We are working with Cambridge Assessment International Education towards endorsement of this title Cambridge Primary Mathematics Packed with activities, including estimating, drawing and labelling, these workbooks help your students practise what they have learnt Specific exercises develop thinking and working mathematically techniques 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 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 ✓ P rovides learner support as part of a set of M This resource is endorsed by Cambridge Assessment International Education Emma Low & Mary Wood 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_9781108746311 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 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 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/9781108746311 © 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 978-1-108-74631-1 Paperback with Digital Access (1 Year) Additional resources for this publication at www.cambridge.org/9781108746311 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_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title Contents Contents How to use this book Thinking and Working Mathematically The number system 8 1.1 1.2 Understanding place value Rounding decimal numbers 2D shape and pattern 17 PL E 2.1 Triangles 2.2 Symmetry 13 17 24 Numbers and sequences 31 3.1 3.2 3.3 Counting and sequences Square and triangular numbers Prime and composite numbers 31 36 40 4 Averages 44 Mode and median Addition and subtraction 49 5.1 5.2 Addition and subtraction including decimal numbers Addition and subtraction of positive and negative numbers 3D shapes 59 6.1 Nets of cubes and drawing 3D shapes Fractions, decimals and percentages 66 7.1 7.2 7.3 Understanding fractions Percentages, decimals and fractions Equivalence and comparison SA M 4.1 44 49 54 59 66 70 76 8 Probability 81 8.1 Likelihood 8.2 Experiments and simulations 81 86 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title Contents Addition and subtraction of fractions 93 9.1 Addition and subtraction of fractions 93 10 Angles 98 10.1 Angles 98 11 Multiplication and division 103 103 108 111 PL E 11.1 Multiplication 11.2 Division 11.3 Tests of divisibility 12 Data 114 12.1 Representing and interpreting data 12.2 Frequency diagrams and line graphs 114 126 13 Ratio and proportion 136 13.1 Ratio and proportion 136 14 Area and perimeter 144 M 14.1 Area and perimeter 144 15 Multiplying and dividing fractions and decimals 151 15.1 Multiplying and dividing fractions 15.2 Multiplying a decimal and a whole number 151 156 SA 16 Time 160 16.1 Time intervals and time zones 160 17 Number and the laws of arithmetic 169 17.1 The laws of arithmetic 169 18 Position and direction 175 18.1 Coordinates and translation 175 Acknowledgements 182 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 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 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 1.1 Understanding place value You will also find these features: 16 Worked example Important words that you will use Find the missing numbers a 0.9 × = 3.5 Time hundredth decimal place place value decimal point tenth M b 350 ÷ Step-by-step examples a showing a way to solve 100s a problem =9 decimal 10s 1s s 10 s 100 16.1 Time intervals and time zones Use a place value grid to help you To move digits one column to the left you multiplyWorked by 10 example Mai, Yared and Susan live in different time zones The time on Yared’s clock is hours ahead of the time on Mai’s clock 0.9 × 10 = s 10 s 100 SA b 100s 10s 1s There are often many different ways to solve a problem The time on Susan’s clock is hours behind the time on Mai’s clock To move digits two columns to the right you The time in Mai’s time zone is 15:07 What is the time for Yared and Susan? divide by 100 Yared’s time is hours ahead of Mai’s Susan’s time is hours behind Mai’s 350 ÷ 100 = 3.5 These questions will help you develop your skills of thinking and working mathematically Add hours to 15:07 The time for Yared is 17:07 Subtract hours from 15:07 The time for Susan is 12:07 Exercise 16.1 time interval Focus time zone Universal Time (UT) 1.1 Understanding place value Circle the amount of time to correctly 11 Draw a ring around the odd one out complete each sentence a 0.5 minutes is the same as: 368.4 368.4 tenths 3684 hundredths 30 seconds b seconds 50 seconds 36.84 368 tenths and hundredths 0.5 hours is the same as: Explain your answer minutes 30 seconds c 30 minutes 1.5 days is the same as: day and hours Challenge day and 12 hours day and 15 hours 12 Write down the value of the digit in each of these numbers a 72.3 b eighty-four point zero three 159 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 13 Arun has these cards We are working with Cambridge Assessment International Education towards endorsement of this title Additionand and Working subtraction Thinking Mathematically PL E Thinking and Working Mathematically There are some important skills that you will develop as you learn mathematics Specialising is when I choose an example and check to see if it satisfies or does not satisfy specific mathematical criteria SA M Characterising is when I identify and describe the mathematical properties of an object Generalising is when I recognise an underlying pattern by identifying many examples that satisfy the same mathematical criteria Classifying is when I organise objects into groups according to their mathematical properties Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title Thinking and Working Mathematically PL E Critiquing is when I compare and evaluate mathematical ideas, representations or solutions to identify advantages and disadvantages Improving is when I refine mathematical ideas or representations to develop a more effective approach or solution SA M Conjecturing is when I form mathematical questions or ideas Convincing is when I present evidence to justify or challenge a mathematical idea or solution These characteristics are reproduced from the Cambridge Primary Mathematics curriculum framework (0096) from 2020 This Cambridge International copyright material is reproduced under licence and remains the intellectual property of Cambridge Assessment International Education Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title PL E The number system 1.1 Understanding place value Worked example decimal hundredth Find the missing numbers decimal place place value a 0.9 × decimal point tenth =9 b 350 ÷ Use a place value grid to help you M a = 3.5 100s 10s 1s s 10 s 100 To move digits one column to the left you multiply by 10 SA b 0.9 × 10 = 100s 10s 1s s 10 s 100 To move digits two columns to the right you divide by 100 350 ÷ 100 = 3.5 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title 1.1 Understanding place value Exercise 1.1 Focus Write the missing numbers in this sequence ÷ 10 190 19 ÷ 10 ÷ 10 ÷ 10 You may find a place value grid helpful for these questions PL E 1900 Tip Write these numbers in digits a fifteen point three seven b one hundred and five point zero five c thirty four point three four Write the missing numbers a SA × M 75 b 25 000 ì100 ì10 ì10 ữ ữ100 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title 16 Time 10 Use the table and clocks from Question to help you calculate the day and time in: a Cape Town if it is 08:13 on Wednesday in Lima PL E b Chennai if it is 10.37 p.m on Saturday in Cape Town c Sao Paulo if it is 17:28 on Tuesday in Tokyo d Lima if it is 9.09 a.m on Friday in Adelaide SA M 168 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title PL E 17 Number and the laws of arithmetic 17.1 The laws of arithmetic Worked example Are the following statements true or false? a × = × Explain your answers a True commutative law distributive law regroup The commutative law states that when two numbers are added or multiplied, you can the calculation in any order b False The learner has added and to give 10, then multiplied by The order of operations is multiplication before addition, so the answer is + 16 = 24, not 80 SA decompose M Answers: b + × = 80 associative law Exercise 17.1 Focus Look at each number sentence Write true or false for each one a × = × b 28 ÷ = ÷ 28 c × × = × × 169 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title 17 Number and the laws of arithmetic Write the missing number 13 × 36 = 13 × ×9 Use single digits to complete this number sentence 25 × 15 = × Calculate a + × = b 12 − × = c 14 + ữ = Practice ì ì PL E Complete these calculations 21 × × 7 b M a × × = × = ×7 × = 160 + ×8 = SA = = Sofia knows that 48 × 20 = 960 Show how she can use this fact to calculate 48 ì 19 170 Original material â Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title 17.1 The laws of arithmetic Use numbers and operation signs from the box to make three calculations giving different answers + × PL E You can only use each number once in each calculation, but you can use the same operation sign more than once M = SA = = Use +, −, ×, ÷ to complete these number sentences × Example: a 12 c − 6=6 = 12 3=9 b d 10 = 42 2=3 171 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title 17 Number and the laws of arithmetic Ali, Bashir, Petra and Tara calculate 25 × using different methods Which method you prefer? You must explain the advantages of your chosen method Ali’s method Bashir’s method 20 × = 160 25 × = × × + 5×8 + 40 Petra’s method 25 × 25 × – 50 = 100 × = 200 SA = 200 – Tara’s method 25 × = 25 × × M 25 × 10 = × 40 = 200 = 200 = 250 PL E 25 × 172 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title 17.1 The laws of arithmetic Challenge 10 Explain whether each calculation will give an answer equal to the product of 12 and b 12 × × c + 10 × PL E a × × M 11 Use the distributive law to help you work out these calculations Show your working SA a 39 × b 38 × c 29 × 173 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title 17 Number and the laws of arithmetic 12 Use the associative law to help you work out these calculations Show your working b 50 × 12 × c 25 × 19 × PL E a × 17 × 13 Write the missing numbers c + × = 41 − = 18 SA e × + = 19 M a × b × − d 16 ÷ f 13 − 12 ÷ = 29 −3=1 =9 174 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title PL E 18 Position and direction 18.1 Coordinates and translation Worked example The coordinates of three vertices of a rectangle are (3, 1), (4, 1) and (3, 5) What are the coordinates of the fourth vertex? coordinates translation Check the definition of a rectangle y Plot the coordinates on a grid Join the points with straight lines M A rectangle has four sides and four vertices It has two pairs of opposite equal parallel sides and four right angles (3, 5) SA (3, 1) 0 (4, 1) x 175 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title 18 Position and direction Continued y The other two sides must make right angles with the first sides For this question, each line can be drawn in only one direction Draw the other two sides (3, 5) 0 y (4, 1) PL E (3, 1) x The fourth vertex is where the sides of the rectangle meet (3, 5) 0 (4, 1) M (3, 1) 1 x SA Answer: The fourth vertex has coordinates (4, 5) Exercise 18.1 y Focus Write the coordinates that are inside the circle on the grid ⎛ ⎝ ⎛ ⎝ , ⎛ ⎛ ⎝ ⎝ , ⎛ ⎛ ⎝ ⎝ , ⎛ ⎛ ⎝ ⎝ , ⎛ ⎝ , ⎛ ⎛ ⎝ ⎝ , ⎛ ⎝ 0 x 176 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title 18.1 Coordinates and translation 2 a Draw two lines to complete the square on the grid y PL E 2 x b Two of the coordinates at the vertices of the square are (1, 1) and (1, 4) What are coordinates of the other two vertices? ⎛ ⎝ , ⎛ ⎛ ⎝ ⎝ , ⎛ ⎝ Draw a ring around the numbers and words that describe the translation from shape A to shape B M a A B SA A b / / squares right / left / up / down B / / squares right / left / up / down c B A / / squares right / left / up / down and / / squares right / left / up / down 177 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title 18 Position and direction Practice The coordinates of three vertices of a rectangle are (0, 1), (0, 4) and (4, 4) What are the coordinates of the fourth vertex of the rectangle? PL E 4 5 A cross is marked at point (50, 50) on the grid Estimate the coordinates of points A, B and C (50, 50) B M y SA C A x a A is approximately ⎛ ⎝ , ⎛ ⎝ b B is approximately ⎛ ⎝ , ⎛ ⎝ c C is approximately ⎛ ⎝ , ⎛ ⎝ 178 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title 18.1 Coordinates and translation PL E Look at this picture of a shape that has been translated Draw a ring around True or False for each statement about translating shapes Translated shapes travel in a straight line True / False A shape gets larger when it is translated True / False A shape rotates when it is translated True / False The lines joining the vertices of the first shape to the translated shape are parallel True / False M Translate each shape according to the instructions left 5, down SA right 2, down right 12, up right 3, up right 1, down left 2, up 179 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title 18 Position and direction Challenge A farmer keeps his sheep safe by putting them no more than 20 metres away from the farmhouse and not too close to the river or the road Tip 10 River Farmhouse 10 m Road 1 10 11 12 Write the coordinates for five points where the sheep will be safest SA M Use the scale on the map to work out distances PL E y Two vertices of an isosceles triangle are at (2, 2) and (4, 2) Find the coordinates for the possible positions of the third vertex on this grid ⎛ ⎝ , ⎛ ⎛ ⎝ ⎝ , ⎛ ⎛ ⎝ ⎝ , ⎛ ⎝ , ⎛ ⎛ ⎝ ⎝ , ⎛ ⎛ ⎝ ⎝ , ⎛ ⎝ ⎛ ⎝ , ⎛ ⎛ ⎝ ⎝ , ⎛ ⎛ ⎝ ⎝ , ⎛ ⎝ ⎛ ⎝ 3 x 180 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title 18.1 Coordinates and translation 10 Translate the triangle four times to reach the finish point of the maze Tip Finish SA M Write your directions using the number of squares right or left, then the number of squares up or down for each translation PL E Start 181 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 We are working with Cambridge Assessment International Education towards endorsement of this title 18 Position and direction Acknowledgements SA M PL E Cover illustration: Pablo Gallego (Beehive Illustration); 182 Original material © Cambridge University Press 2021 This material is not final and is subject to further changes prior to publication ISBN_9781108746311 ... 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 41 42 49 50 57 58 PL E This is an by number grid 35 36 37 38 39 40 43 44 45 46 47 48 51 52 53 54 55 56 59 60 61 62 63... 13 23 29 71 65 51 45 15 92 25 31 37 16 14 PL E 2 11 5 a Find two different prime numbers that total + =9 M b Find two different prime numbers that total 50 + = 50 SA Show that 15 is a composite... Area and perimeter 144 15 Multiplying and dividing fractions and decimals 151 15. 1 Multiplying and dividing fractions 15. 2 Multiplying a decimal and a whole number 151 156 SA 16 Time 160 16.1