We are working with Cambridge Assessment International Education towards endorsement of this title Cambridge Primary Mathematics Packed with activities, including drawing angles, completing sequences and working out ratios, these workbooks help your students practise what they have learnt Specific exercises develop thinking and working mathematically skills Focus, Practice and Challenge exercises provide clear progression through each topic, helping learners see what they’ve achieved Ideal for use in the classroom or for homework • Activities take an active learning approach to help learners apply their knowledge to new contexts • Three-tiered exercises in every unit get progressively more challenging to help students see and track their own learning • Varied question types keep learners interested • Write-in for ease of use • Answers for all activities can be found in the accompanying teacher’s resource PL E CAMBRIDGE Primary Mathematics Workbook For more information on how to access and use your digital resource, please see inside front cover ✓ P rovides learner support as part of a set of resources for the Cambridge Primary Maths curriculum framework (0096) from 2020 ✓ H as passed Cambridge International’s rigorous quality-assurance process ✓ Developed by subject experts ✓ For Cambridge schools worldwide 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 SA M This resource is endorsed by Cambridge Assessment International Education Mary Wood, Emma Low, Greg Byrd & Lynn Byrd Visit www.cambridgeinternational.org/primary to find out more Second edition Digital access Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title PL E CAMBRIDGE Primary Mathematics Workbook SA M Mary Wood, Emma Low, Greg Byrd & Lynn Byrd Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title 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 314–321, 3rd Floor, Plot 3, Splendor Forum, Jasola District Centre, New Delhi – 110025, India 79 Anson Road, #06–04/06, Singapore 079906 PL E 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/9781108746335 © Cambridge University Press 2021 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 2014 Second edition 2021 20 19 18 17 16 15 14 13 12 11 10 Printed in Dubai by Oriental Press M A catalogue record for this publication is available from the British Library ISBN 978-1-108-74633-5 Paperback with Digital Access (1 Year) Additional resources for this publication at www.cambridge.org/9781108746335 SA 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 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 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 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title Contents Contents Thinking and Working Mathemetically The number system 1.1 1.2 Place value Rounding decimal numbers 13 Numbers and sequences 18 2.1 2.2 2.3 Counting and sequences Special numbers Common multiples and factors 18 23 27 3 Averages PL E How to use this book 32 Mode, median, mean and range 32 Addition and subtraction (1) 38 4.1 4.2 Positive and negative integers Using letters to represent numbers 38 43 2D shapes48 M 3.1 5.1 Quadrilaterals48 5.2 Circles53 5.3 Rotational symmetry60 Fractions and percentages65 SA 6.1 Understanding fractions 6.2 Percentages 6.3 Equivalence and comparison 65 69 73 Exploring measures 77 7.1 Rectangles and triangles 7.2 Time 77 83 Addition and subtraction (2)89 8.1 8.2 Adding and subtracting decimal numbers Adding and subtracting fractions 89 94 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title Contents 9 Probability98 9.1 Describing and predicting likelihood 98 10 Multiplication and division (1)107 107 111 114 PL E 10.1 Multiplication 10.2 Division 10.3 Tests of divisibility 11 3D shapes119 11.1 Shapes and nets 11.2 Capacity and volume 119 127 12 Ratio and proportion136 12.1 Ratio 12.2 Direct proportion 136 140 13 Angles146 13.1 Measuring and drawing angles 13.2 Angles in a triangle 146 154 M 14 Multiplication and division (2)160 14.1 Multiplying and dividing fractions 14.2 Multiplying decimals 14.3 Dividing decimals 160 164 167 SA 15 Data171 15.1 Bar charts, dot plots, waffle diagrams and pie charts 15.2 Frequency diagrams, line graphs and scatter graphs 171 182 16 The laws of arithmetic194 16.1 The laws of arithmetic 194 17 Transformations199 17.1 Coordinates and translations 17.2 Reflections 17.3 Rotations 199 208 215 Acknowledgements219 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title How to use this book How to use this book PL E 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 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 You will also find these features: M Important words that you will use SA Step-by-step examples showing a way to solve a problem There are often many different ways to solve a problem These questions will help you to develop your skills of thinking and working mathematically Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title Thinking and Working Mathematically PL E 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 M Characterising is when I explain how a group of things are the same SA Generalising is when I explain a rule or pattern Classifying is when I put things into groups Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title Thinking and Working Mathematically PL E 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 SA M 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 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title PL E The number system 1.1 Place value Worked example compose decimal point decompose Paulo is thinking of a number digit hundredths place value He says, ‘If I divide my number by 10 and then by 100, the answer is 0.375.’ regroup tenths thousandths M What number is Paulo thinking of? 0.375 × 100 × 10 10 0.1 0.01 0.001 SA 100 7 5 To find Paulo’s number, reverse the operations You could replace × 100 × 10 by × 1000 × 100 × 10 0.375 × 100 × 10 = 375 Answer: Paulo is thinking of 375 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title 1.1 Place value Exercise 1.1 Focus Draw a ring around the expression that is equivalent to 0.67 10 + 60 10 10 10 100 60 100 100 + 70 100 PL E + + What does the digit in 3.065 represent? Magda regroups 56.079 in different ways but two of her answers are wrong Which answers are wrong? A: 5607 tenths + thousandths B: 56 ones and 79 thousandths C: 56 + 0.79 M D: 50 + 6.079 E: 50 + + 0.07 + 0.009 SA Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title 17.1 Coordinates and translations SA M PL E Draw axes from –6 to +6 on squared paper Plot the points A (0, 1), B (2, 1) and C (4, –2) a W rite down the coordinates of D so that A, B, C and D are the vertices of an isosceles trapezium b W rite down two possible coordinates of D so that D is a point on the line segment AB Tip You can use fractions or decimals in coordinates 205 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title 17 Transformations c Write down two possible coordinates of D so that A, B, C and D are the vertices of a parallelogram Challenge PL E d Is it possible to find coordinates for D so that A, B, C and D are the vertices of a rectangle? Explain your answer M (-1, 3) and (3, 1) are the coordinates of two vertices of a square What could the other vertices of the square be? Find all the possible solutions The diagram shows shape P on a coordinate grid y SA P –5 –4 –3 –2 –1 1 x Erin translates shape P squares right and squares up She labels the shape Q 206 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title 17.1 Coordinates and translations a What translation should Erin to take shape Q back to shape P? Explain how you worked out your answer i PL E b Erin translates shape Q squares right and square up She labels the shape R Erin thinks that she could use the single translation squares right and squares up to take shape P to shape R Is Erin correct? Explain your answer SA M ii What you notice about the single translation P to R, and the two translations P to Q and Q to R? Rectangle K has vertices as the points (-2, -1), (-5, -1), (-5, -3) and (-2, -3) Shen translates K four times, using these four different translations A, B, C and D A squares right and squares up B squares right and squares up C squares right D square left and square down 207 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title 17 Transformations After which translation will K and the new rectangle be: a touching end to end b touching corner to corner c overlapping PL E d not touching or overlapping? 17.2 Reflections Worked example diagonal mirror line SA M Reflect this triangle in the diagonal mirror line Take one vertex of the triangle at a time Draw arrows (black) to the mirror line, then draw the same length arrows (grey) the other side of the mirror line Join the vertices with straight lines to complete the reflected triangle 208 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title 17.2 Reflections Exercise 17.2 Focus Which drawings show correct reflections of triangle A? a b A c PL E A d A SA M A 209 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title 17 Transformations Reflect each shape in the mirror lines They have all been started for you b PL E a d M c Is A, B or C the correct reflection for each of these? i SA A B C 210 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title 17.2 Reflections ii iii B C PL E A SA A M B C 211 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title 17 Transformations Practice Reflect the shape in the horizontal and vertical mirror lines d M c b PL E a This is part of Jose’s homework Question: Reflect shape A in the diagonal line of symmetry Label your answer shape B SA B A Has Jose drawn shape B correctly? Explain your answer 212 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title 17.2 Reflections Reflect the shape in the diagonal mirror lines b PL E a d c 7 a Describe the mirror line for each of these reflections ii SA M i iii Tip Is the mirror line horizontal, vertical or diagonal? b Draw in the correct mirror line for each reflection 213 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title 17 Transformations Challenge Draw in the correct mirror line for each reflection b c PL E a 9 a Reflect the shapes in the mirror lines to complete the pattern i ii i M b What is the order of rotational symmetry of the completed pattern? ii 10 The diagram shows shape A on a coordinate grid. A SA a Reflect shape A in the mirror line Label the new shape B b Translate shape B squares left and square down Label the new shape C c Reflect shape C in the mirror line Label the new shape D d Describe the translation that takes shape D back to shape A e What you notice about your answer to part d and the translation you carried out in part b? 214 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title 17.3 Rotations 17.3 Rotations Worked example anticlockwise centre of rotation A C clockwise corresponding rotate PL E Rotate triangle A 90° anticlockwise about the centre of rotation marked C Label your answer triangle B Step Step A A M C C Start turning the tracing paper 90° (a quarter turn) anticlockwise Step Step SA Trace the shape, then put your point of your pencil on the centre of rotation A A B C C Once the turn is completed make a note of where the new triangle is Draw the new triangle onto the grid and label it B 215 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title 17 Transformations Exercise 17.3 Focus In each of these diagrams, shape A has been rotated to shape B around centre C Write down if the rotation is clockwise or anticlockwise a b A B C Tip A C Clockwise: PL E B c d B C A B A C Anticlockwise: a M Complete these rotations of 90° clockwise about the centre C b C SA C Complete these rotations of 90° anticlockwise about the centre C a C b C Practice Rotate the shapes 90° clockwise about the centre C a b C c C C 216 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title 17.3 Rotations Rotate the shapes 90° anticlockwise about the centre C a b c C C C This is part of Alysha’s homework The centre of rotation is shown by a dot (•) Question: Rotate shape A 90° clockwise about the centre of rotation (•) Label the shape B Answer: Has Alysha got her homework correct? Use diagrams to help you explain your answer B M A PL E SA Challenge Rotate the shapes 90° about the centre of rotation C, using the direction shown a anticlockwise b C clockwise C 8 a Follow these instructions to make a pattern Rotate the shape 90° clockwise about C Draw the new shape Rotate the new shape 90° clockwise about C C 217 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title 17 Transformations Draw the new shape Rotate the new shape 90° clockwise about C Draw the new shape b What is the order of rotational symmetry of your completed pattern? 9 a Rotate triangle A1B1C, using the same instructions as question 8a. Label the vertices of the three new triangles A2, B2, C then A3, B3, C then A4, B4, C C B1 PL E A1 b On your completed diagram, join A1 to A2 to A3 to A4 to A1 with straight lines What shape have you just drawn? c On your completed diagram, join B1 to B2 to B3 to B4 to B1 with straight lines What shape have you just drawn? SA M d Do you think that whatever shape you rotate, if you rotate it 90° clockwise or anticlockwise three times, then the shape you get when you join corresponding vertices will always be the same? Explain your answer You can use diagrams to help your explanation 218 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment International Education towards endorsement of this title 17.3 Rotations SA M PL E Acknowledgements 219 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 ... research at the highest international levels of excellence www .cambridge. org Information on this title: www .cambridge. org/9781108746335 © Cambridge University Press 2021 This publication is in copyright... Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746335 We are working with Cambridge Assessment... Delhi – 110025, India 79 Anson Road, #06–04/06, Singapore 079906 PL E Cambridge University Press is part of the University of Cambridge It furthers the University’s mission by disseminating knowledge