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Youll find explanations of mathematical skills and plenty of opportunities for practice, investigation and mental maths throughout. The accompanying .Youll find explanations of mathematical skills and plenty of opportunities for practice, investigation and mental maths throughout. The accompanying .
3 k2 CAMBRIDGE UNIVERSITY PRESS CAMBRIDGE Primary Mathematics CAMBRIDGE UNIVERSITY PRESS CAMBRIDG Primary Mathematics CAMBRIDGE UNIVERSITY PRESS University Printing House, Cambridge C82 88S, United Kingdom (ne Liberty Plazo, 20th Floor, New York, NY 10006, USA 477 Wiliomstown Road, Port Melbourne, VIC 3207, Australia 314-321, 3d Floor, Plt 3, Splendor Forum, sola District Centre, New Delhi 110025, ndio 103 Penong Road, #05-06/07, Vsionerest Commercial Singapore 238467 Cambridge Univesity Press is part ofthe University of Cambridge It furthers the University’s mission by disseminating knowledge inthe pursuit of education, learning and research atthe highest international levels of excellence wwwwcambridge org Information on this ttle: www.cambridge org/9781108745291 (©Cambridge University Prese 2021 This publication is in copyright, Subjectto statutory exception tnd tothe 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 11 109.87 Printed in Malaysia by Vivor Printing ‘Acatologue record for this publication i availabe from the British Library ISBN 978-1-108-74529-1 Poperback with Digital Access (1 Year) ISBN 978-1-108-96416-6 Digitol Learner's Book (1 Yeor) ISBN 978-1-108-96417-3 Learner's Book eBook ‘Additional resources for this publication at wwnw.camibridge-org/9781108745291 Combridge University Press has no responsibilty for the persistence or accuracy ‘of URLS for external or thitd-porty 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, ond 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 Projects and their accompanying teacher guidance have been written by the NRICH Team, [RICH 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 ønd discussion:rịch.motheorg CCombridge International copyright moteral in this publication is cepraduced under licence ond remains the intellectual property of Cambridge Assessment Intemational Education NOTICE TO TEACHERS IN THE UK Itis legal to reproduce any part ofthis work in material form (including photocopying and electronic storage) except under the following circumstances: (where you are abiding by a licence granted to your schoo! or institution by the Copyright Licensing Agency: (i) where no such licence exists, oF where you wish to exceed the terms of a licence, ‘ond you have gained the written permission of Cambridge University Press: (i) where you ore ollowed to reproduce without permission under the provisions ‘of Chapter ofthe Copyright, Designs ond Patents Act 1988, which covers, for ‘exemple, the reproduction of short passages within certain types of educational “onthology and reproduction forthe purposes of setting examination questions @ Introduction Introduction Welcome to Stage 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 are negative numbers and when are they used? How can you quickly find out if 1435 is in the 25 times table? Which is bigger: half a cake or 50 percent of a cake? What might you be doing at the time 23:30? What shape is a cone? Whatis a dot plot? What comes between the points north, east, south and west on a compass? 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 and Emma Low Contents 10 26 38 39 54 61 74 75 s7 88 99) How to use this book ‘Thinking and Working Mathematically Numbers and the number system 1.1 Counting and sequences 1.2 More on negative numbers 1.3 Understanding place value Project 1: Deep water Time and timetables 24 Time 2.2 Timetables and time intervals Project 2: Rolling clock Addition and subtraction of whole numbers 3.1 Using a symbol to representa missing number or operation 3.2 Addition and subtraction of whole numbers 33 Generalising with odd and even numbers Probability 4.1 Lielhood ‘5 Multiplication, multiples and factors 5.1 Tables, multiples and factors 5.2 Multiplication Project 3: Square statements 2D shapes 61 2D shapes and tessellation 62_Symmetry Project 4: Always, sometimes or never true? Fractions 7.1 Understanding fractions 7.2 Froctions as operators @ Angles &1 Comparing angles 82 Acute and obtuse 83 _ Estimating angles Number Geometry and measure Number Statistics and probability Number ‘Geometry and measure Number Geometry and measure Contents 113 123 124 132 144 156 166 179 194 195 208 220 235 246 ° Comparing, rounding and dividing 9.1 Rounding, ordering and comparing whole numbers 9.2 _ Division of 2-digit numbers Project 5: Arranging chairs 10 Collecting and recording data 1041 How to collect and record data 1" Fractions and percentages 11.1 Equivalence, comparing and ordering fractions 11.2 Percentages 12 Investigating 30 shapes and nets 12.1 The properties of 3D shapes 12.2_ Nets of 3D shapes 13 ‘Addition and subtraction 13.1 Adding and subtracting efficiently 13.2 Adding ond subtracting fractions with the some denominator 14 ‘Area and perimeter 14.1 Estimoting and measuring area and perimeter 142 Area and perimeter of rectangles 16 Special numbers 15.1 Ordering and comparing numbers 15.2 Working with special numbers 15.3 Tests of divisibilty Project 6: Special numbers 16 Data display and interpretation 16.1 Displaying and interpreting dato ” Multiplication and division 17.1 Using an efficient column method for multiplication 17.2_Using an efficient method for division 18 Position, direction and movement 48.1 Position and movement 18.2 Reflecting 2D shapes Glossary ‘Acknowledgements, Number Statistics and probability, Number Geometry and measure Number Geometry and measure Number Statistics and probability, Number Geometry and measure How to use this book } In this book you will find lots of different features to help your lear Questions to find out what you know already —————+ 1g: Read here nanber you prt then wre ach number in wed Wet te number yu mate whan you put the paces cade ogee What you will learn in the ti => Important words that you will use» Step-by-step examples showing a way to solve problem, ——————+ There are often many different ways to solve a problem These questions will help you develop your skills of thinking and working mathematically ‘walt method of ox 285 174 3001009 409 ca ‘ecompose the numbers ‘Aad the hundreds, tens ond ones together ‘Then compose the parts =—==— seers ow rts each ter ano ety eet? bp An investigation to carry ————> ‘out with a partner or in groups Where this icon appears “XY, the activity will help develop your skills of thinking and working How to use this book vế cre tl go down te+ha uhU “ác Er~) i m2) Oo mathematically Questions to help you think about how you learn —————+ This is what you have learned in the unit —————> Questions that cover what you have learned in the unit ———> At the end of several units, there ialprojectforyou tocanyout using what you have learned You might make something oe ỹ Project vero ge sain pref bene nin Tee TEEErtriLctretcs Tre” Projects and their accompanying ¬ : teacher guidance have been written by the NRICH Team NRICH is an innovative collaboration between the Faculties of’ Mathematiesiand Education Gt) i won monedaef i Bef wos Ro the University of Cambridge, which | focuses on problem solving and on | Ktbewecaimn su onec eur 2on see how uch Creating opportunities for students | "=" "srt menirtiw menwatdttenmese noe to learn mathematics through exploration and discussion: nrich.maths.org jing and Worl 1g Mathematically 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 > Characterising is when I identify and describe the mathematical properties of an object Generalising is whenI 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 >> Thinking and Working Mathematically Critiquing is when I compare and evaluate mathematical ideas, representations or solutions to identify advantages and disadvantages Improving is whenI refine mathematical ideas or representations to develop a more effective approach or solution Conjecturing is when I form mathematical questions or ideas Convincing is when I present evidence to justify or challenge a mathematical idea or solution ve Numbers and the number system Getting storted Write the term-to-term rule for finding the next term in these sequences a 185,180, 175, b 235, 245, 255, © 901,801, 701, Read these numbers to your partner, then write each number in words b 299 a 601 c 111 Write the number you make when you put the place-value cards together ° Bab — ay Copy and comy plete these number sentences +60+/| 305 = 300 + the missing numbers 16x10= 56x Numbers and the number system This unit is all about our number system You will look at linear sequences and non-linear sequences, negative numbers, multiplying and dividing by 10 and 100, and place value Imagine you save $2 each week Can you write a number sequence for how much you have at the end of each week? You add the same amount each time, so this is a linear sequence The term-to-term rule is ‘add If you save a different amount each time, the sequence will be non-linear One of the main ideas in place value is that the value of a digit depends on its position in the number Think about what the digit is worth in $7 and $70 Do you have enough money to buy the bike? & There are $7 in the bag Think about the numbers 126 and 162 đ What is the value of the digit in each number? The bike costs $70 Numbers and the number system > > 1.1 Counting and sequences dre goïng to nt on and bac f tens, hundrec You will continue counting forwards and backwards in steps of constant size and you will start to use negative numbers Around the coasts of Antarctica temperatures are between -10°C and ~30 °C Try counting back in tens starting at 30 and linear sequence negative number non-linear sequence Cee Carlos writes a number sequence ‘The first term in his sequence is He uses the rule ‘subtract 2' to work out the next term What is the fifth term in his sequence? 2 from difference ending with -30 Worl thousands starting 2 BRE ác Vệ vo Answer: The fifth term is rule sequence spatial pattern square number term term-to-term rule Start with and subtract each time until you have five terms 1.1 Counting and sequences 'Worked example ‘The numbers in this sequence increase by 50 each time +50 +50 +50 —> 60 ——» 110 ——> 160 What is the first number greater than 1000 that is in the sequence? Explain how you know 60, 110, 160, 210, 260, Write down the first few terms (You could write down all the terms in the sequence, but it would take a long time.) Answer: The terms all end in 10 or 60 so the first number greater than 1000 is 1010 Exercise 1.1 1a _ Mia counts on in steps of 100 She starts at 946 Write the next number she says b ¢ Kofi counts back in steps of 100 He starts at 1048 Write the next number he says Bibi counts on in steps of 1000 She starts at 1989 wr the next number she says d_ Pierre counts back in steps of 1000 e Tara counts back in ones He starts at 9999 Write the next number he says She counts 3, 2, 1, Write the next number she says 13 Numbers and the number system Copy and complete this square using the rule ‘add across and add down’ ‘What you notice about the numbers on the diagonal? Discuss with your partner #Ì X > +2 — Draw two more by squares and choose a rule using addition Predict what the numbers on the diagonal will be before you complete the squares Choose any two of these three sequences How are they similar to each other and how are they different? X Look at these sequences Which could be the odd one out? Explain your answer eee ee ee? pope Ì 8,11, 14, 17, Think about \Jour ansWwers to questions and DU 70/00/77 14 > | 1.1 Counting and sequences Use Can a b c d different first terms to make sequences that all have the term-to-term rule ‘add 3° you find a sequence for each of the following? Where the terms are all multiples of Where the terms are not whole numbers Where the terms are all odd Where the terms include both 100 and 127 Abdul makes a number sequence The first term of his sequence is 397 His term-to-term rule is ‘subtract Abdul says, ‘If | keep subtracting from 397 | will eventually reach 0." Is he correct? Explain your answer Which sequences are linear and which are not? Write the next term for each sequence Explain your answers to your partner a Add five: 4,9, 14, b Subtract four: 20, 16, 12, Add one more each time: 2, 3, 5, Multiply by three: 2, 6, 18, Subtract one less each time: 50, 41, 33 Divide by two: 32, 16, 8, Here is a spatial pattern Draw the next term in the pattern What number does it represent? 15 Numbers and the number system > Think like a mothemdtician These sets of beads have consecutive numbers in the circles ‘The numbers add up to the number in the square Example: «You will show you are specialising when you identify examples that fit the criteria ‘The numbers add up to the numbers in the square’ + You will show you are generalising when you notice a way of finding the middle number Complete these sets of beads “0008 * @0000 Consecutive numbers are next to each other Mu and Describe to a partner how to find the middle number of each set of beads * You will show you are specialising when you identify examples that fit the criteria ‘The numbers add up to the numbers in the square * You will show you are generalising when you notice a way of finding the middle number 117-0727 lon-linear sequen 16> 1.2 More on negative numbers > 1.2 More on negative numbers We dre goïng to In this section, you will use negative numbers in contexts such as temperature or being above or below sea level, An iceberg There is much more ice below sea level than there is above sea level The temperature in England is 11°C The temperature in Iceland is 15° colder What is the temperature in Iceland? deel 15 + la mois ey, 1011 Answer: The temperature in Iceland is ~4°C Draw a number line to help Startat 11 The temperature is colder, so you jump back 15 places 17 > Numbers and the number system Exercise 1.2 Look at the number line Tứ tr — T T—T -10-9 -8 -7 -6 -5 -4 -3-2-1 6789 ‘these moves line ‘Write where you would land on the number rete a start count on start countback © start ® count on start @ ‘© Hereis a number line B | ¬ A count back @