CARIBBEAN Primary MATHEMATICS Second edition Student's Book 3 Laurie Sealy and Sandra Moore BRIGHT SPARKS SB3 prf4.indd 1
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: 978-0-230-40115-0 Pack ISBN: 978-0-230-42867-6 CD ISBN: 978-0-230-42868-3 Text Laurie Sealy and Sandra Moore 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 & Illustrators and Macmillan Education Typeset by Orchard Publishing, South Africa Illustrated by Oxford Designers & Illustrators, Clive Goodyer & 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/VStock p74, Alamy/Dennis Cox p149; Norman Livingstone pp13, 14, 36, 100, 131; Laurie Sealy p 67; Studio8 pp 64, 83, 86, 166; Tips Images/Guido Alberto Rossi p 92. Printed and bound in Malaysia 2016 2015 2014 2013 2012 10 9 8 7 6 5 4 3 2 1 BRIGHT SPARKS SB3 prf4.indd 2
Note to parents Children learn Mathematics best when they are encouraged to use it in the world around them. For example, if children point to each button as they count from 1 to 20, it is much better than simply reciting the words one to twenty. If students start to learn to add by using objects which they see and feel, and by talking about what they are doing, they will learn to add mentally in a way that will be useful. The written number sentence, such as 5 + 6 = 11, should only be taught later, after their understanding of the concept is strong. The same is true for other concepts in Mathematics. First we build understanding, and then we practise the written form. Parents can help students build their mental Mathematics skills, and their understanding of the concepts of Mathematics, by encouraging them to use their senses as they learn. When walking, help children notice and name the shapes you see. Ask questions to help children think mathematically. For example, draw a circle and look at a ball. Talk about how both the circle and ball are round, but the circle is a flat shape (2D). Ask how the ball is different. In ways such as these, children need to be encouraged to ask questions, to notice details, and to talk about what they know without fear of being wrong. Make up games when you go out, such as counting the number of light poles along a certain road. Or, you might start at ten, and count back one each time you see a white car, trying to see who gets to zero soonest. In this way the concept of zero and the early steps towards subtraction are both practised, in a fun way. 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 explore 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. When you help your child with homework, talk about ideas and what makes sense. Use objects, draw pictures or diagrams, and be encouraging. Homework in the Bright Sparks Workbook ties directly to the lesson that would have been done in class using the Student s Book. Looking over both together can help students recall the lesson and their steps of understanding. The Student s CD gives extra practice on key mathematical ideas for this year group. Students are given different activities, which keeps it interesting, and have challenges to stretch their learning. Curiosity, asking questions, not being afraid to try out an idea these are the traits that encourage children to love Mathematics and be successful. BRIGHT SPARKS SB3 prf4.indd 3
Contents Scope and sequence 7 How to use Bright Sparks for students 9 Introduction for teachers 10 How to use this CD-ROM 11 Unit 1: Patterns and numbers Counting in twos 13 Counting in threes 14 Counting in 5s 15 Counting in 10s 15 Number patterns 16 Continuing sequences 17 More number patterns 18 Comparing numbers 19 Equal numbers 20 Comparing: practical situations 21 Sets 22 Odd and even numbers 23 Counting on: practical situations 24 Working backwards 25 Writing number words 26 Ordinal numbers 27 Unit 1 Check and summary 28 Assessment 1 29 Unit 2: Number Place value 31 Value 33 Expanded numbers 34 Expanded numbers practice 35 Rounding 36 Rounding cents to the nearest ten 37 Rounding to the nearest hundred 37 Rounding to the nearest dollar 38 Making ten 39 Simple addition 40 Algebra missing addends 41 Unit 2 Check and summary 42 Assessment 2 43 Unit 3: Operations addition and subtraction Addition regrouping tens 45 Addition regrouping tens in 3-digit numbers 46 Subtraction review 47 Algebra missing numbers 48 Subtraction with 2-digit numbers 48 Practise regrouping 49 Subtraction with regrouping 50 Subtraction with hundreds regrouping hundreds 52 Subtraction practice 53 Addition and subtraction practice 53 Fact families for + and 54 Problem solving 56 Unit 3 Check and summary 57 Assessment 3 58 Unit 4: Operations multiplication Calculator fun 60 Multiplication times 61 2-digit multiplication 62 Multiplication with regrouping 63 Multiplying by 3 64 Multiplying by 4 65 Multiplying regrouping to hundreds 66 Multiplying by 5 67 Multiplying by 10 68 Multiplying using arrays 69 Multiplying 6, 7, 8 and 9 (Enrichment) 70 Problem solving 71 Unit 4 Check and summary 72 Unit 5: Operations division Division as sharing 73 Division as grouping 75 Dividing a 2-digit number by 2 77 Dividing with a remainder 78 Dividing by 2 regrouping tens 79 Problem solving 80 More regrouping tens 81 Dividing by 3 82 Dividing a 2-digit number by 3 83 Mixed problems 84 Dividing by 3 with a remainder 85 4 Contents BRIGHT SPARKS SB3 prf4.indd 4
Dividing by 4 86 Dividing by 5 87 Dividing by 4 and 5 using columns 88 Dividing by 4 and 5 with a remainder 89 Fact families for and 91 Unit 5 Check and summary 93 Assessment 4 94 Unit 6: Money Money overview 96 Finding the total coins 97 Drawing coins 98 Finding the total notes 99 Writing sums of money 100 Drawing change and totals 101 Shopping practice 102 Spending money 104 Making change from $10 or $20 105 Practice making change 106 Larger notes 107 Rounding cents to the nearest dollar 108 Calculator activities money 109 Unit 6 Check and summary 110 Assessment 5 111 Unit 7: Geometry Congruence 113 Lines of symmetry 114 Drawing symmetrical shapes 116 Lines and angles 117 Right angles 118 Plane shapes (2D) 119 Identifying plane shapes (2D) 120 Solid shapes (3D) 121 Solid shapes cylinders and spheres 122 Solid shapes properties 123 Solid shapes in the environment 124 Unit 7 Check and summary 125 Unit 8: Measurement Distance 126 Practical measurement 127 Estimating and measuring distance 128 Practice with distance 129 Capacity 130 Practice with capacity 131 Mass 132 Practical activity: mass 133 Customary and metric units (Enrichment) 134 Temperature 135 Unit 8 Check and summary 136 Assessment 6 137 Unit 9: Measurement perimeter and area Perimeter 139 Measuring perimeter 140 Perimeter practical situations 141 Area 142 Area in cm 2 143 Area practice 144 Assessment 7 145 Unit 10: Measurement time Making clocks 147 Writing the time 147 Quarter past the hour 148 Quarter to the hour 149 Writing quarter to 150 Practice 151 Understanding time in practical terms 152 Calendar: months 153 More calendar and time 154 Units 9 and 10 Check and summary 155 Unit 11: Statistics Collecting information from interviews 156 Pictographs 157 Collecting information from observations 158 Making a table 159 Block graphs 160 Making a block graph 161 Contents 5 BRIGHT SPARKS SB3 prf4.indd 5
Reading bar graphs (Enrichment) 162 Making a bar graph 163 Assessment 8 164 Unit 12: Fractions Parts of a whole 166 Part of a group 167 Part of a set 168 Equivalency 169 Comparing fractions 170 Ordering fractions 171 Adding fractions 172 Adding and subtracting fractions (Enrichment) 173 Units 11 and 12 Check and summary 174 Assessment 9 175 Final assessments 177 Self-check progress graph 183 Index 184 6 Contents BRIGHT SPARKS SB3 prf4.indd 6
Scope and sequence Major Concept Sub-concepts Knowledge and Skills Number Patterns, Functions, Algebra Operations and Relations Money Skills Counting and Naming Place Value / Value Ordering, Comparing Rounding Relations Operations (computation) addition subtraction multiplication division Estimation Count / write numbers to 100 Write numbers less than 100 using numerals and words Apply counting skills to practical situations Use ordinal numbers 1st to 99th State the value (total value) of a numeral in a 3-digit number Name the place value to 1000 Write 2-digit and 3-digit numbers in expanded form Compare and order 1- to 3-digit numbers Identify and order odd and even numbers Compare 1- to 3-digit numbers using <, =, > Use skill of more/less (fewer) in practical situations Round to nearest ten or hundred Round money to the nearest dollar Recognise and extend patterns in a series of numbers or shapes Recognise and complete odd/even patterns ascending or descending Calculate missing values in sequences (counting in 2s, 5s or 10s) Skip count to 100 Create a pattern with 3 to 4 variables Solve for unknown represented by a symbol Use mental Mathematics strategies demonstrating number sense Use operations to solve simple word (story) problems Use arithmetic skills to complete fact families using addition and subtraction, multiplication and division Compare addition and subtraction processes Compare multiplication and division processes Explain multiplication using an array model, and as repeated addition Understand division using a repeated subtraction model Demonstrate skill at using a calculator to solve simple equations with addition and subtraction Combine numbers to make 10s in a series of three 1-digit numbers Use the commutative property of addition Mentally complete addition pairs up to a sum of 20 Add 1- to 3-digit numbers with or without regrouping up to a total of 999 Mentally complete subtraction pairs up to 20 Subtract 1- or 2-digit numbers from 2- or 3-digit numbers, with or without regrouping Multiply a 2- or 3-digit number by a 1-digit number, with or without regrouping State and use multiplication (times) tables of 1, 2, 3, 4, 5, (6), 10 Use a division algorithm to divide a 2-digit number by 2, 3, 4, 5, (6) Estimate a reasonable answer to a simple word problem Use rounding skills to estimate and check answers in calculations Recognise the use of money in shopping situations Recognise and calculate with coins in use in own country 1, 5, 10, 25, (50 ), $1 Combine coins up to 100 cents Recognise and use ($1), $5, $10, and $20 notes/bills Combine notes/bills up to $100 Write the notation for a sum of money under $5 Use a calculator to add or subtract dollars Round to the nearest dollar and estimate total cost Calculate change from totals up to $20 Calculate total cost (coins and bills) Show equivalence using notes/bills up to $100 Scope and sequence 7 BRIGHT SPARKS SB3 prf4.indd 7
Major Concept Sub-concepts Knowledge and Skills Measurement Time Distance Area Mass Tell the time to the hour, half hour, quarter hour (to and past) Fill in the clock face for a given time Discuss and calculate elapsed time one hour before, or after Know the months of the year, and how to write the date Know days of the week Use a ruler or metre stick to correctly measure to the nearest cm, m Compare lengths using cm, m Explain and calculate perimeter, measuring sides Count squares to determine area on a square centimetre grid Use a balance to compare which object is heavier, using non-standard, and standard units of mass Choose appropriately when to use g or kg with practical objects Compare mass using 1 kg, 2 kg, 1 1 4 kg, 2 kg and a balance scales Geometry Fractions Statistics and Probability Capacity Use 1 l, 2 l, Temperature 1 4 l, 1 2 l to measure and compare the capacity of containers Describe and compare recorded temperatures (e.g. ice) Discuss customary units of measurement Recognise angles in plane figures, identifying those smaller, the same or larger than a right angle Identify lines, curves, open and closed shapes Recognise, describe and name plane figures (circle, square, rectangle, triangle) Recognise and compare solid shapes (sphere, cube, cuboid, cone, cylinder) Identify solid shapes in the environment Make models of solid shapes from nets Describe the faces on solid shapes and compare to plane figures Count the faces, (edges) (vertices) on solid (3D) shapes Compare flat surfaces, using tessellation Recognise and draw a line of symmetry in plane figures (one line) Recognise congruence in simple plane figures Explore and predict with simple transformations (flip, slide) Understand the concept of a fraction, and name the numerator or denominator Recognise and name fractions as parts of a whole or group Fold, cut, draw equal parts in a whole Shade parts of a whole to a given unit fraction Name the fraction represented in a set of objects Compare fractions using models Add, subtract fractions with like denominators, using manipulation if needed Identify and solve real-world problems using fractions Discuss data collected through observations and interviews Use tally chart and frequency tables to record data Understand how data is represented on pictographs, block graphs and bar graphs Use a key representing more than one unit in graphs Choose and draw graphs to represent data collected Discuss, read and interpret information displayed in these graphs Decide if something is possible or impossible, given different scenarios of probability 8 Scope and sequence BRIGHT SPARKS SB3 prf4.indd 8
How to use Bright Sparks for students Your book is set out in units. The unit headings tell you the topic. The lesson title is given blue. You can also use the table of contents or the index to find a particular skill. Unit 2: Number and operations You find explanations in green boxes at the beginning of the lesson. Green example boxes show you a question, and how it is solved. Words that you will need to use when talking about Mathematics are in Mathematical language boxes. Challenge boxes have questions that are a little harder, sometimes like a puzzle that not everyone will be able to solve. tells you where you can find extra activities in the CD-ROM, and tells you when you might use a calculator. Hint / THINK boxes help you build your mental Mathematics and problemsolving skills. Review boxes allow you to revisit topics. Remember boxes have important ideas to keep in mind. Discuss boxes give you a chance to talk over your ideas, and to explain your reasoning or your strategies. Activities and Partner Activities give you a fun chance to practice your skills. Enrichment pages and Enrichment boxes show you extra topics connected to the Mathematics you are learning. Summary boxes list the key points you need to learn. Check up tests you on the unit. Use the Summary box when you revise your work. Keep track of your scores on all of the Check ups and Assessments and compare them to see where you are strong. Assessments are spaced throughout the book in different ways, with final assessments at the end. How to use Bright Sparks for students 9 BRIGHT SPARKS SB3 prf4.indd 9
Introduction for teachers Through real-life situations and everyday problems, Bright Sparks builds an understanding of Mathematics as a worthwhile and purposeful skill, and as an integrated way of thinking. It encourages discussions of mathematical concepts, and provides opportunities to use variety in problem-solving approaches to form the basis for discovery, reasoning and learning. The confidence and skills that students build through these practices strengthens their ability to use Mathematics comfortably, and allows them to apply their learning in multiple situations. The teamwork and listening skills they practise during mathematical discussions enhance their ability to reason mentally, and to appreciate thinking approaches different from their own. Research on brain development suggests that what is already known about the topic needs to be stimulated, recalled and reviewed before new knowledge can be successfully introduced. In this way, the new information fits into a pattern of existing understanding and prior knowledge, and is more readily available to the student in future. This sequential developmental model is the structural framework for the Bright Sparks series. The liberal use of explanations and examples allows students the opportunity to practise on their own. For homework, parents are able to use the examples as models, if needed. The problem-solving abilities, developed through finding solutions to real-world situations, can be easily transferred to other subject areas and life situations. Bright Sparks engages Caribbean students through the use of culturally and geographically familiar word problems, appropriate to the students age. Students like the colourful and interesting design, and the Challenge boxes are particularly popular. The new edition adds photographs to further stimulate interest and icons to suggest where technology can be used. Consistent colours are used for each feature. What is new in Bright Sparks 2nd editions: Caribbean teachers are benefitting from new research in Mathematics education. Curricula are expanding and changing, and as in the case of the OECS, there is a new and harmonised vision for Mathematics learning. The second edition takes these various changes into account and offers a fuller and wider curriculum, with the scope and sequence for each level included. The exercises are set out so teachers can use all or only a part of each concept area, based on their needs. The teaching stories shared by teachers in workshops throughout the region have been heard and specifically addressed in the new editions. For example, the books have more fraction practice exercises and models. The newly added Teacher s Books, and the Teacher Resource website, provide practised lesson ideas for active learning. They include extensions, differentiated approaches and games to encourage and support teachers in using activities to reinforce and practise Mathematics in a variety of ways. Each Student s Book above the K level has a CD-ROM included, with many varied activities, utilising different learning styles. The Workbooks are now expanded and carefully crossreferenced to the Student s Books to make them easier to use for practice and homework. Workbooks 1 and 2 have been added for the Infant years, and Book K is now KA and KB with a range of learning to fit Early Childhood Education needs. 10 Introduction for teachers BRIGHT SPARKS SB3 prf4.indd 10
How to use this CD-ROM Insert the disk in the disc drive. When the Autoplay box opens, use the mouse to click on Run. The title page will open. Click the number in the centre. Choose a unit topic. Click on the letter. Choose a topic. Click on the name. If there is a drop-down box, click on the arrow. Then select your choice. Sometimes there are lines to match. Click on a box, then click your answer and the line will show. Sometimes you need to click the answer and drag it to the correct spot. Or, if there is a box to check, you just click the answer once. Sometimes you need to click on a box and enter your answer. Lastly, click Check. See if you have all answers correct. If you have something to change, it will show you. If you have all correct, you will hear clapping. Then click OK and Back to choose a new topic, or Quit to leave. How to use this CD-ROM 11 BRIGHT SPARKS SB3 prf4.indd 11
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Unit 1: Patterns and numbers Counting in twos Use squared paper and copy the number square, or use the one in Workbook 3. Colour every second number, starting with 2. Look at the pattern you have made. The numbers coloured are all even numbers. Practise counting using only these numbers. You are counting in twos. 1.1 1 The first coloured number is. 3 The second number coloured is. 2 The third coloured number is. 4 The tenth number coloured is. Fill in the missing numbers: 5 2, 4, 6,,, 12 8 86, 84, 82,,, 6 20,,, 26,, 30 9 90,,, 96,, 7 42, 44,, 48,, 52 10 50, 48,,, 42, Unit 1: Patterns and numbers 13 BRIGHT SPARKS SB3 prf4.indd 13
Counting in threes Take your number square and circle every third number, starting with 3. Look at the pattern. Is it different from the pattern when counting in twos? How is it different? Practise counting in threes. 1.2 1 The fifth number coloured is. 3 Is the number 55 coloured? Yes / No 2 The last number coloured is. 4 Is the number 63 coloured? Yes / No Fill in the missing numbers: 5 3, 6,, 12,, 18 8 42, 45,,, 54, 6 30,, 36, 39,, 9 51,, 45,, 39, 36 7 18,,, 27,, 33 10 99, 96,,, 87, 84 14 Unit 1: Patterns and numbers BRIGHT SPARKS SB3 prf4.indd 14
Counting in 5s Copy the number square on page 13 and colour every fifth number. Start with the number 5. Look at the pattern you made this time. Count using only these numbers. You are counting in 5s. 1.3 1 All the coloured numbers end with either or. 2 The fifth number coloured is. 3 The tenth number coloured is. 4 Is the number 51 coloured? Yes / No Fill in the missing numbers: 5 5, 10,, 20, 25, 8 85,, 75,, 65, 6 60, 55,,, 40, 35 9 50, 55,,, 70, 75 7 20, 25, 30,,, 10 100, 95,,,, 75 Counting in 10s On the same number square used for counting in 5s, circle each number for counting in 10s. Start with 10. It will already be coloured. Practise counting in 10s. 1.4 1 10,, 30,,, 60 6 comes before 100. 2,, 80,,, 50 7 comes before 60. 3 comes after 50. 8 comes after 40. 4 comes before 90. 9 All of these numbers end with. 5 comes between 20 and 40. 10 The number after 100 will be. Challenge Why are the 10s already coloured in this square? Unit 1: Patterns and numbers 15 BRIGHT SPARKS SB3 prf4.indd 15