then ask them to write the
same number sentence in words.
Have each pair bring their number sentences and clues to a designated space on the
floor. Mix up the written and symbolic number sentences, then have pairs take turns to
match them up.
Paste matched written and symbolic number sentences together as a chart.
Resources
Add any you find suitable.
Websites
Check all websites before recommending them to students.
Add any you find suitable.
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
2
Teacher notes
Returns
Student sheet 1 – Finding the mystery number – Activity 1
Student sheet 3 – Creating number sentences – Activity 3
Student sheet 4 – Problem-solving – Activity 5
Student sheet 5 – Problem-solving – Reflection
Checking up sheet
personal tape or recording – Reflection, Checking up
Supervisor and Student Feedback sheets
the guide (if you ask for it)
Checking up answers
Audio response
Explain the steps you use to find mystery numbers.
Suggested steps:
•
Underline important data
•
Write number sentence
•
Work backwards
•
Check by placing missing value in original number sentence
From Checking up sheet
1
a
b
c
65 + 20 – 3 = 82
1
16 – ( of 36) = 4
3
(15 + 3) x 2 = 36
d
1
of [(5 x 8) – (2 x 10)] = 10
2
2
a
b
c
3
2.6
2.5
3
a
b
c
d
(4 x 6) + 52 = 76
(5 x 8) – 18 = 22
4 x 7 = 30 – 2
45 ÷ 5 = 27 ÷ 3
4
a
b
(104 ÷ 4) – 2 = 24 students in each class
24 groups of 4; no students left over.
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
3
Teacher notes
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
4
Teacher notes
Student's name:
Assessment record
Using Maths Tracks, Stage 3B – Unit 40
Patterns and Algebra
Entry 3: Writing Number Sentences
Circle the numbers of the activities the student was asked to complete.
1
2
3
4
5
The student:
Indicator
Activity
Comment
•
completes number sentences
Introduction,
that involve more than one
1, 2, 3, 4,
operation by calculating missing Checking up
values
(PAS3.1b)
•
Introduction,
constructs a number sentence
1, 3, 4
to match a problem that is
presented in words and requires
finding an unknown
(PAS3.1b)
•
solves a number sentence
by working backwards and
describes the strategy
(WMS3.2, WMS3.3)
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
Adapted from: Mathematics K–6 Syllabus, © Board of Studies NSW 2002.
5, Reflection
5
Teacher notes
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
6
Teacher notes
Maths K–6
Stage 3B – Unit 40
Patterns and Algebra
Entry 3: Writing Number Sentences
Supervisor notes
and
Student and supervisor guide
P/M 3B 43885
Centre for Learning Innovation
Number: 43885
Title: Using Maths Tracks Stage 3B Unit 40
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 pp 1,
5, Supervisor notes
p5
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
Supervisor notes p
7, Student sheet 2b,
p 17
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:
Illustrators/Photographers
Desktop Publishing:
Averil Griffith
Maree Camilleri, Nicholas Perkins
Tom Brown, 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 2006.
Stage 3B – Unit 40
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
Words you need to know
Your student’s teacher may have selected the appropriate activities from 1 to 5 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
may 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
Activity 5 – can provide extra challenge
Reflection and Checking up – for all students
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
1
Supervisor notes
Answer guide
This guide helps you give your student feedback on questions and tasks in the unit or in
the Maths Tracks Student Book, especially where answers will vary.
Introduction
Problem
a
Half of my number
then added to 5 is 11.
b
3 times my number
3
is of 16.
4
c
12 added to my
number is double 9.
Number sentence
(? ÷ 2) + 5 = 11
Rewrite, Solve and check
(11 – 5) x 2 = 12
Check: 12 ÷ 2 + 5 = 11
3x?=
3
x 16
4
3
of 16) ÷ 3 = 4
4
3
Check: 3 x 4 = of 16
4
(
? + 12 = 9 x 2
9 x 2 – 12 = 6
Check: 6 + 12 = 9 x 2
Activity 1
a
5
b
8
c
6
d
2
e
10
Activity 1 – Student sheet 1
a
c
9 – 6 = 15 ÷ 5
1
12 + 8 = of 40
2
3x4=5+7
d
11 x 2 = 4 x 5 + 2
b
Activity 3 – Student sheet 3
Problem
Number sentence
If you multiply me by 3 and
add 5 the answer is 20.
? x 3 + 5 = 20
Work backwards: (20 – 5) ÷ 3 = 5
Check: 5 x 3 + 5 = 20
If you divide me by 6 and
add 8 the answer is 11.
? ÷ 6 + 8 = 11
Work backwards: (11 – 8) x 6 = 18
Check: 18 ÷ 6 + 8 = 11
If you divide me by 8 and
then multiply by 3 the
answer is 9.
?÷8x3=9
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
2
Work backwards and Check
Work backwards: 9 ÷ 3 x 8 = 24
Check: 24 ÷ 8 x 3 = 9
Supervisor notes
Multiply me by 9, divide by
2 and the answer is 18.
? x 9 ÷ 2 = 18
Work backwards: 18 x 2 ÷ 9 = 4
Check: 4 x 9 ÷ 2 = 18
Divide me by 6 and
multiply by 5 to get 30.
? ÷ 6 x 5 = 30
Work backwards: 30 ÷ 5 x 6 = 36
Check: 36 ÷ 6 x 5 = 30
Divide me by 4 and
multiply by 5 to give 25.
? ÷ 4 x 5 = 25
Work backwards: 25 ÷ 5 x 4 = 20
Check: 20 ÷ 4 x 5 = 25
Activity 5 – Student sheet 4
Jocum – 53 kg
Yling – 38 kg
Nyaguay – 35 kg
Brett – 42 kg
Greatest mass to least mass: Jocum, Brett, Yling, Nyaguay
Reflection
Examples of word problems.
If you multiply me by 3 and add
4 the answer is 19.
Divide me by 12, multiply by 4
and the answer is 32.
Add 24 to me and divide by 6 to
give an answer of 6.
Subtract 2 from me and divide
by 12 to give the answer of 4.
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
3
Supervisor notes
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
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
Activity
•
complete number sentences that
involve more than one operation by
calculating missing values
(PAS3.1b)
Introduction,
1, 2, 3, 4,
Checking up
•
construct a number sentence to
match a problem that is written in
words and requires finding a missing
value
(PAS3.1b)
Introduction,
1, 3, 4
•
describe how working backwards
can be used to solve a number
sentence
(WMS3.2, WMS3.3)
5, Reflection
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
5
with
difficulty
(Tick along line)
with
independently
help
Adapted from: Mathematics K–6 Syllabus, © Board of Studies NSW 2002.
Did your student:
Supervisor notes
Feedback
Help your student
to give feedback
on their learning
for completed
activities.
Student
In this unit I learnt about __________________________________________________
______________________________________________________________________.
Some strategies that I use to find missing values in number sentences are:
__________________________________
__________________________________
__________________________________
I enjoyed Activity ___________________________ because _____________________
______________________________________________________________________.
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
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 40
Patterns and Algebra
Entry 3: Writing Number Sentences
2
Write a number sentence for each problem, then write the answer.
a
I am three less than the sum of twenty and sixty-five. __________________
b
I am added to one-third of thirty-six to make sixteen. __________________
c
I am twice the sum of 15 and three. _______________________
d
I am half the difference between five times eight and double ten. _________
Write the missing value in these balances to make them even.
a
3
4
b
c
Write a number sentence and find the missing value. What must be:
a
Added to four groups of six to make seventy-six? _____________________
b
Subtracted from five lots of eight to make twenty-two? _________________
c
Multiplied by four to make thirty minus two? _________________________
d
Divided by five to make twenty-seven divided by three? ________________
Write number sentences for these problems. In Year 6 there are 104 students in
four classes.
a
If two students in each class were absent, how many students were in each
class?
b
The teachers of each class put the students who were present that day into
groups of four. How many groups of four were there in all of Year 6 and how
many students were left over?
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
7
Supervisor notes
Adapted from: Maths Tracks Teacher’s Resource Book Stage 3B © Harcourt Education, 2004.
1
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
8
Supervisor notes
Stage 3B – Unit 40
Student and supervisor guide
Unit contents
About this unit
ii
What you’ll do ................................................................................ ii
What you need .............................................................................. iii
Words you need to know .......................................................... iii
Icons .................................................................................................. iii
Using this guide ............................................................................ iv
Returns ............................................................................................. iv
Introduction
....................................................................................
..........................................................................................
1
Activity 1
.................................................................................................
3
Activity 2
.................................................................................................
5
Activity 3
.................................................................................................
7
Activity 4
.................................................................................................
9
Activity 5
..............................................................................................
10
Reflection
.............................................................................................
11
Checking up
.......................................................................................
Student sheets
................................................................................
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
i
12
13
Student and supervisor guide
About this unit
What you’ll do
√
Introduction
•
discuss strategies for making a number sentence to solve a word
problem
•
work backwards to find a missing number
•
solve mystery number problems
Activity 1
•
compare number sentences with missing values on a balance scale
•
use the answer of one side to find the missing value on the other
side
•
write word problems as number sentences
Activity 2
•
match missing values with number sentences to play ‘Missing
Values’
Activity 3
•
use the known values in number sentences to find the unknown
values
•
match number sentences with mystery number problems
•
rewrite number sentences and write the answers
•
write a number sentence to solve a problem
Activity 4
•
write a number sentence for a word problem and find the mystery
number
•
write number sentences to solve problems
•
write story problems to match number sentences
Activity 5
•
use the Work backwards problem-solving poster to solve a more
complicated word problem
√
√
Reflection
•
write word problems to match number sentences
Checking up
•
discuss steps used to identify mystery numbers
•
write number sentences to solve problems
•
write missing values on balances to make both sides equal
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
ii
Student and supervisor guide
What you need
Activity 2
•
counters in two different colours
Activity 3
•
Maths Tracks Student Book Stage 3B, page 94
Activity 4
•
Maths Tracks Student Book Stage 3B, page 95
Activity 5
•
Work backwards problem-solving poster
Words you need to know
number sentence
problem
missing value
operations
difference
greatest
least
2x
1
2 of 12
Icons
Record this for the teacher.
Return this to the teacher.
Use the page in the Maths Tracks Student Book.
Page x
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
iii
Student and supervisor guide
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 1 – Finding the mystery number – Activity 1
Student sheet 3 – Creating number sentences – Activity 3
Student sheet 4 – Problem-solving – Activity 5
Student sheet 5 – Problem-solving – Reflection
Checking up sheet
personal tape or recording – Reflection, Checking up
Supervisor and Student Feedback sheets
this guide (if your teacher asks for it)
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
iv
Student and supervisor guide
Introduction
In this unit you will make number
sentences to match word problems that
ask you to find a missing value.
You will use the facts you know to find
what is unknown.
I’m thinking…when I am
doubled and have 5 added,
the answer is 25. What
value am I?
Read the following problem in the
speech bubble.
The important information in this word problem
is doubled, 5 added and answer is 25.
Underline the words in the speech bubble.
The number sentence for the above problem
would look like this:
x 2 + 5 = 25
Notice the missing value has a symbol to
represent it.
So something multiplied by 2 plus 5 equals 25.
To solve the above problem you will need to
work backwards.
25 – 5 is 20, divided by 2 is 10.
The missing value is 10.
This can be rewritten as 25 – 5 ÷ 2 = 10.
You can check this number sentence is correct
by replacing the symbol with the number in the
original number sentence.
Check: 10 x 2 + 5 = 25
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
1
Student and supervisor guide
Write number sentences for the following
problems. Use a symbol for the missing number
and work backwards:
Problem
a
Half of my number
then added to 5 is
11.
b
3 times my number
3
is of 16.
4
c
12 added to my
number is double 9.
Number sentence Rewrite and Solve
Refer to the Answer guide
in the Supervisor notes.
Provide feedback for this
activity on the Feedback
sheet.
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
2
Student and supervisor guide
Activity 1
In this activity you will calculate missing values
in number sentences that involve more than one
operation.
These are called equivalent number sentences.
For example: 45 ÷ 5 x
= 36
45 ÷ 5 x _____ = 36
Solve the first part:
45 ÷ 5 = 9.
Now see how many 9s
are in 36.
Supply the missing numbers in each
number sentence.
a
3x
= 15
b
27 +
c
7x
d
16 x 2 –
= 30
e
(6 x 7) –
= 32
= 35
+ 3 = 45
2x
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
3
1
2 of 12
Student and supervisor guide
You need to find the missing value to balance
the number sentences on the balance on the
previous page. The number sentences need to
equal each other.
Your student should point
to the right side of the
balance.
Which side does not have a missing value?
1
of 12, which is 6 and use the
2
6 to find the missing value.
You need to find
2x?=
1
of 12
2
We know that
1
of 12 is 6 so 2 x ? = 6
2
The missing number must be three.
The correct number sentence is 2 x 3 =
Read the problem shown on
the next balance:
5 times my number is 8 + 2.
Solve the known side (8 + 2)
and use that value to find the
missing value.
5x
= 10
1
of 12.
2
8+2
5x
The missing value is 2.
The correct number sentence is 5 x 2 = 8 + 2.
Find Student sheet 1 and use the balances to
help find the following mystery numbers.
Write each number sentence in the space below
each balance.
a
b
c
d
6 taken from my number is 15 divided by 5.
8 added to my number is half of 40.
3 groups of 4 is my number plus 7.
Double 11 is 4 times 5 plus my number.
Refer to the Answer guide
in the Supervisor notes.
Provide feedback for this
activity on the Feedback
sheet.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
4
some
help
no
help
Student and supervisor guide
Activity 2
Something is missing...
what is it?
Find Student sheet 2a and cut out the two sets
of 1-12 numeral cards. Find Student sheet
2b and use the gameboard to play the game
‘Missing values’ with your supervisor.
You will need
1 gameboard
•
1 set of 1-12 numeral cards each
•
different-coloured counters for each player
•
Aim
To find the missing value.
•
How to play
Cut out and shuffle the numeral cards.
•
Player 1 turns over the top card and tries
•
to complete one of the sentences on the
gameboard.
12
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
5
Student and supervisor guide
•
•
•
If the number fits as a missing value, put a
counter on that space.
Player 2 then has a turn.
Continue until one player occupies 4
spaces in a row, diagonally, horizontally or
vertically.
Provide feedback for this
activity on the Feedback
sheet.
6
4
12
7
2
9
8
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
6
some
help
no
help
Student and supervisor guide
Activity 3
Read this word problem.
I am thinking of a number
so that when I double it
and add 6 the answer is 14.
What is the number?
To solve this word problem you need to create
a number sentence. This helps you find the
missing number or value.
As you can see important data has been
underlined to help.
The number sentence would be
x 2 + 6 = 14
The first thing to do is work backwards.
Subtract 6 from 14 to get 8 and then you would
halve it or divide by 2 to get 4.
This is rewritten as (14 – 6) ÷ 2 = 4.
The missing number is 4. You can check this by
placing 4 in the original number sentence.
Check 4 x 2 + 6 = 14
Find Student sheet 3 and create number
sentences to match a problem that is presented
in words. Don’t forget that it helps to underline
important information.
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
7
Student and supervisor guide
Find page 94 in the Maths Tracks Student Book.
Page 94
1
Find four different coloured pencils. First,
read the sentences about mystery numbers
in the first column. Match these to the
number sentences in the second column.
Then rewrite the number sentences and
write the mystery number answers in the
third column.
2
Read the problems and match each one
by writing a, b, c or d above the matching
number sentence. Write the answers in the
space provided.
3
Underline the important words in each
problem. Write a number sentence to solve
each problem.
Mark your answers for this page at the back of
the Maths Tracks Student Book. Have another
try if you went off the track.
For example;
I am four less than six
times six; is matched to
? = (6 x 6) – 4; which is
then rewritten as
32 = (6 x 6) – 4.
The Mystery number is 32.
Match all three by
colouring in the boxes the
same colour.
Provide feedback for this
activity on the Feedback
sheet.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
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some
help
no
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Student and supervisor guide
Activity 4
Find page 95 in the Maths Tracks Student Book.
Page 95
1
Write a number sentence for each problem
and then find the mystery number.
2
Write a number sentence for each problem
and then solve it.
3
Write a story problem for each number
sentence.
You will need to check
your student’s stories as
problems will vary.
Mark your answers for this page at the back of
the Maths Tracks Student Book. Have another
try if you went off the track.
Provide feedback for this
activity on the Feedback
sheet.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
9
some
help
no
help
Student and supervisor guide
Activity 5
Find your Work backwards problem-solving
poster. It may help you solve the following
problems.
Show your working out on Student sheet 4.
Scenario:
•
Jocum, Yling, Nyaguay and Brett have
a total mass of 168 kg. Jocum is 15 kg
heavier than Yling. The difference between
Yling (who has a mass of 38 kg) and
Nyaguay is that Yling is 3 kg heavier.
•
Arrange the four students in order, from
greatest mass to least mass. Write their
exact masses.
Refer to the Answer guide
in the Supervisor notes.
Provide feedback for this
activity on the Feedback
sheet.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
10
some
help
no
help
Student and supervisor guide
Reflection
Find Student sheet 5. Look at the number
sentences and write word problems for each
number sentence.
Record your answers to the following for your
teacher.
•
•
•
Read a number sentence and matching
word problem from Student sheet 5.
What was the missing value?
How did you check that you found the
correct missing value for each number
sentence?
Refer to the Answer guide
in the Supervisor notes.
Provide feedback for this
activity on the Feedback
sheet.
Stop the recording now.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
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some
help
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Student and supervisor guide
Checking up
Record this for your teacher.
Explain the steps you use to find mystery
numbers.
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 40
© NSW DET 2006
12
some
help
no
help
Student and supervisor guide
Name:
Activity 1
Adapted from: Maths Tracks Teacher’s Resource Book Stage 3B © Harcourt Education, 2004.
Finding the mystery number
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
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Student sheet 1
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
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Student sheet 1
Name:
Activity 2
Missing values
1
2
3
4
6
7
8
9 10
5
11 12
1
2
3
4
6
7
8
9 10
5
11 12
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
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Student sheet 2a
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
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Student sheet 2a
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
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Student sheet 2b
Missing values
Name:
Activity 2
Adapted from: Maths Tracks Teacher’s Resource Book Stage 3B © Harcourt Education, 2004.
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
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Student sheet 2b
Name:
Creating number sentences
Problem
Number
sentence
Activity 3
Work backwards and
Check
If you multiply me
by 3 and add 5 the
answer is 20.
If you divide me by 6
and add 8 the answer
is 11.
If you divide me by 8
and then multiply by 3
the answer is 9.
Multiply me by 9,
divide by 2 and the
answer is 18.
Divide me by 6 and
multiply by 5 to get
30.
Divide me by 4 and
multiply by 5 to give
25.
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
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Student sheet 3
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
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Student sheet 3
Name:
Activity 5
Problem-solving
Use this page to solve the problem.
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
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Student sheet 4
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
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Student sheet 4
Name:
Reflection
Problem-solving
Write word problems to match each number sentence. Then find
the missing values.
? x 3 + 4 = 19
Missing value:
(? ÷ 12) x 4 = 32
Missing value:
(? + 24) ÷ 6 = 6
Missing value:
(? – 2) ÷ 12 = 4
Missing value:
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
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Student sheet 5
Using Maths Tracks, Stage 3B, Unit 40
© NSW DET 2006
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Student sheet 5
Centre for Learning Innovation
NSW Department of Education and Training
51 Wentworth Road
Strathfield NSW 2135