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Look at the picture
on the cover. Work in
pairs and answer the
questions.
Activity box
1 What numbers can you see?
2 How many odd numbers are there?
3 What is the biggest number you can see?
4 How many football boots can you see?
5 David scored 2 goals. Zara scored 4 more than David. How many goals did
Zara score?
6 Half a match was 10 minutes long. How long was the whole game?
Cambridge Primary
Mathematics
Second Edition
Learner’s
Book 2
Catherine Casey
Steph King
Josh Lury
Series editors:
Paul Broadbent
Mike Askew
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ISBN: 978 1 3983 0094 1
© Catherine Casey, Steph King, Josh Lury 2021
First published in 2017
This edition published in 2021 by
Hodder Education,
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Printed in Italy
A catalogue record for this title is available from the British Library.
9781398300941_HCP_MATH_S2_LB.indb 2
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Contents
How to use this book
4
Term 1
Unit 1 Numbers to 100
6
Unit 2 Addition and subtraction
13
Unit 3 Shapes, direction and movement
28
37
Unit 4 Statistical methods and chance Unit 5 Multiplication and division
43
Unit 6 Time and measurement
58
Term 1 Review66
Term 2
Unit 7 Addition and subtraction
68
Unit 8 Money
81
Unit 9 Number patterns and place value
88
Unit 10 Time and measurement
100
Unit 11 Shapes, direction and movement
112
Unit 12 Fractions
120
Term 2 Review125
Term 3
Unit 13 Statistical methods and chance
127
Unit 14 Number patterns and place value
137
Unit 15 Addition and subtraction
147
Unit 16 Multiplication and division
161
Unit 17 Fractions
178
Unit 18 Time and measurement
182
Term 3 Review194
Mathematical dictionary
Thinking and Working Mathematically (TWM) skills vocabulary
9781398300941_HCP_MATH_S2_LB.indb 3
196
200
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How to use this book
This book will help you to learn about mathematics.
Explore the picture
or problem.
What do you see?
What can you find?
Understand new
Maths words.
The Mathematical
dictionary at the
back of the book
can help you.
Unit 11 Shapes, direction and movement
Position and movement
Explore
Where is
the parrot?
Maths words
turn
clockwise
anticlockwise
whole turn
half turn
quarter turn
This icon shows
you that the
activity links with
other subjects
in your school
curriculum.
Learn
A turn changes
the direction you
are facing.
Your position
stays the same.
115
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Unit 5 Multiplication and division
Learn new
mathematics skills
with your teacher.
Look at the pictures
to help you.
Learn
There are 10 baseball bats.
We can put them in groups of 2.
How many groups can we make?
2
4
6
8
10
10 divided into groups of 2 is
5 groups, so: 10 ÷ 2 = 5.
Can we put the 10 baseball
bats in groups of 5?
How many groups can we
make this time?
10 ÷ 5 =
Practise
The shaded
questions show
you what you
need to do.
1 You will need 20 counters. Find how many groups each time.
Make groups of 5.
a Make groups of 2.
20 ÷ 5 = 4
b Make groups of 10.
20 ÷ 2 =
20 ÷
=
2 There are 30 tennis rackets. Maris puts 10 in each basket.
How many baskets will she use? Write the division sentence.
3 a Look at the basketballs in groups of 5.
How many groups are there?
b Complete the division sentence.
Remember to write
any answers in
your notebook, not
in this textbook.
÷5=
Let’s talk
What can David do to help him make groups of 5 or 10 for division?
Try out your ideas to solve:
I can count in twos
and 60 ÷ 10 =
30 ÷ 5 =
to help make groups
of 2 for division.
54
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4
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How to use this book
Do the Practise
activities to
learn more.
Work like a
mathematician.
Unit 4 Statistical methods and chance
Practise
David asked his friends what their favourite fruit is.
Fruit
Number of
children
ll
llll
llll lll
l
Try this activities
make you think
carefully about
mathematics.
llll
1 Write the totals.
2 Use your results to draw a block graph.
3 Answer these questions about the
block graph.
a How many children like mangoes?
b How many children like oranges?
c Which is the most popular fruit?
d Which is the least popular fruit?
e How many more children like
oranges than mangoes?
f How many children did David ask?
Try this
Ask your friends what their favourite fruit is.
Create a block graph.
This star shows
you the activities
that require you
to Think and Work
Mathematically.
How will you collect the data? Which categories
or types of fruit will you choose?
For Let’s talk
activities, talk
about your ideas.
Let’s talk
You have looked at tally charts, block graphs and pictograms.
Which do you like best? Why? Use your critiquing skills.
Which is most useful? When would you use each one?
39
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Do each Quiz to
find out how much
you have learnt.
This icon shows you that
audio material is available.
Listen and you will learn.
Mathematical dictionary
Unit 1 Numbers to 100
Quiz
1 Make these numbers on ten frames.
a Seven
b Twelve
2D shapes two-dimensional geometric
shapes; flat shapes with sides and angles
c Seventeen
2 a Write the missing numbers.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
28
29
30
31
32
33
34
35
36
37
38
39
40
43
44
45
46
47
48
49
41
51
52
53
54
55
56
57
58
61
62
63
64
65
66
67
71
72
73
74
75
76
77
78
81
82
83
84
85
86
87
88
91
92
93
94
95
96
97
98
circle
triangle
square
rectangle
pentagon
hexagon
3D shapes three-dimensional
geometric shapes; solid shapes with
faces, edges and corners; see also face,
edge and corner
cube
59
60
69
70
79
80
99
100
sphere
cuboid
triangular prism
cylinder
square-based
pyramid
A
addition a calculation of the sum of
two numbers or things
amount the total of things such as
numbers, size or value
anticlockwise in the
opposite direction to
the hands of a clock
array an arrangement
made up of rows and columns
90
b Explain how you know what the missing numbers are.
3 Estimate how many people are in your class. Count to check.
4 a Estimate how many books are on a shelf. Count to check.
b Estimate how many pencils are in the class. Count to check.
12
9781398300941_HCP_MATH_S2_LB_01.indd 12
cone
B
block graph a diagram to show
information
C
calculation a way of finding the
number of something
calendar a chart or pages that show
the months and days of a whole year
capacity the largest amount that
something can contain
Carroll diagram a table used for
sorting things
Multiple of 5
Not a multiple of 5
10, 20, 30
2, 6, 12
Not an even 5, 15, 25
number
3, 7, 11
Even
number
category a division, class or certain
type of thing; music has categories
such as hip hop, folk, blues, pop
cent(s) a coin value
centimetre (cm) there are
100 centimetres in a metre
chance a possibility of
something happening
clockwise in the same
direction as the hands
of a clock
coin a piece of metal used as money
196
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5
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1
Numbers to 100
Reading and writing numbers to 20
Explore
Look at the picture of a night sky.
Can you see different groups of stars?
Say how many stars are in each group. Count them to check.
Are there different ways to count each group?
Do you need to count one by one?
Learn
One ten frame is full.
The other ten frame has 9 counters.
Maths words
count
twenty
estimate
19 is 10 and 9 more.
Now take 18 counters.
Show the different ways you can make 18 on 2 ten frames.
6
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Unit 1 Numbers to 100
Practise
1 Make these numbers on ten frames. Draw each pattern you make.
b 5
11
a 1
2 a Find the matching pairs.
20
twelve
12
seventeen
7
four
15
c
11
17
fourteen
eleven
10
20
14
twenty
seven
b Which card does not match?
3 How many cubes are there? Estimate. Then count to check.
Copy the table and write your answers.
I estimated …
a
b
c
I counted …
d
Try this
Draw a space picture.
Show groups of stars that add up to 20.
Then add some other space objects.
Let’s talk
Challenge a partner to estimate how many stars
there are in each group in your space picture.
Then count the groups of stars together aloud.
7
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Unit 1 Numbers to 100
Reading and writing numbers to 100
Maths words
hundred
numeral
thirty
forty
fifty
Explore
Look at the hundred (100) number grid.
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
Which numbers
do you know?
Can you see any
number patterns?
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
Learn
Point to and say each numeral on the number track.
Find the matching words.
10
20
30
ten
twenty
seventy
40
thirty
eighty
50
60
forty
ninety
70
fifty
80
90
100
sixty
hundred
Now practise counting from 21 to 29.
21
22
23
24
25
26
27
28
29
Twenty-one, twenty-two … How do I go on?
8
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Unit 1 Numbers to 100
Practise
1 Say each number aloud.
31
32
33
34
35
36
37
38
39
40
48
49
58
59
2 Write the missing numbers in words and numerals.
a
41
b
51
43
44
52
45
54
47
56
3 Which numbers are wrong?
61
62
63
65
64
66
67
68
69
70
71
27
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
98
90
91
92
93
94
95
96
97
89
99
100
Try this
Let’s talk
Use 2 of the cards below
to make a number.
How many different
numbers can you make?
A numeral is a figure
or symbol that
stands for a number.
1
3
0
7
I made thirteen.
I made seventy-three.
You need a large
100 grid and counters.
Play with a partner.
Take turns to cover 5 numbers
on the 100 grid.
Write the hidden numbers
in words and as numerals.
Score a point for each correct
word or numeral.
9
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Unit 1 Numbers to 100
Estimating and counting to 100
Explore
David and Zara are counting to 100.
Thirty-eight, thirty-nine, thirty-ten, …
I am lost! Please help me.
I see a pattern in the
numbers. This helps
me to count correctly.
Estimate the number of marbles, then count to check.
Learn
The paperclips fell out of the box.
Discuss the children’s estimates. Then count to check.
I can see a lot
more than 10.
Is it nearly 100?
Practise
1 Use a 100 grid to practise these counting patterns.
a Start on 1. Count up to 50. b Start on 63. Count up to 83.
c Start on 25. Count up to 45. d Start on 100. Count back to 1.
10
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Unit 1 Numbers to 100
Practise (continued)
2 Estimate. Then count to check.
b
a
c
d
Try this
Make your own number grid.
Invent a different pattern for placing the numbers.
Challenge your classmates to count on your number grid.
Let’s talk
Work in a group. Use 100 cubes or counters.
Place some of the cubes or counters in a circle.
All group members must estimate how many there are.
Then count together to check.
11
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Unit 1 Numbers to 100
Quiz
1 Make these numbers on ten frames.
a Seven
b Twelve
c Seventeen
2 a Write the missing numbers.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
28
29
30
31
32
33
34
35
36
37
38
39
40
43
44
45
46
47
48
49
58
59
60
69
70
79
80
41
51
52
53
54
55
56
57
61
62
63
64
65
66
67
71
72
73
74
75
76
77
78
81
82
83
84
85
86
87
88
91
92
93
94
95
96
97
98
90
99
100
b Explain how you know what the missing numbers are.
3 Estimate how many people are in your class. Count to check.
4 a Estimate how many books are on a shelf. Count to check.
b Estimate how many pencils are in the class. Count to check.
12
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2
Addition and subtraction
The relationship between addition
and subtraction
Explore
Let’s also buy
some lemonade!
Lemonade
2 friends join you in the line to buy lemonade.
How many children are in the line now?
When the first 3 children have paid for their lemonade,
how many are left in the line? What do you notice?
Learn
Maths word
inverse
In the Explore box above: 5 + 3 = 8 and 8 – 3 = 5.
+3 children
0
1
2
3
4
5
6
7
8
9
10
8
9
10
–3 children
0
1
2
3
4
5
✗
6
✗
7
✗
When we add 3 and then subtract 3, we go back to the start.
Addition and subtraction are inverse operations because one
operation undoes the other.
13
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Unit 2 Addition and subtraction
Practise
1 Give the addition and subtraction sentences to match each pair
of number lines.
a
0 1 2 3 4 5 6 7 8 9 10
✗ ✗
0 1 2 3 4 5 6 7 8 9 10
✗ ✗
b
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
+
=
–
=
–
=
+
=
2 Copy these inverse addition and subtraction wheels.
Look at the example and then complete them.
Write the matching addition and subtraction sentences.
a
b
c
add
add
add 3
add 4
2
5
subtract 3
5
7
6
subtract
subtract 4
6
9
subtract
Let’s talk
What could the missing numbers be in this set of related facts?
+
= 9 9 –
=
+
= 9 9 –
=
Share your ideas with the group.
Have you all picked the same numbers? Why?
14
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Unit 2 Addition and subtraction
Addition and subtraction facts for 10
Explore
Maths words
total
amount
complement
Look at the children’s
number cards!
7
6
What are the missing numbers?
2+
+ 6 = 10
= 10
10 = 2 +
10 =
What other totals of 10 can
you make?
2
3
+6
4
0 10
1
9
5
8
Learn
We can use the addition number facts for 10 to find the
subtraction facts.
6 + 4 = 10
10 – 4 = 6
When we take away 4 from 10, it leaves 6. The number line shows
that we subtracted the same amount that we added.
6 + 4 = 10
0
1
2
3
4
5
6
7
8
9
10
10 – 4 = 6
15
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Unit 2 Addition and subtraction
Practise
1 Write the addition and subtraction facts.
a
+
= 10 b
–
=
c
+
= 10 d
–
=
2 Look at the hands. Write an addition and subtraction fact.
a
b
8 + 2 = 10
7+
10 – 2 = 8
10 – 3 =
= 10
+
10 –
= 10
=
3 Here are 2 number facts for the flowers.
2 + 8 = 10 and 10 – 8 = 2
Write 2 number facts for each row of flowers.
a
b
c
16
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Unit 2 Addition and subtraction
Try this
Let’s talk
We say that two numbers
that total 10 are
complements of 10.
How many complements
of 10 can you remember?
Show a friend how you
answered these questions
using number facts for 10.
a Annay has 10 stickers and
gives away 3. How many
does he have left?
b There are 10 cars in the
car park and 8 drive away.
How many are left?
c Viti has 10 cents.
She spends 5 cents.
How many cents does she
have left?
Pairs that total 20
Explore
Zara and Annay want to
put 20 pencils in a pot.
Which 2 packs of pencils
can they put together
to make 20?
Which other pairs
of pencils make 20?
Can they fill 5 pots?
17
9
3
20
20
pencils
11
20
pencils
13
5
7
15
20
pencils
pencils
20
pencils
6
17
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Unit 2 Addition and subtraction
Learn
We can use what we know about complements of 10 to help us
find complements of 20. Look at the examples.
What do you notice?
What is the same?
What is different?
20 is 10 more than 10.
16 is 10 more than 6.
6 + 4 = 10
16 + 4 = 20
What number is 10 more than 4?
Can you use this to make
another complement of 20?
Practise
1 Find the missing numbers to complete the complements of 20.
b
c
d
a
20
20
20
20
11
3
6
7
2 a Complete the number sentences.
12 +
= 20
3+
= 20
+ 6 = 20
2+
= 20
13 +
= 20
+ 16 = 20
b What patterns do you notice?
Let’s talk
What should you look for when finding complements of 20?
Make up some rules that will help others.
18
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Unit 2 Addition and subtraction
Addition and subtraction with numbers to 20
Explore
Maths words
Zara and Jack play a game.
part-part-whole model
They number 20 stones from 1 to 20.
regroup
Zara always adds the two numbers
that she turns over.
Jack always subtracts the smaller number
that he turns over from the larger number.
Who will make a number more than 10?
Who will make a number less than 15?
20
4
What numbers did the children make?
5
9
What other numbers could they
make on their next turn?
Play the game with a partner.
Learn
On her first turn, Zara adds 9 and 4.
She uses a number line to help her.
0
1
2
3
4
5
6
7
8
+1
9
+3
10 11 12 13 14 15
She adds 1 and then she adds 3.
Why do you think she does this?
The part-part-whole model also shows
Zara’s addition:
Zara makes a 10. She can regroup
(break up) the 4 into 1 + 3
because she knows that 9 and 1
is a complement of 10.
4
9
+
1
+
3
= 13
10
19
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Unit 2 Addition and subtraction
Practise
Oh look, 7 + 6 is a bit more than
6 + 6. We say that 7 + 6 is a near
double. Can you spot any other
near doubles in the questions?
1 Complete these additions.
Draw number lines or
part-part-whole models
to help you.
a 11 + 4 =
b 12 + 4 =
8+ 7 =
d 9 + 10 =
c
2 Complete the additions. How will you regroup the red sticks
of cubes to help you make a 10?
b
c
a
+
+
+
3 a A bag of stones is 6 kg heavier than a 13 kg bag of sand.
What is the mass of the bag of stones?
b A crayon is 5 cm shorter than a pencil.
The crayon is 8 cm long. How long is the pencil?
Try this
Which additions have totals greater than 15? Do not calculate.
8+5
13 + 1
9+8
16 + 4
5+6
3 + 13
6 + 10
Explain to a partner how you know.
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Unit 2 Addition and subtraction
Learn
Jack subtracts 6 from 14. He uses a number line to help him.
–2
0
1
2
3
4
5
6
7
8
9
–4
10 11 12 13 14 15
He subtracts 4. Then he subtracts 2. Why do you think he does this?
Practise
1 Complete these subtractions. Draw number lines or
part-part-whole models to help you.
a
20 – 7 =
b
15 – 6 =
19 – 7 =
15 – 7 =
18 – 7 =
14 – 6 =
–7=
14 –
=7
2 Annay has $17. Maris has $16.
Annay spends $4 on a book and then $8 on a ball.
Maris spends $12 on a game.
Who has more money left? How much more?
Try this
Jack continues to play the 1 to 20 stones game
from Explore on page 19. He says he must always
regroup (break up) the smaller number to help
him subtract it from the larger number.
Do you agree? Can you think of other methods
you could use? Give some examples.
20
5
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Unit 2 Addition and subtraction
Adding small numbers
Explore
Zara and David want
to buy some balloons.
Which balloons can
the children buy?
Can they buy
2 balloons each?
Can they buy 3 each?
How will you add the
numbers to check?
5
2
9
8
4
3
I want my balloons to
have a total of more
than 15 but less than 20.
2
5
8
6
1
7
4
3
I want my balloons to have
a total of less than 15.
Learn
When we add small numbers, it helps
to look for pairs that total 10 first.
8+2+6=
8 and 2 total 10.
Can you see a pair that
totals 10 in this example?
Remember that we can
add in any order.
5
+4+
5
10
10 and 6 total 16, so 8 + 2 + 6 = 16
Can you also see a double?
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Unit 2 Addition and subtraction
Practise
1 Complete these additions. Draw number lines or
part-part-whole models to help you.
a
+
+
Make an estimate
b
+
+
first. Will the total
c
+
+
be greater than 10
d
each time? Will it
+
+
be less than 20?
2 Use ten frames and counters to add
How do you know?
these. First find a pair that totals 10.
a 4+6+7=
b 3+3+7=
c 8+1+9=
d 5+ 3 + 7 + 5 =
3 Maris has some ribbon: 7 metres of red,
8 metres of blue and 3 metres of yellow.
How many metres of ribbon does she have in total?
Try this
Rewrite these additions
to show the order you
will add them.
3+4+6=
2+5+3=
1+3+9+2=
2+5+5+8=
Let’s talk
Sometimes you will not find a pair of
numbers that total 10 straight away.
What can you do to help you complete
these additions?
3 + 4 + 3 7+2+1
3 + 2 + 5 6+8+6
Share your ideas with a partner.
Can you make up some other examples
that you might add in a similar way?
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Unit 2 Addition and subtraction
Adding multiples of 10
Explore
Annay is exploring patterns.
He makes rows of circles and triangles.
Maths words
multiple of 10 equal
How many circles do I use in each pattern?
How many triangles? How many shapes altogether?
What other patterns can
you make with the rows?
Talk about the number
of circles and triangles
each time.
Learn
There are 10 shapes in each row of Annay’s patterns.
We can count the rows in tens.
A number that can be counted in tens is called a multiple of 10.
There are 10 rows of ten in each pattern. 10 tens is equal to 100.
Look at the diagrams below. They show other number facts to 10
to help you add multiples of 10.
+
=
4 ones + 3 ones =
7 ones
+
=
4 tens + 3 tens =
7 tens
What is the same about these additions? What is different?
4 tens is equal to 40.
3 tens is equal to 30.
7 tens is equal to 70.
So, 40 + 30 = 70.
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Unit 2 Addition and subtraction
Practise
Complete the matching number sentences each time.
1 Here are some more of Annay’s patterns.
a
tens +
tens =
tens
+
= 100
b
tens +
+
tens =
tens
= 100
c
tens +
+
2 a
tens =
= 100
ones +
+
So,
tens +
and
+
b
ones +
+
tens
So,
tens +
and
+
ones =
tens =
ones
tens
=
ones =
tens =
ones
tens
=
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Unit 2 Addition and subtraction
Practise (continued)
c
ones +
+
So,
tens +
and
+
ones =
ones
tens =
tens
=
3 Complete these additions.
a 30 + 40 =
b 20 + 70 =
c 50 +
= 60
40 + 30 =
70 + 20 =
10 +
= 60
50 + 30 =
70 + 30 =
+ 50 = 70
4 A farmer planted 70 seeds.
20 seeds grew into plants.
How many seeds did not grow?
Try this
Sort these calculations into sets by their totals.
20 + 60
90 + 10
Total is 80
40 + 60
10 + 80
Total is 90
50 + 40
20 + 80
Total is 100
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Unit 2 Addition and subtraction
Quiz
1 Complete these number sentences:
a 4 + 7 = 11 so
–
b 5 + 6 = 11 so
–6=
c 8 + 3 = 11 so
–
=4
=
2 Write the addition and subtraction facts for each of these.
b
c
a
10
10
10
3
7
6
4
1
9
3 True or false?
a 12 + 8 = 20 b 14 + 5 = 20 c 7 + 12 = 20 d 8 + 12 = 20
4 Complete these additions and subtractions.
a 11 + 6 =
d 6+
= 17
b 9+8=
c 15 –
e 20 – 8 =
f 15 – 7 =
= 11
5 There are 14 goats on the mountain. Five more goats arrive.
How many goats are on the mountain now?
6 Complete each number sentence.
a 3 + 5 = 8, so 30 + 50 =
b 4 + 3 = 7, so 40 +
= 70
c 5 + 5 = 10, so
+
= 100
d 8 + 2 = 10, so
+
= 100
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3
Shapes, direction
and movement
2D and 3D shapes
Explore
Look at the pictures that the children are holding.
They show different shapes!
Maths words
corner
curved
side
face
edge
Name the 2D shapes that you can see.
Name the 3D shapes that you can see.
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Unit 3 Shapes, direction and movement
Learn
This table shows the features of 2D shapes.
Object
Name of shape Description/features
Circle
0 corners
1 curved side
Triangle
3 corners
3 sides
Square
4 square corners
4 sides of equal length
Rectangle
4 square corners
4 sides
Opposite sides of equal length
Hexagon
6 corners
6 sides
This table shows the features of 3D shapes.
Object
Name of shape Description/features
Cone
1 circle face, 1 curved surface
Cuboid
8 corners, 6 faces, 12 edges
Sphere
1 curved surface
Cylinder
2 circle faces, 1 curved surface
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Unit 3 Shapes, direction and movement
Learn (continued)
Circles are all around us.
A circle has a centre point.
The distance from the centre
to any point on the curved side
is always the same.
centre point
The table below shows one way to sort these shapes.
Shapes that have 4 corners Shapes that do not have 4 corners
Practise
1 Which shapes are circles?
a
b
c
d
f
g
h
i
e
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Unit 3 Shapes, direction and movement
Practise (continued)
2 Complete a table like this.
Shape
Number Number
of corners of faces
0
Cylinder
Number of edges
3
2
Cuboid
Triangularbased prism
Triangularbased pyramid
3 Write two special features of each shape.
square
a
cube
b
d
octagon
e
pentagon
4 corners
4 sides
c
square-based
pyramid
triangular
prism
4 What 2D shapes are the faces of these 3D shapes?
b
a
square
triangle
c
rectangle
d
hexagon
Some 3D shapes have
different face shapes.
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Unit 3 Shapes, direction and movement
Practise (continued)
5 Sort each set of shapes into 2 groups. Explain your groups.
a
bicycle wheel
textbook
car tyre
clock
window
button
square-based
pyramid
sphere
cube
cone
cuboid
cylinder
cardboard box
ball of string
box of tissues
golf ball
traffic cone
football
b
c
6
This shape has
This shape has
straight sides.
straight sides.
It has 3 corners.
It has 4 corners.
a What is the same about the shapes?
b What is different about the shapes?
Try this
Jack and Maris are
playing draughts.
How many
squares can
you see?
Let’s talk
Look at the shapes
around you. How many
circles can you find?
Explain the features of
a circle to a partner.
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Unit 3 Shapes, direction and movement
Patterns and pictures
Explore
Jack and Annay are decorating bags.
They have printed patterns.
What shape is next in Annay’s pattern?
What shape is next in Jack’s pattern?
How are the patterns different
to each other?
Learn
Patterns and sequences are made from shapes
or numbers repeating.
Maths words
pattern
sequence
What shape is next?
What is the pattern
that is repeated?
What shape is next?
What is the pattern
that is repeated?
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Unit 3 Shapes, direction and movement
Learn
The picture shows a racing car track!
What 2D shapes
can you see?
What 3D shapes
can you see?
This picture shows a jungle model that Elok made! What 3D shapes
can you see?
What 2D shapes
can you see?
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Unit 3 Shapes, direction and movement
Practise
Draw the next shape in each sequence for questions 1 and 2.
1 a
b
c
2 a
b
c
3 What shapes do you see in the picture?
a
b
e
c
d
d
b
a
e
f
c
f
Try this
Let’s talk
Use modelling clay to make
3D shapes. Can you make an
animal from your shapes?
What is the pattern?
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Unit 3 Shapes, direction and movement
Quiz
1 a Which 2D shapes is the robot made of?
b How many sides does each shape have?
c How many corners does each shape have?
2 a Write the name of each shape, A and B.
b How many faces does each shape have?
c How many edges does each shape have?
d How many corners does each shape have?
A
B
3 Sort these shapes in 2 different ways.
4 Copy the pattern and draw the next shape each time.
a
b
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4
Statistical methods
and chance
Pictograms and block graphs
Explore
The children are having fun at the beach!
Maths words
popular
tally chart
tally
data
block graph
pictogram
category
Tally chart
Fishing
||||
In the sea ||||
What is the most popular activity?
Which activity do you like best?
Look at the tally chart. Have you used one?
Flying a kite |||
Reading
||
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Unit 4 Statistical methods and chance
Learn
Zara asked her friends what their favourite colour is.
She made a tally. The picture shows you how she did this.
What is your favourite colour?
Blue
|||
Red
|||| ||
Orange ||
Green
Record or keep track of
each person as a line.
Remember that the
fifth line goes across
the first four lines.
||||
Zara used the information or data to draw a block graph and
a pictogram.
Number of children
A block graph to show children’s
favourite colours
10
9
8
7
6
5
4
3
2
1
0
A pictogram to show children’s
favourite colours
Blue
Red
Orange
Green
Blue
Red
Orange
Favourite colours
Green
Key:
= 1 person
What is different about the
block graph and the pictogram?
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Unit 4 Statistical methods and chance
Practise
David asked his friends what their favourite fruit is.
Fruit
Number of
children
ll
llll
llll lll
l
llll
1 Write the totals.
2 Use your results to draw a block graph.
3 Answer these questions about the
block graph.
a How many children like mangoes?
b How many children like oranges?
c Which is the most popular fruit?
dWhich is the least popular fruit?
eHow many more children like
oranges than mangoes?
f How many children did David ask?
Try this
Ask your friends what their favourite fruit is.
Create a block graph.
How will you collect the data? Which categories
or types of fruit will you choose?
Let’s talk
You have looked at tally charts, block graphs and pictograms.
Which do you like best? Why? Use your critiquing skills.
Which is most useful? When would you use each one?
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Unit 4 Statistical methods and chance
Venn diagrams and Carroll diagrams
Maths words
Venn diagram
Carroll diagram
Explore
How have these shapes been sorted?
What could the sorting labels be?
Learn
We use Venn diagrams and Carroll diagrams for sorting numbers
or objects. For example, look at these numbers:
2 5 14 10 25 6 15 20 12 35
Which numbers are even numbers?
Which numbers are multiples of 5?
The numbers have been sorted in these diagrams.
Venn diagram
Carroll diagram
Even numbers
2
6
12
14
Multiples of 5
10
20
5
25
35
15
Multiples
of 5
Even
numbers
Not even
numbers
10
20
5 15
25 35
Not multiples 2 6
of 5
12 14
Where would you put the number 30? Where would you put 21?
What do you notice about the diagrams?
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Unit 4 Statistical methods and chance
Practise
1 Complete a Venn diagram like this. Use these numbers:
Odd numbers
5
Multiples of 5
3
20
9
11
1
10
15
7
25
2 Complete a Carroll diagram like this. Use the numbers given:
3 5 12 20 17 13 2 8
10 or bigger
Not 10 or bigger
Even
Not even
Try this
Use a handful of 2D shape tiles.
Choose a shape and place it into
a blank Venn diagram. Repeat.
How many shapes can you put into the
Venn diagram before your partner guesses your rule?
Let’s talk
Use your critiquing skills. What is different about Venn diagrams
and Carroll diagrams? What is the same about them?
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Unit 4 Statistical methods and chance
Quiz
1 This tally chart shows children’s favourite animals.
Animal
Tally
Elephant
llll l
llll llll
lll
llll lll
Zebra
Rhino
Lion
a Use the tally chart to draw a block graph.
b Write the most popular animal.
c Write the least popular animal.
d How many children like lions the most?
e How many more children like zebras
than rhinos?
2 Complete a Venn diagram like this. Use these numbers:
15 or bigger
Even
8
18
5
12
15
16
20
14
3 Choose 12 numbers to complete a Carroll diagram like this.
20 or bigger
Not 20 or bigger
Even number
Not an even number
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5
Multiplication and division
Counting in twos, fives and tens
Maths word
total
Explore
The market sells fruit.
I’m going to buy
some strawberries!
I’m going to buy
some pineapples!
David has 7c. Zara has 35c. How much can they buy?
Learn
When Annay visits the market in Explore, he buys 6 oranges.
We can count in fives to help us find out how much he spends.
cents
0
5
10
15
20
25
30
Annay also buys 3 passion fruits. How much does he spend in total?
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Unit 5 Multiplication and division
Learn (continued)
We can carry on counting in fives from 30.
cents
30
35
40
How much change
will Annay get
from 50 cents?
45
Annay spends 45 cents in total.
Practise
Look at Explore on page 43 to answer questions 1 and 3.
1 How much do the fruits cost in total? Use counting to help you.
a 7 strawberries
b 3 passion fruits and 4 oranges
c 5 pineapples
d 5 pineapples and 3 bananas
e 7 strawberries and 2 more strawberries
2 Answer these. Count back to zero each time:
a in fives from 25; how many fives did you count?
b in tens from 90; how many tens did you count?
c in twos from 16; how many twos did you count?
3 Maris has 80 cents. She buys 6 passion fruits and 4 oranges.
How much money does she have left?
Let’s talk
David counts in twos from zero. Zara counts in fives from zero.
Which of these numbers will the children say:
40 24 20 15 21 10 9?
Which numbers will they not say? Can you think of other numbers
they will not say? Convince your partner.
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Unit 5 Multiplication and division
Multiplication as repeated addition
Explore
At the animal sanctuary, the
helpers pack boxes of fruit for
the animals to eat, 1 box has:
1 watermelon 2 melons
3 grapefruits 4 plums
5 pineapples 6 passion fruits
7 bananas
8 kiwi fruits
9 mangoes
10 guavas
How many of each fruit
are needed for 2 boxes?
What patterns do you notice?
Learn
There are 2 melons in each box. We can count in twos to find
how many melons we need for more than 1 box.
+2
+2
+2
+2
+2
+2
+2
+2
+2
+2
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
For 2 boxes, we need 4 melons.
We can write this as a repeated addition: 2 + 2 = 4
For 3 boxes, we need 6 melons. We can write this as a repeated
addition: 2 + 2 + 2 = 6
What patterns do you notice?
Maths words
Write a repeated addition sentence to show
repeated addition
the number of melons for 4 boxes.
multiplication
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Unit 5 Multiplication and division
Practise
1 Each box has 2 melons. Write the
repeated addition for how many in:
a 6 boxes?
b 7 boxes?
c 9 boxes?
d 10 boxes?
Use the number line
in Learn to help you.
2 A box has 5 pineapples in it.
a Draw a number line to show the count of 5 up to 50.
b Fill in a table like this.
Number of boxes Repeated
Total number of
addition sentence pineapples
2
5 + 5 = 10
10
5
6
10
3 A box has 10 guavas in it.
a Draw a number line to show the count of 10 up to 100.
bComplete a table like this.
Number of boxes Repeated
Total number of
addition sentence guavas
2
4
7
10
Try this
I think:
2 + 2 + 2 + 2 + 2 + 2 + 2 = 15
Do you agree with David?
Explain your thinking.
I don’t need to check Viti’s addition.
I know she has made a mistake.
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Unit 5 Multiplication and division
Learn
4 boxes have 20 pineapples because: 5 + 5 + 5 + 5 = 20
0
5
box
10
box
15
box
5 is the size of each group.
4 is the number of groups.
20 is the total number
of pineapples.
We can write this using the
multiplication (×) sign as:
5 × 4 = 20
20
box
We can also say that
5 multiplied by 4 is 20.
Practise
1 How many pineapples? Write a repeated addition sentence and
a multiplication sentence each time.
b
a
c
d
2 True or false?
a 2+2+2=2×3
b 2+2+2+2=2×5
c 2+2+2+2+2+2+2=2×6
d 2+2+2+2+2+2+2+2+2=2×9
Try this
Jack’s multiplication sentences show what fruit to pack in boxes.
5 × 6 = 30 2 × 8 = 16 10 × 7 = 70 5 × 9 = 45
Which digits show the group size? Which show the number of
groups? Write the repeated addition sentences to match.
Why do you think Jack wrote multiplication sentences?
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Unit 5 Multiplication and division
Using arrays to show multiplication
Explore
These stamps were
designed to celebrate
the Olympic Games.
Maths words
array
equal
How can you find the total
number of stamps in each set?
Is there a different way?
What do you notice about the
way the stamps are arranged?
How can this help you?
Learn
An array has equal rows and columns. This array has 3 rows of 5.
We write: 5 + 5 + 5 or 5 × 3
How many counters in total?
We can also see 5 columns of 3.
We can write:
3+3+3+3+3=3×5
3 × 5 = 15 and 5 × 3 = 15
3×5=5×3
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Unit 5 Multiplication and division
Practise
1 Complete the addition and multiplication sentences for
each array. Look at the example.
2
+ 2
+ 2
2
× 3
= 6
+
+
×
=
+
=
×
=
+
+
a
b
c
+
+
= 6
+
=
+
=
×
=
Think about the number of groups
and the group size each time.
2 Write 2 multiplication sentences
for each set of stamps.
b
a
c
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Unit 5 Multiplication and division
Practise (continued)
3 Use counters to make arrays that match each pair of
multiplication sentences.
a 2 × 5 = 10
b 2 × 6 = 12
c 2 × 7 = 14
5 × 5 = 25
5 × 6 = 30
5 × 7 = 35
d Which 2 arrays come next in this pattern?
Write the multiplication sentences.
Try this
Choose 2 numbers.
1
2
3
4
5
10
Write a multiplication calculation. Use counters to make an array.
Can you use the same total number of counters to make a different
array? Write the new multiplication sentence.
Let’s talk
This array
shows 5 × 4.
Talk to a partner:
Do you agree or disagree with Jack?
Why might Jack think he is correct?
Why is Jack wrong?
Can you improve Jack’s array?
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Unit 5 Multiplication and division
Division as sharing
Explore
Maths words
share
divide
The owl needs to feed the 5 owlets.
How many worms
must the owl find
so that the owlets
get an equal share?
Learn
The owl collects 15 worms. It shares
them equally between the owlets.
Each owlet gets 3 worms.
15 divided equally between 5 is 3.
We can write: 15 ÷ 5 = 3
We can show this as a bar model
with 5 equal parts.
3
15 worms
3
3
3
The ÷ sign
means divide.
3
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Unit 5 Multiplication and division
Practise
1 You will need 20 counters.
a Share them equally between 2 groups.
How many are in each group?
20 ÷ 2 =
b Share them equally between 5 groups.
How many are in each group?
20 ÷ 5 =
c Share them equally between 10 groups.
How many are in each group?
20 ÷
=
2 The owl collects 30 worms.
The owl divides the worms equally between the 5 owlets.
How many for each owlet? Write the matching division sentence.
3 Write the matching division each time.
b
c
a
8
10
30
4
4
2 2 2 2 2
? ? ? ? ? ? ? ? ? ?
Try this
Maris cuts a 50 cm length of ribbon into 5 equal pieces.
How long is each piece? Write the division sentence.
Maris then cuts each piece in half.
Explain why the division sentence is now: 50 ÷ 10 =
Let’s talk
Dividing equally between 2
is the same as halving.
Do you agree?
Use some examples to help convince your partner.
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Unit 5 Multiplication and division
Division as grouping
Explore
Sort the sports balls into groups.
Maths word
sort
group
Put an equal number of balls in each basket.
How many baskets will you use each time?
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Unit 5 Multiplication and division
Learn
There are 10 baseball bats.
We can put them in groups of 2.
How many groups can we make?
2
4
6
8
10
10 divided into groups of 2 is
5 groups, so: 10 ÷ 2 = 5.
Can we put the 10 baseball
bats in groups of 5?
How many groups can we
make this time?
10 ÷ 5 =
Practise
1 You will need 20 counters. Find how many groups each time.
Make groups of 5.
a Make groups of 2.
20 ÷ 5 = 4
b Make groups of 10.
20 ÷ 2 =
20 ÷
=
2 There are 30 tennis rackets. Maris puts 10 in each basket.
How many baskets will she use? Write the division sentence.
3 a Look at the basketballs in groups of 5.
How many groups are there?
b Complete the division sentence.
÷5=
Let’s talk
What can David do to help him make groups of 5 or 10 for division?
Try out your ideas to solve:
I can count in twos
and 60 ÷ 10 =
30 ÷ 5 =
to help make groups
of 2 for division.
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Unit 5 Multiplication and division
Division as repeated subtraction
Explore
A group of 20 children visit the fun park
for a day. Here are some of the rides.
Maths word
repeated subtraction
Teacup ride
5 people in each car
House of Mirrors
10 people at a time
Fun drive
ride
2 people
in each c
ar
All the children want to go on the 3 rides.
How many cars will the children need for each ride?
How many groups of 10 for the House of Mirrors?
Learn
We can count back in fives to find how many Teacup ride cars
20 children will need.
–5
0
–5
5
–5
10
–5
15
20
25
30
We need 4 cars for 20 children.
We can count back (subtract) 4 groups of 5 and no children will be left.
We can write this as a repeated subtraction: 20 – 5 – 5 – 5 – 5 = 0
How many cars are needed for 15 children? And for 10 children?
What patterns do you notice?
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Unit 5 Multiplication and division
Practise
1 Write repeated subtraction sentences each time.
How many Fun drive ride cars are needed for:
a 14 children b 16 children c 18 children d 22 children?
2 Write a repeated subtraction sentence to match each number line.
– 10
– 10
– 10
– 10
a
0
b
10
– 10
0
c
20
– 10
10
– 10
0
– 10
20
– 10
10
30
– 10
30
– 10
20
40
– 10
40
– 10
30
– 10
50
– 10
40
60
– 10
50
– 10
60
70
3 Zara has 80 cents to spend. She spends 10 cents on each ride.
How many rides is this? Write the repeated subtraction sentence.
Try this
The Teacup ride can take 5 people per car.
The Fun drive ride can take 2 people per car.
Convince a partner that 26 people cannot be on the Teacup ride,
but 26 people can be on the Fun drive ride.
Let’s talk
I can use repeated subtraction
to solve a division.
Do you agree with Annay?
Try his idea for 30 ÷ 10 and 18 ÷ 2.
15 ÷ 5 = 3
15 – 5 – 5 – 5 = 0
I subtracted 3 lots of 5,
as there are 3 fives in 15.
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Unit 5 Multiplication and division
Quiz
1 Count on in twos from 0 to 24. How many twos?
2 Count back in tens from 50 to 0. How many tens?
3 Count on in fives from 0 to 45. How many fives?
4 Write repeated addition and multiplication sentences to match
each array of cupcakes.
a
b
5 A baker packs bread rolls into bags.
Each bag has 4 rolls in it.
a How many bread rolls are in 2 bags?
b How many bread rolls are in 5 bags?
c How many bread rolls are in 10 bags?
6 a The baker bakes 60 biscuits.
She puts 10 on each tray.
How many trays does she use? 60 ÷ 10 =
b The children take 2 biscuits each from one of the
trays in part a.
How many children can take 2 biscuits?
7 The baker bakes 30 cupcakes.
She divides them equally between 5 plates.
How many cupcakes are on each plate? 30 ÷ 5 =
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6
Time and measurement
Time
Explore
Make a paper plate clock!
You need
l paper plate
l felt-tip pen
l split pin paper fastener
l sheet of coloured card
l pair of scissors
Method
1 Write the numbers 1 to 12
around the paper plate.
Space them evenly, as on
a clock face.
2 Draw and cut out an hour
hand and a minute hand
from the coloured card.
3 Use the split pin to attach
the minute and hour
hands to the paper plate.
4 Check that the hands can
move easily. Choose a
time and set the hands of
the clock to show this time.
Maths words
hour hand
minute hand
year
month
week
day
hour
minute
seconds
Look at the
finished clock.
What time does
it show?
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Unit 6 Time and measurement
Learn
1 year = 365 days
1 year = 12 months
1 week = 7 days
1 day = 24 hours
55
minute hand
0
1 hour = 60 minutes
1 minute = 60 seconds
5
50
10
45
15
40
20
35
30
hour hand
25
What time is it? How do you use the numbers on a clock?
The time on an analogue clock
The time on a digital clock
The hour hand is
pointing to the 4.
The minute hand
is pointing to the 12.
It is 4 o’clock.
It is 4 o’clock.
The hour hand is
pointing past the 4.
The minute hand
is pointing at the 2.
It is 10 minutes past 4.
It is 10 minutes past 4.
The hour hand is
pointing between
the 4 and 5.
The minute hand
is pointing to the 8.
It is 4:40 or 40 minutes past 4.
It is 4:40 or 40 minutes
past 4.
hour
minutes
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Unit 6 Time and measurement
Practise
1 Match the time on each analogue clock to the digital clock.
a
1
b
2
c
3
d
4
e
5
f
6
g
7
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Unit 6 Time and measurement
Practise (continued)
2 Which is longer?
a 1 day or 1 hour
c 1 minute or 1 second
e 1 month or 1 year
g 1 day or 1 week
b 1 hour or 1 week
d 1 second or 1 year
f 1 year or 1 week
Try this
Time yourself.
How long does it take you to
write the numbers 1 to 20?
Compare your time with
others in your group.
How could you show
your results?
Let’s talk
Work with a partner. Answer the questions.
1 The aeroplane took off at 3 o’clock.
It landed at 8 o’clock.
How long was the flight?
2 The film started at 4 o’clock.
It finished 2 hours later.
What time did it finish?
Can you write a time question for your partner?
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Unit 6 Time and measurement
Length
Explore
Learn
Jack and Annay are having
a jumping challenge.
Using non-standard units
How many counters fit along
the pencil?
I think I can jump
about 60 metres (m).
Using centimetres and a ruler
cm
0
cm 10
20
30
40
50
60
70
80
I think I can jump about
60 centimetres (cm).
cm 10
20
30
40
50
60
70
5
10
15
The tip of the pencil is in line
with the 12.
The pencil is 12 cm in length.
Non-standard units
are all different.
80
Who made a good estimate?
How far did each child jump?
Who jumped the furthest?
Maths words
metre (m) centimetre (cm)
length
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Unit 6 Time and measurement
Practise
1 How long is each item?
a Estimate in counters.
Then use counters to
measure.
b Estimate in centimetres.
Then measure each item.
book
hand span
shoe
2 How high can you jump? Estimate and then measure.
Learn
B
Compare the sunflowers.
Put the sunflowers in order from
shortest to tallest.
The shortest sunflower is 28 cm .
A
C
The next is 42 cm .
The tallest sunflower is 63 cm .
42
42 cm
63
63 cm
28
28cm
cm
1 metre (m) = 100 centimetres (cm)
The 3 sunflowers are all shorter than 1 metre.
Point to something that
is shorter than 1 metre.
B
A
C
Point to something that
is taller than 1 metre.
You can also put the sunflowers
in order from tallest to shortest.
shortest
28 cm
28
tallest
42cm
cm
42
63cm
cm
63
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Unit 6 Time and measurement
Practise
1 Estimate which items are taller or longer than 1 metre.
2 Put each set of lengths in order from shortest to longest.
Use a ruler and metre stick to compare them.
b 1 m, 10 m, 5 m
a 4 cm, 8 cm, 6 cm
d 10 m, 20 m, 15 m
c 18 cm, 16 cm, 14 cm
f 20 m, 30 m, 25 m
e 24 cm, 28 cm, 26 cm
h 35 m, 40 m, 33 m
g 34 cm, 38 cm, 36 cm
3 a Estimate how many metres each item is:
l the length of the classroom
l the height of the door.
b Measure each item in metres.
Try this
Measure and order different
lengths of string.
You need a ruler, some string
and a pair of scissors.
Measure and cut pieces of string
in these lengths:
l 5 cm
l 10 cm l 15 cm
l 20 cm
l 25 cm.
Then put your measured lengths
in order from shortest to longest.
Let’s talk
How many items can you
find in the classroom that are:
l taller or longer than 1 metre?
l shorter than 1 metre?
How could you
record this?
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Unit 6 Time and measurement
Quiz
1 Match the time on each analogue clock to the digital clock.
a
1
b
2
c
3
2 Put each set of lengths in order from shortest to longest.
a 3 cm, 9 cm, 12 cm, 6 cm
b 13 m, 19 m, 22 m, 16 m
c 23 cm, 29 cm, 32 cm, 26 cm
3 Find 3 pencils of different lengths.
Use a ruler to measure each pencil in centimetres.
cm
0
5
10
15
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Term
Review
1
Units 1–6
1 Take a large handful of counters. Place them in a pile.
Estimate how many there are. Then count to check.
Write the number as tens and ones.
2 Write the related subtraction facts.
a 7 + 3 = 10 à 10 –
=
b 8 + 2 = 10 à 10 –
=
c 4 + 6 = 10 à 10 –
=
d 9 + 1 = 10 à 10 –
=
3 Do these calculations.
a 19 – 4 =
c 13 +
b 14 + 6 =
d 18 – 5 =
= 17
4 What are the next 2 shapes in each sequence?
a
b
c
5 Sort the shapes into a table like this.
3 or more corners
a
b
Not 3 or more corners
c
d
e
f
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Term 1 Review
6 Complete a Venn diagram like this. Use these numbers:
Odd numbers
30 or more
5
10
12
35
50
38
17
7 Write the multiplication to match each array.
a
b
c
8 Jack has 15 marbles. He gives 5 marbles to each
of his friends. How many friends will get 5 marbles?
9 Match the units of time.
1 year
7 days
1 week
24 hours
1 day
60 minutes
1 hour
12 months
10 Give the digital time
for the clock.
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7
Addition and subtraction
Addition and subtraction facts for 20
Explore
I will put some more
shells in my bucket so
that I have 20 altogether.
Maths words
complement
inverse
How many shells could David
have to start with? How many
more did he collect?
David then puts the same number
of shells back on the beach.
How many does he have left
in his bucket?
Learn
We can use complements of 20 to help us think about the number
of shells David has to start with and how many more he collects.
+
= 20
The number line below shows a possible solution.
15 shells add 5 shells is 20 shells.
15 + 5 = 20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
20 – 5 = 15
We can also see that 20 shells take away 5 shells leaves 15 shells.
Subtraction ‘undoes’ addition so we can use our addition facts
to find out subtraction facts.
We say that addition and subtraction are inverses.
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Unit 7 Addition and subtraction
Practise
1 Write the addition and subtraction fact to match.
a
b
+
=
+
14 15 16 17 18 19 20
–
=
13 14 15 16 17 18 19 20
=
–
=
2 a Complete these bar models to show complements of 20.
20
20
20
?
?
?
10
11
8
b Write matching addition and subtraction sentences for each.
3 Complete these.
a 16 +
= 20 20 – 4 =
b 15 +
c
= 20
+ 6 = 20 – 5 = 15
20 – 6 =
Try this
Write 5 pairs of items that will balance the scales.
17 g
1g
3g
20 g
10 g
2g
10 g
19 g
16 g
18 g
4g
Write addition sentences and the matching subtractions.
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Unit 7 Addition and subtraction
Adding and subtracting multiples of 10
Explore
The children are playing with blocks of tens.
Maris adds 2 extra blocks to her pile.
What is the value of her pile
now?
Annay uses a ball to knock
blocks off his pile.
What could the value of his
pile be now?
Maths word
multiples of 10
Learn
We can use addition facts to 10 to help us add multiples of 10.
The total is 10 times as big.
+
=
1 + 9 = 10
+
10 + 90 = 100
=
10 – 9 = 1
100 – 90 = 10
Subtraction is the inverse of addition,
so we can write:
1 + 9 = 10
10 – 9 = 1
10 + 90 = 100
100 – 90 = 10
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Unit 7 Addition and subtraction
Practise
1 Answer these additions and subtractions.
a 80 + 20 =
b 100 – 20 =
c 80 + 10 =
70 + 30 =
100 – 30 =
90 – 10 =
60 + 40 =
100 – 40 =
90 – 80 =
2 Work out the related facts for each number sentence.
a 40 + 60 = 100
= 100
60 +
100 – 60 =
100 –
b 30 + 70 = 100
+ 30 = 100
= 30
100 –
=
– 30 = 70
100 –
=
100 –
= 60
c 20 + 80 = 100
+
= 100
Try this
Jack starts on 40 and adds a multiple of 10.
Viti starts on a number and subtracts a multiple of 10.
My new number is the same
as your starting number!
That’s strange.
How many ways can you make this true?
Let’s talk
10
20
30
40
50
60
70
80
90 100
Use counters on the track to convince a friend each time.
a 30 + 70 = 100 and 100 – 70 = 30 b 60 + 20 = 80 and 80 – 20 = 60
What other addition and subtraction facts can you make?
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Unit 7 Addition and subtraction
Making estimates
Explore
Maris and David are making buns.
I need to make 4 buns
for Grandpa and 5 buns
for Auntie. Is there
enough space in my tin?
Maths word
estimate
I need to make 3 buns for
Gran and 8 buns for Uncle.
Is there enough space
in my tin?
What do you think? How can Maris and David check?
Can they use estimates to help them? Talk about it.
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Unit 7 Addition and subtraction
Learn
Maris knows that double 5 is 10. David knows that 3 and 7
are a pair that total 10.
How does that help her?
How does that help him?
4 is less than 5, so 4 + 5 must be
less than double 5 (or 5 + 5).
8 is more than 7, so 3 + 8 must
be more than 3 + 7.
Practise
1 Will the answers to these additions be more or less than 10?
Write the number fact you use to help you.
a 6+3
b 6+5
c 8+4
d 2+7
e 5+5+1
2 Write less or more to complete these sentences.
than 10.
a Double 5 is 10, so 5 + 6 is
than 8.
b Double 4 is 8, so 4 + 3 is
than 12.
c Double 6 is 12, so 6 + 6 + 1 is
than 20.
d Double 10 is 20, so 9 + 8 is
3 Will the answers to these subtractions be more or less than 10?
Write the number fact you use to help you.
a 9–3
b 18 – 10 c 18 – 7
d 12 – 4
e 20 – 11
Try this
Look at: 20 – 5 = 15.
Will 20 – 8 be less or
more than 15?
Will 20 – 4 be less or
more than 15?
Explain how you know.
Let’s talk
I know that 10 + 5 = 15, so
9 + 6 must be more than 15.
What do you think about Viti’s
estimate? How can you improve it?
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Unit 7 Addition and subtraction
Adding small numbers
Explore
Play a game.
Throw 3 bean bags into
3 numbered buckets.
What different total scores could you get?
How can you show that you have
found all the different total scores?
Maths word
double
Learn
You can add numbers in any
order: 3 + 2 = 2 + 3
When adding sets of numbers,
look for complements of 10
or doubles.
For example: 3 + 4 + 3 + 6 =
First think about an estimate.
double 3 = 6
3 + 4 + 3 + 6 = 16
4 + 6 = 10
Practise
1 Copy the numbers and add them. Write the answers.
a 3+2+8+3=
b 4+3+7+4=
4+2+8+4=
5+3+7+5=
5+2+8+5=
6+3+7+6=
6+2+8+6=
7+3+7+7=
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Unit 7 Addition and subtraction
Practise (continued)
2 The children are playing a game. They try to knock over as
many skittles as they can. Who has the highest score?
Name
David
Viti
Jack
Maris
Throw
1st 2nd
4
2
6
6
3
3
2
8
3rd
6
3
1
4
4th
2
7
9
4
Total
score
3Zara is playing a game.
She throws 3 balls at the target.
What can her total score be?
Try to make an estimate first.
Will the score be more than 15?
Write some possible numbers of throws.
Try this
Let’s talk
3
7
2
2
Jack catches 3 fish
with these numbers:
5
6
8
10
4
1
What is his total?
Viti also catches 3 fish.
9
Two of her numbers are
1 and 8 .
a What can the number on Viti’s
third fish be?
b Write all the possible totals that
Viti can make.
I know that we can
add numbers in any
order. I don’t think
we can subtract
numbers in any order.
How can you
convince Maris that
she is correct?
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Unit 7 Addition and subtraction
Adding two-digit and one-digit numbers
Explore
The children spin
a 1 to 6 spinner.
Annay moves his
counter on 3 spaces.
What number is his
counter on now?
Zara spins the spinner and moves on this number of spaces.
What number can her counter be on now?
Learn
32 + 4 = 36 Remember that you can do addition in any order.
You can count on from the larger number on a number line.
Count on 4.
30
31
32
33
34
35
36
37
38
39
40
You can also use addition facts to help you.
2 + 4 = 6, so 32 + 4 = 36
Maths word
addition
=
+
32
4
36
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Unit 7 Addition and subtraction
Practise
1 Copy the calculations. Write the answers.
a 22 + 3 =
b 33 + 2 =
c 40 + 5 =
23 + 3 =
33 + 4 =
41 + 5 =
24 + 3 =
33 + 6 =
42 + 6 =
34 + 3 =
43 + 6 =
42 + 7 =
2 Write the number sentence and the answer.
a
b
24
25
26
27
28
3 Write the number
sentence and
the answer.
a
29
23
24
25
26
27
28
29
b
+
+
Try this
Annay writes a number. He adds 5. His new number is 29.
What number did he write? Make up your own problem like this.
Let’s talk
Jack says that 23 + 6
= 29
How many other additions can you make to give the answer 29?
Use a two-digit number and a one-digit
+
= 29
number each time. 77
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Unit 7 Addition and subtraction
Subtracting a one-digit number from
a two-digit number
Maths word
subtraction
Explore
What can you see
in the picture?
How many cars are
in the car park?
How many cars can
drive away so there
are more than 20
cars left?
Give as many
answers as you can.
Learn
27 – 3 = 24 Always do subtraction in the order it appears.
You can count back from the first number on a number line.
Count back 3.
20
21
22
23
24
You can also use subtraction
facts to help you.
7 – 3 = 4, so 27 – 3 = 24
25
26
27
28
29
30
27 – 3 = 24
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Unit 7 Addition and subtraction
Practise
1 Copy the calculations. Write the answers.
a 29 – 4 =
b 38 – 7 =
c 49 – 5 =
28 – 4 =
38 – 6 =
47 – 5 =
27 – 4 =
38 – 5 =
48 – 6 =
37 – 4 =
38 – 4 =
48 – 8 =
2 Write the number sentence and the answer.
a
31
32
33
34
35
36
37
38
41
42
43
44
45
46
47
48
b
3 Write the number
sentence and
the answer.
a
b
Try this
Viti writes a number. She subtracts a number less than 10.
What number could she have written? My answer is 22!
Let’s talk
Talk about any patterns you notice.
How can you use the patterns to find the answer
to 48 – 5? Can you continue the pattern?
18 – 5 = 13
28 – 5 = 23
38 – 5 = 33
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Unit 7 Addition and subtraction
Quiz
1 Complete these calculations.
a 10 + 10 =
b 12 +
c
à 20 – 10 =
= 20 à 20 – 8 =
+ 5 = 20 à 20 – 5 =
d 17 +
= 20 à 20 –
= 17
2 Use 4 of these numbers once to make each number
sentence correct.
80
40
10
50
a 60 – 50 =
c 90 –
= 50
30
b 20 +
= 100
d 50 +
= 80
3 100 passengers board an aeroplane. 30 are carrying a suitcase.
How many passengers are not carrying a suitcase?
4 Complete these additions and subtractions.
b 31 + 6 =
a 39 – 4 =
c 42 +
= 45
d 49 –
= 47
5 There are 45 pens in a box. Zara takes 4.
How many are left?
6 A T-shirt costs $22. A game costs $6 more.
How much is the game?
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8
Money
Understanding coins and notes
Explore
Maths words
coin
note
cent
dollar
I have been
saving up for …
What coins and notes can you see?
Which is worth more: 1 cent or 1 dollar?
Do you ever save or spend money?
What would you like to save for?
Why do some people give money away?
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Unit 8 Money
Learn
We can use addition facts to 10 to help add multiples of 10.
The total is 10 times as big.
I wonder how many
1c coins this is worth?
Practise
1 Sort these coins in order from least value to greatest value.
2 Which has the least value?
Try this
Let’s talk
I am thinking of a coin or
note. It is worth more than
10 cents, but less than $10.
What could it be?
Has one of these machines broken?
Discuss with a partner.
Find all the
possible answers.
COIN CHANGER
COIN CHANGER
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Unit 8 Money
Working out the total amount
Explore
Maths words
total
amount
The children are at the market!
What questions
could you ask these
children at the
market?
Learn
Annay has these coins. That is 11c in total.
0
1
2
3
4
5
6
7
8
9
10
11
12
Jack has these coins.
How much is the total amount?
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Unit 8 Money
Practise
1 Work out the total for each bar model.
b
a
d
c
e
2 Work out the total amounts of money.
a
b
c
d
3 Work out how much money is in each bowl.
Sort the total amounts in order.
b
c
d
a
4 Work out the mystery coins.
a
50 cents
b
?
e
75 cents
?
Try this
Use coins or toy coins. Choose 5 coins at random.
Challenge your partner to work out the total amount.
Then try it with 6 coins at a time.
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Unit 8 Money
Making amounts
Explore
Annay and Maris are shopping. They have notes to spend!
What would you buy? What notes would you have to use?
What could the children buy?
Learn
Which coins could make exactly 35c?
What notes could you use to buy the bear?
35c
$14
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Unit 8 Money
Practise
1 Draw coins or notes to make each of these amounts.
a 11c
b 19c
c 21c
d$16
26c
e 50c
f $30
g $21
h $49
$18
$16
$1
2 Choose 2 items to buy.
4
$16
$1
$16
4
$1
$18
$18
$18
$15
$16
$17
$15
$1
4
$15
$18
4
$1$15
7
$
17 would use.
a Work out the total cost. Show the notes you
Choose 3 items to buy. Work out the notes you would
b
use to make
$1the exact amount.
$15
$17
7
Price list:
pen 20c
pencil 15c
ruler 25c
eraser 10c
notepad 30c
3 Zara buys 3 items from the price list.
She pays using these coins.
Which 3 items did Zara buy?
Try this
Let’s talk
Zara invents her own money
for a game. She only uses 2c,
5c and 30c coins.
What different amounts can
she make?
Are there any amounts that
she cannot make?
Set up your own shop
with price labels.
Role-play shopping for the
different items.
Make your own coins and
notes of different values.
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Unit 8 Money
Quiz
1 Look at this selection of coins and notes.
a Sort them from smallest to largest value.
b Sort the money from largest to smallest.
2 How much money is there each time?
a
b
3 Draw 2 different ways to make 26c from these coins.
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Number patterns and
place value
9
Tens and ones
Explore
How many tens
can you see?
Maths words
tens
ones
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Unit 9 Number patterns and place value
Learn
16 is 1 full ten and 6 ones.
The 1 stands for 1 ten. The 6 stands for 6 ones.
26 is 2 full tens and 6 ones.
What do the 3 and the 6 stand for in 36?
How would you write a number with 6 full tens and 2 ones?
I can use rods and
cubes to show
tens and ones.
Practise
1 Write these numbers as tens and ones.
a
b
c
d
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Unit 9 Number patterns and place value
Practise (continued)
2 Write these numbers as tens and ones.
a
b
c
3 Write these as numbers.
a 2 tens and 3 ones
c 9 tens and 1 one
d
b 4 tens and 9 ones
d 8 tens and 0 ones
4 Represent (show) the number 32 in as many ways as you can.
Use equipment, drawings, numbers and words.
Try this
Let’s talk
Write the different numbers
that David and Maris might
have.
Write each number as tens
and ones.
ten
My number
has 6 tens.
My number
has 6 ones.
twenty
thirty
forty
fifty
sixty
seventy
eighty
ninety
What does the 0 stand for
in each number?
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Unit 9 Number patterns and place value
Counting in tens and ones
Explore
Let’s look for tens!
Thirty
Ten
Twenty
10
20
Fifty
Sixty
Forty
30
50
40
One
hundred
Eighty
Seventy
60
70
Ninety
80
90
100
First count aloud in tens!
Then use counting
equipment to make
each number.
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Unit 9 Number patterns and place value
Learn
Look at this counting pattern. How would it continue?
3
13
23
33
I wonder why 10
more is always
underneath?
Practise counting on and back in tens in this pattern.
Make the numbers using counting equipment.
Practise
1 Make each pattern and write the next numbers.
a
4, 14, 24, 34,
b
,
,
,
,
,
6, 16, 26, 36,
,
,
,
,
,
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Unit 9 Number patterns and place value
Practise (continued)
2 Use a 100 grid. Then answer the questions below.
a Choose any starting number in
the top row. Count on in tens.
Write the counting pattern you used.
b Choose any number in the bottom row.
Count back in tens. Write the counting
pattern you used.
3 Copy each number track and fill in the missing numbers.
a
7
b
31
61
c
88
58
d 100
17
37
67
81
28
60
10
3535
Try this
Some of this number is hidden.
Write all the numbers it could be.
There
There
areare
3 tens
3 tens
and
and
5 ones.
5 ones.
Let’s talk
What would you say to explain how to
count on and back in 1s from any number?
I can count back
from 25, but what do
I do when I reach 21?
21 22 23 24 25 26 27 28 29 30
I can count on in ones from
25, but what do I do after 30?
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Unit 9 Number patterns and place value
Counting in fives
Explore
Let’s count in fives!
Maths word
fives
How many fingers in each row?
How many fingers in total?
Estimate. Then count to check.
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Unit 9 Number patterns and place value
Learn
The number track shows the counting pattern in fives.
5
1
11
21
31
41
51
61
71
81
91
10
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
15
20
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
25
30
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
35
40
45
50
9 10
19 20
Use your skills of
29 30
conjecturing and
39 40 characterising.
49 50
59 60
69 70
79 80
89 90
99 100
Find the fives counting pattern on the 100 grid.
What do you notice? Now start on 1. Count in fives.
Look at the pattern on the 100 grid.
Practise
1 Count forwards and backwards in fives.
Point to each number as you count.
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
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Unit 9 Number patterns and place value
Practise (continued)
2 Continue these counting patterns.
a 2, 7, 12, 17,
,
,
,
,
,
,
,
b 3, 8, 13,
,
,
,
,
,
,
,
,
c 4, 9, 14,
,
,
,
,
,
,
,
,
3 Zara starts on 99. She counts down in fives.
Which of these numbers will she say?
98 50 44 95 89 59 34 84 75 4 5 10 19
Try this
A bee has 5 eyes.
Count how many
bees you see.
How many eyes
do all the bees
you counted have?
A group of bees fly away.
When you count the eyes of those left in the hive, there are fewer
than 20. How many bees could there be in the hive?
Let’s talk
Spread out a large number of counters or cubes.
Sort them into piles of 5 to make counting them easier.
Try this with different numbers of objects.
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Unit 9 Number patterns and place value
Counting in twos
Explore
Discuss different ways to count the penguins.
How can you make sure that you are correct?
Maths words
twos even odd
Learn
Count the pile of counters in twos. How many in total?
We can sort the counters into pairs. Count them in twos.
How many in total?
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Unit 9 Number patterns and place value
Learn (continued)
The numbers in the circles are even numbers.
What do we call the numbers
in between the even numbers?
We call them
odd numbers.
Practise
1 aCount forward in twos on these rows of a 100 grid.
What patterns do you notice?
bCount back in twos from 40. Can you predict the numbers
you will say? What if you count back from 39?
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
2 a Write all the even numbers between 30 and 50.
b Write all the odd numbers between 30 and 50.
3 Take 24 counters. Share them into 2 equal groups.
Now try to share 27 counters into 2 equal groups.
What do you notice?
Try this
Predict which numbers can be shared equally between 2 groups.
Then predict which numbers leave 1 left over.
Can you explain what you find out?
31
32
33
34
35
36
37
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Unit 9 Number patterns and place value
Quiz
Use this picture to help you answer the questions below.
1 Choose 2 players. Write each number as tens and ones
in tables like this.
a 10s
1s
b 10s
1s
2 Estimate how many players are on the field.
3 Count the players in ones.
4 a Draw 25 footballs.
b Count them in fives.
5 Count the players’ kit bags in twos.
6 Write 3 even and 3 odd numbers that you see in the picture.
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10
Time and measurement
Time
Explore
Maths words
hour
minute
seconds
Look at all these clocks!
01:05
03:35
Can you read the time on each clock?
What different types of clocks can you see?
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Unit 10 Time and measurement
Learn
55
0
50
5
minute hand
10
hour hand
45
15
40
20
25
35
30
What time is it? What are the numbers on the outside of the clock?
The time on an analogue clock
The time on a digital clock
The hour hand is
pointing to the 10.
The minute hand
is pointing to the 4.
It is 20 past 10.
It is 20 past 10.
The hour hand is
pointing past the 4.
The minute hand
is pointing at the 3.
It is 15 minutes past 4.
It is four fifteen.
The hour hand is
pointing between
the 4 and 5
The minute hand
is pointing to the 8.
It is four forty.
It is 4:40 or 40 minutes
past 4.
hour
minutes
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Unit 10 Time and measurement
Practise
1 Match the time on each analogue clock to the digital clock.
1
2
3
4
a
b
c
5
6
d
e
f
7
g
h
8
2 Write each time as it would be on digital clocks like this.
b
a
twenty past four
c
quarter past six
d
three o’clock
Try this
How many seconds
can you go without
blinking?
Work with a partner
to time each other.
half-past eight
Let’s talk
Is there a clock in the
classroom? What time is it now?
What time do you have lunch?
What time do you finish school?
What is your favourite time of
the day? Explain why.
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Unit 10 Time and measurement
Length
Explore
Maths words
centimetres
metres
difference
Which items would you measure in centimetres?
Which items would you measure in metres?
Which measuring tools are best for each measuring task?
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Unit 10 Time and measurement
Learn
We can use a ruler to measure an item in centimetres.
The carrot is 12 cm.
Use a ruler to draw the line.
How to draw a line that is 8 cm long
1 Put the ruler flat on the paper and hold
it still.
2 Put your pencil on 0 cm and make a dot.
3 Put your pencil on 8 cm and make a dot.
4 Join the 2 dots, drawing along the ruler.
We can add lengths together.
0
1
2
30
1
2
3
4
5
0
1
2
3
4
5
6
7
8
3 cm + 5 cm = 8 cm
We can find the difference between 2 lengths.
0
0
1
1
2
2
3
3
4
4
5
6
6 cm – 4 cm = 2 cm
The difference is 2 cm.
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Unit 10 Time and measurement
Practise
1 How long is the brinjal, the sweet potato and the carrot in
centimetres?
b
a
c
2 How tall is each flower in centimetres?
a
b
c
3 Draw a line for each length.
a 3 cm
b 6 cm
e 10 cm
d 12 cm
c 9 cm
f 7 cm
4 Complete these additions.
a 7 cm + 3 cm =
b 5 cm + 9 cm =
c 14 cm + 2 cm =
d 18 cm + 4 cm =
e 5 cm + 7 cm =
f 9 cm + 3 cm =
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Unit 10 Time and measurement
Practise (continued)
5 Find the difference between each pair of straws.
a
8 cm – 2 cm =
cm
b
7 cm – 3 cm =
cm
c
3 cm – 1 cm =
cm
Try this
In April the flower was 12 cm tall.
In May the flower was 20 cm tall.
How much had the plant grown?
Viti is 133 cm tall.
Zara is 125 cm tall.
How much taller is Viti than Zara?
Let’s talk
How many items can you find in the
classroom that are:
l taller or longer than 10 centimetres
l shorter than 10 centimetres?
How could you
record this?
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Unit 10 Time and measurement
Mass
Maths words
mass
gram (g)
kilogram (kg)
heaviest
lightest
Explore
Nuts for sale!
Viti has __
​​  12 ​​
a kilogram.
Viti has 500 g.
Viti has 5 kg.
Who is correct? Explain why.
How much will Viti’s nuts cost?
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Unit 10 Time and measurement
Learn
We measure the mass of an object in grams (g) and in kilograms (kg).
We can use a scale to measure how heavy an object is.
Look at the scale on the right.
What is the mass of the parcel?
The red arrow points to 80 g.
The parcel weighs 80 g.
90
0
80
10
20
70 grams 30
60
50
40
We can use signs to compare mass:
< is less than > is greater than
50 g > 2 g
100 g > 10 g
4 g < 25 g
3 g < 60 g
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Unit 10 Time and measurement
Practise
1 Write the mass of each parcel.
b
a
90
80
0
90
10
20
80
70 grams 30
60
40
50
0
10
20
70 grams 30
60
40
50
2 Use weighing scales to find the mass of 5 objects.
Record your results in a table like this.
Remember to estimate the mass first.
Object
I estimated …
Mass
100 g
90 g
175
150
125
0
g
25
100
50
75
glue
3 Annay has weighed these objects.
10 g
200 g
300 g
75 g
50 g
a Which object has the heaviest mass?
b Which object has the lightest mass?
c Write the objects in order from lightest to heaviest.
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Unit 10 Time and measurement
Practise (continued)
4 Copy these statements.
Complete them by filling in either < or >.
a 10 g
11 g
b 20 g
25 g
c 90 g
90 kg
d 20 kg
20 g
e 10 kg
9 kg
f 20 g
15 kg
5 Use the <, > or = signs to write a statement for each pair.
b
a
50 kg
100 kg
50 kg
50 kg
c
Try this
50 kg
40 kg
Let’s talk
Would you measure these
in grams or kilograms:
l feather
l pencil
l Zara
l large sack of potatoes?
Think of 5 other items that
you would weigh in:
l grams
l kilograms.
The children picked and
then weighed tomatoes.
Viti’s tomato weighed 65 g.
Zara’s tomato weighed
10 g less than Viti’s.
Jack’s tomato weighed
20 g more than Zara’s.
How much did Jack’s
tomato weigh?
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Unit 10 Time and measurement
Quiz
1 Match each analogue clock to the digital clock.
2 Use a ruler to
measure the
length of each
pencil.
b
a
c
3 Write the mass of the parcel.
90
80
0
10
20
70 grams 30
60
40
50
4 Put the objects in order from lightest to heaviest.
a
c
b
10 g
350 g
d
e
240 g
75 g
500 g
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11
Shapes, direction
and movement
Symmetry
Explore
Maths words
line of symmetry
symmetrical
What a beautiful butterfly!
What shapes
can you see?
Learn
Lines of symmetry are all around us.
Symmetrical means that something
is the same on two or more sides.
A line of symmetry shows that the
shape or picture is symmetrical.
It is the same on both sides when
you fold it in half down the line
of symmetry.
line of symmetry
line of symmetry
line of symmetry
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Unit 11 Shapes, direction and movement
Practise
1 Copy each shape. Then draw a line of symmetry.
b
c
d
a
2 Copy the table. Draw 4 shapes under each heading.
Shapes with lines
of symmetry
Shapes with no lines
of symmetry
3 Make a symmetrical pattern.
4 Which lines of symmetry are correct? Write the letters.
b
a
c
d
5 On which shapes can you draw a line of symmetry?
Complete a table like this.
Shape
✗ or ✓
Shape
a
b
c
d
e
f
✗ or ✓
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Unit 11 Shapes, direction and movement
Practise (continued)
6 Part of each shape is missing. The dotted line is a line of
symmetry. Copy each shape and complete it.
b
c
a
7 Part of the picture is missing.
The dotted line is a line of symmetry.
Copy the picture and complete it.
Try this
Look at the symmetrical shape.
Use 10 cubes to make your own
symmetrical shape.
Draw a picture of it.
Let’s talk
All rectangles have a line of symmetry.
Is Viti correct?
Explain your answer.
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Unit 11 Shapes, direction and movement
Position and movement
Explore
Where is
the parrot?
Maths words
turn
clockwise
anticlockwise
whole turn
half turn
quarter turn
Learn
A turn changes
the direction you
are facing.
Your position
stays the same.
115
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Unit 11 Shapes, direction and movement
Learn (continued)
You can turn in different ways.
You can turn clockwise and anticlockwise.
Clockwise
Anticlockwise
You can turn in different amounts.
You can do a whole turn, a half turn or a quarter turn.
Whole turn
Half turn
Quarter turn
A right angle is the same as a quarter turn.
A quarter
turn, clockwise
You can turn shapes and objects.
You can find right angles in many places.
90°
90°
90°
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Unit 11 Shapes, direction and movement
Learn (continued)
Annay turns a square through a whole turn.
The square looks the same 4 times.
Try turning a rectangle through a whole turn.
How many times does it look the same?
Practise
1 Look at the shape.
Annay turns the shape a quarter turn.
Did he turn it clockwise or anticlockwise?
b
a
Think of the hands of
a clock. They move in
a clockwise direction.
2 Look at the shape.
Viti turns it clockwise.
Did she turn it a half turn
or a quarter turn?
a
b
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Unit 11 Shapes, direction and movement
Practise (continued)
3 Look at the shape: The teacher turns the shape:
He turned it a
quarter of a turn.
He turned it
half of a turn.
Who is correct?
4 How many times does the shape look the same through a
whole turn of the shape?
b
c
d
a
rectangle
pentagon
equilateral
triangle
cross
shape
Try this
Which shapes have right angles? How do you know?
a
b
c
d
Let’s talk
How many right angles can you find around the classroom?
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Unit 11 Shapes, direction and movement
Quiz
1 Copy each shape and draw a line of symmetry.
a
b
c
d
e
f
2 Draw the bee after each turn.
a A quarter turn clockwise
b A half turn anticlockwise
3 Which of these shapes have right angles?
a
b
c
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12
Fractions
Equal parts
Explore
Folding is fun!
Maths words
fraction
half
halve quarter
equal
Fold a square of paper in half. Then fold it in half again.
We can say that we halve the paper and then halve it again.
What will you see when you unfold the paper?
Try this with different shapes and sizes of paper.
Learn
Two of these 3 shapes are
divided into equal parts.
The equal parts are fractions
of the whole shape.
Two of these shapes are
broken up into 4 equal parts.
Each part is a quarter.
One shape is not divided
into equal fractions.
Can you see why?
One of the shapes is divided
into 4 parts, but they are not
equal. Can you see why?
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Unit 12 Fractions
Practise
1 Copy each shape and show one way to break up each shape
into quarters.
a
b
c
d
2 a None of these shapes is broken up into quarters.
Copy the table and sort the shapes.
Not 4 parts
Not equal parts
b Explain why we can say:
This shape is not divided into quarters.
3 Use 3 or more different lengths of string.
Fold them in half, then in half again. Compare each quarter of
the lengths of string. What do you notice? Explain what you see.
Try this
How many ways can you fold a square
of paper into 4 equal parts?
Experiment with different ways of folding.
Can you make these shapes?
Let’s talk
Use tape, chalk or ropes to divide these school spaces into quarters:
l the school hall l your desk l the playground.
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Unit 12 Fractions
Fractions of a group
Explore
The teams are
ready to play!
Learn
You can find fractions of a group.
Find half of 8 marbles.
Half of 8 is 4.
__
​​  12 ​​of 8 is 4.
Find a quarter of 8.
So a quarter of 8 is
1
​​ __
4​of 8 is
.
.
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Unit 12 Fractions
Practise
1 Use cubes or counters to find these.
Draw your fractions to show the whole and the parts.
1
a​ __
2 ​​of 6 counters
1
b​ __
2 ​​of 12 counters
1
c​ __
4​of 20 counters
1
d​ __
4​of 16 counters
2 Write a fraction statement for each picture.
b
c
a
3
Do you agree with Zara?
Explain why this is wrong.
Try this
Which sets of books can we
share into equal quarters?
What do you notice?
Can you continue the pattern?
I have found a quarter
because there are 4 cakes
on each plate. A quarter
of 12 cakes must be 4.
Let’s talk
Work out these pairs of fractions
using counters or cubes.
What do you notice?
1
__
2 ​​of 12 is
1
__
4​of 20 is
__
​  14​of 12 is
__
​  12 ​​of 40 is
__
​  12 ​​of 20 is
__
​  41​of 40 is
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Unit 12 Fractions
Quiz
1 Draw a picture of a shape broken up into quarters.
2 Draw a picture of a shape not broken up into quarters.
3 Explain why one shape shows quarters and the other
does not.
4 Find a quarter of all the fish in the picture.
Use cubes or counters to show how to solve this.
5 Choose a group of counters. Show whether you can break up
the group into halves or quarters.
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Term
Review
2
Units 7–12
1 Choose pairs of numbers that total 20.
5
14
0
2
15
20
6
18
2 Find the totals. Think about the numbers you will add
together first.
a 3+4+7=
b 6+5+5=
c 1+9+4+3=
d 3+1+8+2=
3 Draw 2 different ways to make each amount.
a 15c
b 40c
c $35
4 Ask up to 10 children to stand in a line.
Then ask them to wave gently with both hands.
Count all the fingers in 5s.
Now count in 10s.
Is there an odd number or an even number of fingers?
5 How long is the pencil in centimetres?
cm
6 Draw a line for each length.
a 4 cm long
b 8 cm long
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Term 2 Review
7 Jack’s sunflower is 35 cm tall.
Annay’s sunflower is 33 cm tall.
b
a
33 cm
35 cm
How much taller is Jack’s sunflower?
8 This picture is symmetrical. Copy the picture and complete it.
9 Collect 20 counters.
Sort them into equal halves. Then sort them into equal quarters.
What is half of 20?
What is a quarter of 20?
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13
Statistical methods
and chance
Pictograms and block graphs
Explore
Look at all the different fish!
How many blue fish? How many spotted fish?
How many orange fish? How many blue, spotted
and orange fish altogether?
How many more orange fish than blue fish?
Maths words
tally chart
pictogram
block graph
common
category
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Unit 13 Statistical methods and chance
Learn
We can make a tally chart.
Fish
Tally
We can make a pictogram.
Number of fish
llll llll llll
Pink fish
llll llll llll
Pink fish
llll llll llll
Blue fish
Spotted fish
Striped fish
Yellow fish
Stingray
llll llll llll llll
ll
Blue fish
llll
lll
l
Spotted fish
Striped fish
Yellow fish
Stingray
We can make a block graph.
Pink fish
Blue fish
Spotted fish
Striped fish
Yellow fish
Stingray
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
How many pink fish did the diver see?
How many yellow fish did the diver see?
Which was the most common fish?
Which was the least common fish?
How many fish did the diver see altogether?
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Unit 13 Statistical methods and chance
Practise
1
This graph shows children’s favourite sports.
y
Block graph to show children’s favourite sports
12
Number of children
10
8
6
4
2
x
0
Tennis
Football
Cricket
Favourite sports
Cycling
Archery
a Which is the most popular sport?
b Which is the least popular sport?
c How many children like cycling?
d How many more children like football than cycling?
e How many more children like cricket than archery?
f How many children answered the questions altogether?
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Unit 13 Statistical methods and chance
Practise (continued)
2 The table shows the number of T-shirts sold.
Complete a table like this.
Then answer the questions.
Day
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
Tally
ll
T-shirts
2
8
3
5
4
10
0
sold
a How many T-shirts were sold on Friday?
b On which day were the most T-shirts sold?
c On which day were the least T-shirts sold?
d How many T-shirts were sold on Saturday and Thursday?
e How many T-shirts were sold in total?
f Why do you think no T-shirts were sold on Sunday?
g Draw a pictogram to show the data in the table.
Try this
Ask your friends what their favourite type
of book is. Then create a block graph.
I like reading
animal stories.
How will you collect the data?
What categories or types of
books will you choose?
Let’s talk
What do you think would happen if you did not pick categories
before collecting data? Why is it important to pick categories
before asking a question about collecting data?
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Unit 13 Statistical methods and chance
Venn diagrams and Carroll diagrams
Explore
How many different ways could you sort
these animals?
Which animals
live in water?
Maths words
Venn diagram
Carroll diagram
Which animals
have legs?
Learn
We use Venn diagrams and Carroll diagrams for sorting
objects and numbers.
Which shapes are circles? Which shapes are blue?
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Unit 13 Statistical methods and chance
Learn (continued)
The shapes have been sorted
in a Venn diagram.
Blue
Circle
The shapes have been sorted
in a Carroll diagram.
Blue
Not blue
Circle
Not a circle
Practise
1 Complete a Carroll diagram like this.
Red
Not red
4 or more corners
Not 4 or more
corners
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Unit 13 Statistical methods and chance
Practise (continued)
2 a Copy the Venn diagram.
6 or bigger
Even number
8
b Spin a spinner twice to get 2 numbers. Add the numbers.
c Write the number on the Venn diagram.
d Repeat to fill the diagram with more numbers.
Try this
Choose a two-digit number.
Write your number on a blank Venn diagram. Repeat.
Can your partner guess what your rules are?
Let’s talk
Talk to your partner. How could you sort the animals?
What headings would you use in the Carroll diagram?
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Unit 13 Statistical methods and chance
Chance
Explore
Let’s play marbles!
Maths words
likely
will not happen
will happen
might happen
chance
Use your conjecturing skills to answer these questions.
Do you think Zara will pick a blue marble from the bag next?
Do you think Viti will pick a red marble from the bag next?
Who do you think will win?
Play a game of marbles with a friend.
Learn
There are 4 red marbles and 4 green marbles in the bag.
Annay picks a marble from the bag without looking.
How likely is he to pick a red marble? It might happen.
How likely is he to pick a marble? It will happen.
How likely is he to pick a white marble? It will not happen.
What chance does Annay have of picking a green marble?
There are 4 green marbles and 8 in total, so he has
4 out of 8 chances of picking a green marble.
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Unit 13 Statistical methods and chance
Practise
1 David picks a counter from the bag. Use these words.
It will not happen
It might happen
It will happen
a How likely is it that he will pick an orange counter?
b How likely is it that he will pick a blue counter?
c How likely is it that he will pick a white counter?
d How likely is it that he will pick a counter?
2 Look at each set of counters. Is there a pattern?
Describe the pattern in your own words.
a
b
c
Try this
Make sure you put
Put 5 blue and 5 red counters the counter back in
in a bag. Pick 1 but do not look. the bag each time.
What colour could it be? How
likely is it that it will be a blue
counter, a red counter or a
How could
green counter? How likely is
you record it?
it that it will be a counter?
Pick out 1 counter 10 times.
What chance do you have
You could
of picking a red counter …
keep a tally.
and a blue counter?
Let’s talk
Use your skills of characterising.
Can you think of some things that will happen today,
that might happen today and that will not happen today?
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Unit 13 Statistical methods and chance
Quiz
1 Use this block graph to answer the questions.
Number of flowers
y
13
12
11
10
9
8
7
6
5
4
3
2
1
0
a How many red flowers were sold?
b Which was the most popular colour?
c Which was the least popular colour?
d How many orange and white
flowers were sold?
e How many more orange flowers
were sold than purple flowers?
x f How many flowers were sold
Red Purple Yellow White Orange
altogether?
Colour of flowers
Flowers sold
2 Complete a Carroll diagram like this.
Blue shapes
4 sides or more
Not 4 sides or more
Not blue shapes
3 Annay spins a 1 to 6 spinner.
Answer each question with a statement.
It will not happen
It might happen
It will happen
How likely is it that he will spin:
a a number?
b the number 4?
c the number 20?
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14
Number patterns and
place value
Patterns and ordinals
Explore
Maths words
pattern
first, second,
third, …
7
8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
Viti makes a pattern.
She continues like this.
What shape will cover 99?
What about the number 100?
How do you know?
91 92 93 94 95 96 97 98 99 100
Learn
Point to the people in the picture and say the position words:
First, Second, Third, Fourth, Fifth, Sixth,
Seventh, Eighth, Ninth,
Tenth, Eleventh …
1st, 2nd, 3rd, 4th, 5th,
6th, 7th, 8th, 9th,
10th, 11th …
Practise saying these
position numbers:
21st, 22nd, 23rd, 24th, 25th, 26th, 27th, 28th, 29th, 30th, ….
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Unit 14 Number patterns and place value
Practise
1 Point to each place on the track.
Say: 1st, 2nd, 3rd, …
2 What shape is:
a 5th
b 14th
c 19th
d twelfth
e twenty-first?
3 a In what position are
Annay, Viti and Jack
standing?
Annay is in
position.
Viti is in
position.
Jack is in
position.
b What shapes are they covering?
4 Later, Jack stands on the 45th square.
Viti stands on the 50th square.
What shapes are they covering?
Try this
You will need a blank 100 grid.
Create your own repeating pattern of shapes on it.
What would be in 25th, 75th and 99th position on your square?
Invent your own patterns to challenge a partner.
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Unit 14 Number patterns and place value
Tens and ones
Explore
Maths words
decompose
compose
What is the same?
What is different?
Learn
We can decompose 24 into
2 tens and 4 ones.
We can compose 3 tens and
2 ones to make 32.
24
32
20
4
This is 20 and 4.
20 + 4 = 24
30
2
30 and 2 make 32.
30 + 2 = 32
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Unit 14 Number patterns and place value
Practise
1 Decompose each number into tens and ones.
a
b
17
?
?
c
?
?
d
42
?
?
23
74
?
?
2 Compose these parts to make wholes.
b
a
?
50
c
6
60
d
?
90
?
9
7
?
40
8
3 Complete these additions.
a 20 + 5 =
b 30 + 5 =
c 40 + 5 =
d
e
f 44 = 40 +
= 40 + 5
= 50 + 4
g 90 +
= 94
h
i 4+
= 74
j 44 = 4 +
+ 4 = 84
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Unit 14 Number patterns and place value
Try this
The number 31 has been regrouped in different ways.
See how many different ways you can find to regroup
these numbers.
32
41
70
Let’s talk
No. I think it means
30 + 0, which is 30.
I think this shows 300.
?
30
0
Do you agree with David or Viti? Discuss this with a partner.
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Unit 14 Number patterns and place value
Comparing and ordering numbers
Explore
What do you notice about the order of the
shirts on the washing line?
Maths words
order
compare
What shirt number could be on the ground?
Learn
Choose a number line that will help you
to put each set of numbers in order.
Set A
35 32 40
24 is less than 28.
28 is greater than 24.
Set B
39 24 9 70
Compare the number lines before choosing.
What is similar? What is different?
20
30
30
40
0
10
20
30
40
50
60
70
80
90 100
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Unit 14 Number patterns and place value
Practise
1 Put the shirts
in order.
2 Put each set of numbers in order from smallest to largest.
0
10
20
30
40
50
60
70
80
90 100
a 25, 14
b 26, 62, 4
c 72, 27, 5, 18
d 16, 61, 11, 39, 35 e 34, 12, 38, 26, 62 f 33, 37, 13, 63, 36
3 The table shows each child’s time of running a race.
Child
Zara
David
Viti
Annay
Jack
Time
76 seconds
71 seconds
85 seconds
83 seconds
67 seconds
a Who was first?
b Who was second?
c Who was third?
d Zara finished between David and
Annay. What was her time?
Let’s talk
19 28 37 46 55
Use the number cards above to complete these sentences.
is less than
. is greater than
.
How many more number sentences can you make?
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Unit 14 Number patterns and place value
Round to the nearest 10
Explore
How far can they throw?
I got just
over 20 m.
10 m
20 m
30 m
I threw halfway between
30 m and 40 m.
40 m
Maths word
round
Learn
24 rounds to 20
Look at the number 24. It is between 20 and 30. because it is nearer
Is it nearer 20 or 30?
20 than 30.
20
30
Who do you agree with?
24 rounds to 30
because it is above 20.
29 is so close to 30
that it must round up.
25 is exactly halfway
so we can’t decide.
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Unit 14 Number patterns and place value
Practise
1 Round each number to the nearest 10. Use the number track.
10
20
30
40
50
60
70
80
a
23
b 57
c
d
41
e 98
f 66
g
82
h 25
i
j
94
k 36
l 87
40
54
60
35
3 Round each number
to38the nearest 10.
30
40
a 10s
b 10s
1s
9
6
3
100
73
2 The arrows are pointing to different numbers.
Write each number and round to the nearest 10.
b
a
B
C
A
B
A
30
90
C
70
1s
4
d
c
70
5
40
Try this
Find all the possible answers.
My number has 2
tens and some ones.
It rounds to 30.
50
My number is even.
It rounds to 70.
My number is odd.
It rounds up to 40.
My number has 5
as one of the digits.
It rounds to 50.
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Unit 14 Number patterns and place value
Let’s talk
Use your critiquing skills. Talk to a partner about the diagram.
How does it help to explain how to round numbers?
30 31 32 33 34 35 36 37 38 39 40
multiple of 10
multiple of 10
Quiz
1 Look at a 100 grid to answer these questions.
a What is the 2nd even number?
b What is the 21st odd number?
2 Decompose each number into tens and ones.
a 41
b 57
c 80
3 a Use 0 to 9 digit cards to make
5 numbers between 10 and 100.
b Put your numbers in order.
0
7
1
4
b
?
50
?
40
?
6
9
c
?
3
5
8
4 Each number rounds to 50.
What are the missing parts?
a
2
?
?
9
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15
Addition and subtraction
Using mental strategies to add and subtract
Explore
The children are talking about different
ways to solve calculations.
We can use
pairs that total
10 to help.
We can count on to
find the difference.
Maths words
calculation doubles
difference
We can also use what
we know about doubles.
And we can
count in tens!
Which calculation is each child talking about?
Can they use their ideas for more than one calculation?
Talk about other calculations you can solve in this way.
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Unit 15 Addition and subtraction
Learn
We can use different mental strategies to help us add and subtract.
Counting in tens helps us to add or subtract a number of tens.
56 + 20 = 76
+ 10
+ 10
+
56
50
55
76
66
60
56 – 10 = 46
65
70
75
– 10
46
40
45
56
50
55
60
We can use doubles to help us find near doubles.
4
1
+
3
3
3
= double 3 + 1
Practise
1 Write the missing numbers.
a 36 –
= 26
b 36 +
= 46
36 –
= 16
36 +
= 56
36 –
=6
36 +
= 66
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Unit 15 Addition and subtraction
Practise (continued)
c 45 –
= 35
d 45 +
= 55
45 –
= 25
45 +
= 65
45 –
= 15
45 +
= 75
2 Use doubles to help you calculate these.
a 3+3+5=
b 5+6=
c 6+6+5+5=
d 8+9=
3 Make a ten each time to help you calculate.
a 7+6+3+2
b 1+8+9
c 5 + 4 + 10 + 5
d 8+9+1+2
4 Count up from the smaller number each time to find
the difference. What do you notice?
a 16 – 14 =
b 26 – 24 =
c 36 – 34 =
16 – 13 =
26 – 23 =
36 – 33 =
16 – 12 =
26 – 22 =
36 – 32 =
Try this
I cannot see any pairs that total 10.
I will have to use another way to add.
5 + 7 + 2 + 1 4 + 5 + 1 8 + 1 + 6 + 1 3 + 4 + 2 + 3
What do you think? Can you help David to add the numbers?
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Unit 15 Addition and subtraction
Making estimates
Explore
It’s market day! The children are making
estimates to see what they can buy.
Maths words
estimate
more
less
I have 75 cents
to spend.
I have 50 cents
to spend.
I have 99 cents
to spend.
Does Zara have enough to buy 1 apple and 1 lemon?
Which 2 items can Jack buy?
Does Maris have enough money to buy any 2 items?
Learn
Jack wants to buy an orange for 45 cents and a lemon for 24 cents.
Jack estimates: 45 rounds up to 50; 24 rounds down to 20.
His estimate is: 50 + 20 = 70.
Will the actual total be more or less than 70 cents? 45 + 24 =
Work out the answer and check against Jack’s estimate.
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Unit 15 Addition and subtraction
Practise
1 A banana costs 52 cents. Estimate the total cost for:
a 1 apple and 1 banana
b 1 orange and 1 banana
c 1 banana and 1 lime
d 2 bananas
2 Make an estimate each time.
a 32 + 51 =
b 68 – 42 =
c 23 + 76 =
d 94 – 52 =
e Now calculate and check the answer against your estimate.
Try this
Use estimates to sort these subtractions by their answers:
Less than 30
Between 30 and 60
More than 60
76 – 32 98 – 77 43 – 22 62 – 9 38 – 19 84 – 19
Will the actual answer be more or less each time?
Make up another subtraction for each group.
Let’s talk
Zara is finding answers to some additions.
48 + 36 =
37 + 34 =
41 + 38 =
She uses rounding to make estimates first.
Her estimate is 70 because 40 + 30 = 70
Which of the 3 additions match her estimate?
Now make estimates for her other additions.
Talk about the methods you use.
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Unit 15 Addition and subtraction
Adding pairs of two-digit numbers
Explore
Maths word
decompose
5
6
7
8
9 10 11 12 13
14
18 19 20
2
1
4
16
0
3
17
The children are playing a game.
27
22 23 24 25 26
28
37 38 39 40 41 42
43
45 4
48
6 47
36
32 33 34 35
44
49
29
30 31
50
Help Viti to move her counter on to match the total of the
3 numbers that she spins.
How much does she add in total?
Now help Jack to move his counter.
How much does he add in total?
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Unit 15 Addition and subtraction
Learn
We can add two-digit numbers in another way.
35 + 24 =
Decompose the numbers into tens and ones.
35
35 24
24
There are
3 tens
and and
5 ones.
2 tensare
and 2
4 ones.
There
are
3 tens
5 ones.There areThere
tens and 4 ones.
Add the tens:
3 tens + 2 tens = 5 tens
30 + 20 = 50
Add the ones:
5 ones and 4 ones = 9 ones
5
+
4
= 9
Add these together:
50 + 9 = 59
The answer is 59.
35 + 24 = 59
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Unit 15 Addition and subtraction
Practise
34
1 Use cubes to help you complete these additions. + 23 is a
different way of
22 + 15 =
a 25 + 12 =
writing 34 + 23.
35 + 12 =
b
34
+ 23
32 + 15 =
34
+ 25
44
+ 23
44
+ 25
2 Draw number lines to help you complete these additions.
Look at the example.
+ 10
35 + 22 = 57
+ 10
35
+2
57
a 35 + 23 =
b 42 + 21 =
c 42 + 23 =
d 42 + 25 =
3 The stall holder buys 23 oranges and 45 passion fruits from
the farmer. How many fruits does she have in total?
First make an estimate.
Try this
+
Let’s talk
4
5
2
1
6
6
Find at least 3
other additions
like this with
the answer 66.
Look together at the additions
and your answers for Practise
question 1b. What patterns do
you notice? Try to continue any
patterns you find.
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Unit 15 Addition and subtraction
Subtracting two-digit numbers
Maths word
subtract
Explore
A shop sells these items.
10 cups
10 cups
10 cups
10 cups
10 glasses
10 glasses
10 glasses
10 glasses
There are more cups than
glasses. How many more?
The shop sells 15 cups. How
many are left on the shelf?
The shop also sells some of
the boxes of glasses and
3 of the single glasses.
How many glasses could be
left on the shelf?
Learn
The cubes show
the total number
of cups on the
shelf.
The shop sells 15
cups, so we subtract
a 10 and 5 ones.
There are 32 cups left.
We can write 47 – 15 = 32 or 47
– 15
32
We can do the same calculation on the number line.
–5
– 10
30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
We count back 10 and then use the subtraction fact 7 – 5 = 2
to take away the ones.
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Unit 15 Addition and subtraction
Practise
1 Use cubes to help you solve these subtractions.
a 45 – 13 =
b 58 – 22 =
45 – 23 =
58 – 32 =
45 – 33 =
58 – 42 =
45 – 43 =
58 – 52 =
c
57
– 24
67
– 34
Look for numbers
that are close
together.
Sometimes it is
easier to count on to
find the difference.
77
– 44
87
– 54
2 Complete these subtractions by counting back on the number line.
Look at the example.
77 – 22 = 55
–2
– 10
55 57
– 10
67
77
a 87 – 24 =
b 97 – 26 =
c 65 – 34 =
d 55 – 23 =
e 45 – 12 =
f 76 – 31 =
3 Complete these. Which method will you use this time?
a 27 – 26 =
b 65 – 64 =
c 18 – 17 =
27 – 25 =
65 – 63 =
18 – 16 =
27 – 24 =
65 – 62 =
18 – 15 =
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Unit 15 Addition and subtraction
Try this
I am using the number
line to calculate 39 – 16.
–6
– 10
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
I think Annay has made a mistake.
What mistake has Annay made?
Draw a number line to show the correct answer.
Let’s talk
The answer to 56 – 24 is about
30 because 50 – 20 = 30.
The answer is about 40 because 60 – 20 = 40.
The answer is between 30 and 40.
What did the children do to make their estimates?
Can you use the children’s ideas to estimate the answer to 48 – 33?
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Unit 15 Addition and subtraction
Addition and subtraction facts to 100
Explore
It is a busy day in the
city. Many people use
the bus to travel from
place to place.
More than 20 people
get off the bus.
The same number
get on the bus.
How many people could
be on the bus now?
Explain your thinking.
Maths word
inverse
Learn
To start with, there are 36 people on a bus.
Look what happens when 22 people get off the bus.
–2
– 10
– 10
14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
We write: 36 – 22 = 14. There are 14 people left on the bus.
The same number of people get on the bus.
We write: 14 + 22 =
+ 10
+ 10
+2
14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
What is the same and what is different about the 2 number lines?
14 + 22 = 36 is the inverse addition sentence for 36 – 22 = 14.
What is the inverse subtraction sentence for 14 + 22 = 36?
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Unit 15 Addition and subtraction
Practise
1 Write the inverse addition sentence for each subtraction.
a 25 – 13 = 12
b 36 – 16 = 20
c 49 – 27 = 22
d 55 – 24 =
e 67 – 36 =
f 79 – 48 =
2 True or false?
a 45 + 12 = 57 so 45 – 12 = 57
b 56 + 23 = 79 so 23 – 79 = 56
c 67 + 31 = 98 so 98 – 31 = 67
3 Write a number sentence to match each number story.
a There are 35 people on a bus.
14 more get on. Then 14 get off.
b There are 47 people on a bus.
24 get off. Then 24 more get on.
Try this
Look at these bar models. Find the 2 addition sentences and the
subtractions for each bar model.
75
50
25
20
80
60
93
51
42
Let’s talk
I think you can use an inverse subtraction
sentence to check an addition.
What do you think? Try out some examples.
How can David check a subtraction? Explain your idea.
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Unit 15 Addition and subtraction
Quiz
1 Complete these calculations.
a 10 + 53 =
20 + 53 =
30 + 53 =
b 84 – 10 =
84 – 20 =
84 – 30 =
c 67 – 63 =
57 – 53 =
47 – 43 =
d 33 + 33 =
33 + 34 =
33 + 32 =
2 Complete these additions. Make an estimate first.
c
62
a 43 + 26 = ?
+ 27
b 55 + 32 = ?
?
3 Complete these subtractions. Make an estimate first.
c
67
a 46 – 23 = ?
– 25
b 59 – 32 = ?
?
4 Write the inverse subtraction sentences each time.
a 43 + 22 = 65
b 35 + 21 = 56
c 54 + 32 = 86
5 Write the inverse addition sentences each time.
a 46 – 25 = 21
b 75 – 32 = 43
c 68 – 45 = 23
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16
Multiplication and division
Multiplication as doubling
Explore
Monday
Tuesday
Wednesday
Thursday
Friday
Each day, Jack catches twice as
many fish as the day before.
How many fish does he catch
on Thursday and Friday?
Maths word
doubles
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Unit 16 Multiplication and division
Learn
×2
two lots of
double
2 groups of
twice
Double
Counters
Double 1
As an
addition
1+1=2
As a
As a
multiplication division
1×2=2
2÷2=1
Double 2
2+2=4
2×2=4
4÷2=2
Double 3
3+3=6
3×2=6
6÷2=3
Double 4
4+4=8
4×2=8
8÷2=4
Double 5
5 + 5 = 10
5 × 2 = 10
10 ÷ 2 = 5
Double 6
6 + 6 = 12
6 × 2 = 12
12 ÷ 2 = 6
Double 7
7 + 7 = 14
7 × 2 = 14
14 ÷ 2 = 7
Double 8
8 + 8 = 16
8 × 2 = 16
16 ÷ 2 = 8
Double 9
9 + 9 = 18
9 × 2 = 18
18 ÷ 2 = 9
Double 10
10 + 10 = 20 10 × 2 = 20
20 ÷ 2 = 10
Try to learn these doubles facts!
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Unit 16 Multiplication and division
Practise
1 Write the answers to these doubles. See the example.
+
a
= 2 glasses of juice
+
+
c
=
=
+
++
=
b
++
= +=
d=
+
=+=
=
==
=
2 How many counters are there in each picture?
Write a number sentence to match.
a
b
c
d
e
3 Complete the addition sentences.
a 2+2=
×
b 5+5=
c 6+6=
×
d 10 + 10 =
×
×
Let’s talk
You know that double 10 is 20 and double 3 is 6.
How does that help you to find double 13?
How can you use double 10 and other doubles you know to find:
double 11 ?
double 12 ?
double 14 ?
double 15 ?
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Unit 16 Multiplication and division
Multiplication tables of 1 and 2
Explore
What is different about the 2 cycles?
How many wheels are on 3 monocycles?
What do you notice about the number
of monocycles and the number of wheels?
Maths words
repeated addition
multiplication
times table
Learn
This number line shows the
number of wheels on three
bicycles.
The number line shows the
number of wheels on three
monocycles.
+1
0
+1
1
+1
2
+2
3
4
5
0
+2
2
+2
4
6
Repeated addition can help us to write the multiplication tables.
1×1=1
1×2=2
1×3=3
1×4=4
1×5=5
1
1+1
1+1+1
1+1+1+1
1+1+1+1+1
This is part of the
1 times table.
2×1=2
2×2=4
2×3=6
2×4=8
2 × 5 = 10
2
2+2
2+2+2
2+2+2+2
2+2+2+2+2
This is part of the 2 times
table. I can see some doubles!
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Unit 16 Multiplication and division
Practise
1 Complete the multiplication
tables. Use repeated
addition to help you.
2 Write the multiplication
fact to match each
sentence.
1×1=
2×1=
a 3 groups of 1 is
1×2=
2×2=
b 4 groups of 2 is
1×3=
2×3=
c 5 groups of 1 is
1×4=
2×4=
d 6 groups of 2 is
1×5=
2×5=
1×6=
2×6=
1×7=
2×7=
1×8=
2×8=
1×9=
2×9=
1 × 10 =
2 × 10 =
Try this
True or false?
1×4=2×2
Can you make other number
sentences like this using
multiplication facts you know?
3 2 × 5 = 10
Which division sentence
also tells us that there are
5 groups of 2 in 10?
2 ÷ 10 = 5 10 ÷ 1 = 10
10 ÷ 2 = 5 10 ÷ 10 = 1
Let’s talk
I have 7 bags with 1 apple
in each. There are 7 apples.
I have 7 bags with 2 apples
in each. I have double the
number of apples as David!
Do you agree with Zara?
Draw or write something
to convince your partner.
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Unit 16 Multiplication and division
Multiplication tables of 5 and 10
Explore
The children are making
trains with blocks.
What can the totals
of their trains be?
How many blocks must
they each use for the
totals to be the same?
What do you notice?
10
5
5
5
5
5
5
5
10
10
10
10
5
5
5
10
10
10
10
10
Learn
We can use the fives blocks
and repeated addition to help
build the 5 times table.
5×1=5 5
5 × 2 = 10 5 5
5 × 3 = 15 5 5 5
5 × 4 = 20 5 5 5 5
How does the pattern
continue?
We can also use the tens
blocks to help build the
10 times table.
10 × 1 = 10 10
10 × 2 = 20 10 10
10 × 3 = 30 10 10 10
10 × 4 = 40 10 10 10 10
How does the pattern continue?
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Unit 16 Multiplication and division
Practise
1 Complete and compare the
multiplication tables.
2 Write the multiplication fact
to match each sentence.
5×1=
10 × 1 =
a
5×2=
10 × 2 =
b 3 groups of 10 is
5×3=
10 × 3 =
c
5×4=
10 × 4 =
d 6 groups of 10 is
5×5=
10 × 5 =
5×6=
10 × 6 =
5×7=
10 × 7 =
5×8=
10 × 8 =
5×9=
10 × 9 =
5 × 10 =
10 × 10 =
3 groups of 5 is
6 groups of 5 is
3 aOne bucket holds 5 litres
of water: What is the
total for 3 buckets?
b One box holds 10 kg
of rocks: What is the
total for 5 boxes?
What is the total
for 10 boxes?
Try this
Let’s talk
Jack has some 10 cent coins.
Viti has some 5 cent coins.
The children have an equal
number of cents in total.
Find different ways to make
this true.
What patterns do you notice?
Make up some word problems
to match these multiplication
facts.
5 × 7 = 35 10 × 6 = 60
Convince another pair that
your word problems match.
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Unit 16 Multiplication and division
Using arrays
Explore
The children are visiting the animal sanctuary shop.
There are many things to buy.
Postcards
$2
Maths word
array
$10
Badges
$1
$5
$5
What do you notice about the way the items are arranged?
How many are there of each item?
How much will it cost to buy 2 of each item?
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Unit 16 Multiplication and division
Learn
At the animal sanctuary,
each penguin eats 2 fish.
How many fish will the
sanctuary volunteer need
if there are 4 penguins?
2×4
⎫
A pair of penguins being fed fish
⎪
by a sanctuary volunteer
⎬ The array shows 8 fish.
⎪ 2×4=8
⎭ This is one of the facts in the 2 times table.
Practise
1 Each penguin eats 2 fish. Use the arrays to work out how many
fish the volunteer will need each time, for:
b 6 penguins
a 5 penguins
2×5=
2×6=
c 7 penguins
d 8 penguins
2×7=
2×8=
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Unit 16 Multiplication and division
Practise (continued)
2 Each monkey eats 5 bananas.
Draw an array and write a matching multiplication sentence.
Show how many bananas the volunteer will need each time.
a 2 monkeys will need: 5 × 2 =
b 3 monkeys will need: 5 × 3 =
Remember, you should
also think about the
multiplication tables
that you know!
c 4 monkeys will need: 5 × 4 =
d 5 monkeys will need: 5 × 5 =
e 6 monkeys will need: 5 × 6 =
3 The children line up in 4 rows of 10 to visit the sanctuary.
How many children in total? Write the multiplication sentence.
Try this
Let’s talk
Use the array to complete the
multiplication sentence:
×
=
×
How could you change the
array to show 10 × 2 = 20?
How many different arrays can
you make with 30 counters?
Use your skill
of specialising.
Write a multiplication sentence
each time.
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Unit 16 Multiplication and division
Sharing for division
Explore
Maths words
share
equal
division
divide
Viti is playing Animal snap with 20 cards.
How many cards does
Viti have when she plays
on her own? The other
children join in one
at a time. They share
the cards so they each
get an equal number.
What happens?
Learn
20 ÷ 4
We can use sharing for division.
If we divide or share 20 equally between 4 groups, we get 5.
20
5
5
5
5
That’s the same as
finding quarters!
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Unit 16 Multiplication and division
Practise
1 Use sharing for division. Explain your method to a friend.
a 10 ÷ 2 =
b 10 ÷ 5 =
c 10 ÷ 10 =
d 40 ÷ 4 =
e 40 ÷ 5 =
f 40 ÷ 10 =
2 Write the matching division sentences. Explain how you know.
a
b
16
16
c
25
d
50
3 Which is the odd one out? Explain your decision.
18 ÷ 2 90 ÷ 10 8 ÷ 1 45 ÷ 5
Try this
Viti has 2 packs of 20 animal cards. She invites some friends
to play. How many friends could play a game so they each have
the same number of cards? All the cards need to be used.
Let’s talk
10 ÷ 1 =
I think the answer is
1 because there will
only be one group.
I think the answer is 10 because there are
no other groups to share 10 between.
Do you agree with Annay or Maris? Discuss with a partner.
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Unit 16 Multiplication and division
Grouping for division
Explore
It’s a beautiful day for a balloon ride.
What different number sentences can you make about the picture?
What if 100 people went on a balloon ride that day?
How many balloons would there be?
Learn
There is 1 group of 10 people in each balloon.
There are 5 groups of 10 in 50 because 10 × 5 = 50.
50 divided into groups of 10 is 5.
50 ÷ 10 = 5
50
10
10
10
10
10
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Unit 16 Multiplication and division
Practise
1 Complete these divisions. Explain your method each time.
a
8÷1=
7÷1=
6÷1=
b
16 ÷ 2 =
14 ÷ 2 =
12 ÷ 2 =
c
40 ÷ 5 =
35 ÷ 5 =
30 ÷ 5 =
d 80 ÷ 10 =
70 ÷ 10 =
60 ÷ 10 =
Think about the
multiplication
facts you know.
2 Write number sentences. Explain your method each time.
a There are 18 sandbags. Each balloon has 2 sandbags.
How many balloons are there?
b There are 60 blankets. Each balloon has 10 blankets.
How many balloons are there?
c There are 45 pairs of binoculars. Each balloon has 5 pairs.
How many balloons are there?
Try this
Look at Zara’s division.
Do you agree with her?
Explain your thinking.
Correct Zara’s work if you
think she is wrong.
35 ÷ 5 = 6
I know that 5 x 6 = 35,
so there are 6 fives in 35
Let’s talk
Use your skill of classifying.
Which of these numbers can you group in twos? 25, 16, 40, 9
Talk about the numbers that you can group in fives or in tens.
What do you notice? Which number is the odd one out? Why?
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Unit 16 Multiplication and division
Division as repeated subtraction
Explore
Different animals are together
at a watering hole.
Maths words
repeated subtraction
Soon all the animals
will be gone.
How many groups
of animals leave the
watering hole when
they walk away in:
l ones?
l twos?
l fives?
l tens?
Learn
We can use repeated subtraction to show the animals walking
away from the watering hole.
What does this number line show us?
0
5
10
How many animals walk away in each group?
How many groups are there?
Write this as a division sentence.
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Unit 16 Multiplication and division
Practise
1 Imagine 20 animals at the watering hole. How many groups
leave the watering hole when the animals walk away in:
a ones?
b twos?
c fours?
d fives?
e tens?
2 Write each division as a repeated subtraction.
Look at the example.
15 ÷ 5 = 3 15 – 5 – 5 – 5 = 0 a 25 ÷ 5 = 5
b 30 ÷ 10 = 3
d 6÷2=3
c 50 ÷ 10 = 5
e 10 ÷ 2 = 5
3 Write the matching repeated subtraction sentence:
There are 18 gloves in a basket.
How many children can take a pair?
Try this
÷
How many ways can
you make this true?
=4
Make up a repeated subtraction number story
to match one of your solutions.
Let’s talk
Maris uses repeated subtraction to solve a division:
–
–
–
= 0 What could the division be?
Work together to find at least 3 solutions.
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Unit 16 Multiplication and division
Quiz
1 Complete these sets of multiplications.
a 1×3=
b
2×3=
1×4=
2×4=
1×5=
2×5=
c 5×5=
d 10 × 5 =
5×6=
10 × 6 =
5×7=
10 × 7 =
2 Sketch an array for each of these.
Write the total each time.
a 5×3
b 2×6
c 10 × 4
3 At a school, 8 teams have 5 players each.
How many players are there in total?
4 Write the division number sentence each time.
a The teacher puts 20 children into teams of 5.
How many teams are there?
b How many groups of 10 can you take from 90?
c There are 16 oranges in a box.
Elok shares them equally between 2 children.
How many oranges does each child get?
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17
Fractions
Divide to find fractions
Explore
What is the whole?
This is half
of my shape.
This is one
quarter of
my shape.
Maths word
one quarter
Learn
Divide 6 by 2
Find half of 6
I will share 6
between 2.
Compare these problems:
12 ÷ 4 =
Find __
​​  14​of 12.
I will use 6 counters.
But is my problem
like yours?
1
​ __
4​is one quarter.
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Unit 17 Fractions
Practise
1 Solve these fraction problems using cubes, counters and drawings.
1
a Find ​​ __
2 ​​ of 10.
c
1
​​ __
4​of 12 is
b What is __
​​ 12 ​​ of 16?
.
1
d​​ __
4​of 8 is
.
2 There are 16 children in a class. Divide them into 4 equal teams.
Write your answer as a fraction number sentence.
3 Complete the missing information.
1
a ​​ __
2 ​​ of
is 5.
1
b​​ __
4​ of
1
c ​​ __
2 ​​ of
is 2.
d
is 5.
of 4 is 1.
Try this
Explore the whole numbers up to 20.
Which whole numbers can you divide into halves?
Which whole numbers can you divide into quarters?
Let’s talk
Are all these shapes broken up into quarters?
Discuss this with a partner.
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Unit 17 Fractions
One quarter, two quarters, three quarters …
Explore
Think about equal parts. Draw one of these shapes.
Colour in 2 equal parts.
What fraction have you coloured in?
Learn
Place fractions on a number line. Where does half go?
1
2
3
4
__
__
__
__
0
4​
4​
4​
4​
1
Compare two quarters and one half (​​ __
2 ​​). They are equivalent.
1
__
4​
2
__
4​
3
__
4​or three quarters
4
__
4​
1
__
2
Which fraction is less than one half?
Which fraction is greater than one half?
Maths word
two quarters
equivalent
three quarters
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Unit 17 Fractions
Practise
1 a Draw a number line from 0 to 1.
b Label it with quarters and halves in the correct places.
2 a Say the name of each fraction.
1
__
2
__
​
b Find a pair of equivalent fractions.
​
4
4
4
__
1
__
c Write the fractions in order.
4​
2
3
__
4​
3 First Viti painted 1 half yellow.
Then Zara painted 1 more quarter blue.
a What fraction is painted? b What fraction is not painted?
4 Copy each shape.
a
b
Colour half of each shape yellow.
Colour 1 more quarter of each shape blue.
c
d
What fraction have you shaded?
What fraction is left blank?
Try this
Practise counting from 0 to 1 in quarters. Draw a number line to
help you. Try counting forwards and backwards.
2
1
__
instead
of
Try saying __
4
2 when you count.
Quiz
1
1 Find ​​ __
4​of each number: a 8
b 12
c 20
2 Draw one quarter, two quarters, and three quarters.
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18
Time and measurement
Time
Maths words
calendar
day
week
month
year
Explore
The calendar shows the month of July.
What is happening in July?
JULY
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
1
2
3
4
5
6
8
7
Jade’s
party
Jade’s
birthday
9
10
11
12
13
14
Gran 15
coming
to stay
16
17
18
Sports
day
19
20
21
22
23
24
25
26
27
28
29
Haircut
30
Dentist
31
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Unit 18 Time and measurement
Learn
rN
ctobe ovembe
O
r
r
be
Saturda
y
January
Feb
mber
e
c
ru
e
D
ugust Sep
uly A
tem
eJ
un
ay Wed
sd
y
day Monday T
n
u
ue
S
There are 52 weeks and
12 months in a year.
h Apri
l
M
a
Marc
yJ
ary
There are 7 days in a week.
There are 24 hours in a day.
There are 60 minutes in an hour.
There are 60 seconds in a minute.
y Thursday Fri
da
sda
ne
Practise
The calendar shows the month of January.
1 Which day comes after Wednesday?
JANUARY
2 Which day comes after Friday?
SUN MON TUES WED THU FRI SAT
3 Which day comes before Monday?
1 2 3 4
4 Which day comes before Friday?
5 6 7 8 9 10 11
5 Which month comes after January?
6 Which month comes before January? 12 13 14 15 16 17 18
19 20 21 22 23 24 25
7 Which month comes after June?
26 27 28 29 30 31
8 Which month comes before June?
Let’s talk
What day of the week is it today? What day will it be in 10 days?
How could you work it out? Which month of the year is it now?
What month will it be in 6 months? How can you check?
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Unit 18 Time and measurement
Capacity
Explore
David, Annay and Zara water the plants.
They each use 4 litres of water.
Maths words
litres
capacity
measuring cylinder
measuring scale
millilitres
Annay fills his watering can 4 times.
Zara fills her watering can twice.
David fills his watering can once.
How much water does each watering can hold?
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Unit 18 Time and measurement
Learn
Capacity is the amount that a container can hold.
We can measure capacity by counting how many
cups of water fill a container.
The cups must be the same size and shape.
Remember to fill the cup each time.
Remember that you can only
compare containers if you
measure them in the same way.
The bowl holds 2 cups. The jug holds 3 cups.
The bucket holds 4 cups. It holds the most water.
It has the largest capacity.
We can also measure capacity using a measuring cylinder.
It has marks or lines to show you how much is in it.
We call these lines a measuring scale.
A measuring scale is similar to a continuous number line
where the in-between marks have values.
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Unit 18 Time and measurement
Learn (continued)
We measure capacity in litres (ℓ) and millilitres (ml).
We use the symbol ℓ for litres. We use the symbol ml for millilitres.
We use measuring jugs and measuring cylinders to measure the
capacity of containers.
The water level in the measuring jug is at the 300 ml mark.
The measuring jug holds 300 ml of water.
ml
Using the symbols makes
it quick and easy to write
the measurement.
450
350
250
150
50
500
400
300
200
100
Practise
1 Use a table like this. Fill in the answers to the questions.
Container
Estimate
Number of cups
__________________________________________________________________
watering
canwatering
watering
can
watering
can can
watering can
jam jar
jam
jar
jam
jam jar
jam jar
jar
jug
jug jug
water
jug
water
water
bottle
bottle
jug
water
bottlebottle
water bottle
a Estimate which container holds the most water.
b Find out exactly how many cups of water each container
holds. How will you do this?
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Unit 18 Time and measurement
Practise (continued)
2 Which container holds the most water?
3 Which container holds the least water?
4 Put the containers in order from:
holds the least  to  holds the most.
5 Estimate each time.
a How many jam jars of water will fill the watering can?
b How many bottles of water will fill the jug?
c Does the watering can or the jug hold the most water?
6 How much water is in each measuring container?
a ml
500
450
350
250
150
50
b
ml
500
450
400
350
300
400
300
It is important to
measure correctly.
200
100
Put the measuring
container on a flat
surface. Use a table
or counter. Never just
hold it in your hand!
250
200
150
100
50
c
ml
500
Always measure at
eye level, looking
straight at it. Bend
down if you need to.
450
400
350
300
250
200
150
100
50
Pour in the liquid
until it is exactly at
the measuring line,
not above or below it.
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Unit 18 Time and measurement
Practise (continued)
7 Copy the number sentences. Use <, > or = to compare amounts.
a 100 ml
c 3ℓ
50 ml
b 100 ml
d 2ℓ
1ℓ
150 ml
1ℓ
8 Use <, > or = to compare the amounts.
b
a
450
350
250
150
50
250 ml
250
ml
250 ml
250
ml
300 ml
300
ml
c
500
400
300
200
100
500
500 ml
ml
250 ml
d
300 ml
300
300ml
ml
200
200200
ml ml
ml
300 mlml
300
300 ml
200 ml
Let’s talk
I think the measuring
cylinder has the largest
capacity. It is the tallest.
Is Jack correct? Explain why or why not.
measuring
cylinder
bottle
cup
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Unit 18 Time and measurement
Measures
Explore
Can you name these measuring instruments?
What could you use each measuring instrument to measure?
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Unit 18 Time and measurement
Learn
Measurement Measuring instrument
Unit
Length
Centimetres
Metres
Kilometres
Mass
Grams
Kilograms
Capacity
Millilitres
Litres
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Unit 18 Time and measurement
Practise
1 Annay is baking a cake. Which measuring instrument should he
use to weigh the butter?
a
b
c
2 Zara is measuring the length of the classroom.
Which measuring instrument should she use?
a
b
c
3 Jack is measuring out some water.
Which measuring instrument should he use?
a
b
c
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Unit 18 Time and measurement
Practise (continued)
4 How long is each pencil?
a
b
5 How heavy is each letter? What is its mass?
a
b
Let’s talk
Match each measuring instrument a
to the correct unit of measurement.
c
centimetres
metres
millilitres
b
d
grams
What could you use each measuring instrument to measure?
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Unit 18 Time and measurement
Quiz
1 Which month comes after February?
2 Which day comes before Tuesday?
3 Which month is after July?
4 Which month is before April?
5 How much water is in the
measuring cylinder?
ml
500
450
400
350
300
250
200
150
100
50
6 Copy these capacity
sentences and fill in the
<, > or = signs to compare
the amounts.
a 5 litres
10 litres
b 400 ml
300 ml
c 5 litres
1 litre
7 Write which instrument you would use to do these things.
a Measure the length of a piece of ribbon.
b Weigh a parcel.
c Measure an amount of water.
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Term
3
Review
Units 13–18
Even numbers
1 Complete a Venn diagram,
like the one on the right.
Use these numbers:
23, 42, 4, 6, 12, 28, 31
2 Viti spins a 1 to 6 spinner.
How likely is it that she:
a spins and gets a number?
b spins and gets an 8?
c spins and gets a 3?
Choose from these words to
answer each time.
It will not happen
1
20 or more
2
6
3
5
4
It might happen
It will happen
3 How many children are in your class today?
Round the number to the nearest 10.
4 Find the missing numbers.
Then write the inverse calculation sentences.
a 100 – 30 =
b 60 +
= 100
c
d 90 –
= 60
50 + 20 =
5 Complete these calculations.
a 52 + 23 =
b
52
+ 25
c
66
– 25
d 68 – 25 =
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Term 3 Review
6 Complete these divisions.
16 ÷ 2 =
b 30 ÷ 5 =
c 60 ÷ 10 =
d 25 ÷ 5 =
a
7 Fill in the missing numbers in these multiplication facts.
a 2×
=8
b 5×
c 10 ×
= 50
d
× 9 = 18
× 9 = 45
f
× 10 = 100
e
= 15
8 Draw a number line to show one quarter, two quarters,
three quarters, 0 and 1.
Explain where half is on the number line.
9 Viti is measuring the length of a table.
Which measuring instrument should she use?
a
c
b
10 How much water is in each jug?
a 1000 ml
b
1000
ml
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Mathematical dictionary
2D shapes two-dimensional geometric
shapes; flat shapes with sides and angles
circle
triangle
square
rectangle
pentagon
hexagon
3D shapes three-dimensional
geometric shapes; solid shapes with
faces, edges and corners; see also face,
edge and corner
cube
sphere
cuboid
triangular prism
cone
cylinder
square-based
pyramid
A
addition a calculation of the sum of
two numbers or things
amount the total of things such as
numbers, size or value
anticlockwise in the
opposite direction to
the hands of a clock
array an arrangement
made up of rows and columns
B
block graph a diagram to show
information
C
calculation a way of finding the
number of something
calendar a chart or pages that show
the months and days of a whole year
capacity the largest amount that
something can contain
Carroll diagram a table used for
sorting things
Multiple of 5
Not a multiple of 5
10, 20, 30
2, 6, 12
Not an even 5, 15, 25
number
3, 7, 11
Even
number
category a division, class or certain
type of thing; music has categories
such as hip hop, folk, blues, pop
cent(s) a coin value
centimetre (cm) there are
100 centimetres in a metre
chance a possibility of
something happening
clockwise in the same
direction as the hands
of a clock
coin a piece of metal used as money
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Mathematical dictionary
common happens often
compare to note similarities and
differences
complement(s) the amount you must
add to something to make it a whole
compose to combine place value
parts, for example:
200 + 40 + 2 = 242
corner where two or more lines meet
and form an angle
count to use numbers to see how
many there are of something
curved round, not straight
D
data information that has been
collected in some way
day there are 24 hours in a day; a day
is one of the 7 days in a week
decompose separate a number into
each of its place value parts
24
20
4
difference the answer when
subtracting one number from another
divide to find how many times a
number is contained in another
number
division to break up a number into
equal parts
dollar a unit of money
double twice as many
doubles numbers added to
themselves, such as 2 + 2 = 4; 4 + 4 = 8;
8 + 8 = 16
E
edge the straight side of a 2D object;
where two faces of a 3D shape meet
equal(s) the same as, shown by the
sign =
equivalent the same as something
else
estimate a sensible guess, or to make
a sensible guess
even the same in size; even numbers
are all numbers ending in 0, 2, 4, 6 or 8
F
face surface of a solid shape
fifty the number 50
first, second, third, … ordinal
numbers, written as 1st, 2nd, 3rd …
fives used when counting 5 numbers
on or back, for example, 5, 10, 15, 20
forty the number 40
1
fraction a part of something
or part of a number, for example, 4
G
gram (g) there are 1000 grams in one
kilogram
group to gather/collect
H
half something divided by 2
half turn not a full turn; half of it
halve to divide something by 2
heaviest weighs the most; has the
most mass
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Mathematical dictionary
hour a unit of time
hour
(60 minutes)
hour hand the shorter arrow on an
analogue clock; points to the hour
hundred the number 100
I
inverse opposite; subtraction is inverse
to addition; multiplication is inverse to
division
K
kilogram (kg) a measurement
of weight (equal to
1000 grams)
0g
500 g
1000 g
L
length how far from one
point to another
less not as many
lightest weighs the least; has the least
mass
likely a good chance of something
happening
line of symmetry a line line of symmetry
that divides something
into two identical halves
litre a unit of measurement
(equal to 1000 millilitres)
M
mass how much something weighs
measuring cylinder a container to
measure liquids
measuring scale marks or lines on a
measuring instrument to show the value,
for example, grams, millilitres or litres;
similar to a continuous number line
where in-between marks have values
metre (m) a unit of length (equal to
100 cm)
might happen used in chance;
will possibly happen
millilitre there are 1000 millilitres in
one litre
minute there are 60 minutes in
1 hour; there are 60 seconds in
1 minute
minute hand the longer arrow on an
analogue clock; points to the minutes
month there are 12 months in a year:
January, February, March, April, May,
June, July, August, September, October,
November, December
more greater in number or size
multiple of 10 a number that can be
divided equally by 10
multiplication an operation that we
can represent as repeated addition or
as an array
N
note(s) paper money
numeral a figure or
symbol that stands
for a number
O
odd all numbers ending in 1, 3, 5,
7 or 9
one quarter one part of something
divided into 4 parts
ones shows the ones place value;
numbers up to 9: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
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Mathematical dictionary
order an arrangement of objects or
numbers from smallest to largest or
largest to smallest
P
part-part-whole model when a whole
is broken up into 2 or more parts, such
as: 2 (part) + 13 (part) = 15 (whole)
15
2
15
13
2
13
pattern a repeated design on fabric
or in numbers
pictogram a picture that
represents a word or a number
popular well liked
Q
quarters something divided into 4
quarter turn a right-angle turn
R
regroup exchange for something with
the same value, for example: regroup
10 ones to make 1 ten
repeated addition to add over and
over again, for example, 2 + 2 + 2
repeated subtraction to subtract over
and over again, usually until you reach
0, such as 20 – 5 – 5 – 5 – 5 = 0
round done to find the nearest whole
number; we can round 28 to 30;
21 to 20, 39 to 40
9781398300941_HCP_MATH_S2_LB.indb 199
S
second comes after first
seconds a minute has 60 seconds;
a second is one sixtieth of a minute
sequence the order in which
something is arranged, such as
numbers or events
share to divide something between
others
side a line of a shape
subtract to take away something
from another
subtraction a way of finding the
difference between two numbers or
things
symmetrical each half is
exactly the same This beetle is
symmetrical.
T
tally a way of keeping a score or
amount llll llll llll
tally chart a chart used to keep
a tally score
tens shows the tens place value
third comes after second and
before fourth
thirty the number 30
three quarters 3 of 4 parts
__
​​  3 ​​ is shaded
of something
4
times table a table showing
numbers multiplied together
total the answer to an addition
calculation
turn to rotate or change position
twenty the number 20
two quarters half of __​​  12 ​​ is shaded
something
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Mathematical dictionary
twos the numbers used when
counting, for example, 2, 4, 6, 8 …
or 11, 13, 15, 17, 19
V
Venn diagram a diagram with
circles to show sets
Even numbers
2
6
Multiples of 5
10
20
12
14
5
25
15
Thinking and Working Mathematically
(TWM) skills vocabulary
characterising identifying and
describing the mathematical properties
of an object
classifying organising objects into
groups according to their mathematical
properties
conjecturing forming mathematical
questions or ideas
35
W
week there are 7 days in a week:
Monday, Tuesday, Wednesday,
Thursday, Friday, Saturday, Sunday
whole turn
whole turn
a full rotation
will happen used in chance;
something that is certain
to happen
will not happen used in chance;
something that is certain not
to happen
Y
year 365 (or 366) days make a year
convincing presenting evidence to
justify or challenge a mathematical idea
or solution
critiquing comparing and evaluating
mathematical ideas, representations or
solutions to identify advantages and
disadvantages
generalising recognising an underlying
pattern by identifying many examples
that satisfy the same mathematical
criteria
improving refining mathematical ideas
or representations to develop a more
effective approach or solution
specialising choosing an example and
checking to see if it satisfies or does not
satisfy specific mathematical criteria
This calendar
shows the
12 months
of a year.
200
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