iMaths National - Firefly Education

Transcription

iMaths 2 Teacher Book – Important Updates
Important changes to iMaths 2 Teacher Book
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Contents
Earlier edition (2012)
New edition (2013)
iMaths Investigations and Topics
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Investigation notes
New edition (2013)
Investigation 2ÛJ`goÛlae]
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Investigation 4 Gone fishing
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Investigation 5 Ff[]ÛmhgfÛYÛ[Ykld]Û
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iMaths 2 Teacher Book – Important Updates
Student Book Answers – Topics
Important
changes to iMaths 2 Teacher
Book
New edition (2013)
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NA5ÛNA8ÛNA9ÛNA10ÛNA11ÛNA12Û
In
2013 we are rolling out our new and improved iMaths 2 Student Book, and you may notice some changes from the
earlier
edition book.
NA22ÛMG4ÛMG14ÛMG15ÛMG16ÛMG19
Why have we made some changes? It’s simple really, you asked us to! We were listening as you told us some of the
Topics were too difficult for Year 2 Students, so we’ve made the necessary changes to bring the iMaths Topics up to the
exacting standards of Australian teachers
and version
of the Australian
Curriculum.
Student
Book3Answers
– Problem
solving strategies
If you purchase digital or hardcopy copies of these books for the 2013 teaching year, these changes will already be
edition who
(2012)
New edition
incorporated.Earlier
For teachers
still possess earlier edition Student Books, or simply want
to revise(2013)
Topics at the end of
this
year, we’ve
attached the altered pages for you
to print.
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Strategy
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Some changes are small, while others are more significant, so we’ve listed them in the table below for you to peruse.
Student Book Answers – Problem solving tasks
NA12ÛNA16ÛMG14ÛMG19
New edition (2013)
Student Book Answers – Challenges
MG19
New edition (2013)
Tracker Book Answers – Topic assessment
NA13ÛNA14ÛNA15ÛÛNA18ÛNA22
New edition (2013)
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iMaths Investigations and Topics
The grid below shows the 12 Investigations and the associated Topics.
Investigation
Page
Topics
1 Marble ramp
20
MG1 Measurement with metres
MG2 Measurement with centimetres
MG11 Classify 2D shapes
MG13 Classify 3D objects
MG16 Drawing 3D objects
MG17 Here, there and everywhere
SP2 Collecting data
SP3 Column graphs
2 Show time
28
NA10 Addition facts
NA11 Mental strategies for addition
NA12 Written strategies for addition
NA13 Subtraction facts
NA14 Mental strategies for subtraction
NA15 Written strategies for subtraction
NA27 Do I have enough money?
MG7 Clocks – quarter past, half past
MG8 Clocks – quarter past, quarter to
3 Quizit
36
NA2 Showing numbers beyond 100
NA3 Counting on number lines beyond 100
NA4 Place value to 1000
NA5 Number lines to 1000
NA6 Number expanders to 1000
NA7 Regrouping numbers to 1000
NA9 Expanded notation to 1000
NA28 Repeating patterns
NA29 Growing patterns
NA30 Odd and even
SP1 Probability
4 Gone fishing
44
NA1 Tens and ones with blocks
NA10 Addition facts
NA16 Backtracking
NA21 Division
MG9 Calendars
MG10 Months and seasons
5 Once upon a castle
52
MG12 Construct 2D shapes
MG14 Making 3D objects
MG15 Faces, edges and corners
MG20 Flip, slide, turn
SP2 Collecting data
6 Treasure trove
60
NA10 Addition facts
NA25 Coins and notes
MG18 Maps
MG19 Map references
7 Up, up and away
68
MG3 Area
SP2 Collecting data
SP3 Column graphs
8 Pizza party
76
NA20 Groups and arrays
NA21 Division
NA22 Models and symbols for fractions
NA23 Fractions as division
SP2 Collecting data
SP4 Picture graphs
9 Waterwise me
84
NA19 Multiplication problem solving
MG4 Litres
SP2 Collecting data
SP5 Interpreting graphs
10
The big squeeze
94
NA18 Multiplication
NA21 Division
MG4 Litres
MG5 Comparing mass
MG6 Kilograms
SP2 Collecting data
11
Dog tales
104
NA18 Multiplication
NA21 Division
MG4 Litres
MG5 Comparing mass
MG6 Kilograms
12
Paint it!
114
NA18 Multiplication
MG4 Litres
The following Topics do not appear in any Investigation: NA8 Place value with an abacus, NA17 The turnaround law, NA24 Make a $1 total,
NA26 Comparing coins.
ISBN 978 1 74135 245 0
iMaths 2 Teacher Book
5
Sample yearly program
The grid below shows a suggested yearly plan containing one or two Investigations per term. An assessment week has been allocated
to each Investigation. Topics that are not included in the Investigations are scheduled for independent teaching and assessment.
Note: The Topics marked with an * contain problem solving tasks.
TERM 1
Duration
(weeks)
Readiness test (Tracker Book 2)
1
2–3
Problem solving strategies – PS1, PS2, PS3, PS4, PS5
Assessment of Topics
2
4–6
Investigation 3 Quizit
Revise NA2, NA3
NA5 Number lines to 1000*
NA30 Odd and even
SP1 Probability
3
Assessment
1
NA24 Make a $1 total*
NA26 Comparing coins*
SP3 Column graphs
Problem solving strategies – PS6, PS7, PS8, PS9, PS10
3
1
7
Semester 1
Investigations and Topics
8–10
Term
weeks
Duration
(weeks)
1–3
Investigation 6 Treasure trove
Revise NA2, NA5*, NA7, NA10, NA11, NA12*, NA14
NA8 Place value to 1000 with an abacus (extra Topic)
NA25 Coins and notes*
MG17 Here, there and everywhere (extra Topic)
MG18 Maps
MG19 Map references*
3
Assessment
1
5–6
NA16 Backtracking*
NA17 The turnaround law
MG3 Area
MG9 Calendars
2
7–9
Investigation 8 Pizza party
Revise SP2
NA21 Division
NA22 Models and symbols for fractions*
SP4 Picture graphs
3
10
Assessment
1
4
Semester 2
Term
weeks
TERM 3
TERM 4
Term
weeks
TERM 2
Term
weeks
1–4
5
6–8
9
Duration
(weeks)
Investigation 2 Show time
NA10 Addition facts
NA11 Mental strategies for addition*
NA12 Written strategies for addition*
NA14 Mental strategies for subtraction*
4
Assessment
1
Investigation 5 Once upon a castle
MG12 Construct 2D shapes*
MG13 Classify 3D objects*
MG14 Making 3D objects*
SP2 Collecting data
3
Assessment
1
ISBN 978 1 74135 245 0
1
2–4
5
6–8
9
Duration
(weeks)
MG5 Comparing mass
MG6 Kilograms
1
Investigation 9 Waterwise me
Revise NA11, NA12*, NA14, NA15, NA23, SP2
NA18 Multiplication*
MG4 Litres
3
Assessment
1
Investigation 11 Dog tales
Revise NA18, NA19, NA20, NA21, NA22, NA23,
MG4, MG5, MG6
3
Assessment
1
13
Introduction to iMaths
Australian Curriculum match
The tables on these pages list the three content strands, their associated sub-strand descriptions from the
Australian Curriculum, and the Topics from iMaths 2 Student Book that match these descriptions.
Strand
Sub-strand
Student Book Topics
Number and Number and place value
Investigate number sequences, NA28 Repeating patterns
Algebra
initially those increasing and
decreasing by twos, threes, fives
and ten from any starting point,
then moving to other sequences.
(ACMNA026)
Recognise, model, represent and NA2 Showing numbers beyond 100
order numbers to at least 1000. NA5 Number lines to 1000
(ACMNA027)
Group, partition and rearrange NA1 Tens and ones with blocks
collections up to 1000 in
hundreds, tens and ones to
facilitate more efficient counting.
NA8 Place value to 1000 with an abacus
(ACMNA028)
NA10 Addition facts
NA16 Backtracking
Solve simple addition and
subtraction problems using a
range of efficient mental and
written strategies. (ACMNA030)
NA10 Addition facts
Recognise and represent
multiplication as repeated
addition, groups and arrays.
NA18 Multiplication
Explore the connection between
addition and subtraction.
(ACMNA029)
(ACMNA031)
Recognise and represent
division as grouping into equal
sets and solve simple problems
using these representations.
NA21 Division
(ACMNA032)
Fractions and decimals
Recognise and interpret
common uses of halves,
quarters and eighths of shapes
and collections. (ACMNA033)
Money and financial
mathematics
Count and order small
collections of Australian coins
and notes according to their
value. (ACMNA034)
NA24 Make a $1 total
NA26 Comparing coins
Patterns and algebra
Describe patterns with numbers
and identify missing elements.
NA30 Odd and even
(ACMNA035)
Solve problems by using number NA12 Written strategies for addition
sentences for addition or
subtraction. (ACMNA036)
18
ISBN 978 1 74135 245 0
The content strand descriptions © Australian Curriculum, Assessment and Reporting Authority 2012. This material is reproduced with the permission of ACARA.
ACARA neither endorses nor verifies the accuracy of the information provided and accepts no responsibility for incomplete or inaccurate information. You can find the
unaltered and most up to date version of this material at http://www.australiancurriculum.edu.au/Home
Strand
Sub-strand
Measurement Using units of measurement
and Geometry Compare and order several shapes
and objects based on length,
area, volume and capacity using
appropriate uniform informal units.
Student Book Topics
MG3 Area
MG4 Litres
(ACMMG037)
Compare masses of objects using
balance scales. (ACMMG038)
MG5 Comparing mass
MG6 Kilograms
Tell time to the quarter-hour, using
the language of ‘past’ and ‘to’.
(ACMMG039)
Name and order months and seasons.
(ACMMG040)
Use a calendar to identify the date
and determine the number of days in
each month. (ACMMG041)
MG9 Calendars
Shape
Describe and draw two-dimensional
shapes, with and without digital
technologies. (ACMMG042)
Describe the features of
three-dimensional objects. (ACMMG043) MG14 Making 3D objects
Location and transformation
Interpret simple maps of familiar
locations and identify the relative
positions of key features. (ACMMG044)
MG18 Maps
MG19 Map references
Investigate the effect of one-step slides MG20 Flip, slide, turn
and flips with and without digital
technologies. (ACMMG045)
Identify and describe half and quarter
turns. (ACMMG046)
Statistics and Chance
Probability Identify practical activities and
everyday events that involve chance.
Describe outcomes as ‘likely’ or
‘unlikely’ and identify some events as
‘certain’ or ‘impossible’. (ACMSP047)
Data representation and
interpretation
Identify a question of interest based
on one categorical variable. Gather
data relevant to the question.
SP1 Probability
SP2 Collecting data
(ACMSP048)
Collect, check and classify data.
SP2 Collecting data
(ACMSP049)
Create displays of data using lists,
table and picture graphs and interpret
them. (ACMSP050)
ISBN 978 1 74135 245 0
SP3 Column graphs
SP4 Picture graphs
19
Investigation 2
Show time
Show day is here again with fairy floss,
rides and show bags galore. Students
will use a show guide to negotiate and
make choices about spending money.
The number concepts of addition and
subtraction are practised in calculating
a $60 budget. This Investigation is best
done at the time of your local show.
Planning the Investigation
Expected duration of Investigation:
3 weeks
Recommended group size:
Pairs
Students will need:
internet access
Tear-out 2 – Show guide
Tear-out 3 – My plan for a day at the show
Tear-out 4 – Wish list
Tear-out 5 – Final budget
BLM 2.1 – Australian notes
BLM 2.2 – Australian coins
play money (notes and coins)
A3 paper
calculator
Topics for this Investigation
Before starting the Investigation, teach the following Topics…
NA10 Addition facts
28
ISBN 978 1 74135 245 0
Investigation
Investigation 2
1
Curriculum match for Investigation 2
The table below shows how the Topics in Investigation 2 match the content requirements of the Australian Curriculum.
Content descriptions
iMaths 2 Topics
Number and Algebra
Number and place value
• Explore the connection between addition and subtraction.
NA10 Addition facts
(ACMNA029)
• Solve simple addition and subtraction problems using a range
of efficient mental and written strategies. (ACMNA030)
Money and financial mathematics
• Count and order small collections of Australian coins
and notes according to their value. (ACMNA034)
Measurement and Geometry
Using units of measurement
• Tell time to the quarter-hour, using the language of
‘past’ and ‘to’. (ACMMG039)
NA10 Addition facts
The table below shows how students will apply the proficiency strands during each task in this Investigation.
Proficiency strands
Investigation 2 criteria
Understanding, Fluency
and Problem Solving
Step 3: Use the information on the Show guide and the Program of events in the
Student Book to complete My plan for a day at the show.
Step 4: Use the Show guide to make a Wish list of show bags, rides, and food and drink.
Find the total cost.
Step 5: Use notes and coins to show different ways to make $60.
Step 5: Create a final budget to make sure you spend as close to $60 as you can.
Reasoning
Step 6: Explain their plan, Wish list, final budget and how they spent the $60.
The content strand descriptions © Australian Curriculum, Assessment and Reporting Authority 2012. This material is reproduced with the
permission of ACARA. The extract is from the Australian Curriculum. ACARA neither endorses nor verifies the accuracy of the information provided
and accepts no responsibility for incomplete or inaccurate information. You can find the unaltered and most up to date version of this material at
http://www.australiancurriculum.edu.au/Home
ISBN 978 1 74135 245 0
29
Investigation 3
Quizit
In this Investigation students work in
teams to compete in the Quizit maths quiz.
Students test their skill and knowledge in
a variety of number concepts including
probability, place value, number lines and
growing and repeating patterns. Positive
social interaction skills are encouraged
as students work cooperatively and
effectively to solve each quiz question in
the given time.
3 weeks
Small groups of 4 or 5 students
Students will need:
internet access
BLM 3.1 – Chance cards
BLM 3.2 – Chance card labels
BLMs 3.3–3.12 – Quiz questions
stopwatch
prizes (such as a trophy, certificate or voucher)
craft materials
NA30 Odd and even
SP1
Probability
36
ISBN 978 1 74135 245 0
Investigation
Investigation 3
1
iMaths 2 Topics
Number and Algebra
• Recognise, model, represent and order numbers to
at least 1000. (ACMNA027)
• Investigate number sequences, initially those increasing and
decreasing by twos, threes, fives and ten from any starting
point, then moving to other sequences. (ACMNA026)
• Group, partition and rearrange collections up to 1000 in
hundreds, tens and ones to facilitate more efficient counting.
(ACMNA028)
• Describe patterns with numbers and identify missing elements.
(ACMNA035)
Statistics and Probability
Chance
• Identify practical activities and everyday events that involve
chance. Describe outcomes as ‘likely’ or ‘unlikely’ and identify
some events as ‘certain’ or ‘impossible’. (ACMSP047)
NA30 Odd and even
SP1 Probability
Proficiency strands
and Problem Solving
Step 3: Match the Chance cards to the labels of possible, impossible, likely or unlikely.
Step 4: Play the game following the rules and answering the questions within
the time limit.
Reasoning
Step 5: Explain the outcomes of the Quizit game and how it differed from the predictions
made at the start of the game.
Step 5: Predict what might happen if they played the game again.
ISBN 978 1 74135 245 0
37
Investigation 4
Gone fishing
Where is everybody? Gone fishing!
Students will read for important
information, work backwards and practise
mental computation strategies to evenly
distribute a catch of fish between friends.
This Investigation can also be used to
raise student’s awareness of sustaining
healthy waterways, fish habitats and the
environmental impact of fishing.
3 weeks
3 students
Optional materials:
highlighters
concrete materials – MABs, counters and blocks
plastic cups
Students will need:
internet access
Data page 1 – Fisherman’s guide
Tear-out 6 – The catch
BLMs 4.1–4.3 – Fish cards
paper, calculators, pencils and ruler
magnets
string and paperclips
sticks, lengths of dowel or rulers
NA1
Tens and ones with blocks
NA16 Backtracking
NA10 Addition facts
NA21 Division
MG9 Calendars
44
ISBN 978 1 74135 245 0
Investigation
Investigation 4
1
iMaths 2 Topics
Number and Algebra
• Group, partition and rearrange collections up to 1000 in hundreds,
tens and ones to facilitate more efficient counting. (ACMNA028)
• Investigate number sequences, initially those increasing and decreasing
by twos, threes, fives and ten from any starting point, then moving to other
sequences. (ACMNA026)
• Solve simple addition and subtraction problems using a range of
efficient mental and written strategies. (ACMNA030)
NA10 Addition facts
• Explore the connection between addition and subtraction. (ACMNA029)
NA10 Addition facts
NA16 Backtracking
• Recognise and represent division as grouping into equal sets and solve
simple problems using these representations. (ACMNA032)
NA21 Division
(ACMNA035)
• Compare and order several shapes and objects based on length, area,
volume and capacity using appropriate uniform informal units. (ACMMG037)
• Use a calendar to identify the date and determine the number of days in
each month. (ACMMG041)
MG9 Calendars
• Name and order months and seasons. (ACMMG040)
Proficiency strands
and Problem Solving
Step 3:
Step 4:
Step 5:
Step 6:
Reasoning
Step 7: Talk about the strategies used to solve the problem and share the fish.
Used the measurements on the Fish cards to draw life-size versions of each fish.
Use the clues to find the number of fish caught each day.
Calculate and check the total number of fish caught over the five days.
Calculate the number of fish each person will take home.
The content strand descriptions © Australian Curriculum, Assessment and Reporting Authority 2012. This material is reproduced with the permission of ACARA.
The extract is from the Australian Curriculum. ACARA neither endorses nor verifies the accuracy of the information provided and accepts no responsibility for
incomplete or inaccurate information. You can find the unaltered and most up to date version of this material at http://www.australiancurriculum.edu.au/Home
ISBN 978 1 74135 245 0
45
Investigation 5
Once upon a castle
This hands-on Investigation allows
students to explore and apply their
knowledge of 2D shapes and 3D objects
as they work in groups to design and
construct a model castle. Communication
skills are practised as students work
cooperatively and interact effectively in
order to complete their project.
3 weeks
Individual, pairs or small groups
Optional materials:
pipe cleaners or pliable wire
modelling clay
strong card for baseboards (cartons are ideal)
cardboard templates of cube and square
pyramid nets (to trace around)
digital camera
Students will need:
internet access
Tear-out 7 – Castle diagram
BLMs 5.1–5.7 – Castle nets (multiple copies to card)
BLM 5.8 – Tally table
craft materials – popsticks, straws, string, matchsticks,
coloured card and paper, sticky tape, scissors, glue
Everyday 3D objects, eg party hats, small sultana box,
cereal box, cardboard tube
SP2 Collecting data
52
ISBN 978 1 74135 245 0
Investigation
Investigation 5
1
iMaths 2 Topics
Shape
• Describe and draw two-dimensional shapes, with and without
digital technologies. (ACMMG042)
• Describe the features of three-dimensional objects. (ACMMG043)
• Investigate the effect of one-step slides and flips with and
without digital technologies. (ACMMG045)
• Identify and describe half and quarter turns. (ACMMG046)
Data representation and interpretation
• Identify a question of interest based on one categorical
variable. Gather data relevant to the question. (ACMSP048)
• Collect, check and classify data. (ACMSP049)
SP2 Collecting data
SP2 Collecting data
Proficiency strands
and Problem Solving
Step 3: Sketch a plan for a castle that uses 2D shapes and 3D objects
for the castle parts.
Step 4: Collect everyday 3D objects and arrange these to create a castle and
working drawbridge.
Step 5: Tally the shapes and objects used in the construction of the castle.
Reasoning
Step 6: Display the castle to the class. Describe the best features and explain
why they were chosen.
ISBN 978 1 74135 245 0
53
Investigation 5
4 Build your castle.
For this step of the Investigation students will need a selection
of 3D objects such as party hats, cardboard tubes, cereal boxes,
toothpaste boxes etc.
If students wish to make their own 3D objects, print multiple
copies of BLMs 5.1–5.7 for each group. Students will also need
coloured card and the other craft materials to create the 3D
castle models. Students should then arrange and glue their 3D
objects and 2D shapes to a baseboard made of sturdy cardboard.
This step gives students the opportunity to take ownership of
experiences and learning, as they make decisions about what
they do and how they do it.
Groups will need to work out how to construct a working
drawbridge. Encourage students to share ideas about
how to make a working drawbridge. Students can visit
imathskids.com.au, click on Investigation 5 and follow the
links to the websites listed to find examples of how to make
a drawbridge.
You may wish to use a digital camera to record each stage of this
Investigation, from the planning to the completed 3D models.
You could display these photos on the school intranet or web
page, along with written comments by the students (recounts,
procedure writing, digital photo story or task reflection).
Allow a sufficient number of sessions to complete the task.
There will be opportune times throughout this stage for student
feedback and sharing. In particular, identify and discuss
clever ideas, creative use of 2D shapes and 3D objects in
representing the variety of features, and effective techniques
for joining and gluing.
Fig 5.2 –Example 3D model castle
Encourage students to experiment with 2D shapes and 3D
objects in various ways. 2D shapes (such as arches, zigzags and
letters ‘L’, ‘Z’ and ‘T’) work well for flipping, sliding and turning to
create decorative features for the castle’s walls and doors. 3D
objects can be chosen and positioned to use space efficiently
and to complement a strong and sturdy design.
Students will use the guess and check problem solving strategy
to help rearrange the 3D objects used to construct their castle.
This will help them identify the most efficient position of edges,
faces and corners and how the different shapes and objects
interact.
Ask the groups to decide on a name for their 3D castle and label it.
3D mode l
5 Tally the shapes.
For this step of the Investigation students will need copies of
BLM 5.8 Tally table. Students should complete the tables using
tally marks to show how many 3D objects and 2D shapes they
used for their model castle (see Fig 5.3).
Fig 5.3 – Example Tally table
BLM 5.8 Investigation 5: Once upon a castle
Tally table
2D shapes
Shape
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ISBN 978 1 74135 245 0
Tally
3D objects
Object
Tally
iMaths 2 Black Line Masters © Mary Serenc and Lena Ford 2011 Firefly Education Pty Ltd
57
Reasoning
Proficiency strands
ISBN 978 1 74135 245 0
Understanding, Fluency and Problem Solving
Teacher comments
Clearly and confidently
explained the castle design
to the class. Gave a detailed
description of the best features
and gave clear and logical
reasons for including them
in the castle design. Always
used the correct mathematical
terms.
Display the castle to
the class. Describe
the best features and
explain why they were
chosen.
Explained their castle design
to the class. Identified some of
the best features and clearly
described why they included
these in the construction of
the castle. Generally used the
correct mathematical terms.
With prompting, identified all
2D shapes and 3D objects
used in the construction of the
castle. Corrected any errors
when tallying and recording
the number of shapes and
objects used.
Without help, identified all
used in the construction of
the castle. Made no errors
when tallying and recording
the number of shapes and
objects used.
Tally the shapes and
objects used in the
construction of the
castle.
Chose a suitable range of
2D shapes and 3D objects to
create a plan for the castle.
Made only minor errors when
drawing and labelling these.
B
Arranged 3D objects to
construct a castle layout.
With prompting, positioned
the edges, faces and corners
of 3D objects efficiently in
relation to each other.
Without help, chose a suitable
range of 2D shapes and
3D objects to create a
complex plan for the castle.
Drew and labelled these
correctly.
A
Name:
Arrange 3D objects
Arranged 3D objects to
efficiently to construct construct a complex castle
a castle.
layout. Independently
positioned the edges, faces
and corners of 3D objects
efficiently in relation to each
other.
Sketch a plan for
a castle that uses
2D shapes and
3D objects for the
castle parts.
Step Ability to...
Investigation 5 Once upon a castle
Gave a simple description
of their castle design to the
class. Identified some of the
best features and gave some
simple reasons for using them
in the construction of the
castle. Mostly used the correct
mathematical terms.
Needed some help to
identify all the 2D shapes
and 3D objects used in the
construction of the castle.
Made some errors when
tallying and recording the
number of shapes and objects
used.
Used 3D objects to construct
a simple castle layout. With
help, positioned 3D objects in
an organised manner.
Chose suitable 2D shapes and
3D objects to create a simple
plan for the castle. Made
some errors when drawing
and labelling these.
C
Showed their castle to the
class. Pointed out some of the
features. Reasons for choosing
these features were often
unrelated to the design and
sometimes confusing. Did
not always use the correct
mathematical terms.
Needed teacher guidance
to identify all the 2D shapes
and 3D objects used in the
construction of the castle.
Made errors when tallying
and recording the number of
shapes and objects used.
Did not always place the
shapes in a suitable layout.
Needed teacher guidance to
choose a suitable range of
Did not always draw and label
these shapes correctly.
D
E
Overall rating
Gave a very brief and
confused description of their
castle. Could not clearly
identify why they chose to
use these particular features.
Did not use the correct
mathematical terms.
Inconsistently identified the
used in the construction of
the castle. Was unable to
accurately tally or record.
Placed none of the shapes in
suitable places.
Chose a random sample of
Labelled some shapes and
objects correctly but drew
them inconsistently.
Due date:
Investigation 5
Rubric
59
Investigation 6
Treasure trove
Students take on the role of a game
designer as they work in teams to
complete and test a pirate board game.
In this game of chance, students roll the
dice and use map references to move
about the game board. Addition and
subtraction concepts are practised as
they play the game and keep a tally of
their winnings.
3 weeks
2 or 3 students
Optional materials:
a variety of board games, eg Snakes and Ladders,
Battleships, Monopoly
fiction and non-fiction books about pirates
strong card
Students will need:
internet access
Tear-out 8 – Game grid
Tear-out 9 – Board game tokens
BLM 6.1 – Chance cards
BLM 6.2 – Dice nets
play money
calculators
snap lock bags
counters
NA10 Addition facts
MG18 Maps
MG19 Map references
60
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Investigation
Investigation 6
1
iMaths 2 Topics
Number and Algebra
• Recognise, model, represent and order numbers to at least
1000. (ACMNA027)
• Group, partition and rearrange collections up to 1000 in
hundreds, tens and ones to facilitate more efficient counting.
(ACMNA028)
• Count and order small collections of Australian coins and notes
according to their value. (ACMNA034)
NA10 Addition facts
• Solve problems by using number sentences for addition or
• Interpret simple maps of familiar locations and identify the
relative positions of key features. (ACMMG044)
MG18 Maps
MG19 Map references
Proficiency strands
and Problem Solving
Step 2: Complete the Game grid, make the dice, collect enough play money and draw
chance card symbols on the grid.
Step 4: Write a set of rules for the game.
Step 4: Play the game and calculate the total winnings accumulated.
Reasoning
Step 5: Evaluate the game.
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61
Investigation 8
Pizza party
This Investigation immerses students in
the familiar and fun context of ordering
pizzas. Fractions, division and collecting
and representing data are the focus as
students explore, identify and practice
sharing of whole parts and collections.
3 weeks
4 or 5 students
Optional materials:
concrete materials – counters, blocks
paper squares and circles, paper strips
Students will need:
internet access
Data page 4 – Pizza Pantry
Tear-out 10 – Favourite pizza
Tear-out 11 – Pizza planner
craft materials – coloured pencils, scissors, glue
NA21 Division
SP2 Collecting data
SP4 Picture graphs
76
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Investigation
Investigation 8
1
iMaths 2 Topics
Number and Algebra
• Recognise and represent multiplication as repeated addition,
groups and arrays. (ACMNA031)
NA21 Division
• Recognise and represent division as grouping into equal
sets and solve simple problems using these representations.
(ACMNA032)
• Recognise and interpret common uses of halves, quarters and
eighths of shapes and collections. (ACMNA033)
SP2 Collecting data
SP2 Collecting data
• Create displays of data using lists, table and picture
graphs and interpret them. (ACMSP050)
SP4 Picture graphs
Proficiency strands
and Problem Solving
Step 2: Collect data for the Favourite pizza table and use the information to
complete a picture graph.
Step 3: Use the information on the Pizza planner to calculate the fraction of
pizza each person will eat.
Step 4: Calculate the number of pizzas you will need to order.
Step 5: Share the garlic bread equally.
Reasoning
Step 6: Explain the pizza order and how they shared the garlic bread.
ISBN 978 1 74135 245 0
77
Investigation 9
Waterwise me
This Investigation takes students from
the classroom to their home, as they
work with family members to collect and
record data on shower water usage.
Students will perform calculations using
litres and the four operations to explore
information, analyse, hypothesise and
think about how their household can
more efficiently use water.
3 weeks
Individuals and small groups
Students will need:
calculators
10 litre buckets
1 litre measuring jugs
Optional materials:
internet access
MG4 Litres
SP2 Collecting data
84
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Investigation
Investigation 9
1
iMaths 2 Topics
Number and Algebra
• Recognise and interpret common uses of halves, quarters and
eighths of shapes and collections. (ACMNA033)
• Solve problems by using number sentences for addition or
• Compare and order several shapes and objects based on
length, area, volume and capacity using appropriate uniform
informal units. (ACMMG037)
• Identify a question of interest based on one categorical variable.
Gather data relevant to the question. (ACMSP048)
MG4 Litres
SP2 Collecting data
SP2 Collecting data
• Create displays of data using lists, table and picture graphs and
interpret them. (ACMSP050)
Proficiency strands
and Problem Solving
Step 2: Describe the method used to measure the volume of shower water collected
in one minute.
Step 3: Record the volume of water, in litres, each family member uses when showering.
Step 4: Calculate how much water could be saved in one day by cutting shower time in half.
Reasoning
Step 5: Explain how each part of the Investigation was solved. Describe the changes that
could be made at home because of what was learned.
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Essential word list
Investigation 9
Waterwise me
Students will need to understand
the following terms:
waterwise
calculate
half
recycle
shower rose
collect
The rubric
Read and discuss the rubric. Discuss
the criteria and have students identify
which step of the Investigation each
one is describing. The rubric should be
revisited after the Understanding the
Investigation stage, both during and
after the Using maths stage and during
the Reasoning and reporting stage.
It’s time to be waterwise.
One way to save water is to cut down
the time you spend in the shower. But
do you know how much water you can
really save by doing this?
How much water could you and your
family save if you cut your showering
time by half?
Now that’s waterwise!
Topics
Before you start the Investigation you need to know…
NA11 Mental strategies for addition ................. p52
NA19 Multiplication problem solving ................. p68
NA12 Written strategies for addition ................. p54
NA23 Fractions as division...................................p76
NA14 Mental strategies for subtraction ............... p58
MG4 Litres ............................................................ p98
NA15 Written strategies for subtraction .............. p60
SP2 Collecting data............................................p134
NA18 Multiplication ............................................. p66
SP5 Interpreting graphs .................................... p140
Understanding the Investigation
1 Read and discuss.
Read and discuss the Investigation introduction above.
What is the Investigation asking you to do?
Teacher note
• Comprehensive lesson notes,
suggestions and resources are
available in iMaths 2 Teacher Book.
Make sure you understand the meanings of: waterwise,
calculate, half, recycle, shower rose and collect.
24 iMaths 2 Student Book
ISBN 978 1 74135 177 4
1 Read and discuss.
Read the introductory text and discuss the premise of the
Investigation.
Teach the Topics (concepts) that provide the knowledge
required to complete the Investigation.
Re-read the introductory text and each step of the
Investigation. Discuss procedures to be used, how data
will be organised and how solutions will be communicated.
Discuss new terms in the context of the Investigation.
continued next page
Focus questions
• What is this Investigation asking you to do?
• Which Topics are really important to this Investigation?
• What do you think you will be good at?
• What do you think you will need help with?
• Do you understand the meanings of the words on page 24?
Read and discuss the rubric. Clarify the criteria to be
assessed. This rubric should be revisited throughout the
investigative process.
Identify and discuss students’ prior knowledge about water
and water saving. Teachers can visit imathsonline.com.au,
click on Investigation 9 and follow the links to the websites
listed to find more information about water-related issues. You
may also wish students to explore some of the websites listed.
86
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4 How much shower water can you save?
In this step of the Investigation, students use the data from
their showering times table to work out how much water their
family would save in a day if they cut their shower time in half.
Working example
There are 4 people in my family.
Our shower rose uses 8 litres of water per minute.
My family is in the shower for a total of 24 minutes per day.
We use a total of 192 litres of water in a day.
Encourage students to make connections, and transfer and
apply their new learning from Step 3 to make reasonable and
informed estimates of how many litres of water could be saved.
Ensure students understand the language used. For example:
“What does it mean to cut something by half? How do we halve
a number?” Make connections with doubling. It is important
that students understand the relationship between the length
of time spent in the shower and the number of litres used.
Focus questions
• What do we already know? (What are the facts?)
• What do we need to find out?
• How can we solve the problem?
Daily water savings
Students will need to use their problem solving skills to find
out how much water their family would save in a day if shower
times were halved. See Fig 9.3 for example strategies and
calculations.
This is an opportune time to observe the thinking process and
strategies that students use to solve problems. Use information
gathered during this observation phase for assessment
purposes.
Fig 9.3 – Example strategies for calculating daily water savings
Division (halving the time)
12 minutes
2 24
So, 12 min x 8 L = 96 L used
per day, and 96 L saved per day.
Guess and check
+
= 192
1. Guess 50 + 50 = 100
2. Guess 80 + 80 = 160
3. Guess 90 + 90 = 180
Halving
192 = 100 + 90 + 2
1
2
1
2
1
2
4. Guess 95 + 95 = 190
5. Guess 96 + 96 = 192
x 100 = 50
x 90 = 45
x2=1
50 + 45 + 1 = 96 L / day saved
Doubling
+
= 24
12 + 12 = 24
+
= 192
96 + 96 = 192
Communicating and reflecting
The following questions are designed to help you assess
students’ proficiency in reasoning.
• How did you calculate how much water could be saved
per day?
• Which strategies did you use to solve the problems?
• What new strategies did you learn?
• Do you feel that your family uses water wisely? Why?
• How does the water your family would save each day
compare with that of other families?
90
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Investigation 9
5 Results – every drop counts.
Students take turns explaining how they solved each part of
the Investigation. This process will take some time and it is best
managed over a series of sessions. Provide the opportunity
for students to comment and ask questions. Communicating
and reflecting questions have been provided throughout this
Investigation to help you assess students’ proficiency in reasoning.
Students should suggest changes their family could make at
home in order to save water. Students’ suggestions should be
based on their results from this Investigation.
Creative thinking strategy
Use the SWOT strategy (Strengths, Weaknesses, Opportunities
and Threats) to more closely examine and reflect on the
water saving efforts of students, their families and the school
(see Fig 9.4). This approach involves grouping the internal
and external factors of a chosen topic. Usually Strengths and
Weaknesses are the internal factors, and Opportunities and
Threats are the external factors.
Fig 9.4 – Example SWOT analysis
Topic: Our water saving efforts
Strengths
• have a water saving
shower rose
• feel that we can make
a difference
• don’t water the grass
anymore
Weaknesses
• let water run when I brush
my teeth
• pour drink bottle leftovers
down the drain
• stay in shower too long
• play with the hose
Opportunities
• collect shower water for
watering plants
• use glass of water when
brushing teeth
• use a shower timer
Threats
• run out of clean water
• be put on restrictions
• no more gardens
Communicating and reflecting
The following questions are designed to help you assess
students’ proficiency in reasoning.
• Is there room for improvement in the use of water in
your family? How?
• Using what you have found out, what changes could
you make at home?
• What difference would these changes make to your
family’s water usage?
• How could you use the information you have found to
convince your family to reduce their shower times?
Students should submit:
table showing shower times and water usage for
family members
calculation of total family shower water usage per day
daily calculation for amount of water saved by halving
shower times.
Inquiry
Students who need an extra challenge could be engaged in the
following activity, which extends the application of the Topics
used in the Investigation.
When you turn on the tap to have a shower, it takes a while for
the hot water to come through.
If you collected this cold water in a bucket each time
you showered, how much water would your household
collect in a day?
How much water would your household collect in a week?
Suggest ways to recycle this water.
Black Line Masters, Data pages & Tear-outs
There are no Black Line Masters, Data pages or Tear-outs for this Investigation.
ISBN 978 1 74135 245 0
91
Proficiency strands
ISBN 978 1 74135 245 0
Reasoning
Understanding, Fluency and Problem Solving
Independently created a
suitable table. Used the
results in Step 1 to accurately
calculate and record the total
litres of shower water used.
Used an efficient strategy
and the results from Step 2
to accurately calculate and
record the total litres of
shower water a family could
save in one day.
Clearly and confidently
described how they solved
each step. Described some
changes they could make at
home and used the data to
explain how these changes
could make a difference.
Record the volume of
water, in litres, each
family member uses
when showering.
Calculate how much
water could be saved
in one day by cutting
shower time in half.
Explain how each part
of the Investigation
was solved. Describe
the changes that
could be made at
home because of
what was learned.
Teacher comments
Clearly explained the detailed
process used to measure
the volume of shower water
collected in a minute and how
the variables affected the
result.
A
Describe the method
used to measure the
volume of shower
water collected in
one minute.
Step Ability to...
Described how they solved
each step. Identified some
changes they could make
at home and gave a
reasonable explanation of
how the changes could make
a difference.
Used a reasonable strategy
and corrected any errors
made when calculating and
recording the total litres of
shower water a family could
save in one day.
With prompting, created a
suitable table. Corrected any
errors made when calculating
and recording the total litres
of shower water used.
Described the process used
to measure the volume of
shower water collected in a
minute. Identified some of
the variables that may have
affected the result.
B
Name:
Made some errors when
explaining how they solved
each step. Identified some
basic changes they could
make at home based on
some of the results of the
Investigation.
Needed help to find a
reasonable strategy. Made
only minor errors when
calculating and recording the
total litres of shower water a
family could save in one day.
With help, created a suitable
table. Made some errors
when calculating and
recording the total litres of
shower water used.
Gave a description of the
simple process used to
measure the volume of shower
water collected in a minute.
Recorded a reasonable result.
Did not discuss the variables.
C
Made several errors when
explaining how they solved
each step. The suggested
changes were not always
related to the results of the
Investigation.
Needed guidance to use
the strategy they were given
to calculate and record the
total litres of shower water a
family could save in one day.
With teacher guidance,
created a suitable table.
Made errors when attempting
to calculate and record the
total litres of shower water
used.
Described a very basic approach
to the task of measuring
collected in a minute. Did not
identify any variables that
affected the result.
D
E
Overall rating
Gave a very confused
explanation of how each
step was solved. Made some
random suggestions which
were unrelated to the results.
to attempt any of the
calculations.
Had to be given a table.
to attempt the calculation.
Made errors when recording
the total litres of shower
water used.
The description of the
method used to measure
was unclear. There was no
evidence of a systematic
approach to the task.
Due date:
Investigation 9
Rubric
93
Investigation 10
The big squeeze
In this Investigation, students will
discover whether it is more economical
to squeeze or buy orange juice.
Understanding of multiplication,
division, kilograms, litres and money
are developed as students roll up their
sleeves to organise a morning tea with
fresh orange juice on the menu.
3 weeks
Pairs, small groups and whole class
Students will need:
internet access
Tear-out 12 – The big squeeze planner
grocery catalogues
balance scales
calculators
1 kg masses
Litre jugs, empty juice containers, buckets with litre
measurements, breadboards, citrus juicers
oranges
plastic cups
NA18 Multiplication
MG4 Litres
MG5 Comparing mass
NA21 Division
MG6 Kilograms
SP2 Collecting data
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Investigation
Investigation10
1
iMaths 2 Topics
Number and Algebra
• Recognise and represent division as grouping into equal
sets and solve simple problems using these representations.
NA18 Multiplication
NA21 Division
(ACMNA032)
MG4 Litres
• Compare masses of objects using balance scales. (ACMMG038)
MG5 Comparing mass
MG6 Kilograms
SP2 Collecting data
SP2 Collecting data
Proficiency strands
and Problem Solving
Step 3: Find the number of oranges needed to make juice for your class.
Step 3: Calculate the number of kilograms of oranges needed for the class and the total cost.
Step 4: Calculate the number of litres of bottled orange juice needed for the class and the
cost of this.
Reasoning
Step 5: Identify which was best and give reasons for the choices.
ISBN 978 1 74135 245 0
95
Investigation 12
Paint it!
Working to a budget and charging by the
hour, this Investigation introduces students
to early lessons in finding important
information, forward planning and earning
wages. Numerous Number and Algebra
Topics are practised and revised as
students work step-by-step to find out how
to paint a fence within a given budget.
3 weeks
Individuals or pairs
Students will need:
internet access
BLM 12.1 – Australian notes
highlighter pens
NA18 Multiplication
MG4 Litres
114
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Investigation
Investigation12
1
iMaths 2 Topics
Number and Algebra
NA18 Multiplication
(ACMNA035)
MG4 Litres
• Tell time to the quarter-hour, using the language
of ‘past’ and ‘to’. (ACMMG039)
Proficiency strands
and Problem Solving
Step 3: Calculate how much paint is needed to cover a 16 m long fence with one
and two coats of paint.
Step 4: Calculate how much it would cost to paint the fence.
Step 5: Work out what time you will finish painting the fence if you start at 8:15 am.
Step 6: Calculate how much you would earn if you completed the job.
Reasoning
Step 7: Explain how you painted the fence for $450 or less.
ISBN 978 1 74135 245 0
115
128
2
3
4
5
6
7
8
9
10
11
12 13
14
15
5
25
30
20
10
0
30
10
40
50
50
45
60
70
70
75
1 Write the missing numbers in the empty boxes.
Draw the missing arrows to show the position of the numbers on the number line.
Try this
0
1
Write the missing numbers to complete this number line.
A number placed on a
number line shows its
value compared to other
numbers. The position of
numbers on a number line
also helps us to sort, order
and compare numbers.
80
16
95
90
90
18
100
20
ISBN 978 1 74135 177 4
17
19
0
820
420
20
820
830
826
429
430
433
31
30
28
840
440
40
860
850
848
453
450
450
48
50
50
860
460
60
870
470
70
880
875
477
470
80
70
880
480
80
890
490
90
888
900
893
490
500
499
95
100
100
Challenge
b 65
c 85
d 99
e 25
50
100
Blank number line: Mark where the number 125 should go on the number line
below. Show any working and explain how you chose where to place your mark.
0
a 10
iMaths 2 Student Book
200
100
Make your mark: Mark these numbers on the number line. Use the space provided in iMaths 2 Tracker
Book to work out your answer.
Problem solving task
802
810
808
401
410
410
7
10
5
ISBN 978 1 74135 177 4
800
c
400
b
a
2 Write the missing numbers in the empty boxes.
Draw the missing arrows to show the position of the numbers on the number line.
41
ISBN 978 1 74135 245 0
Topic NA5
ISBN 978 1 74135 245 0
131
t
O
H
a
H
t
329
O
b
H
204
t
O
1 Complete each abacus or give the missing number.
You do not need to show the unused beads (the white beads) in each place.
Try this
H
3 beads in the hundreds place
0 beads in the tens place
5 beads in the ones place
This abacus shows the number 305.
An abacus is a counting device, usually a frame like
this one threaded with beads. Each line of beads
represents a place value in our system of counting.
t
ISBN 978 1 74135 177 4
O
NA8 Place value to 1000 with an abacus
H
t
t
O
O
Melbourne 801
H
Brisbane 633
How do you start a Teddy Bear race?
O
O
t
t
O
O
Perth 545
H
H
Canberra 86
225
t
t
ISBN 978 1 74135 177 4
R
999
156
H
H
E
308
= T
O
= A
O
A
225
D
210
t
t
Y
111
999
H
345
H
,
T
156
= R
O
= O
O
E
308
D
210
308
H
500
H
t
t
D
210
= E
O
= G
O
Y
111
t
t
t
O
345
!
= D
O
= Y
O
O
O
G
500
210
H
111
H
H
t
Sydney 900
H
Darwin 107
47
Topics NA7–NA8
,
3 Write the number shown on each abacus. Then, write the letter that matches each
answer in the correct boxes below. The first one has been done for you as an example.
t
t
Hobart 290
H
H
Adelaide 425
2 The Teddy Bear Shop has stores in eight Australian cities. Show how many
teddy bears these stores sold last month. Draw beads on each abacus.
Topic NA8
132
200 + 60 + 3
100 + 5
263 =
105 =
= 300 + 50 + 2
= 900 + 90 + 9
352
999
d
e
=
409
c
400 + 9
800 + 80 + 1
881
b
=
627
600 + 20 + 7
900 + 80 + 4
a
=
te ns
984 =
1 Complete the expanded notation.
Try this
7
5
300 + 70 + 5
d red
hun s
Look carefully at these examples.
3
375
ISBN 978 1 74135 177 4
on es
Our modern number system uses place value. This means that a digit has a
different value depending on its place in a number. In the example below you can
see that 375 is 3 hundreds, 7 tens and 5 ones or 300 + 70 + 5. Showing the place
notation.
values of a number in this way is called expanded notation
2
400 + 70 + 5
272
0
100 + 2
125
+7
827
519
d
g
= 500 + 9 + 10
= 7 + 800 + 20
= 30 + 4 + 600
283
146
808
b
e
h
= 8 + 800
= 40 + 6 + 100
= 3 + 200 + 80
500 + 2
475
i
f
c
777
329
456
ISBN 978 1 74135 177 4
49
= 70 + 7 + 700
= 20 + 300 + 9
= 400 + 6 + 50
+5
100 + 20
502
Muddled numbers: The expanded notation is muddled up for this number – 20 + 4 + 800 =
.
Write five more muddled up numbers for a friend to try. Make sure you have the answers written on a
separate piece of paper.
Challenge
634
a
3 The expanded notation is muddled up for these numbers.
Write the number shown by each expanded notation.
200 + 70
+
127
2 Draw a line from each fish to the matching number on a fishing line.
ISBN 978 1 74135 245 0
Topic NA9
ISBN 978 1 74135 245 0
133
2+4 =
k
g
j
6
4
+ 2
6
8
7
+ 1
3+3 =
d
6
5 + 6 = 11
a
l
13
6
+ 7
10
n
5
4
+ 1
7
+ 7
14
o
h 7 + 6 = 13
e 9 + 8 = 17
7
7 + 3 = 10
3 + 7 = 10
b 6+1 =
7
+ 3
m
8 + 2 = 10
2 + 8 = 10
1 Complete these addition facts.
Try this
9 + 1 = 10
1 + 9 = 10
Learn the pairs of numbers that build to 10.
p
5
3
+ 2
i
f
c
r
11
6
+ 5
5
ISBN 978 1 74135 177 4
3+2 =
8 + 3 = 11
2
+ 8
7
2
9
5 + 5 = 10
2
7
9
8 + 2 = 10
10
q
5 + 6 = 11
6 + 7 = 13
6 + 6 = 12
7 + 7 = 14
6 + 4 = 10
4 + 6 = 10
Near doubles
7+2=9
2+7=9
Turnarounds
Tens
Doubles
5+1=6
5+2=7
Count ons
Here’s a reminder of some strategies for learning
addition facts.
facts The most important one is
turnarounds. When you learn a fact like 7 + 2 = 99,
turnarounds
you can do a turnaround and see that 2 + 7 = 9 too.
Here are some strategies with examples.
NA10 Addition facts
5
+ 5
5
+ 3 4+3
7
+ 2
11
+ 11
20 + 1
2
+ 2
21 + 4
9+8
3
4
4
4
5
5
5
6
6
7
7
7
7
6
7
8
8
8
8
8
START
HERE
1+1
7
6
25
+ 3
1+0
20 + 7
6
2+1
23
+ 3
9
9
9
9
10
10
10
ISBN 978 1 74135 177 4
Count ons
Doubles
Near doubles
51
12
Topics NA9–NA10
Tens
11
11
Player 2
8-12
HELP! ... it’s a
p l a t yp u s!
Which strategy? Which addition strategy should you use? Sort these facts and write them
in the boxes below.
4
7
6
8
5
4
3
9
2
7
+ 4
+ 1
+ 4
+ 8
+ 2
+ 5
+ 7
+ 8
+ 9
+ 7
Challenge
2
3
Player 1
2-6
3
+ 2
9
+ 9
8
+ 8
22
+ 2
20
+ 3
5+1
10 + 9
10
+10
8
+ 7
3 With a partner, take turns rolling two dice. Add the numbers
on both dice to find the total. Colour the total on the
chart below. Colour the total no matter whose turn it is.
Neither player scores the 7s but colour them anyway.
The winner is the first player to completely
colour their side.
5
8
+ 3
6+6
9
+ 4
7+7
2 Scientists call this shy Australian creature ornithorhynchus.
To find out what it looks like, complete the dot-to-dot below.
You will have to use addition facts to work out each dot.
Topic NA10
134
6+5+4+5
9+8+1
166
45
136
25
+4
140
+4
+5
+5
+2
50
+2
52
144
32
170 172
+4
30
+2
Build to ten – Jump to the next ten, then add the rest.
10
6 + 5 + 4 + 5
10
9 + 8 + 1
10
2 + 6 + 4
10
10
3 + 5 + 7 + 5
10
Find pairs of numbers that add to 10.
3+5+7+5
2+6+4
2 Friendly pairs
166 + 6
45 + 7
136 + 8
25 + 7
1 Friendly chunks
Try this
ISBN 978 1 74135 177 4
20
18
20
12
Answer
172
52
144
32
Answer
Working out answers in your head is called
mental computation. Try these mental
computation strategies for addition.
( 80 + 10 )
90
+
+
+
+
+
+
64 65
55 + 10 = 65, –1
+10
–1
92 93
83 + 10 = 93, –1
+10
–1
57 58
–1
48 + 10 = 58, –1
(friendly)
(fix)
+10
15 16
6 + 10 = 16, then –1 to fix.
–1
64
92
57
15
Answer
99
67
76
48
Answer
ISBN 978 1 74135 177 4
Add 9 with three-digit numbers: Try adding nine to a three-digit number, like 424 + 9 = 433.
Write ten of these for a classmate to do, then swap. Make sure you have the answers written on
a separate piece of paper.
55
83
48
6
+10
(4 + 5)
9
(3 + 4)
7
(4 + 2)
6
2 + 6 = 8
then add the ones.
To add 9, add 10 then fix by taking away 1.
Challenge
55 + 9
83 + 9
48 + 9
6+9
4 Friendly and fix
84 + 15
( 50 + 10 )
60
(60 + 10)
70
64 + 12
53 + 14
30 + 10 = 40
Add the tens
Add the digits with the same place values.
32 + 16
3 Place value
53
ISBN 978 1 74135 245 0
Topic NA11
ISBN 978 1 74135 245 0
135
s
5
3 3
+2
one
5 tens and 8 ones
3 tens and 5 ones
add 2 tens and 3 ones
We say:
+
9 9
2 6
7 3
7
7
f
6
1
2
+ 5
a tens ones
g
+
8
5
+ 3
9 9
3 8
6 1
9
2
7
b tens ones
h
c
+
+
7 6
3 3
4 3
7 8
2 4
5 4
1 Add the ones, then the tens to complete these additions.
Try this
We show:
t
ens
i
d
+
+
7 9
2 5
5 4
5 5
2 1
3 4
3
+ 2
5
5
3
8
j
e
+
+
8 6
7 2
1 4
8 7
6 5
2 2
ISBN 978 1 74135 177 4
tens ones
We write:
When you are adding two-digit
numbers add the ones first, then
add all the tens. Here’s how to add
35 and 23
23.
7 3
31
30
22
70
78
52
f
b
+
50
73
11
99
9
6
+ 3
45
92
90
69
38
g
c
71
33
54
+
47
5
2
+ 3
88
55
6 9
2 6
3 1
1 2
4
0
4
tens ones
80
91
41
63
h
d
32
20
+
8
1
+ 7
0
5
3
7 8
6
1
0
0
0
tens ones
55
Topics NA11–NA12
d If I join my card collection of 27 cards with
your collection of 62 cards, how many will we
have altogether?
Another 55: The answer to Question 2a at the top of the page is 55.
Write some other two-digit numbers that add up to 55. How many can you make?
Challenge
c I was given 20 dollars for my birthday.
I spent 10 dollars. How much is left?
a In my class there are 14 girls and 13 boys.
b There are 55 shells in my bucket and 44 in
What is the total number of children in the class?
your bucket. How many do we have altogether?
When do you add? Some of these problems need addition. Read each problem carefully.
Colour the ones that can be worked out using addition, write a number sentence, then add to find
the answer. Use the space provided in iMaths 2 Tracker Book to work out your answers.
40
3 2
1 2
2 0
2
1
1
tens ones
When you are
sure that all your
answers are
correct, colour
the word.
+
5
5
2 2
5 1
1
4
3
+ 2
tens ones
ISBN 978 1 74135 177 4
e
a
2 Complete each addition then find the answers
in the shapes below and colour them in.
The first one has been done for you as an example.
What do you call a camel with three humps?
Topic NA12
136
10 – 2 = 8
10 – 8 = 2
j
3
5
– 2
1
9
– 8
4
e 4–0 =
i
1
a 6–5 =
k
6
12
– 6
l
7
7
– 0
f 10 – 9 =
b 6–1 =
1 Complete these subtraction facts.
Try this
10 – 1 = 9
10 – 9 = 9
10
– 7
3
m
1
5
9
15
– 6
n
15 – 7 = 8
12 – 5 = 7
2
3
– 1
7
6
0
8
– 8
p
r
0
2
6
– 4
ISBN 978 1 74135 177 4
5
10
– 5
q
h 15 – 15 =
4
10 – 5 = 5
d 8–4 =
16 – 8 = 8
18 – 9 = 9
10 – 4 = 6
10 – 6 = 4
o
g 14 – 7 =
c 8–2 =
10 – 3 = 7
10 – 7 = 3
Learn the pairs of numbers that build to 10.
Near doubles
7–1=6
9–2=7
Count backs
Tens
Doubles
5–4=1
8–6=2
Count ons
Did you know that all subtraction facts
are related to addition facts
facts?? That’s right,
if you know 7 + 2 = 9, then the related
subtraction facts are 9 – 2 = 7 and 9 – 7 = 2.
Here’s a reminder of some strategies for
learning subtraction facts.
9
–4
7––711
11
–6
11 – 6
7
–2
12
–6
9
–1
8–3
8–3
16
–8
4
–1
5
–3
3
14
–7
1010– 8
–8
9–2
9–2
8–2
7
–5
8
–6
3
–1
5 –54
–4
ISBN 978 1 74135 177 4
start 1
red
blue
yellow
green
pink
orange
brown
purple
white
57
2
3
7 6 54
16
15 14 13 12 11 10 9 8
A dice game for two players
4–4
4–4
6–0
6–0
8
–5
6
–1
8––833
1010
–5
–5
3
9– –49 4
3
9
–9
11
–6
80
– 60 Can you see the pattern? Write ten of the subtraction facts
20 above as ’tens subtraction facts’.
18
17
20
19
BOM B
8
Tens subtraction facts: – 6
2
Challenge
You need:
• two players
• two dice
• two coloured pencils
0
1
2
3
4
5
6
7
8
7
–2
10–10
–5 5
5
–0
6
–3
6
–4
2
–0
9
–7
11
11
– 3– 3
2–1
3 Take turns rolling two dice. Subtract the smaller number from the larger number.
Move along the numbered fuse and colour the number you land on. Continue to
take turns rolling the dice until one player reaches the bomb. The winner is the
other player!
7
–7
10
11 – 6
8
–7
8 –– 44
6
3
6– –2 2
–1
1
5 – 51
7
4––444 – 1
–1
–3
3 –– 333
9 –95
2
10
–5
–2
–6
3
6
5 5– 5
5–2
–6
–5
8
7
–8
–4
3
10
7–1
7–1
–7
9
4–2
4–2
–6
8 –8 4
–4
12–6
5–1
5–1
10
–102– 2
2 Use the colour code to colour each space.
For example, the 8 – 3 on
6
Roxy’s arm is 5, so it should
–1
be coloured orange.
ISBN 978 1 74135 245 0
Topic NA13
ISBN 978 1 74135 245 0
137
90
–2
–2
38 – 10 = 28
38 – 10
82
92 – 10 = 82
92 – 10
ISBN 978 1 74135 177 4
28
35
= 35
10
45 –
45 – 10
63
10
Answer
38
88
58
8
Answer
73 – 10
41
94
62
13
tens ones
3
= 6
–1
–2
–3
40
–4
60
10
To subtract 10, change the digit in the tens place.
38
88
–2
58
8
–2
Back to ten – Jump back to the last ten, then subtract the rest.
tens ones
7
3
–
2 Subtract ten
41 – 3
94 – 6
62 – 4
13 – 5
1 Friendly chunks
Try this
When you work out answers in your head,
computation Try these mental
that's mental computation.
computation strategies for subtraction.
( 90 – 40 )
50
+
+
+
+
+
+
(8 – 7)
1
(6 – 1)
5
(8 – 2)
6
7–3=4
then subtract the ones.
66 – 10 = 56, +1
–10
25 – 10 = 15, +1
–10
66
25
94
ISBN 978 1 74135 177 4
59
Topics NA13–NA14
57
16
85
8
Answer
51
55
36
14
Answer
Subtract 10 with three-digit numbers: Try subtracting 10 from a three-digit number, like
929 – 10 = 919. Write ten of these for a classmate to do, then swap. Make sure you have the
answers written on a separate sheet of paper.
56 57
+1
15 16
+1
–10
94 – 10 = 84, +1
(friendly)
(fix)
+1
17
8
17 – 10 = 7, then +1 to fix.
84 85
7
+1
–10
To subtract 9, subtract 10 then fix by adding 1.
Challenge
66 – 9
25 – 9
94 – 9
17 – 9
4 Friendly and fix
98 – 47
( 70 – 20 )
50
(60 – 30)
30
68 – 32
76 – 21
20 – 10 = 10
Subtract the tens
Subtract the digits with the same place values.
27 – 13
3 Place value
Topic NA14
138
3
6
– 3
2
5
3
tens ones
a
b
4
5
– 1
7
9
2
tens ones
1 Complete these subtractions.
Try this
We show:
c
–
3 0
7 8
4 8
d
–
4 tens and 5 ones
7 tens and 6 ones
subtract 3 tens and 1 one
We think or say:
Subtract means the same as
take away or minus. When you
subtract two-digit numbers it
is important to keep the places
nes under the
lined up. Write the ones
ones
nes. Write the tens under the
tens. Subtract the ones
tens
nes first, then
subtract the tens
tens. Here’s how to
work out 76 subtract 31.
4 1
9 4
5 3
–
We write:
tens ones
e
–
4
7
3
tens
ISBN 978 1 74135 177 4
1 4
8 8
7 4
5
6
1
ones
65
8
85
11
0
2
26
2
2
9
1
6
– 4
9
0
6
2
3
– 2
7
1
4
– 2
tens ones
50
34 58
31
33
j
f
b
21
10
27
47
5
9
– 4
6
8
– 2
5
8
– 3
87
8
8
0
5
8
3
2
8
6
73
52
49
tens ones
20
9
44
19
k
g
c
58
– 36
22
b Grandma and Mum
64
– 12
52
9
4
1
4
3
3
7
4
8 5
9
– 1
8
9
– 1
3
7
– 4
tens ones
–
58
8
50
d Grandma and Emily
Person
Ag e
Grand
ad
64
Grand
ma
58
Dad
37
M um
36
Jack
12
Emily
8
c Grandad and Jack
93
81
30
l
h
d
ISBN 978 1 74135 177 4
What was the question? The answer to a subtraction is 43. Write three possible questions using
two-digit subtraction that would give this answer.
Challenge
37
– 12
25
a Dad and Jack
5
2
7
8
1
7
9
2
7 3
8
– 1
2
7
– 5
4
5
– 1
tens ones
3 Write number sentences to find out the age difference
between members of Emily’s family, then calculate the answer.
3
99
70
i
e
a
2 Complete each subtraction then find the answers in the
shapes below and colour them in.
What kind of coat do you put on only when it is wet?
61
ISBN 978 1 74135 245 0
Topic NA15
ISBN 978 1 74135 245 0
139
63
86
14
63 add 2 makes 65
64
86 add 1 makes 87
87
14 add 2 makes 16
15
3
2
1
51
50 add 2 makes 52
Try this
50
65
16
52
If you add a number then tak
takee away the same number,
you end up where you started. That’s backtracking
backtracking.
NA16 Backtracking
50
15
16
87
64
65
52
ISBN 978 1 74135 177 4
65 take away 2 leaves 63
63
86
14
51
80
27
47
100
29
48
47
48
96
28
29
90
100
30
40
63
Topics NA15–NA16
50
80
27
95
46
Back to backtracking: When Granny was sick the doctor gave her a box of tablets to make her
better. Granny took 2 tablets every day for 7 days. There are 36 tablets left. How many tablets were
in the box that the doctor gave Granny? Use the space provided in iMaths 2 Tracker Book to work out
your answer.
80 add 20 makes 100
90
27 add 2 makes 29
28
95 add 1 makes 96
96
46 add 2 makes 48
ISBN 978 1 74135 177 4
7
6
95
5
46
4
Topic
Topic NAXX
NA16
AXX
ISBN 978 1 74135 245 0
141
3 fives
We show:
3 fours
or
3 groups of 4
We say:
or
3 groups of 5
We say:
1 For 3 bags of 4 bananas, complete the following:
Try this
We show:
or
0
+5
5
+5
10
+5
3 x 5 = 15
15
20
ISBN 978 1 74135 177 4
4 x 3 = 12
We write:
The multiplication sign
3 x 5 = 15
We write:
but with a bit of practice,
multiplication will be much faster.
5
5
+ 5
15
Multiplication can be used whenever the
same number is added again and again. This is
called repeated addition.
I have 3 bags of apples. Each bag contains 5
apples. To find the total number of apples I
could use addition...
NA18 Multiplication
7 x 2
4 groups of 5
f
b
2 x 2
4 groups of 2
g
c
2x4
3x3
2x5
• 6 groups of 4
• 8 groups of 3
• 12 groups of 2
ISBN 978 1 74135 177 4
67
Topics NA17–NA18
Word list: There are plenty of words we use to show ‘groups of ’ things. Words like bundle, team,
herd, collection and so on. Make a big list of words that show groups.
Challenge
• 2 groups of 12
• 3 groups of 8
• 4 groups of 6
3 x 4
2 groups of 6
2x2
h
d
Multiplication with 24: Use different colours to circle the 24 stars into these groups.
Use the space provided in iMaths 2 Tracker Book to work out your answer.
3x5
5 x 3
3 groups of 3
3 Find matching pairs of multiplications. Colour them the same.
e
a
2 Complete these multiplications.
Topic NA18
142
$ 3 x 5 = $15
Using
multiplication
Veggies
fork
6
trowel
$
4
$
rake
5
$
$6 x 5 = $30
d 5 forks
$6 x 4 = $24
a 4 forks
1 Use a calculator to find the cost of these items.
Try this
Using repeated
addition
$3
3
3
3
+ 3
$15
Multiplication is the best way
to solve problems where the
same number is added again
and again.
For my new veggie patch I
needed five packets of seeds
which cost $3 each.
To work out the total cost
we should multiply $3 by 5
which is quicker than using
repeated addition.
$4 x 2 = $8
e 2 trowels
Tomato
Onion
Carro
t
ISBN 978 1 74135 177 4
$5 x 4 = $20
f 4 rakes
$5 x 9 = $45
c 9 rakes
Using a calculator is an
easy way to work out
multiplication answers.
$4 x 5 = $20
b 5 trowels
Radish
Bean
$5 x 8 = $40
$3 x 1 = $3
$2 x 9 = $18
g Nine soft drinks
$1 x 2 = $2
h Two orange juices
Gum Nut Cafe
$5 x 9 = $45
j 9 bags of tomatoes
$3 x 5 = $15
f 5 bags of beans
Hamburger..............................$5
Salad roll ..................................$4
Fish and chips ........................$7
Doughnut ................................. $2
Custard tart...........................$3
Flavoured milk ...................... $3
Soft drinks ..............................$2
Orange juice ...........................$1
$4 x 7 = $28
i 7 bags of onions
$5 x 5 = $25
a bag
ISBN 978 1 74135 177 4
g
Onion
s
ba
$4 a
Radishes
$6
Five of each: At the end of an hour at the markets, the veggie stall owner has sold five bags
of each item. How much money has the owner made?
Challenge
$3 x 7 = $21
f One flavoured milk
$2 x 5 = $10
$7 x 2 = $14
e Seven custard tarts
d Five doughnuts
$4 x 6 = $24
b Six salad rolls
c Two fish and chips
$5 x 4 = $20
a Four hamburgers
$5
Tomaatobaegs
C$a3rarboatsg
e 5 bags of tomatoes
3 Jack works at the Gum Nut Cafe. At lunch time he took
these orders. Work out how much each order cost.
$4 x 5 = $20
h 8 bags of tomatoes
$3 x 4 = $12
$3 x 2 = $6
g 5 bags of onions
d 4 bags of carrots
$6 x 5 = $30
b 5 bags of radishes
c 2 bags of beans
$4 x 4 = $16
a 4 bags of onions
2 Use the price boards to work out
the cost of these vegetables.
$
B3eaabnasg
69
ISBN 978 1 74135 245 0
Topic NA19
ISBN 978 1 74135 245 0
145
e 78
d 14
b 34
a 38
f 58
c 12
This is the number
of parts altogether.
This is the number
of shaded parts.
1 Colour the part of each shape shown by the fraction.
Try this
3
=4
3
4
Three quarters
Five eighths
5
8
Three parts
out of four
Five parts
out of eight
1
2
ISBN 978 1 74135 177 4
One half
One part
out of two
A fraction is a part of something. Fractions can
parts.
be shown by models which contain equal parts
E
H
H
5
8
A
1
4
D
1
8
1 =
A
4
1 =
I
2
A
1
4
H
5
8
O
8
8
3 =
P
8
3 =
T
4
P
3
8
E
7
8
R
4
4
A
1
4
8 =
O
8
2 =
N
8
T
3
4
e
I
1
2
ISBN 978 1 74135 177 4
O
8
8
2
8
N
5 =
H
8
7 =
E
8
75
Topics NA21–NA22
Half a square: How many different ways can you show ‘half’ by colouring half a square?
Challenge
Use the space provided in iMaths 2 Tracker Book to work out your answers.
These shapes are made from triangles that are all the same size.
Which shape has three eigths of the triangles shaded? Circle it.
a
b
c
d
Fraction action: These shapes are made from squares that are all the same size.
Which shape has one quarter of the squares shaded? Circle it.
a
b
c
d
e
7
8
5
8
4 =
R
4
1 =
D
8
2 To solve the riddle, write the fraction symbol for each fraction model shown.
Write the letter that matches each correct answer in the boxes below.
Did you hear about the injured kangaroo
who couldn’t jump anymore?
Topic NA22
ISBN 978 1 74135 245 0
157
1 litre
a
b
2 litres
Cola
4 litres
2 litre milk
container
2 litre soft
drink bottle
c
2L
2L
4L
d
10 litres
1 litre olive
oil bottle
Olive
Oil
1L
4 litre ice-cream
container
Cola
1 How much does each object hold?
Try this
Litres may be abbreviated
as L (no full stop, no ‘s’ for
plural and the L is always a
capital letter).
Language reminder
2L
10 litre
bucket
10 L
4L
ISBN 978 1 74135 177 4
2 litres
1 litre
10 litres
4 litres
1 litre milk
container
1L
4 litre motor oil
container
The litre is the basic unit for measuring volume. To
get an idea of how to measure using litres, it helps
to know how much some everyday objects hold.
MG4 Litres
2L
Cola
2L
ISBN 978 1 74135 177 4
5
4
3
2
1
10
9
8
7
6
99
Topics MG3–MG4
3 A bucket holds more water than a cup. We say that the bucket has a greater capacity than the cup. Sort
the 10 containers you used in the above activity in order from greatest capacity 1 to least capacity 10 .
Number of 1 L needed
to fill container
water, sand or rice
b Containers that hold
more than one litre
10 objects to measure
Number needed
to fill 1 L
A 1 L measure
a Containers that hold
less than one litre
You need:
Cola
2 A one litre milk container makes a great 1 L measure for this activity. Collect 10 objects
for measuring volume. Sort them into two groups: containers less than one litre, and
containers more than one litre.
Topic MG4
Unfolding the pyramid
Unfolding the cube
Net of the pyramid
Cut along these lines
ISBN 978 1 74135 177 4
1 Use scissors to cut a cereal box along its edges. Use the red lines below to guide you.
Unfold the box to create a net.
Try this
Pyramid
Cube
Net of the cube
glue
glue
square pyramid
b
c
ISBN 978 1 74135 177 4
Dice pattern: Look at the totals of various pairs of faces on your cube.
Can you find a pattern in the totals?
Challenge
a
119
Topics MG13–MG14
d
Cube nets: Which of these nets will make a cube? Cut out and fold the nets on page 197 to prove your
choices. There are 2 to find. Circle them. Use the space provided in iMaths 2 Tracker Book to work out
your answers.
glue
3 Remove Tear-out 13: Making 3D objects on page
197. Cut around the outline of the cube. Fold the
net and glue the tabs to make your own dice.
rectangular prism
glue
A 3D object can be unfolded into a flat pattern.
This flat pattern is called a net
net.
cube
2 Match each 3D object to its net. Colour each pair alike.
glue
glue
ISBN 978 1 74135 245 0
glue
glue
167
Topic MG14
168
A cube has 8 corners.
(4 corners at the base
and 4 at the top.)
A cube has 12 edges.
(4 around the base, 4 around
the top and 4 vertical.)
A cube has 6 faces.
(The faces on dice are
numbered 1 to 6.)
Square pyramid
a
faces
edges
corners
5
8
5
b
Rectangular prism
1 How many faces, edges and corners does each object have?
Try this
corner
edge
face
faces
8
ISBN 978 1 74135 177 4
corners
12 edges
6
A line has length. It is one dimensional (1D).
A flat shape has length and width. It is two dimensional (2D).
A solid object has length, width and height. It is three dimensional (3D).
Language reminder
Corner
A corner is a point where
three or more faces of a
3D shape meet.
Edge
An edge is the line segment
where two faces of a
3D object meet.
Face
A face is a 2D shape which
forms part of the surface area.
It is bounded by the edges.
This is a three dimensional (3D) object — a cube. 3D objects
are often classified according to the number of faces
faces,
edges and corners each object has. Some 3D objects have
surfaces or edges that are curved.
Triangular pyramid
Rectangular prism
faces
4
6
4
8
corners
edges
faces
corners
12 edges
6
d
b
1
3
6
5
6
2
Number of faces and
curved surfaces
0
2
12
8
12
1
Number of edges
Triangular prism
Square pyramid
ISBN 978 1 74135 177 4
Sort the edges: Which shapes have only straight edges?
Which shapes have only curved edges? Which shape has no edges?
Challenge
sphere
cylinder
rectangular
prism
pyramid
cube
cone
Shape
3 For each 3D object, count the faces, edges and corners.
Some 3D objects have surfaces or edges that are curved.
c
a
corners
edges
faces
corners
edges
faces
0
0
8
5
8
1
Number of corners
6
9
5
5
8
5
2 Use toothpicks or matchsticks, and plasticine or modelling clay to construct these 3D objects.
Write the number of faces, edges and corners each shape has.
121
ISBN 978 1 74135 245 0
Topic MG15
ISBN 978 1 74135 245 0
169
1 Draw a triangular pyramid.
Try this
How to draw a triangular pyramid –
Draw the base (a triangle).
Features of a pyramid –
• 3D object
• a plane shape as the base
• all other faces are triangles.
2 Draw a square pyramid.
Use a ruler to connect the corners
of the base to the tip.
To draw a 3D object, it helps to know some of the features of
the shape. Let’s describe a prism then identify the features.
ISBN 978 1 74135 177 4
6 Draw a pentagonal pyramid.
4 Draw a rectangular prism.
ISBN 978 1 74135 177 4
123
Topics MG15–MG16
Use a ruler to connect the matching corners
of the two faces.
3D outlines: Try drawing some prisms where the two identical faces overlap.
Challenge
5 Draw a pentagonal prism.
3 Draw a triangular prism.
How to draw a triangular prism –
Draw two identical faces (triangles).
Features of a prism –
• 3D object
• two identical faces
• all other faces are rectangles.
Topic MG16
172
A4
C3
c Bubbling mud pool
e The mountains
D4
a The volcano
d The big tree
b The waterfall
1 Write the map reference for each of these places on the map.
Remember to write the letter first.
Try this
C1
D1
ISBN 978 1 74135 177 4
Maps are often criss-crossed with horizontal and vertical
lines—a grid. This grid is labelled at the edges of the map
using letters and numbers.
The letters and numbers can be used to locate the
position of an object on the map. For example B2 is the
square that contains Fern Valley.
MG19 Map references
C5
D3
E6
E4
F6
F4
F2
G8
ISBN 978 1 74135 177 4
On
ice: Look
at the
above. Make
of inthe
thatit isarefacing
completely
on the
Seagull
flight:
Findmap
the seagull
at B2.aItlist
flies
thesquares
direction
(diagonally)
forice.
6 squares.
Give
the map
reference
for sea,
eachsometimes
one.
Sometimes
it flies
over the
over ice. Write the map references of the four places the
seagull could land on ice.
Challenge
129
On ice: Look at the map above. Make a list of the squares that are completely on the ice. Give the map
reference for each one. Use the space provided in iMaths 2 Tracker Book to work out your answer.
A5
B5
C3
E1
2 Turn to Tear-out 14: Resources on page 199 and cut out the section for Map references.
Carefully separate the 12 pieces and glue them in the correct places on the map below.
The location of each square is shown by the letter and number on each of the pieces.
Colour your completed map.
ISBN 978 1 74135 245 0
Topic MG19
Student Book Answers – Problem solving strategies
Strategy 1 Guess and check
Answer:
1
+
6
+
3
= 10
4
+
6
+
3
= 13
+
7
= 13
+
7
= 14
or
4
+
2
5
+
2
1
+
7
+
6
= 14
4
+
2
+
9
= 15
5
+
2
+
9
= 16
4
+
6
+
7
= 17
Problem solving
or
Strategy 2 Make a table or chart
Answer: 24
Strategy 3 Draw a picture or diagram
Answer: 3 km
Strategy 4 Act out the problem
Answer: The yellow crayon
Strategy 5 Find a pattern
Answer: A = 24, B = 38, C = 69, D = 74, E = 88
Strategy 6 Check for useful information
Answer: June
Strategy 7 Find smaller parts of a big problem
Answer: 9 squares
Strategy 8 Make an organised list
Answer: 6 different sandwiches:
cheese & tomato tomato & lettuce lettuce & ham
cheese & lettuce tomato & ham
cheese & ham
Strategy 9 Solve a simpler problem
Answer: 900
Strategy 10 Work backwards
Answer:
3rd prize is $5
ISBN 978 1 74135 245 0
179
Make your mark: Mark these numbers on the number line.
a 10
b 65
c 85
d 99
e 25
Answer:
0
1
2
3
4
5
10
99
50
25
Guess and check
Make a table or chart
Draw a picture or diagram
Act out the problem
Find a pattern
6
7
8
9
10
65
85
100
Check for useful information
Find smaller parts of a big problem
Make an organised list
Solve a simpler problem
Work backwards
When do you add? Some of these problems need addition. Read each problem carefully. Colour the ones that can be worked out
using addition, then add to find the answer.
Answer: a
b
c
14
55
27
+ 13
+ 44
+ 62
27 children
99 shells
89 cards
1
2
3
4
5
Guess and check
Act out the problem
Find a pattern
6
7
8
9
10
Work backwards
NA16 Backtracking
Back to backtracking: When Granny was sick the doctor gave her a box of tablets to make her better. Granny took 2 tablets every
day for 7 days . There are 36 tablets left. How many tablets were in the box that the doctor gave Granny?
Answer: 50
30
1
2
3
4
5
Day 7
2 tablets
Day 6
2 tablets
36
Guess and check
Act out the problem
Find a pattern
Day 5
2 tablets
Day 4
2 tablets
40
6
7
8
9
10
Day 3
2 tablets
Day 2
2 tablets
Day 1
2 tablets
50
Work backwards
NA18 Multiplication
Multiplication with 24: Use different colours to circle the 24 stars into these groups.
Answer:
1
2
3
4
5
180
Guess and check
Act out the problem
Find a pattern
6
7
8
9
10
Work backwards
ISBN 978 1 74135 245 0
Black squares: This pattern is not finished yet. How many black squares will there be?
Answer: 13
1
2
3
4
5
Guess and check
Act out the problem
Find a pattern
6
7
8
9
10
Work backwards
Let's face it: Complete the table below. Write the number of squares, rectangles, triangles and circles used to make each 3D object.
Answer:
1
2
3
4
5
squares
6
1
0
0
rectangles
0
0
6
1
triangles
0
4
0
0
circles
0
0
0
2
Guess and check
Act out the problem
Find a pattern
6
7
8
9
10
Work backwards
MG14 Nets of 3D objects
Cube nets: Which of these nets will make a cube? Cut out and fold the nets on page 197 to prove your choices.
There are 2 to find. Circle them.
Answer:
a
1
2
3
4
5
182
Guess and check
Act out the problem
Find a pattern
b
6
7
8
9
10
c
d
Work backwards
ISBN 978 1 74135 245 0
Key
Key strategies used to solve the task
Supporting strategies used to solve the task
MG19 Map references
On ice
Look at the map in page 129 of the Student Book. Make a list of the squares that are completely on the ice.
Give the map references for each one.
Answer: A8
E4 E2 E1
F8 F4 F3 F2 F1
G8 G3 G2 G1
H2 H1
Guess and check
Act out the problem
Find a pattern
ISBN 978 1 74135 245 0
6
7
8
9
10
Work backwards
Problem solving
1
2
3
4
5
183
Student Book Answers – Challenges
Dice pattern: Look at the totals of various pairs of faces on your cube. Can you find a pattern in the totals?
Answer: All the pairs of opposite faces total 7.
Sort the edges: Which shapes have only straight edges? Which shapes have only curved edges? Which shape has no edges?
Answer: straight edges: cube, pyramid, rectangular prism
no edges: sphere
curved edges: cone, cylinder
3D outlines: Try drawing some prisms where the two identical faces overlap.
Bunny directions: Tell the bunny between the tables some interesting places to hide.
“Black bunny, run... then... then...”
MG18 Maps
Treasure map directions: Give directions for someone walking from your classroom to the school gate.
Use the words ‘ahead’, ‘left’ and ‘right’ in your directions.
MG19 Map references
Seagull flight: Find the seagull at B2. It flies in the direction it is facing (diagonally) for 6 squares. Sometimes it flies over the sea,
sometimes over ice. Write the map references of the four places the seagull could land on ice.
Answer: D4, E5, G7, H8
Write numbers sdrawkcab: Try to write the numbers from zero to nine in mirror form. Some will be easy,
like 0 and 1, but then it gets tougher. To check, hold the numbers up to a mirror
or look at the reflection in a window.
Answer: 0 1 2 3 4 5 6 7 8 9
SP1 Probability
Take a chance: Make a list of events under the headings ‘Impossible’, ‘Unlikely’, ‘Likely’ and ‘Certain.’
SP2 Collecting data
Pogo power: What other forms of transport might be used to travel to school?
Try to think of some unusual ones.
SP3 Column graphs
Popular transport: What is the most popular form of transport for your class?
Why do you think this is so? List five possible reasons.
SP4 Picture graphs
Simple symbols: Picture graphs use simple symbols to show information.
Simple symbols or icons are often used on signs instead of words.
Can you draw or describe some icons you know?
Pool graph: Draw a column graph showing the different number of people who visit the local
swimming pool during one week. Suggest reasons for the differences on certain days.
188
ISBN 978 1 74135 245 0
a
b
c
d
e
46
71
355
507
889
0
10
20
30
40
NA9 Addition facts
a 900 + 30 + 1 b 300 + 2
50
60
70
90
100
0
10
20
30
40
50
60
70
80
90
100
300
310
320
330
340
350
360
370
380
390
400
500
520
540
800
560
580
g 42
j 90
a
b
145
d red
hun s
1
4
c
e
on s
5
2
4
te ns
0
d
5 7 2
e
5 7
f
5
d red
hun s
5
d red
hun s
te ns
e
on s
d red
hun s
250
5
te ns
7 2
7
h 505
e
on s
0
= 5 hundreds and 72 ones
e
on s
2
i 847
j 169
NA8 Place value with an abacus
a 135
b 529
d 131
e 600
f
g
t
O
i
194
H
t
O
j
H
t
60
+
3
g 563
300
+
10
+
3
h 19 9
600
+
0
+
7
i 728
100
+
90
+
9
j 6 07
700
+
20
+
8
a 5+1= 6
4+1= 5
6+2= 8
5+2= 7
b 2+2= 4
5 + 5 = 10
1+1= 2
4+4= 8
c 4+3= 7
3+2= 5
3+4= 7
5+4= 9
d 8 + 2 = 10
3 + 7 = 10
6 + 4 = 10
10 + 0 = 10
e 7+2= 9
8+1= 9
9+0= 9
5+4= 9
O
7+1= 8
3+3= 6
4+5= 9
9 + 1 = 10
= 5 hundreds, 7 tens and 2 ones
a 300 − 1
b 60 tens
c 17 + 5
d 40 + 30
e 90 hundreds
f 5 tens = 50
g 50 + 50 + 50 = 150
h 100 + 100 + 10 = 210
i 6 fifties = 300
j 100 + 20 + 5 = 125
H
+
= 57 tens and 2 ones
e
on s
te ns
500
e
on s
= 572 ones
2
313
e
on s
4
e 703
NA10 Addition facts
404
d red
hun s
d 495
900
h 52
te ns
f
c 888
600
850
f 18
i 70
g
80
H
t
f
g
h
c 40
h
i
H
t
O
6+3= 9
9
+2
3
+9
8
+3
10
+2
1
+ 10
11
12
11
12
11
7
+7
6
+6
8
+8
9
+9
5
+5
14
12
16
18
10
5
+6
7
+8
6
+7
8
+9
9
+ 10
11
15
13
17
19
11
6
10
4
8 3
7 4 +3 5 8
7 1
j
16
9
9 2
15 8 +7 0 7
6 7
13
14
O
ISBN 978 1 74135 245 0
226 + 8
b
3+5+7
c
6+1+4+9
+4
f
= 234
226
230
234
3 + 5 + 7
= 15
10
10
(40 + 10)
50
47 + 12
+
+
(7 + 2)
9
+10
e
84
+4
g
85
+3
86
90
93
3 + 6 + 7 + 5 + 4
72 + 26
(70 + 20)
90
+
+
(2 + 6)
8
i
15 + 34
(10 + 30)
40
+
+
(5 + 4)
9
j
155 + 9
+10
164
d 67
16
13
13
17
15
12
–6
18
–9
10
–5
14
–7
16
–8
6
9
5
7
8
15
–7
17
–9
15
–8
14
–6
12
–7
8
8
7
8
5
20
–4
16
–8
8
–3
5
–4 = 1
j
20
–7
13
–3
10
–5
5
–1 = 4
e 99
35
20 or 32
45
g
h
+ 22
+ 35
+ 45
+ 22
57
55
77
67
22 or 22
20 or 35
i
j
35
45
+ 32
+ 45
+ 20
+ 32
52
80
77
99
f
165
–2
a
= 49
8
9–8= 1
8–6= 2
7–6= 1
b 6–1= 5
4–1= 3
7–2= 5
5–2= 3
c 4–2= 2
6–3= 3
8–4= 4
10 – 5 = 5
d 6–4= 2
8–5= 3
10 – 4 = 6
10 – 6 = 4
e 9–9= 0
8–0= 8
4–4= 0
7–7= 0
ISBN 978 1 74135 245 0
9–7= 2
68
c
81 – 10
d
89 – 57
e
(80 – 50)
30
+
+
27
–10
37
28
g
89 – 10
h
99 – 33
= 86
93
90
= 79
89 – 10 = 79
(90 – 30)
60
+
+
(9 – 3)
6
= 66
–10
= 15
24 – 9
14
15
+1
j
24
–10
125 – 9
115
125
116
83
57 c
95 d
85
b
a
– 21
– 16
– 63
– 74
62
41
32
11
88
– 45
43
g
59
– 24
35
= 28
–3
86
f
= 32
93 – 7
8–1= 7
6–0= 6
(9 – 7)
2
–4
f
= 68
= 71
81 – 10 = 71
37 – 9
i
8–3= 5
74
70
+1
= 8
–4
74 – 6
+1
2–1= 1
15
10
–2
b
a 5–4= 1
–5
15 – 7
= 98
= 164
155
c 88
= 25
–1
b 75
16
–1
10
10
a 67
19
–2
i
= 93
3+6+7+5+4
h
h
= 59
= 84
75
86 + 7
15
–2
–1
75 + 9
f
14
–1
= 20
6 + 1 + 4 + 9
10
d
g
18
–2
h
85
– 45
40
i
66
– 24
42
= 116
e
97
– 37
60
j
45
– 24
21
195
Tracker Book
+4
a
NA13 Subtraction facts (continued)
NA16 Backtracking
a
a $25
32
30 + 2 = 32
– 2 = 30
b $12
c $14
d $16
Meals Order Form
Kid’s Meals
b
5
2
3
0
1
+ 2 = 15
13
15 – 2 = 13
e $9
c
Cost
$15
$8
$12
$0
$5
Nuggets and chips..................... $3
Spaghetti ..................................... $4
Burger and chips ........................ $4
Chicken and noodles ................. $5
Fish and chips.............................. $5
Desserts
77
78 – 1 = 77
9 Ice-cream and topping............. $2 $18
2 Apple pie and cream................. $3 $6
+ 1 = 78
Drinks
8 Lemonade ................................... $2 $16
1 Orange juice................................ $3 $3
2 Cordial........................................... $1 $2
d
– 2 = 40
42
40 + 2 = 42
e
69
71 – 2 = 69
f 49 − 2 = 47
g 83 + 5 = 88
i 90 + 6 = 96
j 50 + 12 = 62
+ 2 = 71
h 100 − 30 = 70
a
4
x
3
=
12
b
3
x
5
=
15
c
5
x
5
=
25
d
4
x
4
=
16
e
2
x
7
=
14
f 5x3
g 2x4
a 7 + (2 + 8) = 17
NA21 Division
b (5 + 5) + 1 = 11
a
h 3x3
i 10 x 4
j 9x5
b
c 6 + (6 + 4) = 16
d (3 + 7) + 10 = 20
e 4 + (11 + 9) = 24
f 25
g 240
6
h 222
i 1042
NA18 Multiplication
a 5 x 6 b 10 x 8 c 2 x 9
f
j 2953
d 10 x 3
g
d
e 5x4
h
3x4
2x6
c
4
6x3
3
2
e
i
j
3x3
There are other
correct groupings.
2x2
4
f 6
196
g 4
h 12
i 3
j 8
ISBN 978 1 74135 245 0
b
a
d
NA24 Make a $1 total (continued)
c
e
f
g
h
i
j
3
4
$
1
.
20
$
1
.
10
$
1
.
40
$
1
.
30
$
1
.
70
b
a
c
d
a
e
b
f 60c
c
d
g 55c
h 80c
i $20
j $15
NA26 Comparing coins
a
e
b
There are other
correct groupings.
g 1 of 8
8
h 1 of 12
4
NA24 Make a $1 total
a
c
b
i 1 of 10
2
j 1 of 16
4
c
Tracker Book
f 1 of 6
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ISBN 978 1 74135 245 0
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iMaths National - Firefly Education

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