Primary mathematics 6 learners book second edition

Cambridge Primary Mathematics
Whether they are presenting data in a range of formats or exploring cube numbers,
Cambridge Primary Mathematics helps your learners develop their mathematical
thinking skills. They’ll be fully supported with worked examples and plenty of
practice exercises, while projects throughout the book provide opportunities for
deeper investigation of mathematical concepts – including coordinates and angles.
With key word boxes, clear diagrams and supporting illustrations, the course makes
maths accessible for second language learners.

CAMBRIDGE

ãỵ Get learners thinking about what they already know with ‘Getting Started’ boxes
ãỵ Help your learners think and work mathematically with clearly identified
activities throughout each unit
ãỵ Think like a mathematician provides learners with investigation activities
ãỵ Look what I can do! statements in each section and ‘Check your progress’
exercise at the end of each unit help your learners reflect on what they
have learnt
ãỵ Answers for all activities can be found in the accompanying teacher’s resource

Primary Mathematics
Learner’s Book 6

For more information on how to access and use your digital resource,
please see inside front cover.

This resource is endorsed by
Cambridge Assessment International Education
support as part of a set of
Provides
ỵ

resources for the Cambridge Primary Maths
curriculum framework (0096) from 2020

ỵHas
ỵ passed Cambridge Internationals
rigorous quality-assurance process

Developed by subject experts
✓ For Cambridge schools worldwide

Mary Wood, Emma Low,
Greg Byrd & Lynn Byrd

Completely Cambridge
Cambridge University Press works with Cambridge
Assessment International Education and experienced
authors to produce high-quality endorsed textbooks
and digital resources that support Cambridge teachers
and encourage Cambridge learners worldwide.
To find out more visit cambridge.org/
cambridge-international

Registered Cambridge International Schools benefit from high-quality programmes,
assessments and a wide range of support so that teachers can effectively deliver
Cambridge Primary.
Visit www.cambridgeinternational.org/primary to find out more.

Second edition

Digital access


CAMBRIDGE

Primary Mathematics
Learner’s Book 6
Mary Wood, Emma Low, Greg Byrd & Lynn Byrd


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Information on this title: www.cambridge.org/9781108746328
© Cambridge University Press 2021
This publication is in copyright. Subject to statutory exception
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no reproduction of any part may take place without the written
permission of Cambridge University Press.
First published 2014
Second edition 2021
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Printed in Dubai by Oriental Press.
A catalogue record for this publication is available from the British Library

ISBN 978-1-108-74632-8 Paperback with Digital Access (1 Year)
ISBN 978-1-108-96421-0 Digital Learner’s Book (1 Year)
ISBN 978-1-108-96420-3 Learner’s Book eBook
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Cambridge University Press does not guarantee the accuracy of such information
thereafter.
Projects and their accompanying teacher guidance have been written by the
NRICH Team. NRICH is an innovative collaboration between the Faculties of
Mathematics and Education at the University of Cambridge, which focuses on
problem solving and on creating opportunities for students to learn mathematics
through exploration and discussion: nrich.maths.org.
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anthology and reproduction for the purposes of setting examination questions.


Introduction

Introduction
Welcome to Stage 6 of Cambridge Primary Mathematics. We hope this book will show
you how interesting Mathematics can be and make you want to explore and investigate
mathematical ideas.
Mathematics is everywhere. Developing our skills in mathematics makes us better
problem-solvers through understanding how to reason, analyse and reflect. We use
mathematics to understand money and complete practical tasks like cooking and
decorating. It helps us to make good decisions in everyday life.
In this book you will work like a mathematician to find the answers to questions like these:
• What is the value of 2 + 22 + 23?
• Which would you choose 20% of $10 or
• What is a common multiple?

1
10

of $20?

• Why is the answer to 3 × (4 + 5) different to the answer to 3 ì 4 + 5?
ã What time is it in Mumbai when it is 9 am in Mexico City?
• What is a reflex angle?
• How do you draw a waffle diagram?
• How can a shape be translated?
Talk about the mathematics as you explore and learn. This helps you to reflect on what you
did and refine the mathematical ideas to develop a more effective approach or solution.
You will be able to practise new skills, check
how you are doing and also challenge
yourself to find out more. You will be able
to make connections between what seem to

be different areas of mathematics.
We hope you enjoy thinking and working
like a mathematician.
Mary Wood, Emma Low, Greg Byrd and Lynn Byrd

3


Contents

Contents
Page

Unit

6

How to use this book

8

Thinking and Working Mathematically

10

1

The number system
1.1 Place value
1.2 Rounding decimal numbers

Number

20

2

Numbers and sequences
2.1 Counting and sequences
2.2 Special numbers
2.3 Common multiples and factors

Number

35

Project 1: Ordering times

36

3Averages
3.1 Mode, median, mean and range

46

Project 2: Odd sequence

47

4

61

5 2D shapes

Addition and subtraction (1)
4.1 Positive and negative integers
4.2 Using letters to represent numbers

Maths strand

Statistics and probability

Number

Geometry and measure

5.1Quadrilaterals
5.2Circles
5.3 Rotational symmetry

4

81

Project 3: Sneaky statistics

83

6

Fractions and percentages
6.1 Understanding fractions
6.2Percentages
6.3 Equivalence and comparison

Number

97

7

Exploring measures
7.1 Rectangles and triangles
7.2Time

Geometry and measure

112

Project 4: Petal problems

113

8

Addition and subtraction (2)
8.1 Adding and subtracting decimal numbers
8.2 Adding and subtracting fractions

Number


Contents

Page

Unit

Maths strand

122

9

Statistics and probability

132

10 Multiplication and division (1)
10.1Multiplication
10.2Division
10.3 Tests of divisibility

Number

146

11 3D shapes
11.1 Shapes and nets

11.2 Capacity and volume

Geometry and measure

163

12 Ratio and proportion
12.1Ratio
12.2 Direct proportion

Number

176

13Angles
13.1 Measuring and drawing angles
13.2 Angles in a triangle

Geometry and measure

189

Project 5: Animal angles

191

14 Multiplication and division (2)
14.1 Multiplying and dividing fractions
14.2 Multiplying decimals
14.3 Dividing decimals

Number

203

15Data
15.1 Bar charts, dot plots, waffle diagrams
and pie charts
15.2 Frequency diagrams, line graphs and
scatter graphs

Statistics and probability

222

16 The laws of arithmetic
16.1 The laws of arithmetic

Number

228

17Transformation
17.1 Coordinates and translations
17.2Reflections
17.3Rotations

Geometry and measure

248

Project 6: Considering coordinates

251

Glossary

259

Acknowledgements

Probability
9.1 Describing and predicting likelihood

5


How to use this book

How to use this book
In this book you will find lots of different features to help your learning.
Questions to find out what
you know already.

What you will learn
in the unit.

Important words
that you will use.

bisect  diagonal
decompose  justify
parallel  trapezia

Step-by-step examples
showing a way to solve
a problem.

There are often many different
ways to solve a problem.
6


How to use this book

These questions will help
you develop your skills
of thinking and working
mathematically.
An investigation to carry out
with a partner or in groups.
,
Where this icon appears
the activity will help develop
your skills of thinking and
working mathematically.
Questions to help you think
about how you learn.
What you have
learned in the unit.

Questions that cover
what you have learned
in the unit.

At the end of several units,
there is a project for you to carry
out using what you have
learned. You might make
something or solve a problem.
Projects and their accompanying
teacher guidance have been written
by the NRICH Team. NRICH is an
innovative collaboration between
the Faculties of Mathematics and
Education at the University of
Cambridge, which focuses on
problem solving and on creating
opportunities for students to learn
mathematics through exploration
and discussion: nrich.maths.org.

<screenshot of Project box>

7


Thinking and Working Mathematically

Thinking and Working

Mathematically
There are some important skills that you will develop as you learn mathematics.

Specialising is
when I give an example
of something that fits a
rule or pattern.

Characterising
is when I explain how
a group of things are the
same.
Generalising
is when I
explain a rule
or pattern.
Classifying
is when I put things
into groups.

8


Thinking and Working Mathematically

Critiquing is
when I think about
what is good and what
could be better in my work
or someone

else’s work.

Improving is
when I try to make
my work better.

Conjecturing is
when I think of an idea or
a question to develop
my understanding.

Convincing
is when I explain my
thinking to someone
else, to help
them understand.

9


1
The number
system
Getting started
1 What is the value of the digit 9 in these numbers?
a 809.46

b 2021.89

c 123 456.95

2 Write these numbers in words and digits.
a 200 000 + 5000 + 400 + 8 + 0.9
b 500 000 + 70 000 + 30 + 6 + 0.01
3a What number is ten times bigger than 0.01?
b What number is one hundred times smaller than 555?
4 What is the missing number?


100 ì 10 = 10000 ữ

5 Round these lengths to the nearest whole number.
a 6.2 m

b 36.5 cm

c 12.3 m

6 A number with 1 decimal place is rounded to the nearest
whole number.
a What is the smallest number that rounds to 100?
b What is the largest number that rounds to 10?

10

d 10.6 cm


1 The number system

Numbers are important. We use them every day.
• We use a series of digits when we telephone a friend.
• We use decimal numbers when we work out prices.
• We use positive and negative numbers when we use a thermometer.
When do you use numbers? Make a list.
Here are some ideas to help you get started.

11


1 The number system

1.1 Place value
We are going to …
•

explain the value of each digit in numbers with up to 3 decimal places

•

multiply and divide whole numbers and decimals by 10, 100 and 1000

•

compose, decompose and regroup numbers with up to 3 decimal places.

You already know how to read and write
decimal numbers with 1 or 2 decimal places.

compose  decimal point

You can compose, decompose and regroup
numbers, and you can multiply and divide
by 10, 100 and 1000.

hundredths  place value

decompose  digit
regroup tenths  thousandths

The Western Pygmy Blue Butterfly is very
small. Some have a wingspan of only 0.375 inche