Maths K–6
Stage 3B
Stage 3B – Unit 61
Patterns and Algebra
Entry 5: Using Inverse Relationships
This booklet includes:
• Teacher notes
(to be detached before sending to the student and supervisor)
• Supervisor notes
• Student and supervisor guide
P/M 3B 43906
Centre for Learning Innovation
Number: 43906
Title: Using Maths Tracks Stage 3B Unit 61
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 p 7
Photo © Tom Brown
Student and supervisor guide
p 14, Student sheet 4 p 26
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 pp 9, 10
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 61
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:
•
identifying and using inverse operations to assist with the solution of number
sentences
Prior knowledge
•
•
•
Checking solutions to number sentences by substituting the solution into the
original question
Selecting and applying appropriate mental, written or calculator strategies to solve
addition and subtraction problems (inverse relationships)
Applying appropriate mental, written or calculator strategies to solve multiplication
and division problems (inverse relationships)
Language
number sentence, problem, missing value, operation, inverse operation, addition,
subtraction
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
1
Teacher notes
What is needed
Activity 3
•
Maths Tracks Student Book Stage 3B, page 99
Activity 4
•
Maths Tracks Student Book Stage 3B, page 100
Activity 5
•
‘Work backwards’ poster
Activity 6
•
Travel brochures if no Internet access
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
Activity 6: In a satellite lesson, students could exchange problems they have designed
around the cost of a family holiday, asking someone else to solve it using inverse
operations.
Reflection: In a satellite lesson, students could exchange shopping problems to find
solutions using inverse operations.
Resources
Add any you find suitable.
Websites (accessed 21/9/2006)
Check all websites before recommending them to students.
A useful online Maths dictionary:
www.teachers.ash.org.au/jeather/maths/dictionary.html
Add any others you find suitable.
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
2
Teacher notes
Returns
Student sheet 3 – Problem solving – Activity 5
Student sheet 4 – Costing a family holiday – Activity 6
Student sheet 5 – Shopping – Reflection
Checking up sheet
personal tape or recording – Reflection and Checking up
Supervisor and Student feedback sheets
the guide (if you ask for it)
Checking up answers
1
a
$31.99 (jeans)
d
$10.99 (singlet)
$39.99 (bathers)
2
a
shorts
3
a
$43.18
+ $ 6.82
$50.00
b $22.49 (skirt)
$13.59 (t-shirt)
$22.49 (skirt)
b
T-shirts
c
shorts
d
b
$59.23
+ $40.77
$100.00
c
$21.59
x
3
$64.77
d
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
c
3
hat
$26.37
$13.65
+$59.98
$100.00
Teacher notes
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
4
Teacher notes
Student's name:
Assessment record
Using Maths Tracks, Stage 3B – Unit 61
Patterns and Algebra
Entry 5: Using Inverse Relationships
Circle the numbers of the activities the student was asked to complete.
1
2
3
4
5
6
The student:
Activity
Comment
•
uses inverse operations to assist Introduction,
6,
with solving a number sentence
Reflection,
(PAS3.1b)
Checking up
•
solves a problem using the
working backwards strategy
(WMS3.2)
5
•
constructs a number sentence
to match a problem presented
in words that requires finding an
unknown
(PAS3.1b)
6
•
designs problems to be solved
using inverse operations
(PAS3.1b)
•
describes how inverse
Checking up
operations can help find missing
values in number sentences
(WMS3.3)
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
Adapted from: Mathematics K–6 Syllabus, © Board of Studies NSW 2002.
Indicator
6,
Reflection
5
Teacher notes
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
6
Teacher notes
Maths K–6
Stage 3B – Unit 61
Patterns and Algebra
Entry 5: Using Inverse Relationships
Supervisor notes
and
Student and supervisor guide
P/M 3B 43906
Centre for Learning Innovation
Number: 43906
Title: Using Maths Tracks Stage 3B Unit 61
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 p 7
Photo © Tom Brown
Student and supervisor guide
p 14, Student sheet 4 p 26
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 pp 9, 10
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 61
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 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
page x
shows when to refer to the Maths Tracks Student Book pages.
At the end of the unit, ask your student to do the Checking up sheet
independently for return to the teacher. Fill in 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
Activities 5 and 6 – can provide extra challenge
Reflection and Checking up – for all students.
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
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.
Introduction
a
Inverse operations to the number sentences.
87 – 23 = 64
4 x 8 = 32
23 + 34 = 57
b
or
87 – 64 = 23
Inverse operations to find the missing value.
1
2
3
4
÷
+
x
–
c
÷ 4 = 127 + 129
÷ 4 = 256
Solve known part first:
Inverse operation:
Check it:
256 x 4 = 1024
1024 ÷ 4 = 127 + 129
256 = 256
Solve known part first:
Inverse operation:
4 x 63 =
+ 167
252 =
+ 167
252 – 167 = 85
Check it:
4 x 63 = 85 + 167
256 = 256
Activity 3
– 26 = 4
14 +
= 36
26 + 4 = 30
36 – 14 = 22
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
2
Supervisor notes
x 3 = 81
81 ÷ 3 = 27
÷ 3 = 23
3 x 23 = 69
Possible answers for Maths Tracks Student Book Stage 3B, page 99:
3
a
3 x 10 =
+ 12
30 – 12 = 18
3 x 10 =
b
18
+ 12
5x
= 21 + 24
5x
= 45
45 ÷ 5 = 9
5x
c
9
= 21 + 24
= 50
2x
50 ÷ 2 = 25
2x
25
= 50
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
3
Supervisor notes
Activity 4
4
a
2x
+ 6 = 20
20 – 6 = 14
14 ÷ 2 = 7 (Ellie’s number)
7
2x
b
+ 6 = 20
(60 x 12) +
= 850
= 850
720 +
850 – 720 = 130 loose bottles
c
3x
x 3 – 7 = 29
29 + 7 = 36
36 ÷ 3 = 12
12 ÷ 3 = 4
Simon’s number was 4.
d 246 ÷ (8 x 12) =
246 ÷ 96 = 2 albums with 54 cards left over
2 x 96 + 54 = 246
Activity 5
A possible approach to an answer using inverse operations:
Simone’s total marks = 133
Marks for some questions = 25
+ 25 = 133
133 – 25 = 108
108
+ 25 = 133
108 marks for 36 questions
108 ÷ 36 = 3 marks for each question
Check it: 36 x 3 = 108
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
4
Supervisor notes
Activity 6
airfares = $654 + ($3 x $376)
$654 + $1128 = $1782 airfare cost
$2982 – $1782 = $1200 accommodation cost
Reflection
√
√
? + 8 = 42
6 + ? = 13
√
200 – ? = 150
? – 54 = 16
√
?÷8=5
75 ÷ ? = 25
√
√
3 x ? = 24
? x 5 = 1500
Student sheet 5
1
3 x $3.20 = $9.60
$20.00 – $9.60 = $10.40 change
Check:
$10.40 + $9.60 = $20.00
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
5
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
•
explain inverse operations
(PAS3.1b)
Introduction
•
recognise which inverse operation to
apply for a solution
(PAS3.1b)
Introduction
•
solve the known part of a number
sentence first
(PAS3.1b)
Introduction,
3, 4
•
compose number sentences with
missing values
(PAS3.1b)
1, 3
•
recognise an inverse operation
(PAS3.1b)
2, 3
•
solve the known part first, then
use the inverse operation to find a
missing value in a number sentence
(PAS3.1b)
3
•
use the work backwards strategy
(WMS3.2)
5
•
explain how to find missing values in
number sentences by using inverse
operations (WMS3.3)
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
with
difficulty
(Tick along line)
with
independently
help
Adapted from: Mathematics K–6 Syllabus, © Board of Studies NSW 2002.
Did your student:
Reflection
7
Supervisor notes
Feedback
Help your student
to give feedback
on their learning
for completed
activities.
Student
My favourite activity for this unit was ________________________________________
because _______________________________________________________________.
I had difficulty with _______________________________________________________
because _______________________________________________________________.
Something I have learnt about inverse operations is ____________________________
______________________________________________________________________.
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
8
Supervisor notes
Student's name:
Checking up
Using Maths Tracks, Stage 3B – Unit 61
Patterns and Algebra
Entry 5: Using Inverse Relationships
Adapted from: Maths Tracks Teacher’s Resource Book Stage 3B © Harcourt Education, 2004.
Make sure your
student completes
this work
independently
for return to the
teacher.
Underline the important information first.
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
9
Supervisor notes
3
Use inverse operations to check your answers to the questions in 2.
b
c
d
Adapted from: Maths Tracks Teacher’s Resource Book Stage 3B © Harcourt Education, 2004.
a
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
10
Supervisor notes
Stage 3B – Unit 61
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 ....................................................................................................5
Activity 2 ....................................................................................................8
Activity 3 ....................................................................................................9
Activity 4 ................................................................................................. 11
Activity 5 ................................................................................................. 13
Activity 6 ................................................................................................. 14
Reflection ................................................................................................ 15
Checking up .......................................................................................... 17
Student sheets ................................................................................... 19
I can do this part!
5 x 36
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
i
Student and supervisor guide
About this unit
What you’ll do
√
Introduction
•
find missing values in number sentences, using inverse operations
Activity 1
•
play a card game that involves solving number sentences using
inverse operations
Activity 2
•
match number sentences with their inverse operation
Activity 3
•
revise using addition and subtraction as inverse operations
•
revise using multiplication and division as inverse operations
•
match number sentences with their inverse operation
•
find missing values in number sentences by completing the known
part first and then solving the unknown part using an inverse
operation
Activity 4
•
revise inverse operations using +, –, x, and ÷
•
solve problems using inverse operations
Activity 5
•
use the working backwards strategy to help solve a problem
Activity 6
•
use an inverse operation to solve a problem
•
design problems, using costs of travel and accommodation, for
others to solve using inverse operations
√
√
Reflection
•
investigate number sentences that can be solved using inverse
operations
•
write shopping problems that can be solved using inverse
operations
Checking up
•
describe how inverse operations can help to solve number
sentences
•
use inverse operations to find missing items on a list
•
solve shopping problems and use inverse operations to check your
answers
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
ii
Student and supervisor guide
What you need
Activity 1
•
Maths Tracks Student Book Stage 3B, page 99
Activity 4
•
Maths Tracks Student Book Stage 3B, page 100
Activity 5
•
‘Work backwards’ problem-solving poster
Activity 6
•
Access to the Internet or travel brochures
Words you need to know
number sentence
problem
missing value
operation
inverse operation
addition
subtraction
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 Maths Tracks, Stage 3B, Unit 61
© 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 3 – Problem solving – Activity 5
Student sheet 4 – Costing a family holiday – Activity 6
Student sheet 5 – Shopping – Reflection
Checking up sheet
personal tape or recording – Reflection and Checking up
Supervisor and Student Feedback sheets
this guide (if the teacher asks for it)
13 + 5 = 18
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
iv
Student and supervisor guide
Introduction
Tell your supervisor what you know about
inverse operations.
In this unit, you will use inverse operations to
solve number sentences.
Look at the following:
13 + 5 = 18
You can apply the inverse operation to check
that the number sentence is correct.
Subtraction is the inverse of addition.
18 – 13 = 5
or 18 – 5 = 13
Now look at the following multiplication:
6 x 4 = 24
You can apply the inverse operation to check
that the number sentence is correct.
Division is the inverse of multiplication.
24 ÷ 6 = 4 or 24 ÷ 4 = 6
a
Write an inverse operation below each of
the following number sentences to check
they are correct.
64 + 23 = 87
87 –
32 ÷ 8 = 4
4x
57 – 34 = 23
23 +
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
1
Student and supervisor guide
Look at the number sentence below which
contains a missing value:
34 + ? = 78
You can use the inverse operation to find the
missing value in the number sentence.
78 – 34 = 44
You can then check if it is correct by putting your
answer in the original number sentence.
34 + 44 = 78
Read through the following examples that show
inverse operations using all four operations.
+ 126 = 493
Inverse operation: 493 – 126 = 367
Check it: 126 + 367 = 493
– 37 = 96
Inverse operation: 96 + 37 = 133
Check it: 133 – 37 = 96
x 8 = 120
Inverse operation: 120 ÷ 8 = 15
Check it: 15 x 8 = 120
÷ 9 = 52
Inverse operation: 9 x 52 = 468
Check it: 468 ÷ 9 = 52
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
2
Student and supervisor guide
b
Write beside each example below the
inverse operation you would use to find the
missing value.
1
? x 11 = 110 __________________
2
? – 6 = 13
__________________
3
? ÷ 4 = 10
__________________
4
? + 18 = 64 __________________
If the number sentence has a known part, solve
it first. Then use an inverse operation to find
the solution.
5 x 36 = 53 +
Solve the known part first:
5 x 36 = 180
180 = 53 +
Now use the inverse operation.
180 – 53 = 127
Check it: 5 x 36 = 53 + 127
180 = 180
I can do this part!
5 x 36
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
3
Student and supervisor guide
4x
Refer to the Answer guide in
the Supervisor notes.
Provide feedback for this
activity on the Feedback
sheet.
= 500 – 180
Solve the known part first:
500 – 180 = 320
4x
= 320
Now use the inverse operation:
320 ÷ 4 = 80
Check it: 4 x 80 = 500 – 180
320 = 320
c
Find the missing value in the next two
number sentences yourself.
÷ 4 = 127 + 129
4 x 63 =
+ 167
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
4
some
help
no
help
Student and supervisor guide
Activity 1
Find Student sheet 1 and cut up the cards.
You will need the numeral and operation cards
as well as the blank cards and cards with a
question mark.
You will use the cards to make number
sentences using the four operations, as well as
to find solutions using inverse operations.
Follow the four steps below:
1
Choose two numeral cards. Then find the
‘+’ and ‘=’ operation cards as well as one ‘?’
card.
Make a number sentence with them.
For example:
3+8=?
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
5
Student and supervisor guide
2
Write the solution to the number sentence
on a blank card and put that card into the
number sentence.
In this example, it would be ‘11’:
3 + 8 = 11
3
Replace one numeral card with a ‘?’ card.
For example, if you remove the numeral 3,
you would have:
+ 8 = 11
4
Now find a solution using the inverse
operation.
Rearrange the cards to do this.
For the example above, you would have:
11 – 8 = 3
Follow these four steps again, but this time
begin with a minus (‘–’) operation card in the
number sentence.
The inverse operation will need a ‘+’ operation
card.
Repeat the process, first using a ‘x’ sign and
then using a ‘÷’ sign.
When you feel confident, take turns with your
supervisor or another person.
You make the first number sentence with one
missing value. Have a question mark card in
that position.
Ask the other person to solve it by using the
cards to make a number sentence containing the
inverse operation.
Then give the other person a turn at making a
number sentence with a missing value for you to
solve using the inverse operation.
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
6
Your student may make
number sentences with
a minus or division sign
which can’t be solved by an
inverse operation
e.g. 8 – ? = 4.
Explain that this number
sentence can be solved by
another means but not by
using an inverse operation
because of the position
of the missing number.
The same applies with an
example like this:
9 ÷ ? = 3.
Student and supervisor guide
3 + 8 = 1
1
Replace a numeral with ‘?’.
For example, if you remove
the numeral 3, you will
have:
If there is no other suitable
partner, be available to
work with your student,
taking turns to create
number sentences and then
have the other solve them
using inverse operations.
Provide feedback for this
activity on the Feedback
sheet.
? + 8 = 1
1
Now show a solution using
the inverse operation.
Rearrange the cards to do
this. You will have:
1
1
–
8 = 3
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
7
some
help
no
help
Student and supervisor guide
Activity 2
You will need a partner for this activity.
You will need to be available
to work with your student
if another partner is not
available.
Provide feedback for this
activity on the Feedback
sheet.
Find Student sheet 2 and cut up the cards.
1
Shuffle the cards and lay them face down in
a 5 x 8 array.
2
Player 1 turns over two cards.
3
If the cards are the inverse operation of
each other, Player 1 names the missing
value and keeps the pair.
4
If they are not the inverse of each other,
return them to the array face down.
5
Player 2 then has a turn.
6
Continue until all the pairs have been
matched. The winner is the player with the
most matched pairs.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
8
some
help
no
help
Student and supervisor guide
Activity 3
When you see a number sentence with a missing
value, it may be possible to use the inverse
operation to find a solution.
Plus and minus are inverse operations.
In the examples below, use the inverse
operations to find solutions.
– 26 = 4
14 +
= 36
Multiplication and division are inverse
operations.
Use the inverse operations to solve the examples
below:
Refer to the Answer guide
in the Supervisor notes.
x 3 = 81
÷ 3 = 23
Find page 99 in the Maths Tracks Student Book.
Page 99
1
Draw lines to match number sentences
containing inverse operations.
2
Write the inverse operation for each number
sentence.
3
Find the missing value, then write the
number sentence for each balance.
Use inverse operations to check your
answers.
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
9
If necessary, help your
student read and interpret
the instructions.
Answers will vary.
Refer to the Answer guide
in the Supervisor notes for
possible answers.
Student and supervisor guide
7+?=3x4
This is the known part.
4
Solve the known part first. Then find the
missing values using the inverse operation.
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 61
© NSW DET 2006
10
some
help
no
help
Student and supervisor guide
Activity 4
Find page 100 in the Maths Tracks Student Book.
Page 100
1
Use the inverse operation to solve each
number sentence.
2
To find the missing values, solve the known
part first and then use the inverse
operation.
3
Write ‘8’ in each number sentence as the
missing value, then use the inverse
operation to check your answer.
Tick if the answer is correct. Put a cross if it
is incorrect.
4
Read tasks a, b, c and d, underlining the
important data in each problem.
Write the number sentence for each
problem. Use the inverse operation to help
find a solution or to check your answer to
each problem.
If needed, help your student
read and interpret the
instructions.
Which is the
important data?
Look, I’ve
underlined it.
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
11
Student and supervisor guide
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 ways to solve
the problems in Task 4.
Discuss possible reasons for
different answers and praise
successes.
Provide feedback for this
activity on the Feedback
sheet.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
12
some
help
no
help
Student and supervisor guide
Activity 5
I can solve this problem
by working backwards!
Use your ‘Work backwards’ problem-solving
poster to help you solve this problem.
Find Student sheet 3 and show how you would
solve this problem.
Provide feedback for this
activity on the Feedback
sheet.
There were 50 questions in a maths test.
Each question was worth the same number of
marks.
Simone’s total score was 133.
She got full marks for 36 questions and a total
of 25 marks for the remaining questions.
How much was each question worth?
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
13
some
help
no
help
Student and supervisor guide
Activity 6
Find Student sheet 4.
1
Show how to solve the following problem on
Student sheet 4.
A family of one adult and three children
went on a holiday to Noosa.
The airfares per person were: adults $654,
and children $376.
If the airfares and accommodation cost
a total of $2982, how much was the
accommodation?
2
Refer to the Answer guide
in the Supervisor notes.
Use the Internet or travel brochures to
find the cost of travelling to a holiday
destination and the cost of accommodation
there. Using that information, design two
problems around the cost of a holiday for
your family.
Ask someone else to solve your problems
using inverse operations.
Feedback:
lots of
help
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
14
some
help
no
help
Student and supervisor guide
Reflection
When we are asked to find a missing value in
a number sentence, we can try to use inverse
operations to do this.
Look at the number sentences below and tick
the ones where you can find the missing value
by using the inverse operation with the given
numbers.
I don’t think I can solve all
these using inverse operations.
+ 8 = 42
6+
= 13
200 –
= 150
– 54 = 16
÷8=5
75 ÷
3x
= 25
= 24
x 5 = 1500
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
15
Student and supervisor guide
Record the following for your teacher.
How did you find the missing value in each of
the number sentences above?
Which ones could you solve by using the inverse
operation with the given numbers?
Refer to the Answer guide in
the Supervisor notes.
Stop the recording now.
Find Student sheet 5.
$3.20 each
In the spaces provided on Student sheet 5, solve
the following problems:
1
I bought three packets of biscuits.
How much change did I get from $20.00?
2
Using the shopping chart, create two
problems for a partner to solve using
inverse operations.
Ask them to check if they are correct using
inverse operations.
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 61
© NSW DET 2006
16
some
help
no
help
Student and supervisor guide
Checking up
Record this for your teacher.
Describe how inverse operations can help to find
missing values in number sentences.
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 yourself 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 61
© NSW DET 2006
17
some
help
Student and supervisor guide
no
help
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
18
Student and supervisor guide
Numeral and operation cards
1
6
1
6
+
?
2
7
2
7
–
?
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
3
8
3
8
x
?
19
Activity 1
4 5
9
4 5
9
÷ =
?
Student sheet 1
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
20
Student sheet 1
Inverting and matching
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
Activity 2
21
Student sheet 2
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
22
Student sheet 2
Name:
Problem solving
Activity 5
Find your ‘Work backwards’ problem-solving poster and use the strategy
to help you solve this problem.
There were 50 questions in a maths test.
Each question was worth the same number of marks. Simone’s total score
was 133. She got full marks for 36 questions and a total of 25 marks for
the remaining questions.
How much was each question worth?
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
23
Student sheet 3
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
24
Student sheet 3
Name:
Costing a family holiday
Activity 6
Show how you will solve this problem below.
1
A family of one adult and three children went on a holiday to Noosa.
The airfares per person were: adults $654, and children $376.
If the airfares and accommodation cost a total of $2982, how much
was the accommodation?
2
Use the Internet or travel brochures to design two problems similar to
the one you have just solved. Write them below.
a
b
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
25
Student sheet 4
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
26
Student sheet 4
Name:
Shopping
milk $2.50
cheese $4.51
Reflection
toilet paper
(9 rolls) $4.50
biscuits $3.20
potatoes $5.38
tomatoes $4.30
washing powder$4.60
eggs $3.20
bread $4.20
salmon $3.20
Write your answers to the following in the spaces provided.
1
I bought three packets of biscuits.
How much change did I get from $20.00?
Check your answer using the inverse operation.
2
Write two shopping problems for someone else to solve using
inverse operations.
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
27
Student sheet 5
Using Maths Tracks, Stage 3B, Unit 61
© NSW DET 2006
28
Student sheet 5
Centre for Learning Innovation
NSW Department of Education and Training
51 Wentworth Road
Strathfield NSW 2135