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CAMBRIDGE
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Primary Mathematics Workbook 2
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Cherri Moseley & Janet Rees
Second edition
Digital access
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
LE P M A
S Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
LE
CAMBRIDGE
P
Primary Mathematics Workbook 2
S
A
M
Cherri Moseley & Janet Rees
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
University Printing House, Cambridge CB2 8BS, United Kingdom One Liberty Plaza, 20th Floor, New York, NY 10006, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia 79 Anson Road, #06–04/06, Singapore 079906
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314–321, 3rd Floor, Plot 3, Splendor Forum, Jasola District Centre, New Delhi – 110025, India
Cambridge University Press is part of the University of Cambridge.
It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9781108746465 © Cambridge University Press 2021
First published 2021
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This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Printed in ‘country’ by ‘printer’
A catalogue record for this publication is available from the British Library
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ISBN 978-1-108-74646-5 Workbook with Digital Access
Additional resources for this publication at www.cambridge.org/9781108746465
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Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Information regarding prices, travel timetables, and other factual information given in this work is correct at the time of first printing but Cambridge University Press does not guarantee the accuracy of such information thereafter.
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NOTICE TO TEACHERS It is illegal to reproduce any part of this work in material form (including photocopying and electronic storage) except under the following circumstances: (i) where you are abiding by a licence granted to your school or institution by the Copyright Licensing Agency; (ii) where no such licence exists, or where you wish to exceed the terms of a licence, and you have gained the written permission of Cambridge University Press; (iii) where you are allowed to reproduce without permission under the provisions of Chapter 3 of the Copyright, Designs and Patents Act 1988, which covers, for example, the reproduction of short passages within certain types of educational anthology and reproduction for the purposes of setting examination questions. NOTICE TO TEACHERS The photocopy masters in this publication may be photocopied or distributed [electronically] free of charge for classroom use within the school or institution that purchased the publication. Worksheets and copies of them remain in the copyright of Cambridge University Press, and such copies may not be distributed or used in any way outside the purchasing institution.
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
Contents
Contents
5 6
1
Numbers to 100
8
1.1 1.2 1.3
Numbers to 100 Counting up to 100 objects Comparing and ordering numbers
8 15 22
2
Geometry
27
2.1 2.2 2.3
3D shapes 2D shapes and symmetry Fractions of shapes
3
Measures
3.1 3.2
Length Drawing and measuring lines
52 63
4
Statistics
71
4.1
Carroll diagrams and tally charts
71
5
Working with numbers to 100
77
5.1 5.2 5.3 5.4
Addition Subtraction Multiplication Division
77 84 92 100
6
Money
107
6.1
Money
107
7
Time
114
7.1
Units of time and the calendar
114
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How to use this book Thinking and Working Mathematically
27 39 43
52
3
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Contents
Numbers to 100 (2)
122
8.1 8.2
Numbers in words, rounding and regrouping Fractions of numbers
122 128
9
Statistics (2)
133
9.1 9.2
Venn diagrams, lists and tables Statistics
133 142
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8
10 Calculating
148
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10.1 Adding and subtracting two 2-digit numbers 10.2 Connecting addition and subtraction 10.3 Multiplication 10.4 Division
169
11.1 Angles and turns 11.2 Circles
169 179
12 Telling the time
181
12.1 Telling the time
181
13 Measures (2)
188
13.1 Mass and temperature 13.2 Capacity
188 200
14 Pattern and probability
207
14.1 Pattern and probability
207
15 Symmetry, position and movement
213
15.1 Symmetry, position and movement
213
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11 Geometry (2)
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148 154 161 165
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How to use this book
How to use this book
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This workbook provides questions for you to practise what you have learned in class. There is a unit to match each unit in your Learner’s Book. Each exercise is divided into three parts:
• Focus: these questions help you to master the basics • Practice: these questions help you to become more confident in using what you have learned • Challenge: these questions will make you think more deeply.
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You might not need to work on all three parts of each exercise. You will also find these features:
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Important words that you will use.
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Step-by-step examples showing a way to solve a problem. There are often many different ways to solve a problem.
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These questions will help you develop your skills of thinking and working mathematically.
5
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Thinking and Working Mathematically
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Thinking and Working Mathematically There are some important skills that you will develop as you learn mathematics.
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Specialising is when I give an example of something that fits a rule or pattern.
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Characterising is when I explain how a group of things are the same.
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Generalising is when I explain a rule or pattern.
6
Classifying is when I put things into groups.
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
Thinking and Working Mathematically
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Critiquing is when I think about what is good and what could be better in my work or someone else’s work.
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Improving is when I try to make my work better.
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A
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Conjecturing is when I think of an idea or question to develop my understanding.
Convincing is when I explain my thinking to someone else, to help them understand. 7
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1
Numbers to 100
1.1 Numbers to 100
representation row
Focus 1
Write the missing numbers. 3
=
=
4
0
+
+
9
Write the missing numbers.
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2
0
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2
place holder
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Exercise 1.1
column digit
25
30
51
55
60
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A
21
8
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1.1 Numbers to 100
Worked example 1 Answer:
This is a column from the 100 square. 1
1
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Write the missing numbers.
11
11 21 31
Count on in tens. 11, 21, 31 ... The number of ones stays the same. The number of tens changes.
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41
91
61 71 81 91
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51
9
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1 Numbers to 100
3
Write the missing numbers. 6
10
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3
50
56
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53
A
100
Which 2-digit numbers are represented below?
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4
10
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1.1 Numbers to 100
5
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Draw a different representation of this number.
41
1
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40
Show your representation to a partner or carer.
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How is your representation the same as others? How is it different?
Practice
Write the missing numbers.
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6
8
=
5
9
=
=
7
0
+
0
+
0
+
8
3
11
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1 Numbers to 100
7
Here are some rows and columns from a 100 square. Write the missing numbers.
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80
20
8
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4
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74
12
88
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1.1 Numbers to 100
Draw a representation of 23 and a representation of 32.
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8
How they are the same? How they are different?
Discuss your representations with a partner or carer. Here are some pieces of a 100 square.
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9
Write the missing numbers. 23
74
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A
57
88
37
13
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1 Numbers to 100
Challenge 10 Here is a mostly blank 100 square. Write these numbers in the correct places. 53
90
75
46
69
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37 81
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1
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100
11 Use the digit cards to make 6 different 2-digit numbers. Write these numbers in the correct places in the 100 square from question 10. 2
14
4
8
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1.2 Counting up to 100 objects
1.2 Counting up to 100 objects Exercise 1.2 1
Write the missing numbers. 1 ten →
10
order
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3 tens →
5 tens →
collection
Use the table to help you count in tens from 10 to 100.
2 tens →
4 tens →
accurate, accurately
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Focus
6 tens →
A
7 tens → 8 tens →
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9 tens →
10 tens →
15
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1 Numbers to 100
Which tens number is 1 ten more than 8 tens?
3
Which tens number is 1 ten fewer than 6 tens?
4
Sofia and Zara make some numbers. Sofia chooses the tens. Zara chooses the ones.
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2
Write each number they make in a part whole diagram.
10 cents
10 cents
10 cents
1 dollar
1 dollar
1 dollar
1 dollar
1 cent
1 cent
1 cent
1 cent
1 dollar
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A
b
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a
c
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Sofia chooses four tens. Zara chooses zero ones.
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1.2 Counting up to 100 objects
Worked example 2 Arun scoops some stones out of a tray. How many stones does he scoop out? Estimate then count.
More than 10, but fewer than 50. I estimate 20.
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Estimate
10
20
50
100
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Count
Count in tens: 10, 20. Count on in ones: 21, 22, 23, 24, 25, 26, 27.
Answer: 27 stones.
17
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1 Numbers to 100
5
How many cubes are in the collection? Estimate then count to check. Estimate 20
50
100
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10
Count
Compare your estimate and count with another person's. Do you both agree? Sofia counts 100 beads in twos.
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6
Draw a ring around any numbers she said.
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24 59 36 42 17 78 12
Practice 7
Write the tens numbers in order, from 100 to 10. 10
A
100
Marcus and Arun make some numbers. Marcus chooses the tens. Arun chooses the ones.
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8
They make 53 and 87. How many tens does Marcus choose?
How many ones does Arun choose? 18
and
and
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1.2 Counting up to 100 objects
9
How many beans are in the collection? Estimate then count to check. Estimate 20
50
100
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10
Count
Compare your estimate and count with another person's. Do you both agree?
2 more than an odd number is always an odd number.
Numbers with 1, 3, 5, 7 or 9 ones are even numbers.
0 is an odd number.
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An even number of objects can be sorted into 2 equal groups.
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10 Tick the correct sentences.
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Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1 Numbers to 100
Challenge 11 How many large spots are in the box? How many small spots are in the box?
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Estimate, then use the two boxes below to help you count the big spots and then the small spots.
Tip
You could count in twos, fives or tens to find the total.
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Estimate
20
50
100
Count
Estimate 10
20
50
100
Count
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10
Compare your estimate and count with another person's. Do you both agree?
20
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1.2 Counting up to 100 objects
12 Draw or lightly colour a shape joining 5 small squares on the 100 square.
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
72
73
74
75
76
77
78
79
80
82
83
84
85
86
87
88
89
90
96
97
98
99 100
81 91
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71
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1
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Only 1 number inside your shape can be odd.
92
93
94
95
Draw your shape again in a different place.
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A
This time only one of the numbers inside your shape can be even.
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1 Numbers to 100
1.3 Comparing and ordering numbers
close, closer end, stop, finish
Exercise 1.3
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extend order or ordering numbers
Focus
ordinal numbers sequence start, beginning
Worked example 3
0
10
20
30
40
50
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Answer:
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Estimate and show where 32 is on this number line.
S
A
32 is 3 tens and 2 ones.
0
22
10
60
70
80
90
100
32 is after 30 and close to it, but not next to it – that would be 31. It is more than 30 but fewer than 40.
32
20
30
40
50
60
70
80
90
100
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1.3 Comparing and ordering numbers
1
Estimate and show where 15, 43 and 78 are on this number line.
0
10
20
30
40
50
Draw a ring around the 3rd elephant.
3
Arun is last in a queue of 32 people.
70
80
90
100
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2
60
Worked example 4
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Write the ordinal number for Arun’s place in the queue.
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A number sequence starts at 35. It counts on in tens and stops at 65. What are the numbers in this sequence?
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I used a 100 square to help me.
All the numbers have 5 ones. They are all odd. 35, 45, 55, 65.
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Answer: 35, 45, 55, 65.
4
A number sequence starts at 42. It counts on in tens and stops at 72. Write the numbers in the sequence.
23
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1 Numbers to 100
5
A number sequence starts at 32. It counts on in twos and stops at 38. Write the numbers in the sequence.
Draw a ring around the correct words for the number sequence in question 4.
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6
All the numbers are odd even.
All the numbers have the same number of ones tens. 7
Compare 35 and 53.
Tip
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Order these numbers from smallest to greatest. 35
12
A
8
For questions 7 and 8, you can use the number line or place value chart below to help you.
P
Which number is greater?
21
53
S
0
24
10
20
30
40
Tip Remember to use a pencil for any writing or drawing – you can erase your working and reuse the diagrams!
50
60
70
=
+
=
+
80
90
100
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1.3 Comparing and ordering numbers
Practice Estimate and show where 3 and 49 are on this number line.
0
10
20
30
40
50
60
70
80
90
100
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9
10 Draw a ring around the last leaf. Draw a line under the 4th leaf.
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Tick the 1st leaf.
11 Zara’s number sequence is 78, 76, 74, 72, 70.
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Complete the description of Zara’s number sequence. at 78. Count
in
. Stop at
S
A
12 Compare 63 and 36. Which is the smaller number?
13 Order these numbers from smallest to largest. 64
75
46
57
.
Tip For questions 12 and 13, you can use the number line or place value chart at the bottom of the previous page to help you.
19
25
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1 Numbers to 100
Challenge
0
10
20
30
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14 Arun marks two numbers on the number line. Estimate and write Arun's numbers in the boxes.
40
50
60
70
80
90
100
15 Sofia and Zara join a queue to get tickets for the school disco. There are 51 people in front of them.
Where are Sofia and Zara in the queue?
P
16 Write a sequence of 5 numbers.
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Complete the sentences to describe your sequence.
at
. Count
in
. Stop at
.
A
17 Order these numbers from greatest to smallest. 82
48
28
42
S
84
26
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2
Geometry
2.1 3D shapes
edge
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Exercise 2.1
curved surface face
Focus Worked example 1
vertex, vertices
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P
Match these shapes to their names.
cube cuboid pyramid cylinder sphere
S
A
I know a sphere because it’s like a ball.
A cylinder can roll.
I know a cube because it has six faces that are the same.
There is a shape with a vertex at the top.
It has a square face. That is a pyramid.
That means that the last one is a cuboid. 27
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2 Geometry
cuboid
a
Describe this 3D shape.
sphere
cylinder
square-based pyramid
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1
cube
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Continued
.
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This shape is a
faces.
It has
edges.
It has
vertices.
A
It has
b Choose one of these 3D shapes. Name and describe it using edges, faces, vertices and curved surfaces.
S
1
28
Cereal
D e ez B A KE D B EA N S
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2.1 3D shapes
2
Draw a ring around the correct word to name each shape.
cube
pyramid
sphere
cuboid
cube
sphere
cylinder
cuboid
M
cube
sphere
pyramid
sphere
pyramid
cube
S
A
cuboid
cuboid
cylinder
P
sphere
cube
LE
sphere
29
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 Geometry
3
Look around you. Find as many 2D and 3D shapes as you can. Choose 3 of each. Draw what you see. Name of 2D shape
M
P
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Name of object
Name of 3D shape
S
A
Name of object
30
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2.1 3D shapes
Complete the number of faces, edges, curved surfaces and vertices in this table. Shape
Faces
0
Edges
Curved surfaces
Vertices
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4
0
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P
0
8
S
A
5
8
12
31
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2 Geometry
Practice 5
Tony has a 3D shape. One face of the shape is a square.
b
What am I? A
B
D
E
C
P
a
I have more than 2 faces
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6
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What could the shape be?
None of my faces are circles I have 1 square face
Some of my faces are triangles
A
What am I?
c
I am a
I have more than 2 vertices I have no triangular faces
S
All my faces are the same size I have no curved surfaces What am I?
32
I am a
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2.1 3D shapes
7
Use the Venn diagram to sort the shapes. You can draw the shapes or write their names.
M
P
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curved surfaces
S
A
33
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2 Geometry
8
Find 4 3D shapes that are near to you. What 2D shapes can you find on them? For example, a cuboid has 2 square faces and 3 rectangular faces.
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Draw and write what you have found in this table. Name of 3D shape
2D shapes you can see
A
M
P
Name of object
S
Challenge 9
Susie says that her 3D shape has 12 edges. Max says that it can be a square-based pyramid, a cube or a cubopid. Is Max correct? Explain your answer.
34
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2.1 3D shapes
10 Look at each pair of shapes. Can you say what is the same and what is different about the shapes in each pair? Use the table to record your ideas. What is the same?
P
Both have 6 faces, 12 edges and 8 vertices.
M
What is different?
LE
Shapes
S
A
35
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 Geometry
11 Sort the shapes using a Venn diagram. Write or draw the shapes in the correct places.
M
P
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Only flat faces
cube
pyramid
cylinder
sphere
cuboid
Which shapes belongs outside the circle?
A
Write what you notice about the shapes outside the circle.
S
Which shapes belong inside the circle? Write their names.
36
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2.1 3D shapes
12 Look for and find any of these shapes in or outside your house. Draw what you find. Write the name of 2D shapes that can be found on your 3D shapes.
Name
Picture
2D shapes I can see
S
A
M
P
3D shape
LE
Name these 3D shapes.
37
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 Geometry
Write what 2D shapes you can make from your 3D shapes. Look for and find any of these shapes in or outside your house. Draw what you find. Name
Picture
3D shapes I can make
S
A
M
P
LE
2D shape
Write what 3D shapes you can make from your 2D shapes. 38
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2.2 2D shapes and symmetry
2.2 2D shapes and symmetry Exercise 2.2
hexagon
horizontal
line of symmetry
mirror image octagon
Focus Worked example 2 Where is the line of symmetry in this shape?
symmetry, symmetrical vertical
LE
polygon
pentagon
P
If we fold this shape along the dotted line, the 2 sides will match exactly.
1
M
That’s called the line of symmetry. Some shapes have more than one.
Draw a line of symmetry on these pictures.
S
A
Use a mirror to help you.
39
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 Geometry
2
Name the shapes. Write words to describe these shapes.
LE
Use words like side, vertices, right angle, vertical lines.
Practice 3
P
Tick the symmetrical pictures, cross pictures that are not symmetrical.
the
.
S
A
M
Draw one line of symmetry on the pictures you ticked
40
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2.2 2D shapes and symmetry
Draw a line to join each shape with the matching symmetrical half.
P
LE
4
Challenge
M
Complete and colour these pictures so that they are symmetrical.
S
A
5
41
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 Geometry
6
Complete the drawing to make it symmetrical.
LE
Colour the completed face.
Tip
S
A
M
P
Remember to make the picture symmetrical. You need to think about the colours as well as the shapes.
42
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2.3 Fractions of shapes
2.3 Fractions of shapes Exercise 2.3
equal parts
fraction quarter three quarters
LE
Focus Worked example 3
P
Is each shape divided into halves or quarters?
The shapes that have 2 equal parts show halves.
M
The shapes with 4 equal parts show quarters.
Look at each shape and count the number of equal parts. Draw stripes on one of the halves.
S
A
Draw dots on one of the quarters.
43
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 Geometry
Colour one half of each shape red.
LE
1
Draw 2 more things you can cut in half.
S
A
M
P
Colour one half of each red.
44
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2.3 Fractions of shapes
2
This shows 2 halves of a square. Each part is labelled a 1
1 2
LE
2
1 2
1 + 1 = 1 whole 2 2
S
A
M
P
Find and draw the halves of these shapes and write the number sentence below them.
45
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 Geometry
Colour one quarter of each shape blue.
LE
3
Draw 2 more things you can cut into quarters.
S
A
M
P
Colour one quarter of each blue.
46
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
