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ďťż
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Original material Š Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
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S Original material Š Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
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CAMBRIDGE
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Primary Mathematics Workbook 5
S
A
M
Emma Low & Mary Wood
Original material Š 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/9781108746311 © Cambridge University Press 2021
First published 2014 Second edition 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’
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A catalogue record for this publication is available from the British Library ISBN 978-1-108-74631-1 Paperback
Additional resources for this publication at www.cambridge.org/9781108746311
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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. NOTICE TO TEACHERS IN THE UK
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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.
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
Contentsďťż
Contents How to use this book
5
Thinking and Working Mathematically
6
The number system 8
1.1 1.2
Understanding place value Rounding decimal numbers
2
2D shape and pattern 17
2.1 Triangles 2.2 Symmetry
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1
8 13
17 24
Numbers and sequences 31
3.1 3.2 3.3
Counting and sequences Square and triangular numbers Prime and composite numbers
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3
31 36 40
Mode and median
44
5
Addition and subtraction 49
5.1 5.2
Addition and subtraction including decimal numbers Addition and subtraction of positive and negative numbers
6
3D shapes 59
6.1
Nets of cubes and drawing 3D shapes
59
7
Fractions, decimals and percentages 66
7.1 7.2 7.3
Understanding fractions Percentages, decimals and fractions Equivalence and comparison
S
A
4.1
M
4 Averages 44
49 54
66 70 75
8 Probability 80 8.1 Likelihood 8.2 Experiments and simulations
80 85
3
Original material Š Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
Contents
9
Addition and subtraction of fractions 92
9.1
Addition and subtraction of fractions
92
10 Angles 97 10.1 Angles
97
11.1 Multiplication 11.2 Division 11.3 Tests of divisibility
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11 Multiplication and division 102
102 107 110
12 Data 113 12.1 Representing and interpreting data 12.2 Frequency diagrams and line graphs
113 125
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13 Ratio and proportion 135 13.1 Ratio and proportion
135
14 Area and perimeter 143
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14.1 Area and perimeter
143
15 Multiplying and dividing fractions and decimals 150 15.1 Multiplying and dividing fractions 15.2 Multiplying a decimal and a whole number
150 155
16 Time 159
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16.1 Time intervals and time zones
159
17 Number and the laws of arithmetic 168 17.1 The laws of arithmetic
168
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18 Position and direction 174 18.1 Coordinates and translation
174
Acknowledgements 181
4
Original material Š Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
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
1 The number • Challenge: these questions will make you think very hard. system
Each exercise is divided into three parts. You might not need to work on all of them. Your teacher will tell you which parts to do.
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1.1 Understanding place value
16
You will also find these features: Worked example 1
decimal
Important words that you will use. Find the missing numbers. a
0.9 ×
decimal place decimal point
=9
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Step-by-step examples b 350 ÷ showing a way to solve a 100s a problem.
= 3.5
10s
1s
1 s 10
0
9
1 s 100
The time in Mai’s time zone is 15:07. What is the time for Yared and Susan?
10s
1s
3
5
0
A
100s
1 s 10
1 s 100
5
0
There are often many different ways to solve a problem. 3
S 8
These questions will help you develop your skills of thinking and working mathematically.
tenth
16.1 Time intervals and time zones
The time on Susan’s clock is 3 hours behind the time on Mai’s clock.
0.9 × 10 = 9
350 ÷ 100 = 3.5
hundredth place value
Worked example 1 Use a place value grid to help you. Mai, Yared and Susan live in different time zones. To move digits one column to the left you multiplyThe by time 10. on Yared’s clock is 2 hours ahead of the time on Mai’s clock.
9
b
Time
Yared’s time is 2 hours ahead of Mai’s. To move digits two columns to the right you The100. time for Yared is 17:07. divide by Susan’s time is 3 hours behind Mai’s.
Add 2 hours to 15:07.
Subtract 3 hours from 15:07.
The time for Susan is 12:07.
Exercise 16.1
time interval
Focus
time zone
1
Universal Time (UT)
Circle the amount of time to correctly complete each sentence. a
0.5 minutes is the same as: 30 seconds
b
5 seconds
50 seconds
1.1 Understanding place value
0.5 hours is the same as: 11 Draw a ring around the odd one out. 5 minutes 30 seconds 30 minutes
c
1.5 days is368.4 the same tenthsas: 1 day and 5 hours 36.84
368.4
3684 hundredths
1 day and 12 hours 1 day and 15 hours 368 tenths and 4 hundredths
Explain your answer.
159
Challenge 12 Write down the value of the digit 3 in each of these numbers. a
72.3
5
eighty-four point zero three Original material © Cambridge University Press 2020. This material isb not final and is subject to further changes prior to publication.
5 Additionand and Working subtraction Thinking 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 test examples to see if they fit 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 can explain and use a rule or pattern to find more examples.
6
Classifying is when I put things into groups and can say what rule I have used.
Original material Š 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 maths better.
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A
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Conjecturing is when I think of an idea or question linked to my maths.
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.
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1 The number system 1.1 Understanding place value Worked example 1 Find the missing numbers. =9
b 350 ÷
= 3.5
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a
100s
10s
hundredth
decimal place
place value
decimal point
tenth
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a 0.9 ×
decimal
1s
1 s 10
0
9
1 s 100
Use a place value grid to help you. To move digits one column to the left you multiply by 10.
A
9
100s
10s
1s
3
5
0
S
b
0.9 × 10 = 9
8
3
1 s 10
1 s 100
5
0
To move digits two columns to the right you divide by 100.
350 ÷ 100 = 3.5
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1.1 Understanding place value
Exercise 1.1 Focus 1 Write the missing numbers in this sequence.
÷ 10
19 ÷ 10
190
2 Write these numbers in digits. a fifteen point three seven
÷ 10
÷ 10
You may find a place value grid helpful for these questions.
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1900
Tip
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b one hundred and five point zero five c thirty four point three four 3 Write the missing numbers. a
×
M
75
×100
A
×10
b
25 000
×10
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÷
÷100
9
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1 The number system
4 Complete the table to show what the digits in the number 47.56 stand for. 4
tens
5
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6 7 5 Write the missing number.
6.58 = 6 +
+ 0.08
Practice
500 5.00 0.50 0.05
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7 Divide 3.6 by 10.
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6 Draw a ring around the number equivalent to five hundredths.
8 Write the missing numbers.
38.14 = 30 + 8 +
+
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9 Here are four number cards.
33.300
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Draw a ring round the card that shows the number that is 100 times bigger than 33.3 3330
333.00
33300
10 Find the missing numbers.
10
a 7.2 × 100 =
b 0.75 × 100 =
c 4.28 × 10 =
d 270 ÷ 100 =
e 151 ÷ 100 =
f
6.6 ÷ 10 =
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1.1 Understanding place value
11 Draw a ring around the odd one out.
368.4 tenths 368.4 3684 hundredths
36.84 368 tenths and 4 hundredths Explain your answer.
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Challenge
12 Write down the value of the digit 3 in each of these numbers.
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a 72.3
b eighty-four point zero three
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13 Arun has these cards.
2
5
Write all the numbers he can make between 0 and 40 using all four cards.
A
3
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14 Write the missing numbers. a
× 0.6 = 6
b 103 ÷
c
× 0.13 = 13
d 76 ÷
e
× 4.1 = 410
f
0.09 ×
= 1.03 = 7.6 =9
11
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1 The number system
15 Look at this number line. Write the number that goes in the box. 4
16 Heidi makes cakes for a snack bar.
5
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3
a It costs $1.50 to make one chocolate cake.
How much does it cost to make 100 chocolate cakes?
b It costs $19.00 to make 100 small cakes.
How much does it cost to make 10 small cakes?
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c It costs $0.75 to make a sponge cake.
How much does it cost to make 100 sponge cakes?
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17 Arun and Marcus each write a decimal number between zero and one. Arun says, ‘My number has 9 hundredths and Marcus’s number has only 7 hundredths so my number must be bigger.’
Arun is not correct. Explain why.
S
A
12
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1.2 Rounding decimal numbers
1.2 Rounding decimal numbers Worked example 2
nearest
A number with 1 decimal is rounded to the nearest whole number.
round
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a What is the smallest number that rounds to 10? b What is the largest number that rounds to 20? You can use a number line to help you.
10
11
19
20
21
P
9
If the tenths digit is 5, 6, 7, 8 or 9 the number rounds up to the nearest whole number.
a 9.5 b 20.4
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If the tenths digit is 0, 1, 2, 3 or 4 the number rounds down to the nearest whole number.
Exercise 1.2
A
Focus
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1 Here is part of a number line. The arrow shows the position of a number.
33
34
35
Complete the sentence for this number. rounded to the nearest whole number is
 .
13
Original material Š Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1 The number system
2 Zara has four number cards. 36.5
36.4
35.4
35.1
She rounds each number to the nearest whole number.
Which of her numbers rounds to 36?
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3 Draw an arrow to match each number to the nearest whole number. 9.9
10.1
8.5
8
9.4
9
10
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7
8.2
P
7.4
10.7
11.5
11
12
4 Write a number with 1 decimal place to complete each number sentence.
A
rounds to 1
rounds to 10
Practice
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5 Round these lengths to the nearest whole centimetre. a 4.1 cm
c 10.1 cm
14
cm cm
b 6.6 cm
cm
d 8.5 cm
cm
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1.2 Rounding decimal numbers
6 Here are three number cards. 9
5
Use each card once to make a number that rounds to 20 to the nearest whole number.
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1
7 A number with 1 decimal place is rounded to the nearest whole number a What is the smallest number that rounds to 100?
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b What is the largest number that rounds to 100? Challenge
A
B
C
D
E
F
G
H
I
J
K
L
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10.1
9.3
11.1
10.4
7.8
8.8
9.3
19.8
1.9
10.7
9.6
99.9
A
10.8
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8 Write the letters of all the numbers that round to 10 to the nearest whole number. What word is spelt out?
O
P
Q
R
S
T
U
V
W
X
Y
Z
1.8
9.2
10.6
9.1
10.5
7.9
9.5
19.9
16.2
10.9
20.3
8.9
9.4
S
N
15
Original material Š Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1 The number system
9 Here are eight numbers.
19.4 19.9 21.1 20.4 20.3 19.7 21.4 10.1
Draw a ring round the number that these clues are describing. • The number rounds to 20 to the nearest whole number.
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• The tenths digit is odd. • The sum of the digits is less than 18. • The tens digit is even. 10 Rashid has these number cards. 1.4
2.4
3.4
4.4
He chooses two cards.
He adds the numbers on the cards together.
He rounds the result to the nearest whole number.
His answer is 7.
Which two cards did he choose?
M
P
and
.
11 Arun rounds these numbers to the nearest whole number. 3.3 3.5 3.7 3.9 4.4 4.5 4.9
A
He sorts them into 3 groups and places them in a table.
Complete the table.
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Rounds to . . .
16
Rounds to . . .
Rounds to . . .
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2.1 Triangles Worked example 1
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2 2D shape and pattern equilateral triangle
Is this triangle isosceles?
scalene triangle
M
P
isosceles triangle
A
4 cm
5 cm
Measure the length of each side of the triangle. In an isosceles triangle, two sides have the same length.
S
6 cm
The sides are all different lengths. Answer: No, the triangle is not isosceles.
17
Original material Š Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 2D shape and pattern
Exercise 2.1 Focus
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1 Is this triangle isosceles?
How do you know?
M
P
2 Draw a ring around the scalene triangles.
S
A
A
18
E
B
C
F
D
Original material Š Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2.1 Triangles
A
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3 Label the angle at each vertex of these triangles ‘acute’, ‘obtuse’ or ‘right-angle’.
P
B
A
Practice
M
C
S
4 Draw a scalene triangle using a ruler and pencil.
19
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 2D shape and pattern
5 On each of these isosceles triangles, circle the angles that are the same size. You could use tracing paper to compare the sizes of the angles.
B
D
A
M
C
P
LE
A
S
6 a Write a sentence about the sides of an equilateral triangle.
b Write a sentence about the angles of an equilateral triangle.
20
Original material Š Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2.1 Triangles
Challenge
P
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7 a Draw an isosceles triangle with two sides 6 cm long and the other side shorter than 6 cm.
S
A
M
b Draw an isosceles triangle with two sides 6 cm long and the other side longer than 6 cm.
21
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 2D shape and pattern
S
A
M
P
LE
8 Trace the triangles in this tessellating pattern. Make templates of the triangles and complete the pattern.
22
Original material Š Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2.1 Triangles
9 This is a crossword is filled in with words about triangles. Write the clues for the crossword.
4
t
e
s
2
i
3
a
s
s
n
i
o
g
d
s
e
l
a
e
c
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1
5
t
e
s
r
e
i
l
a
e s
P
n
g
s
c
a
l
e
n
e
M
6
e
Across
4
A
6
Down
1
2
3
5
S
23
Original material Š Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 2D shape and pattern
2.2 Symmetry Worked example 2
line of symmetry symmetrical
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Colour the squares to make a symmetrical pattern where the dashed line is a line of symmetry.
M
P
Place a small mirror along the mirror line to see what the complete symmetrical pattern will look like.
A
Reflect the shaded squares across the mirror line.
Squares that are next to the mirror line are reflected to squares that are next to the mirror line on the other side. Squares that are one square away from the mirror line are reflected to squares that are one square away from the mirror line on the other side.
S
Answer:
24
Original material Š Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2.2 Symmetry
Tip
Focus
Place a small mirror on the mirror line.
1 Spot the difference. Draw shapes on the right side of the picture to make it a reflection of the picture on the left.
Check that the picture on the right looks the same as the image in the mirror.
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Exercise 2.2
M
P
mirror line
A
2 Zara says that she is thinking of a triangle with three lines of symmetry. Draw a ring around the name of the triangle that Zara is thinking of. scalene isosceles equilateral right-angled
S
3 Shade squares to make a pattern with one line of symmetry. mirror line
25
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 2D shape and pattern
4 Predict where the reflection of the triangle will be after it is reflected over each of the mirror lines. Draw your predictions using a ruler. mirror line
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mirror line
mirror line
Check your predictions by placing a mirror along each of the mirror lines in turn. Look at how the triangle is reflected. Tick the predicted reflections that are correct. Use a different colour pencil to correct the predictions that are wrong.
Practice
M
P
mirror line
A
5 Use a ruler to draw all of the lines of symmetry on these triangles.
S
A
C
26
B
D
E
Original material Š Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2.2 Symmetry
6 Shade 5 squares in each of the empty quadrants to make a pattern with two lines of symmetry.
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mirror line
P
mirror line
M
7 Reflect the square, triangle, rectangle and pentagon over both the horizontal and vertical mirror lines until you make a pattern with reflective symmetry.
S
A
mirror line
mirror line
27
Original material Š Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 2D shape and pattern
Challenge 8 Choose four colours. Use coloured pencils or pens to shade in the squares and half squares marked with a star (*). Reflect the pattern over the mirror lines and colour all the squares to make a pattern with two lines of symmetry.
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mirror line
Tip
M
P
You could rotate the pattern so that the mirror lines appear vertical and horizontal.
mirror line
9 Sofia says that a right-angled triangle cannot have a line of symmetry.
S
A
a Draw a triangle to show that Sofia is wrong.
b W rite the name of the triangle you have drawn and draw the line of symmetry onto it.
28
Original material Š Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2.2 Symmetry
10 This is a chessboard. a How many lines of symmetry does a chessboard have?
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b Where could you place a counter on the chessboard so that the chessboard still has two lines of symmetry? Mark the place with a blue circle. c Where could you place a counter on the chessboard so that the chessboard has no lines of symmetry? Mark the place with a red circle.
P
d Where could you place a counter on the chessboard so that the chessboard has only one line of symmetry? Mark the place with a green circle.
S
A
M
11 a Colour two more squares so that this pattern has exactly 1 line of symmetry.
29
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 2D shape and pattern
P
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b Colour two more squares so that this pattern has exactly 2Â lines of symmetry.
Shade the grid to show your solution.
S
A
M
c What is the fewest number of squares that have to be shaded to make this pattern have exactly 4 lines of symmetry?
30
Original material Š Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
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3 Numbers and sequences 3.1 Counting and sequences Worked example 1
linear sequence
Marcus counts back in eights starting at 50:
sequence term
P
50 42 34 ….
term-to-term rule
What is the first negative number Marcus says? How do you know?
Another way to think about this question is:
M
Six jumps of 8 is 48 so after counting back six lots of 8 Marcus says the number 2.
10 is 2 more than a multiple of 8 and if you count back in 8s you get to 10, then 2 and then −6.
A
The next number Marcus says is −6.
Each term is 2 more than a multiple of 8.
Answer: −6
S
Exercise 3.1 Focus
1 What is the next number in this sequence?
8, 6, 4, 2, 0, …
How do you know?
31
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
3 Numbers and sequences
2 This is an 8 by 8 number grid. 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
LE
2
P
1
a Colour the multiples of 7.
M
b What do you notice?
c If you continued the sequence would 100 be in it?
A
3 This pattern makes a sequence.
You count the squares in each row of the staircase.
The sequence starts 1, 3, 5, ‌
S
a Complete the table.
32
Row number
1
2
3
Number of squares in row
1
3
5
4
5
6
7
Original material Š Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
3.1 Counting and sequences
b Continue the sequence to show your results.
1, 3, 5,
,
,
,
,
,
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c What is the term-to-term rule for the sequence?
Practice 4 A sequence starts at 19.
9 is subtracted each time.
What is the first number in the sequence that is less than zero?
P
5 Zara counts back in steps of equal size.
Write the missing numbers in her sequence. ,
, 61, 52,
, 34
M
6 a Here are some patterns made from sticks. Draw the next pattern in the sequence.
1
2
3
A
b Complete the table. Pattern number
Number of sticks
1
S
2 3 4
c Find the term-to-term rule.
33
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
3 Numbers and sequences
d How many sticks are in the 10th pattern?
7 A sequence starts at 400 and 90 is added each time. 400, 490, 580, 670, …
What is the first number in the sequence that is greater than 1000?
LE
Challenge
P
8 a Draw the next pattern in the sequence.
1
2
3
M
b Complete the table.
Pattern number
Number of hexagons
1 2
A
3 4
S
c Find the term-to-term rule.
d How many hexagons are in the 8th pattern?
34
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
3.1 Counting and sequences
9 Sofia counts in threes starting at 3.
3, 6, 9, 12, …. Zara counts in fives starting at 5.
5, 10, 15, 20, …. They both count on.
What is the first number greater than 100 that both Sofia and Zara say?
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Explain your answer.
P
10 Zara writes a sequence of five numbers. The first number is 2.
The last number is 18.
Her rule is to add the same amount each time.
Write the missing numbers.
M
2,
,
,
, 18
A
11 Arun writes a sequence of numbers.
His rule is to add the same amount each time.
Write the missing numbers. −1,
,
, 14
S
35
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
3 Numbers and sequences
3.2 Square and triangular numbers Worked example 2
spatial pattern square number
The sequence starts 1, 3, 6 …
triangular number
LE
Look at these patterns made from squares.
a Draw the next term in the sequence.
b Write the next three numbers in the sequence. a
M
b 10, 15, 21
P
Each term has an extra column that is one square taller.
The sequence 1, 3, 6, 10, 15, 21 … is the sequence of triangular numbers
Exercise 3.2
A
Focus
S
1 Draw the next term in this sequence.
36
What is the mathematical name for these numbers?
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3.2 Square and triangular numbers
2 Draw the next term in this sequence.
What is the mathematical name for these numbers?
LE
3 Write the next two terms in these sequences. a 1, 4, 9, 16, 25,
,
b 1, 3, 6, 10,
,
P
Practice
M
4 This pattern is made by adding two consecutive triangular numbers.
1
1+3=4
3+6=9
Tip Remember that consecutive means next to each other.
6 + 10 = 16
a Look at the total in each term and complete this sentence. The terms in the sequence are the
A
numbers.
b What are the next two numbers in the sequence? 2
5 Find the value of 8 .
S
37
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3 Numbers and sequences
6 Solve these number riddles.
• a square number
• a multiple of 3
• less than 25
LE
a The number is:
b The number is:
• a square number
• an even number
• a single digit number
c The number is: • a square number
• a 2-digit number
the sum of the digits is 13
P
7 Zara has a lot of small squares all equal in size.
She uses the small squares to make big squares.
She can use 9 small squares to make a big square.
M
a Which of these numbers of squares could Zara use to make a big square? 64
14
4
24
100
60
66
18
81
9
90
S
A
46
b Can Zara make a big square using 49 small squares?
38
Explain how you know.
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3.2 Square and triangular numbers
Challenge 8 Write the missing numbers in the table. 1 more than the product
1×3=3
4
2×4=8
9
3 × 5 = 15
Equivalent square number 2
2 =4
LE
Product of two numbers
2
3 =9 2
=
2
=
4×6=
×
P
2
=
=
a c
+
= 10
b
+
= 20
+
= 40
d
+
= 50
+
= 80
f
+
= 90
+
= 100
A
e
M
9 Find two square numbers to make each of these calculations correct.
g
S
10 Find the 10th term in this sequence.
1, 3, 6, 10, 15,
39
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3 Numbers and sequences
3.3 Prime and composite numbers Worked example 3
composite number
Here are four digit cards. 9
2
multiple
LE
3
factor 1
prime number
Use each card once to make two 2-digit prime numbers. and The prime numbers are:
Start by writing a list of prime numbers
Answer: 13 and 29
Choose two of these numbers that satisfy the criteria.
P
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ‌
There is more than one correct answer.
M
You could also have chosen
31 and 29
or
19 and 23
S
A
You are specialising when you choose a number and check whether it satisfies the criteria.
40
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3.3 Prime and composite numbers
Exercise 3.3 Focus 1 Here is a grid of numbers.
14
2
13
5
8
15
3
1
11
15
1
11
19
7
6
9
17
9
15
12
12
5
16
4
14
LE
Shade all the prime numbers. What letter is revealed?
P
M
2 Write each number in the correct place on the diagram.
Composite numbers
A
Prime numbers
S
2, 3, 4, 5, 6
3 Complete this sentence.
A number with only two factors is called a
number.
41
Original material Š Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
3 Numbers and sequences
Practice 4 Here is a grid of numbers. Draw a path between the two shaded numbers that passes only through prime numbers.
You must not move diagonally. 4
6
8
13
3
23
29
71
65
1
51
45
7
5
15
92
25
1
2
31
37
16
14
11
P
2
LE
5 a Find two different prime numbers that total 9. +
=9
M
b Find two different prime numbers that total 50.
+
= 50
A
6 Show that 15 is a composite number.
Challenge
S
7 Use the clues to find two prime numbers less than 20.
42
Prime number 1: Subtracting 4 from this prime number gives a multiple of 5.
Prime number 2: This prime number is one more than a multiple of 4, but not 1 less than a multiple of 3.
Prime number 1 is
Prime number 2 is
Original material Š Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
3.3 Prime and composite numbers
8 Multiples of 6 are shaded on this grid. 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
LE
1
Ingrid looks at the grid and says, ‘One more than any multiple of 6 is always a prime number.’
Ingrid is wrong.
Explain how you know.
P
9 Arun chooses a prime number.
He rounds it to the nearest 10 and his answer is 70.
Write all the possible prime numbers Arun could choose.
M
A
10 Write each whole number from 1 to 20 in the correct place on this Venn diagram.
S
Triangular numbers
Prime numbers
Even numbers
43
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4 Averages average
Worked example 1
median
What is the mode of these areas? 2
LE
4.1 Mode and median 2
2
2
2
2
mode
2
45 cm , 36 cm , 18 cm , 36 cm , 21 cm , 45 cm , 36 cm 2
One area is 18 cm
Count how many there are of each area.
2 2
Three areas are 36 cm 2
Two areas are 45 cm
The mode is the area that appears the most often.
P
One area is 21 cm
2
M
Answer: The mode is 36 cm .
Exercise 4.1 Focus
A
1 This box contains some numbers. a How many 3s are in the box?
S
b How many 4s are in the box? c What is the mode of the numbers in the box?
44
3 4 343 4 3 4
3
4 3
3
4 3
4
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4.1 Mode and median
2 a Write these numbers in order from smallest to greatest.
117 109 120 118 121
b Draw a rind around the middle number. What is the median of the numbers?
LE
3 Complete the sentences about this set of numbers.
20 21 22 23 24 24 25 a The mode (most frequent) is b The median (middle) is
.
.
M
P
4 This is how many sweets Tom found in each packet.
11
11
12
13
14
14
Complete the sentences about the average number of sweets in a packet.
A
11
a The mode is
b The median is
.
.
S
Practice
5 Explain in words how to find the median of a set of data.
First
Then
45
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4 Averages
6 Tick the sets of numbers that have a mode of 8 and a median of 9. A 10, 7, 9, 8, 11, 8, 12
LE
B 8, 9, 8, 10, 8, 12, 8 C 10, 8, 8, 9, 10, 9, 10 D 11, 8, 8, 7, 9, 10, 7, 10, 10, 8, 8, 11, 11
P
7 Write your own set of numbers that has a mode of 8 and a median of 9.
8 Seven children reviewed a book about dinosaurs. They gave the book a score out of 5. These are the scores.
M
Dinosaurs
4 1 3 5 5 1 1
a What is the mode of the scores?
A
b What is the median of the scores?
S
c Would you use the mode or the median to describe the scores? Why?
46
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