Pupil s Book 0.2 Maths 5A 3rd Edition 2O% OFF Dr Fong Ho Kheong Gan Kee Soon Chelvi Ramakrishnan APPROVED BY MINIS OF EDUCATION for use from 207 202
Preface My Pals Are Here! Maths (3rd Edition) is a comprehensive, task-based and learner-centred programme designed to provide pupils with a solid foundation in mathematics and opportunities to become efficient problem solvers. My Pals Are Here! Maths (3rd Edition) continues to make learning mathematics fun and rewarding through the use of engaging illustrations, photographs, hands-on activities and interactives that help reinforce and consolidate learning for pupils of different abilities. A calculator may be used when For the Pupil: A Multiply 2 3 by 3. Express your answer as a mixed number. Then, check your answer using a calculator. appears. NEW! Practise new concepts learnt in parallel questions with help from your teacher in! Put On Your Thinking Cap! Anna cycled from school to home. She stopped by the post office, then went back to the mall to buy lunch. She then headed home from the mall. Use the following clues to find how far Anna s home is from her school. School Mall Post office Home 2 3 3 3 2 3 3 3 5 B Multiply. Express your answer in its simplest form. a 3 5 6 3 2 5 b 4 3 2 3 5 5 c 3 4 3 8 5 d 28 3 5 2 7 5 e 2 5 9 3 6 5 9 f 2 3 7 5 Challenge yourself to solve non-routine questions by applying relevant heuristics and thinking skills in Put On Your Thinking Cap! The post office is 2 2 km from Anna s school. 5 The mall is km from the post office. Anna s home is 2 3 km from the mall. 2 Rehna spent 5 of her money on 8 pencils and 2 markers. The cost of each marker is twice the cost of each pencil. She bought some more markers with 5 of her remaining money. How many markers did Rehna buy 8 altogether? 3 Andrea has a box of coins. She wrote down the number of coins she has but spilled her drink over her paper. Maths Sharing The model shows 4 2. Express a mixed number as a product. a Express this mixed number as a product of another mixed number and a whole number. 4 2 5 3 2 b Use the same method to find the missing mixed number below. 8 4 5 3 2 Share with your partner how you found the missing mixed numbers. 82 Chapter 4 Multiplication of Whole Numbers, Fractions and Mixed Numbers Workbook A: Practice 3, pages 55 56 Chapter Wrap-Up Coin Number of Coins 20 9 50 However, she knows that 3 of her coins are 50 and the rest are 20 coins. Also, she has more than 50 but fewer than 0 coins. How many coins does she have? Big Idea The area of a triangle is given by half the product of a base and the corresponding height. Workbook A: Put On Your Thinking Cap! pages 83 84 Review 2, pages 85 88 Chapter 5 Fractions: Word Problems NEW! Share your thoughts with your teachers, create your own mathematics questions and become aware of your own mathematical thinking in Maths Sharing! Consolidate the concepts you have learnt in each chapter in Chapter Wrap-Up! Base and Height Any side of a triangle can be its base. The height is perpendicular to the base. Example A B height C Z base Area of a Triangle Finding the Area Composite Figures The area of a triangle We can find the area is half the area of a of a composite figure rectangle with the by dividing it into same base and rectangles, squares or height or 2 3 base 3 triangles. height. F 4 cm E 2 cm G D Area of triangle DEF 5 3 Area of 2 rectangle DEFG 5 3 EF 3 DE 2 5 3 base 3 height 2 5 2 3 4 3 2 5 4 cm 2 E D A 8 cm B C 3 cm 4 cm Area of figure ABCDE 5 Area of rectangle BCDE Area of triangle ABE Area of rectangle BCDE 5 8 3 4 5 32 cm 2 Area of triangle ABE 5 2 3 8 3 3 5 2 cm 2 Area of the figure 5 32 2 5 44 cm 2 6 Chapter 6 Area of a Triangle
4 Chapter For the Teacher: Multiplication of Whole Numbers, Fractions and Mixed Numbers This recipe serves. How can I f ind the amount of each ingredient for 3 servings? NEW! Use scenarios pupils can relate to in the chapter openers to capture their interest, provide an engaging introduction to the topics and jump-start learning. NEW! Introduce concepts through context-based tasks in Before you learn. At the end of each task, a question is posed to develop pupils creative and critical thinking skills. Lessons Product of a Fraction and a Whole Number and a Whole Number 2 Product of Two Fractions 3 Product of a Mixed Number Big Idea Whole numbers, fractions and mixed numbers can be multiplied in any combination. Teach concepts in concise steps using real-life contexts, manipulatives and meaningful visuals in LEARN. 3 Lesson Order of operations LEARN Order of Operations Before you learn... Ally and Joe worked out the value of the expression 8 20 4 4 2 2. Ally s answer was 5. Joe s answer was. Whose answer is correct? Explain. For the following problems, Ally and Joe solved them differently. Who is correct? a Nellie had stickers. She gave away 4 and bought 5 more. How many stickers did Nellie have in the end? 2 4 5 5? Ally s solution: 2 4 5 6 6 5 5 Nellie had stickers in the end. Joe s solution: 4 5 5 9 2 9 5 Nellie had sticker in the end. Use to check the answer. LearN hands-on activity Work in groups. Station Solve word problems. Read the word problem. Draw a model for the problem. Carry out Hands-On Activity to promote active and collaborative learning. Where possible, pupils will complete station-based activities in rotating groups to best utilise class time. 2 4 5 5 6 5 5 Nellie had stickers in the end. given away bought Lesson 3 Order of Operations 35 example A retailer sold 5 vacuum cleaners. 2 of the vacuum cleaners cost $659 each and the others cost $478 each. How much money did the retailer make from the sale of the 5 vacuum cleaners? $659 $478 Chapter 7 Review? 2 Estimate the answer. 3 Use the model to solve the problem. 4 Compare the answers in 2 and 3 to check for reasonableness. 5 Switch roles. Repeat to 4 with these problems. a Mary bought 24 boxes of beads. Each box contained 245 beads. There were 284 red beads and the rest were blue beads. She used all the blue beads to make 42 bracelets. How many blue beads were used for each bracelet? b Farah baked 72 cupcakes and 55 muffins. She sold 22 cupcakes. She then packed the remaining cupcakes equally into 5 boxes. She gave away 2 boxes of cupcakes. How many cupcakes did she have left? NEW! Assess understanding when pupils apply concepts learnt in Review. The ratio of the number of red caps to the number of black caps is :. The ratio of the number of black caps to the number of red caps is :. 2 Find the missing numbers. a A b A B B A : B 5 : A : B 5 : 3 Express each ratio in its simplest form. a 9 : 6 5 b 8 : 20 : 6 5 44 Chapter 2 Operations of Whole Numbers 4 Find the missing numbers. a 7 : 8 5 2 : b 42 : 49 5 : 7 c 4 : 3 : 7 5 20 : : d 40 : 55 : 5 5 : : 3 42 Chapter 7 Ratio
CONTENTS Whole Numbers 6 Lesson Numbers to Million 7 2 Operations of Whole Numbers 6 Lesson Multiplying by, 0, 00 and Their Multiples 7 Lesson 2 Dividing by, 0, 00 and Their Multiples 27 Lesson 3 Order of Operations 35 Lesson 4 Solving Word Problems 4 3 Fractions and Mixed Numbers 53 Lesson Fractions and Division 54 Lesson 2 Addition of Mixed Numbers 60 Lesson 3 Subtraction of Mixed Numbers 63 4 Multiplication of Whole Numbers, Fractions and Mixed Numbers 70 Lesson Product of a Fraction and a Whole Number 7 Lesson 2 Product of Two Fractions 74 Lesson 3 Product of a Mixed Number and a Whole Number 8
5 Fractions: Word Problems 86 Lesson Solving Word Problems 87 6 Area of a Triangle 2 Lesson Area of a Triangle 3 Lesson 2 Composite Figures 7 Ratio 8 Lesson Finding Ratios 9 Lesson 2 Equivalent Ratios 24 Lesson 3 Comparing Three Quantities 28 Lesson 4 Solving Word Problems 3 8 Volume of Cubes and Cuboids 46 Lesson Volume of a Solid 47 Lesson 2 Drawing Cubes and Cuboids 5 Lesson 3 Volume of a Cube and a Cuboid 59 Lesson 4 Volume of a Liquid 64
Chapter Whole Numbers In the 980s, your grandfather bought a 3-bedroom condominium for $450 000. How much does a 3-bedroom condominium cost now? Type Floor Area (m 2 ) Price ($) 2-bedroom 70 70 000 3-bedroom 93 209 000 4-bedroom 23 599 000 5-bedroom 50 2 080 000 How do I read $ 209 000? Big Idea Lesson Numbers to Million The next two place values after ten thousands are hundred thousands and millions.
Lesson Numbers to Million Reading and writing 6-digit numbers Before you learn... 000 000 There are 47 853 people in a queue. Use 00 000 0 to count aloud 0 000 and show the number of people in the queue. Recall Count in thousands. 00 00 00 00 00 00 00 00 00 00 000 thousands 5 ten thousand LEARN A Count in ten thousands. 000, 20 000, 30 000, 40 000, 50 000, 60 000, 70 000, 80 000, 90 000, 0 000 000 000 000 000 000 000 000 000 000 000 0 000 ten thousands 5 hundred thousand ten thousand 5 thousands ten thousands 5 0 thousands So, hundred thousand 5 0 thousands. LEARN B Count in hundred thousands. 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 000 000 0 000, 200 000, 300 000, 400 000, 500 000, 600 000, 700 000, 800 000, 900 000, 000 000 hundred thousands 5 million hundred thousand 5 0 thousands hundred thousands 5 00 thousands So, 00 thousands 5 million. Lesson Numbers to Million 7
LEARN 0 000 00 000 000 C Count using 000 0. 0 000 000 00 0 0 0 000 000 00 0 0 0 000 000 00 0 0 0 000 00 0 0 0 000 0 Hundred Ten Hundreds Tens Ones 5 3 4 9 2 6 5 hundred thousands 500 000 3 ten thousands 30 000 4 thousands 4000 five hundred and thirty-four thousand 534 926 9 hundreds 900 2 tens 20 nine hundred and twenty-six five hundred and thirty-four thousand, nine hundred and twenty-six 6 ones 6 8 Chapter Whole Numbers
A Write in numerals and in words. 0 000 000 000 00 0 0 0 000 000 000 00 0 0 0 000 000 00 0 0 0 000 000 0 0 0 000 000 0 Numerals: Words: B Write in figures. a six hundred and seventy-three thousand, nine hundred and eleven b c five hundred and eighteen thousand and four two hundred thousand, one hundred and six C Write in words. a 320 76 b 438 830 c 906 095 D Find the missing numbers. a 234 56 5 234 000 b 38 205 5 205 c 482 000 5 482 670 d 780 5 600 780 Lesson Numbers to Million 9
Reading and writing 7-digit numbers Before you learn... Mr Krishnan donated $ 000 000 to a charity. Use 00 000 0 to count 0 000 000 000 aloud and show the amount of money he donated. LEARN A Count in millions. 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 ten millions 000 000, 2 000 000, 3 000 000, 4 000 000, 5 000 000, 6 000 000, 7 000 000, 8 000 000, 9 000 000, 000 000 LEARN 0 000 00 000 000 B Count using 000 0. 000 000 0 000 000 000 00 0 0 000 000 0 000 000 00 0 0 000 000 0 000 000 0 0 000 000 0 000 0 Millions Hundred Ten Hundreds Tens Ones 3 4 6 2 7 5 3 millions 3 000 000 4 hundred thousands 400 000 6 ten thousands 60 000 2 thousands 2000 7 hundreds 700 stands for 5 tens 50 stands for one 3 462 75 three million seven hundred and fifty-one four hundred and sixty-two thousand three million, four hundred and sixty-two thousand, seven hundred and fifty-one Chapter Whole Numbers
LEARN Hands-On Activity Read and write large numbers. Work in groups. 0 000 000 000 Use 00 000 0 to show 458 72. 2 Write in words. Example 3 Switch roles. Repeat and 2 with these numbers. a 543 20 b 359 490 c 645 027 d 2 000 546 A Write in figures and in words. 000 000 0 000 0 000 000 000 0 000 000 0 000 000 000 0 000 000 0 000 000 000 0 0 000 000 000 0 0 000 000 Figures: Words: Lesson Numbers to Million
B Write in figures. a three million, five hundred and sixty-seven thousand and forty-five b c four million, six hundred and five thousand, three hundred and seventy-nine six million, three hundred and twenty-one thousand, five hundred and four C Write in words. a 234 567 b 8 090 909 c 2 653 870 D Find the missing numbers. a 2 300 598 5 2 000 000 598 b 4 26 350 5 26 000 350 c 5 000 000 946 5 5 08 946 d 9 000 000 20 5 9 6 020 Maths Sharing Find examples of numbers in the millions from the Internet and develop a sense of the size of million. Search the Internet for the seating capacity of the Singapore Indoor Stadium. Imagine that a new indoor stadium with a seating capacity of 000 000 will be built. How many times as large as the Singapore Indoor Stadium will the new indoor stadium be? Discuss. 2 Chapter Whole Numbers
2 Look up the Internet for three different examples of numbers in millions up to million. Example The population of Singapore was 5 076 700 in 20. Discuss. Chapter Review Workbook A: Practice, pages 5 6 Write in numerals. a three hundred and seventy-six thousand, two hundred and fourteen b seven million, four hundred and fifty thousand, nine hundred and eighty-six 2 Write in words. a 872 649 b 5 380 70 3 Find the missing numbers. a 578 32 5 578 000 b 4 623 80 5 623 000 80 c 608 5 2 608 d 9 000 000 408 000 5 9 408 326 Workbook A: Chapter Review, page 7 Maths Journal, page 8 Chapter Whole Numbers 3
Chapter Wrap-Up Whole Numbers Big Idea The next two place values after ten thousands are hundred thousands and millions. Reading Hundred Reading and Writing 6-digit Numbers Ten Hundreds Tens Ones 6 3 4 0 5 8 six hundred and thirty-four thousand fifty-eight six hundred and thirty-four thousand and fifty-eight Writing In numerals or figures: 634 058 In words: six hundred and thirty-four thousand and fifty-eight Reading Millions Hundred Reading and Writing 7-digit Numbers Ten Hundreds Tens Ones 4 5 2 0 8 0 four million one hundred and fifty-two thousand eighty four million, one hundred and fifty-two thousand and eighty Writing In numerals or figures: 4 52 080 In words: four million, one hundred and fifty-two thousand and eighty 4 Chapter Whole Numbers
Put On Your Thinking Cap! Carina wants to solve a 7-digit secret code to a safe. Use the clues to help Carina solve the secret code. All seven digits are different. The digit in the ten thousands place is 5. The digit in the thousands place is twice the digit in the hundred thousands place. The digit in the ones place is 2 more than the digit in the millions place. The digit in the millions place is 8 less than the digit in the hundreds place. The digit in the millions place is less than the digit in the tens place. What is the secret code? 2 a Without adding the 99s together, find the value of each of the following. i 99 + 99 ii 99 + 99 + 99 + 99 + 99 + 99 What is the value of the digit in the ones place in each case? b c Find the smallest number of 99s that must be added to get a in the ones place. Without multiplying 99 by 45, explain how you can find the sum of 45 ninety-nines. Workbook A: Put On Your Thinking Cap! pages 9 Chapter Whole Numbers 5