Greg Byrd, Lynn Byrd and Chris Pearce This Cambridge Checkpoint Mathematics Skills Builder 7 workbook provides tailored exercises that help reinforce key skills when studying the Cambridge Secondary 1 Checkpoint Mathematics curriculum framework. By using an active learning approach to help link mathematics to real world scenarios, this workbook builds students’ confidence in performing mathematical operations, enabling them to continue to engage with the Cambridge Secondary 1 Checkpoint Mathematics curriculum framework. Using the workbook in a flexible way with other components in the Cambridge Checkpoint Mathematics series, students can further develop skills and progress at their own pace. A support booklet for teachers and answers to all the exercises are available online for free at education.cambridge.org/9781316637371 Other components in this series: Coursebook 7 Practice Book 7 Challenge 7 Teacher’s Resource CD-ROM
978-1-107-64111-2 978-1-107-69540-5 978-1-316-63741-8 978-1-107-69380-7
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Cambridge Checkpoint Mathematics Skills Builder 7 Byrd, Byrd and Pearce
Cambridge Checkpoint Mathematics Skills Builder 7
Greg Byrd, Lynn Byrd and Chris Pearce
Cambridge Checkpoint
Mathematics
Skills Builder
7
Original material © Cambridge University Press 2017
Original material Š Cambridge University Press 2017
Greg Byrd, Lynn Byrd and Chris Pearce
Cambridge Checkpoint
Mathematics
Skills Builder Workbook
7 Original material Š Cambridge University Press 2017
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 4843/24, 2nd Floor, Ansari Road, Daryaganj, Delhi – 110002, India 79 Anson Road, #06–04/06, Singapore 079906 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 / 9781316637371 (Paperback) © Cambridge University Press 2017 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. First published 2017 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Printed in Spain by GraphyCems
A catalogue record for this publication is available from the British Library ISBN 978-1-316-63737-1 Paperback 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. All Checkpoint-style questions and sample answers within this workbook are written by the authors. notice to teachers in the uk 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 2017
Contents Introduction
5
1 Integers
7
1.1 Multiples 1.2 Factors
7 10
2 Sequences, expressions and formulae 13 2.1 2.2 2.3 2.4
Generating sequences Representing simple functions Constructing expressions Deriving and using formulae
13 15 17 19
3 Place value, ordering and rounding
21
3.1 Multiplying and dividing by 10, 100 and 1000 3.2 Ordering decimals 3.3 Rounding 3.4 Adding and subtracting decimals 3.5 Multiplying decimals
21 24 27 30 33
4 Length, mass and capacity
36
4.1 Knowing metric units 4.2 Reading scales
36 39
5 Angles
44
5.1 Labelling angles 5.2 Calculating angles
44 46
6 Planning and collecting data
48
6.1 Using frequency tables
48
7 Fractions
53
7.1 Simplifying fractions 7.2 Recognising equivalent fractions, decimals and percentages 7.3 Comparing fractions 7.4 Improper fractions and mixed numbers 7.5 Adding and subtracting fractions 7.6 Finding fractions of quantity
53
8 Symmetry
65
8.1 Recognising line symmetry 8.2 Recognising rotational symmetry
65 67
9 Expressions and equations
69
55 57 59 61 63
9.1 Collecting like terms 69 9.2 Expanding brackets 71 9.3 Constructing and solving equations 73 10 Averages
75
10.1 Average and range 10.2 The mean
75 78
11 Percentages
80
11.1 Simple percentages 11.2 Calculating percentages
80 82
12 Constructions
84
12.1 Measuring and drawing lines 11.2 Constructing triangles
84 86
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Contents Unit 7 Fractions
13 Graphs
89
18 Area, perimeter and volume
118
13.1 Plotting coordinates 13.2 Straight lines
89 92
14 Ratio and proportion
95
14.1 Simplifying ratios 14.2 Sharing in a ratio 14.3 Using direct proportion
95 97 99
18.1 Calculating the area and perimeter of rectangles 118 18.2 Calculating the area and perimeter of compound shapes 121 18.3 Calculating the volume of cuboids 123 18.4 Calculating the surface area of cubes and cuboids 125
15 Time
100
19 Interpreting and discussing results 127
15.1 The 12-hour and 24-hour clock 15.2 Timetables
100 103
16 Probability
105
16.1 The probability scale 16.2 Equally likely outcomes
105 108
17 Position and movement
110
17.1 Reflecting shapes 17.2 Rotating shapes 17.3 Translating shapes
110 113 115
19.1 Interpreting and drawing pictograms, bar charts, bar-line graphs and 127 frequency diagrams 19.2 Interpreting and drawing pie charts 131 Glossary 134
44 Original material Š Cambridge University Press 2017
Introduction Welcome to Cambridge Checkpoint Mathematics Skills Builder Workbook 7 The Cambridge Checkpoint Mathematics course covers the Cambridge Secondary 1 Mathematics curriculum framework. The course is divided into three stages: 7, 8 and 9. You can use this Skills Builder Workbook with Coursebook 7 and Practice Book 7. It gives you extra practice in key topics, focusing on those that are the most important, to improve your understanding and confidence. Like the Coursebook and the Practice Book, this Workbook is divided into 19 units. In each unit there are exercises on each topic. There are introductory explanations and either worked examples or guided questions. These explain the skills you need to master and use to solve more complex problems. This Workbook also gives you a chance to try further questions on your own. This will improve your understanding of the units. It will also help you feel confident about working on your own when there is no teacher to help you. At the end of each unit is a link to exercises to attempt in the Coursebook. If you get stuck with a task: •
Read the question again.
•
Look back at the introductory explanations and worked examples or guided questions.
•
Read through the matching section in the Coursebook.
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1 1.1
Integers
Multiples
Look at this sequence: 1 × 3 = 3
2×3=6
3×3=9
4 × 3 = 12
The numbers 3, 6, 9, 12 and 15 are the multiples of 3. Make sure you know your multiplication facts up to 10 × 10 or further.
1
Write in the answers.
a
1 × 5 = ……
2
Write in the answers.
a
2 × 9 = ……
3
Here are some multiplication tables. Fill in the gaps.
a
×
b 3 × 5 = ……
b 3 × 6 = ……
3 3 5
4 12
b
×
6 7
42
c
8 × 5 = ……
d
4 × 5 = ……
c
9 × 2 = ……
d
18 × 1 = ……
4
c
10
×
9
8
3 4
Here are the whole numbers up to 25. Multiples of 3 have been circled. 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 4
Circle the multiples of 4. Two have been done for you. 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
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Unit 1 Integers
5
Circle the multiples of 5.
Remember to start with 5.
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
6
Circle the multiples of 2. 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
7
Circle the multiples of 6. 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
8
Here are two multiples of 8: 8 and 16 Write down another one ……
9
Write down three multiples of 7. …… and …… and ……
Here are the multiples of 3 again. 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 Here are more multiples of 3. 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 10
Circle the multiples of 2. 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
11
Circle the multiples of 5. 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
12
Circle the multiples of 6. 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
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Unit 1 Integers
13 Write down five multiples of 10. 14 Write down five multiples of 8.
15 Write down five multiples of 9. 16 Circle the multiples of 4.
10 16 26 28 30 36
17 Circle the multiples of 5.
15 22 30 45 54 50
18 Draw lines from numbers to their multiples. Two lines have been drawn for you.
Number Multiple
3
12
13
4
14
15
5
16
17
6
18
Now try Exercise 1.3 on page 11 of Coursebook 7.
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Unit 1 Integers
1.2
Factors A factor of a whole number divides into it without a remainder. This means that 1 is a factor of every number. Every number is a factor of itself. Look at these: 1 × 12 = 12
2 × 6 = 12
3 × 4 = 12
The numbers 1, 12, 2, 6, 3 and 4 are factors of 12.
1
Fill in the gaps.
a
3 × 5 = ……
3 and 5 are factors of ……
b
4 × 6 = ……
4 and 6 are ……………… of ……
c
7 × 3 = ……
…… and …… are ……………… of ……
2
Fill in the gaps.
a
28 = 7 × ……
Two factors of 28 are 7 and ……
b
50 = 10 × ……
Two factors of 50 are …… and ……
c
25 = 5 × ……
A factor of 25 is ……
3
Here are some multiplication tables. ×
8
12
×
6
24
2
16
24
4
24
96
3
24
36
1
6
24
Use the tables to help you find the factors of 24.
Can you find eight factors?
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Unit 1 Integers
4
Here are some multiplication tables. ×
5
15
×
10
1
2
10
30
3
30
3
6
30
90
30
300
30
Use the tables to help you find the factors of 30.
5
7 × 9 = 63
6 × 15 = 90
24 × 4 = 96
3 × 19 = 57
13 × 13 = 169
Use these facts to find: a a factor of 90 ……
b a factor of 57 ……
d two factors of 63 …… and …… 6
c a factor of 169 ……
e two factors of 96 …… and ……
Draw lines from the numbers to their factors.
Three lines have been drawn for you.
Number
Factor
14
1 2
16
3 4 5
21
6 7
25
8
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Unit 1 Integers
7
Circle the correct word
in each sentence.
a 6 is a factor/multiple of 18. b 18 is a factor/multiple of 6. c 15 is a factor/multiple of 30. d 8 is a factor/multiple of 4. e 20 is a factor/multiple of 4. f 9 is a factor/multiple of 90.
Now try Exercise 1.4 on page 13 of Coursebook 7.
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2 2.1
Sequences, expressions and formulae
Generating sequences
Here is a sequence of numbers: 4, 6, 8, 10, 12, … The first term of the sequence is 4. The term-to-term rule is ‘Add 2’.
1
A sequence is just a list of numbers that follow a pattern.
The first term is the first number in the list.
You add 2 to each number to get the next number: 4 + 2 = 6, 6 + 2 = 8, 8 + 2 = 10, etc.
Fill in the missing two terms (numbers) in each of these sequences (lists). Also write down the term-to-term rule.
a
5, 10, 15, 20, ……, …… Term-to-term rule ………………
5 + 5 = 10, 10 + 5 = 15, 15 + 5 = 20, … The rule is ‘Add 5’.
b
1, 3, 5, 7, ……, …… Term-to-term rule ………………
1 + ? = 3, 3 + ? = 5, 5 + ? = 7, 7 + ? = ? The rule is ‘Add ?’.
c
6, 10, 14, 18, ……, …… Term-to-term rule ………………
d
20, 28, 36, 44, ……, …… Term-to-term rule ………………
e
10, 9, 8, 7, ……, …… Term-to-term rule ………………
10 – 1 = 9, 9 – 1 = 8, 8 – 1 = 7, 7 – 1 = ? The rule is ‘Subtract 1’.
f
16, 13, 10, 7, ……, …… Term-to-term rule ………………
16 – ? = 13, 13 – ? = 10, 10 – ? = 7, 7 – ? = ? The rule is ‘Subtract ?’.
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Unit 2 Sequences, expressions and formulae
g
20, 18, 16, 14, ……, …… Term-to-term rule ………………
h
50, 45, 40, 35, ……, …… Term-to-term rule ………………
2
Use the given first term and term-to-term rule to write down the next four terms of each sequence.
a
Add 3
5, ……, ……, ……, ……
The first term is 5, then 5 + 3 = 8, 8 + 3 = 11, 11 + 3 = ?, etc.
b
Add 6
2 , ……, ……, ……, ……
The first term is 2, then 2 + 6 = 8, 8 + 6 = ?, ? + 6 = ?, etc.
c
Add 10
12, ……, ……, ……, ……
d
Add 7
0, ……, ……, ……, ……
e
Subtract 2 12, ……, ……, ……, ……
The first term is 12, then 12 – 2 = 10, 10 – 2 = 8, 8 – 2 = ?, etc.
f
Subtract 5 25, ……, ……, ……, ……
The first term is 25, then 25 – 5 = 20, 20 – 5 = ?, ? – 5 = ?, etc.
g
Subtract 1 13, ……, ……, ……, ……
h
Subtract 20 100, ……, ……, ……, ……
3
Fill in the missing terms in each of these sequences.
a
4, 10, 16, ……, 28, ……, 40, 46
b
45, 43, ……, 39, 37, ……, 33
4 + ? = 10, 10 + ? = 16 so the rule is ‘Add ?’. 45 – ? = 43, 39 – ? = 37 so the rule is ‘Subtract ?’.
Now try Exercise 2.1 on page 20 of Coursebook 7. 14 Original material © Cambridge University Press 2017
Unit 2 Sequences, expressions and formulae
Representing simple functions
2.2
The output is the number that comes out of the machine.
Here is a function machine. The input is the number that goes into the machine.
Input 3
Output 9
+6
This machine tells you to add 6 to the input number to get the output number.
1 a
b
c
d
e
Find the missing output numbers in each of these function machines. Input 3
Input 15
Input 8 10
Input 2 8
Input 4 7 19
×2
Output ……
Find the output number by working out: input number × 2, so 3 × 2 = ?
Output ÷3
…… Output
–8
…… ……
15 ÷ 3 = ?
There can be more than one input number, so this time work out both output numbers: 8 – 8 = ? and 10 – 8 = ?
Output ×5
…… …… Output
+2
…… …… …… 15
Original material © Cambridge University Press 2017
Unit 2 Sequences, expressions and formulae
2
Find the missing input numbers in each of these function machines.
a
Input ……
+3
Output 4
b
Input ……
×4
Output 12
12 ÷ 4 = ?
c
Input …… ……
Output 2 5
Input – 6 = output, so output + 6 = input
d
e
Input …… ……
Input …… …… ……
–6
÷2
+7
Find the input number by working backwards: input + 3 = output, so output – 3 = input, so 4 – 3 = ?
Output 3 10
Output 10 14 30
Now try Exercise 2.3 on page 24 of Coursebook 7.
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Unit 2 Sequences, expressions and formulae
2.3
Constructing expressions Here are three bags, each with a different number of balls inside.
This bag has 2 balls. This bag has 4 balls.
1
This bag has b balls. You cannot see how many balls are in this bag, so you can choose any letter to represent the number.
Fill in the missing numbers. If you do not know the number, choose your own letter to represent it.
a
This box has …… counter.
b
This box has …… counters.
c
This box has …… counters.
d
This bag has …… apples.
e
This bag has …… apples.
You do not know how many counters are in this box, so choose your own letter.
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Unit 2 Sequences, expressions and formulae
2
Fill in the gaps to work out the total number of balls in each of these bags after you have added an extra 2 balls.
a
There is 1 ball in the bag. Add 2 balls, so there are now 1 + 2 = …… balls in the bag.
b
There are …… balls in the bag. Add 2 balls, so there are now …… + 2 = …… balls in the bag.
c
There are …… balls in the bag.
Choose your own letter for the number of balls, e.g. x. You cannot work out x + 2, so just leave it as it is.
Add 2 balls, so there are now …… + 2 balls in the bag.
3
A bag has n counters in it. Use a line to join the statement in each rectangle to the correct expression in the ovals. The first one has been done for you.
An expression is a statement that contains letters and sometimes numbers – for example, n + 7.
I add 3 counters to the bag.
I add 1 counter to the bag.
I add 6 counters to the bag.
I add 9 counters to the bag.
I add 7 counters to the bag.
n+7
n+6
n+1
n+3
n+9
Now try Exercise 2.4 on page 26 of Coursebook 7.
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Unit 2 Sequences, expressions and formulae
2.4
Deriving and using formulae An expression is a statement that contains letters and sometimes numbers but has no ‘=’ sign.
x+2
for example: p
n–3
4m
A formula is a statement that contains letters and sometimes numbers and does have an ‘=’ sign. For example: A = 2p
1
y=x–2
v = 5n – 3
R=m+k
Under each of these statements, write ‘E’ if it is an expression or ‘F’ if it is a formula. The first two have been done for you.
a
b
8h E
d
v = 9u
c
9u + 3
f
b–c
F e
m=4+n
G = 2x + y
You can work out the value of an expression by substituting numbers into the expression. For example, the value of x + 2 when x = 5 is: 5+2=7 2
Work out the value of x + 6 when:
a
x=1
x+6=
b
x=2
x+6=
c
x=3
x+6=
d
x=4
x+6=
Substitute the x for the number 5 and then work out 5 + 2.
x+6=1+6=?
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Unit 2 Sequences, expressions and formulae
3
Work out the value of n − 1 when:
a
n=5
n−1=
b
n=6
n−1=
c
n=7
n−1=
d
n=8
n−1=
4
Work out the value of the expression in each rectangle, then use a line to join each rectangle to the correct answer in the ovals. The first one has been done for you.
n–1=5–1=?
y+2 when y = 3
y–2 when y = 10
4+y when y = 2
10 – y when y = 1
y+3 when y = 0
8
6
5
3
9
5
Write down ‘True’ or ‘False’ for each of these. If a statement is false, work out the correct value of the expression. The first one has been done for you.
a
The value of 2m when m = 5 is 7. False, when m = 5, 2m = 10
20
b
The value of 3m when m = 8 is 24.
c
The value of 9p when p = 2 is 11.
d
w The value of 2 when w = 6 is 3.
e
The value of 3 when x = 12 is 6.
2m means 2 × m, so 2 × 5 = 10.
w means w ÷ 2. 2
x
Now try Exercise 2.5 on page 28 of Coursebook 7. Original material © Cambridge University Press 2017
3 3.1
Place value, ordering and rounding
Multiplying and dividing by 10, 100 and 1000 When you multiply a whole number by 10, add one zero on to the number. When you multiply a whole number by 100, add two zeros on to the number.
1
Multiply each of these numbers by 10.
a
7
b
9
c
45
2
Multiply each of these numbers by 100.
a
5
b
30
c
12
3
Divide each of these numbers by 10.
a
80
b
20
c
360
This is the quickest way of multiplying a whole number by 10 and 100.
Adding one zero on to 7 gives 70.
Adding two zeros on to 5 gives 500.
Do the opposite of multiplying and take away one zero from the number: 80 á 10 = 8.
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Unit 3 Place value, ordering and rounding
Place value, ordering and rounding
4
Divide each of these numbers by 100.
a
700
b
3000
c
6500
Do the opposite of multiplying and take away two zeros from the number: 700 ÷ 100 = 7
When you multiply a decimal number by 10, move the decimal point one place to the right.
This is the quickest way of multiplying a decimal number by 10 and 100.
When you multiply a decimal number by 100, move the decimal point two places to the right.
5
Multiply each of these numbers by 10.
a
3.56 3.56 × 10 = 3.5.6 = 35.6
b
4.2
c
15.89
6
Multiply each of these numbers by 100.
a
7.2
b
12.6
c
8.95
d
10.851
7.2 × 100 = 7.2.0. = 720
Once you have moved the decimal point, any empty spaces must be filled with zeros.
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Unit 3 Place value, ordering and rounding
7
Divide each of these numbers by 10. Do the opposite of multiplying and move the decimal point one place to the left:
a
82.5
b
330.9
c
25.66
8
Divide each of these numbers by 100.
a
570
82.5 á 10 = 8.2.5 = 8.25
Do the opposite of multiplying and move the decimal point two places to the left: 570 á 100 = 5.7.0. = 5.70 or just 5.7
b
330.9
c
25.66
If you cannot see a decimal point then imagine one at the end of the number.
Now try Exercise 3.2 on page 34 of Coursebook 7.
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Unit 3 Place value, ordering and rounding
3.2
Ordering decimals 1
Write these numbers in order of size, starting with the smallest. The first one has been done for you. 176
204
23
Start by comparing the numbers in the tens, then the numbers in the hundreds.
498
45
12
12
2
In each of these lists of numbers: i
circle the number that is in the wrong place
ii write the list in the correct order of size, starting with the smallest. a
34 59 70 215 152 251
b
67 88 39 95
c
6 8.2 14.5 67 10.9
101 321
100.7
All the whole number parts are different, so you only need to compare these: 6, 8, 14, 67, 10, 100.
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Unit 3 Place value, ordering and rounding
3 a
Write these measurements in the spaces under the ruler. One has been done for you. 18.6 cm
18.9 cm
18.1 cm
18.5 cm
18 cm
18.3 cm
19 cm
18.3 cm b
Use your answer in part a) to write these numbers in order of size, starting with the smallest. 18.6 18.9 18.1 18.5 18.3
c
Write these numbers in order of size, starting with the smallest. 9.5 9.3 9.8 9.2
d
9.7
Write these numbers in order of size, starting with the smallest. The first one has been done for you. 3.32 3.21 3.56 3.42
The whole number parts are the same, so compare the numbers after the decimal point: 32, 21, 56, 42.
3.21
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Unit 3 Place value, ordering and rounding
4
Complete the workings to write these numbers in order of size, starting with the smallest. 6.5 6.08 6.21 6.1 Start by writing each number out to two decimal places:
6.50, 6.08, 6.21, 6.10
Now write the decimal parts only:
50, 08, 21, 10
Now write in order the decimal parts only:
08, 10, ……, ……
Now write the complete numbers in order:
6.08, ……, ……, ……
5
Write these numbers in order of size, starting with the smallest.
a
4.67 4.21 4.5 4.02
b
12.9 12.41 12.08 12.3
Use the same method as you did in Question 4.
Now try Exercise 3.3 on page 35 of Coursebook 7.
26 Original material © Cambridge University Press 2017
Unit 3 Place value, ordering and rounding
Rounding
3.3
When you round a number you get an approximate value. Look at this section of a number line. The arrow shows the approximate position of the number 27.
20
30
27 is closer to 30 than 20, so you round 27 up to 30. You say that 27 rounded to the nearest 10 is 30.
1
On each of these number lines, draw an arrow to show the approximate position of the given number. Round each number to the nearest 10.
a
23 23 rounded to the nearest 10 is
b
40
50
60
70
10
20
61 61 rounded to the nearest 10 is
d
30
49 49 rounded to the nearest 10 is
c
20
15 15 rounded to the nearest 10 is
15 is exactly half way between 10 and 20, so round up to 20.
e
132 132 rounded to the nearest 10 is
f
130
140
240
250
245 245 rounded to the nearest 10 is
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Unit 3 Place value, ordering and rounding
2
On each of these number lines, draw an arrow to show the approximate position of the given number. Round each number to the nearest 10.
a
82 82 rounded to the nearest 10 is
………
b
………
36 36 rounded to the nearest 10 is
………
c
Start by writing 30 and 40 on the number line.
………
25 25 rounded to the nearest 10 is
d
Start by writing 80 and 90 on the number line.
………
………
………
………
161 161 rounded to the nearest 10 is
3
On each of these number lines, draw an arrow to show the approximate position of the given number. Round each number to the nearest 100.
a
421 421 rounded to the nearest 100 is
b
400
500
600
700
678 678 rounded to the nearest 100 is
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Unit 3 Place value, ordering and rounding
c 120
120 rounded to the nearest 100 is
100
200
300
400
d 350
350 rounded to the nearest 100 is
Now try Exercise 3.4 on page 37 of Coursebook 7.
29 Original material Š Cambridge University Press 2017
Unit 3 Place value, ordering and rounding
Adding and subtracting decimals
3.4
Adding and subtracting decimals is almost the same as adding and subtracting whole numbers. Just make sure you write the numbers one underneath the other, with the decimal points in line.
1
Work out the answers to these whole number additions.
a +
d +
2
b
7
5
2
2
1
2
5
3
1
4
+
e
c
3
6
4
5
5
6
2
3
6
+
+
f
Remember to start from the right – add the units ďŹ rst, then the tens, then the hundreds.
7
9
5
3
2
8
6
7
7
+
Work out the answers to these decimal additions. Use the same method as Question 1. Do not let the decimal point put you off!
a +
3
.
4
2
.
1
b +
5
.
2
3
.
9
. d +
c +
6
.
8
8
.
4
.
4
2
.
5
3
3
.
7
.
e
7 +
.
3
.
7
9
.
1
f +
.
30 Original material Š Cambridge University Press 2017
8
.
4
9
0
.
8
4
.
Unit 3 Place value, ordering and rounding
3
Work out the answers to these decimal additions. a
Use the grid on the right to help you.
+
6
.
1
5
.
7
.
Remember to line up the decimal points in each question so they are underneath each other. The first one has been started for you.
a 6.1 + 5.7
4
c
b 8.3 + 4.8
Work out the answers to these subtractions.
a −
d −
b
7
8
4
2
6
.
7
1 .
4
−
e −
9
2
1
8
.
2
4
.
6
3.21 + 0.58
Start from the right – remember to ‘borrow’ if you need to.
c
4
d
12.9 + 5.3
8
4
3
2
8
2
.
6 3
0
.
4 5
−
f −
31 Original material © Cambridge University Press 2017
Unit 3 Place value, ordering and rounding
5
Work out the answers to these decimal subtractions. Use the grid below to help you.
Remember to line up the decimal points in each question so they are underneath each other.
The first one has been started for you. a 3.9 – 2.5 a –
b 7.4 – 3.8 3
.
9
2
.
5
c 12.92 – 5.35
.
Now try Exercise 3.5 on page 39 of Coursebook 7.
32 Original material © Cambridge University Press 2017
Unit 3 Place value, ordering and rounding
3.5
Multiplying decimals One of the best ways to see the effect of multiplying a whole number by a decimal is to look at some number patterns. 1
a
c
e
Fill in the missing numbers in these number patterns.
200
×
4
=
800
20
×
4
=
80
2
×
4
=
0.2
×
4
=
500
×
3
= 1500
50
×
3
5
×
0.5
b
Look at how the numbers at the end of each pattern get smaller.
300
×
2
=
30
×
2
=
3
×
2
=
0.3
×
2
=
700
×
5
= 3500
=
70
×
5
=
3
=
7
×
5
=
×
3
=
0.7
×
5
=
900
×
2
=
600
×
7
=
90
×
2
=
60
×
7
=
9
×
2
=
6
×
7
=
0.9
×
2
=
0.6
×
7
=
0.8
d
1.5
f
600
6
33 Original material © Cambridge University Press 2017
Unit 3 Place value, ordering and rounding
2
Write out two of your own number patterns in the space below. Make the patterns look the same as those in Question 1, but choose your own numbers. a
b
You could start with 400 × 6 or 800 × 3. It is up to you.
3
Complete the missing steps. The first one has been done for you.
a
0.3 × 6
First work out: 3 × 6 = 18
so 0.3 × 6 = 1.8
b
0.2 × 8
First work out: 2 × 8 = ……
so 0.2 × 8 = ……
c
0.4 × 4
First work out: 4 × 4 = ……
so 0.4 × 4 = ……
d
0.7 × 9
First work out: …… × …… = ……
so 0.7 × 9 = ……
e
0.5 × 5
First work out: …… × …… = ……
so 0.5 × 5 = ……
4
Fill in the missing numbers in this number pattern. 0.1
×
5
=
0.5
0.6
×
5
=
……
0.2
×
5
=
1
0.7
×
5
=
……
0.3
×
5
=
1.5
0.8
×
5
=
……
0.4
×
5
=
2
0.9
×
5
=
……
0.5
×
5
=
……
1
×
5
=
……
To work out 0.2 × 5, do 2 × 5 = 10, so 0.2 × 5 = 1.0, which is the same as 1.
34 Original material © Cambridge University Press 2017
Unit 3 Place value, ordering and rounding
5
Work out the answers to these questions. Show your working in the grid below. The first one has been started for you. 3 × 2
2 7
2
4
1
a
3.2 × 7 = ……
b
4.5 × 2 = ……
c
2.4 × 3 = ……
d
4.6 × 4 = ……
e
8.9 × 5 = ……
f
9.2 × 2 = ……
First work out 32 × 7 = 224, so 3.2 × 7 = 22.4
Now try Exercise 3.6 on page 40 of Coursebook 7.
35 Original material © Cambridge University Press 2017