CARIBBEAN Primary MATHEMATICS Second edition Student's Book 5 Laurie Sealy and Sandra Moore
Macmillan Education Between Towns Road, Oxford, OX4 3PP A division of Macmillan Publishers Limited Companies and representatives throughout the world www.macmillan-caribbean.com ISBN: 978-0-230-40121-1 Pack ISBN: 978-0-230-42910-9 CD ISBN: 978-0-230-42911-6 Text Laurie Sealy 2012 Design and illustration Macmillan Publishers Limited 2012 First published in 2005 This edition 2012 All rights reserved; no part of this publication may be reproduced, stored in a retrieval system, transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publishers. These materials may contain links for third party websites. We have no control over, and are not responsible for, the contents of such third party websites. Please use care when accessing them. Designed by Oxford Designers and Illustrators Typeset by Orchard Publishing, South Africa Illustrated by Oxford Designers and Illustrators, Beehive Illustration and Tek-Art Cover design by Oxford Designers and Illustrators Cover illustration by Clive Goodyer The authors and publishers would like to thank the following for permission to reproduce their photographs: Alamy/Michael Dwyer p205, Alamy/James Jackson p14, Alamy/Motoring Picture Library p128; Corbis/Francesco Venturi p15; Science Photo Library/Babk Tafreshi p18; Superstock p129, Superstock/Nora Scarlett p168. Printed and bound in Malaysia 2016 2015 2014 2013 2012 10 9 8 7 6 5 4 3 2 1
Note to parents An examination year can be challenging to parents as well as students. Encouraging students to take the time to think and building their confidence through reminding them of what they already know are two helpful steps. If students learn Mathematics through connecting these skills to practical activities and situations, they will see and use it in a natural and useful way that extends beyond the classroom or examinations. Parents can help students build their mathematical reasoning skills and their understanding of the concepts of Mathematics by supporting them as they learn. Ask questions to help children think mathematically. Children need to be encouraged to ask questions, to notice details and to talk about what they know without fear of being wrong. When doing word problems, students who ask questions, and discuss what they know and what they need to find out, build confidence that allows them to try different approaches or methods. Often, a strategy or concept learnt in one area might be useful in another area, so connections and exploration are very important. The Student s Book contains many features useful for revision in an examination year. There are Challenge questions to push a student s thinking and stimulate learning, and features that help build mathematical vocabulary or highlight key points to remember. There are also Hint and Strategy features that help students develop critical thinking. Many adults grew up with the idea that there were rigid procedures about how Mathematics must be taught. Partly as a result, Mathematics seemed hard and fear of failure was high. Now we understand that it is better to encourage students to try different approaches and to talk about their reasoning, especially in problem solving. Students today are sometimes encouraged to work with a partner or a group and to use the language of Mathematics in everyday ways. Working together, trying out different ideas or strategies, giving reasons why the final answer makes sense, these are all important life skills that start at an early age. They also lay a strong foundation for the higher Mathematics of secondary school and augur well for success in examinations. One of the best ways you can help with homework is to talk with your child about whether answers make sense and are accurate. Often, successful strategies involve drawing pictures or diagrams, which may be unfamiliar to parents compared to traditional approaches. However, the most successful strategies are those that give precise, accurate results and are well understood by the child. Every child learns differently and teachers offer more than one approach to help all students understand. The Bright Sparks Workbook ties directly to the lessons in class from the Student s Book and includes related unit numbers. Looking over the Student s Book and reviewing the examples there can help students to recall the lesson from class and stimulate their thinking. The Student s CD gives extra practice on key mathematical ideas for this year group. Students are given different styles for presenting answers, which keeps it interesting, as well as several questions that are a challenge. Curiosity, asking questions, not being afraid to try out an idea these are the traits that encourage children to love Mathematics and to be successful.
Contents Scope and sequence 6 How to use Bright Sparks for students 8 Introduction for teachers 9 How to use this CD-ROM 10 Unit 1: Number 1.1 Place value 11 1.2 Value 16 1.3 Expanded form 16 1.4 More expanded numbers with regrouping 20 1.5 Strategy: Forming numbers 21 Assessment 1 22 Unit 2: Patterns, sequence and order 2.1 Ordering numbers 24 2.2 Counting and ordering 25 2.3 Problem solving 26 2.4 Patterns 27 2.5 Revision 28 Unit 1 and Unit 2 check and summary 29 Unit 3: Operations addition and subtraction 3.1 Estimation skills 30 3.2 Properties of addition 32 3.3 Addition with regrouping 33 3.4 Adding large numbers 34 3.5 Subtraction practice 35 3.6 Subtracting large numbers 36 3.7 Regrouping with zeros 37 3.8 Adding and subtracting money 38 3.9 Subtraction practice 38 Unit 3 check and summary 40 Assessment 2 41 Unit 4: Decimals 4.1 Types of numbers 43 4.2 Tenths 44 4.3 Place value: hundredths 45 4.4 Decimals and whole numbers 46 4.5 Rounding decimals 46 4.6 Value 47 4.7 Ordering and comparing decimals 48 4.8 Rounding and estimating decimals 49 4.9 Addition and subtraction of decimal numbers 50 4.10 Problem solving 52 4.11 Group project: A new computer 53 Unit 4 check and summary 54 Assessment 3 55 Unit 5: Multiplication 5.1 Multiples 57 5.2 Multiplication speed tests 59 5.3 Arrays 60 5.4 Square numbers 61 5.5 Square roots 62 5.6 Problem solving: Mental computation 63 5.7 Multiplying large numbers mentally 64 5.8 Multiplying 3-digit numbers 65 5.9 Multiplying large numbers 65 5.10 Multiplying by multiples of 10 66 5.11 Multiplying by 2-digit numbers 67 5.12 Problem solving 68 5.13 Multiplication practice 69 Unit 5 check and summary 70 Assessment 4 71 Unit 6: Division 6.1 Factors 73 6.2 Divisibility 75 6.3 Division: review 77 6.4 Using opposites: multiplication and division 78 6.5 Division speed tests 79 6.6 Division with remainders: review 80 6.7 Dividing larger numbers 81 6.8 Problem solving 82 6.9 Division using zeros 83 6.10 Using long division and zeros 84 6.11 Division with money 85 6.12 Using a calculator 86 6.13 Dividing by 2-digit numbers 87 6.14 Problem solving 89 6.15 Long division practice 90 Unit 6 check and summary 91 Assessment 5 92 Unit 7: Fractions 7.1 Least (Lowest) Common Multiple 94 7.2 Greatest Common Factor (GCF) / Highest Common Factor (HCF) 95 7.3 Prime factors 96 7.4 Common fractions (or proper fractions) 97 7.5 Adding fractions 98 7.6 Decimals and fractions 98 7.7 Equivalent fractions 99 7.8 Reducing fractions to their simplest form 98 7.9 Estimating fractions 100 7.10 Improper fractions and mixed numbers 101 7.11 Equivalent fractions 102 7.12 Comparing fractions 102 7.13 Adding fractions 103 7.14 Subtracting fractions: review 104 7.15 Subtracting fractions with unlike denominators 105 7.16 Estimating and problem solving 106 7.17 Mixed numbers 107 7.18 Subtracting mixed numbers 107 7.19 Problem solving 109 7.20 Practice 110 7.21 Enrichment: Cross multiplication 111 7.22 Working with calculators 113 Unit 7 check and summary 114 Assessment 6 115 4 Contents
Unit 8: Geometry 8.1 Lines 117 8.2 Angles 119 8.3 Measurement of angles 121 8.4 Triangles 122 8.5 Polygons 123 8.6 Naming plane (2D) shapes 124 8.7 Describing movement 125 8.8 Circles: review 126 8.9 Symmetry 127 8.10 Solid (3D) shapes: review 129 8.11 Making nets 130 8.12 Coordinates 131 8.13 Perimeter: Review 132 8.14 Perimeter problem solving 134 8.15 Area and perimeter: review 135 8.16 Calculating area 136 8.17 More area problems 138 8.18 Enrichment: Area of irregular shapes 139 8.19 Area of triangles 140 8.20 Volume 141 Unit 8 check and summary 142 Assessment 7 143 Unit 9: More decimals 9.1 Multiplying decimal numbers 147 9.2 Division by a whole number 148 9.3 Adding zeros to the dividend 149 9.4 Multiplying and dividing decimals by 10, 100, 1000 150 9.5 Enrichment: SI, the metric system 151 9.6 Metric conversions 152 Unit 9 check and summary 154 Unit 10: Measurement 10.1 Units of length 155 10.2 Longer lengths: review 155 10.3 Working with units of length 156 10.4 Practice with longer units of length 157 10.5 Mass 157 10.6 Converting between units of mass 158 10.7 Capacity: review 159 10.8 Converting between units of capacity 160 10.9 Mixed units 160 10.10 Problem solving: different units of measurement 161 Unit 10 check and summary 162 Unit 11: More fractions 11.1 Multiplying fractions 163 11.2 Multiplying whole numbers and mixed numbers by fractions 164 11.3 Cancelling 165 11.4 Drawing a sketch 166 11.5 Dividing fractions 167 11.6 Mixed multiplication and division of fractions 168 11.7 Mixed problem solving 169 11.8 Teamwork: Measurement game 170 Unit 11 check and summary 171 Assessment 8 172 Unit 12: Percent, ratio and proportion 12.1 Percent 174 12.2 Percent and decimals 174 12.3 Percent, decimals, and fractions 175 12.4 Finding the percent of an amount 176 12.5 Problem solving 177 12.6 Comparing fractions 178 12.7 Practice with percent 179 12.8 Activity: Dominoes game 180 12.9 Discount 181 12.10 Problem solving 182 12.11 Wages and salaries 183 12.12 Simple interest 184 12.13 Ratio 185 12.14 Simplifying ratios 186 12.15 Proportion 187 12.16 Working with scale 189 12.17 Problem solving: fractions, ratios and percents 190 Unit 12 check and summary 191 Assessment 9 192 Unit 13: Measurement time 13.1 Review 194 13.2 Enrichment: 24-hour system 194 13.13 Calculating elapsed time 195 Unit 14: Statistics, data and probability 14.1 Finding the mean 199 14.2 Working with the total 200 14.3 Interpreting data and drawing graphs 201 14.4 Making graphs / frequency charts 202 14.5 Enrichment: Interpreting data with a line graph 202 14.6 Circle graphs (pie charts) 203 14.7 Interpreting the circle graph 204 14.8 Using percentages in circle graphs 205 14.9 Probability 206 14.10 Enrichment: Introduction to sets 206 14.11 Enrichment: Types of sets 208 14.12 Displaying data in Venn diagrams 208 14.13 Practice with sets 209 Unit 13 and Unit 14 check and summary 210 Assessment 10 211 Final assessment 1 213 Final assessment 2 217 Final assessment 3 221 Index 224 Contents 5
Scope and sequence Major concept Number Patterns, functions, algebra Operations and relations Money skills Measurement Knowledge and skills Apply counting skills to practical situations Count numbers between two numbers Use ordinal numbers to 100th Read/write numbers to 100000 State the value or place value to 5 digits Write expanded forms for up to 5-digit numbers Write and name decimals to two places Compare and order 1- to 5-digit numbers Recognise and extend patterns in a series of numbers or shapes Calculate missing values in sequences Work with problems involving consecutive numbers or patterns (poles and spaces) Discuss patterns and generalise Create a pattern with up to 5 variables Solve for the unknown represented by a symbol x or variable (n) Substitute values for n in a simple function input/output model Write equations to represent word problems and vice versa Mentally add 2-digit numbers Add up to 5-digit numbers with or without regrouping Mentally subtract from a 1- or 2-digit number from a number up to 100 Subtract up to 5-digit numbers, with or without regrouping Multiply 1- to 3-digit numbers by multiples of 10 Multiply a 1- to 3-digit number by a 1- or 2-digit number, with or without regrouping State and use the times tables to 12 List multiples of a 1-digit number and find the LCM of 2 or 3 whole numbers by listing multiples Divide a 1- to 5-digit number by a 1- or 2-digit numbers using more than one algorithm Deal with the remainder in reasonable ways during problem solving List factors of numbers and explain what they are, and find the GCF/HCF of 2 or 3 numbers Estimate reasonable results to practical situations Round numbers to 4 digits Use rounding skills to estimate and check results Add, subtract and multiply decimal numbers Apply skill with operations to problem solving involving more than one operation Explain why a solution is reasonable Demonstrate skill using a calculator for all four operations Use mathematical language Use mental Mathematics strategies demonstrating number sense Explain problem-solving approaches used and justify answers Use arithmetic skills to complete fact families using addition and subtraction / multiplication and division Compare addition and subtraction inverse processes Compare multiplication and division inverse processes Add a series of numbers, combining to make multiples of 10 Recognise commutative, identity properties of + and Explore the associative and distributive properties of + and Use the distributive property of multiplication to solve equations Use the calculator to add, subtract, multiply dollars and cents Round money to the nearest dollar and estimate total cost Find total cost and make change from $100 Calculate profit and loss Calculate simple hire purchase costs Calculate VAT or tax in simple problems Describe and use notes/bills circulating in own country ($1), $5, $10, $20, ($50), $100 Add, subtract, multiply or divide money using the decimal point, with or without renaming Estimate the total cost of several items given the unit cost, or the rate Review: tell the time in hours and minutes Record time in hours and minutes, and with 24-hour clocks Add, subtract, multiply hours and minutes Discuss and calculate elapsed time, using days, hours or minutes, Convert hours to minutes and minutes to hours Use measurement in problem solving and practical situations Estimate, measure and record lengths using m, cm, mm (metre stick and ruler) Compare lengths using mm, cm, m, km Round to nearest cm or 5 mm 6 Scope and sequence