Maths 5A 3rd Edition

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Dr Fong Ho Kheong • Gan Kee Soon • Chelvi Ramakrishnan

BY

D

D

– e f rom 2017

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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

appears.

For the Pupil:

NEW!

Practise new concepts learnt in parallel questions with help from your teacher in TRY!

ber.

TRY 1A

d num 1 ess your answer as a mixe Multiply 2 3 by 3. Expr lator. sing a calcu

Then, check your answer u

Put On Your Thi 1 Anna cycled from

School

TRY 1B

mplest form. s your answer in its si

Multiply. Expres

a 3 6 3 2 5

c

3 1 4 3 8 5

e 2 9 3 16 5

5

d

1

4 2 5

1 8 4 5

ow many marke

rs did Rehna bu

altogether?

f coins. She wro te down the num drink over her p ber of coins she aper. has

but spilled her

20¢

a

ther mixed number and

mber as a product of ano

3 2 umber below.

of Who Chapter 4 Multiplication

le Numbers, Fractions

Workbook A: Practice 3, pages 55–56 and Mixed Numbers

NEW!

Workbook A: Put On Your Thin king Cap! pages 83–84 Review 2, pag es 85–88 Chapter 5 Fract ions: Word Pro

blems

101

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9

However, she kn ows that 3 of her coins are 50¢ and 10 20¢ coins. Also the rest are , she has more than 50 but few er than 100 coin How many coins s. does she have?

en by Big Idngea le is giv a of a tria a base and the The are of product the height. lf ha onding corresp

Chapter Wrap-Up

Number of Coi ns

50¢

d the missing mixed n

3 2

y

3 Andrea has a box o

er how you found the Share with your partn rs. missing mixed numbe 82

her money on 8 pencils and 2 mar kers. The cost of the cost of eac each

h pencil. She bou ght some more with 5 of her rema markers ining money. H 8

Coin

ethod to fin b Use the same m

5

marker is twice

er as a product.

a Express this mixed nu whole number.

Home

2 Rehna spen 1 t of

Express a mixed numb

1 The model shows 4 2.

2 28 3 5 7 5

9 f 12 3 7 10 5

5

Maths Sharing

3

b 4 3 2 5 5

Post office

is 2 2 km from Ann 5 a’s school. • The mall is 1 1 km from the pos 10 t office. • Anna’s home 3 is 2 km from the 10 mall.

Challenge yourself to solve non-routine questions by applying relevant heuristics and thinking skills in Put On Your Thinking Cap!

1

2 3 3 3 5

Mall

• The post offic e

1

2 3 3 3

nking Cap!

school to home went back to th . She stopped b e m y th Use the followin all to buy lunch. She then head e post office, then g clues to find how ed home from the mall. far Anna’s hom e is from her sch ool.

Consolidate the concepts you have learnt in each chapter in Chapter Wrap-Up!

14/7/16 9:14 am

Area of a Triangle

The area of a triangle is half the area of a rectangle with the same ‘base’ and 1 ‘height’ or 2 3 base 3 height.

Any side of a triangle can be its base. The height is perpendicular to the base.

G

F

Example

Composite Figures

Finding the Area

Base and Height

B

A

A B

E 8 cm

D

height

4 cm Z base

Share your thoughts with your teachers, create your own mathematics questions and become aware of your own mathematical thinking in Maths Sharing!

We can find the area of a composite figure by dividing it into rectangles, squares or triangles.

C

E

2 cm

D

Area of triangle DEF 1 5 2 3 Area of rectangle DEFG 1

5 2 3 EF 3 DE 1 5 3 base 3 height 2 1

523432 2 5 4 cm

3 cm 4 cm

C

Area of figure ABCDE 5 Area of rectangle BCDE 1 Area of triangle ABE Area of rectangle BCDE 5834 2 5 32 cm Area of triangle ABE 1 5 3833 2

5 12 cm

2

Area of the figure 5 32 1 12 2 5 44 cm

ngle Chapter 6 Area of a Tria

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For the Teacher: NEW!

Multiplication of actions , Fr Whole Numbers rs be and Mixed Num

Chapter

4

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.

s 1. How can This recipe serve of each I find the amount servings? ingredient for 3

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.

Lesson

Less

ons

1 2 3

a

Order of operations

Before you learn ... Ally and Joe worked out the value o Ally’s answer was 5. Joe’s answe f the expression 8 1 20 4 4 2 2. r was 11. Whose answer is correct? Explain.

EAR

L

Ide

_04.indd 70

Solve word proble

ms.

Work in groups. Station 1

1 Read the word pro

blem. Draw a mod

el for the problem

. example A retailer sold 5 vacuu m cleaners. 2 of th and the others co e vacuum cleaners st $478 each. How cost $659 each much money did t the sale of the 5 va he retailer make fr cuum cleaners? om $659

10 2 4 1 5 5 ? Ally’s solution: 10 2 4 5 6 6 1 5 5 11 Nellie had 11 stickers in the en d.

Use

to check the answer.

given away

bought

10 2 4 1 5 5 6 1 5 5 11 Nellie had 11 stickers in the end.

Lesson 3 Order of Operatio ns

35

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Chapter 7 Review 1

2 Estimate the a nswer.

NEW!

olve the problem.

4 Compare the answ

ers in 2 and 3 to check for reaso

5 Switch roles. Repe at 1 to 4 with these problems.

nableness.

Assess understanding when pupils apply concepts learnt in Review.

a M ary bought 24 boxe s of beads. Each b There were 2184 re ox contained 245 beads. d beads and the r est were blue beads all the blue beads . She used to make 42 brace lets. How many blu used for each brac e beads were elet? b Farah baked 72 cu pcakes and 55 mu ffins. She sold 22 c She then packed upcakes. the remaining cup cakes equally into She gave away 2 b 5 boxes. oxes of cupcakes. How many cupcak have left? es did she

of black caps

s to the number

umber of red cap

The ratio of the n

:

.

is

The ratio of the n

is

r of red caps

aps to the numbe

umber of black c

:

. bers.

num 2 Find the missing a

b

A

B

A : B 5

a 9 : 6 5

A : B 5

:

.

its simplest form

Chapter 2 Opera tions of Wh

A

B

o in 3 Express each rati

44

Joe’s solution: 4 1 5 5 9 10 2 9 5 1 Nellie had 1 sticker in the end .

?

3 Use the model to s

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.

$478

a N ellie had 10 stickers. She ga ve awa How many stickers did Nellie have y 4 and bought 5 more. in the end?

07_(M)MPaHTB5A

hands-On activity

olved them differently.

Who is correct?

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LearN

1 For the following problems, Ally and Joe s

Whole numbers, d fractions and mixe numbers can be multiplied in any combination.

n and Product of a Fractio a Whole Number tions Frac f Two uct o Prod Number Product of a Mixed er and a Whole Numb

Order of Operations

N

Big

3

Teach concepts in concise steps using real-life contexts, manipulatives and meaningful visuals in LEARN.

:

b 8 : 20 : 16 5

bers.

num 4 Find the missing

ole Numbers

a 7 : 8 5 21 :

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142

b 42 : 49 5 : c 4 : 3 : 7 5 20 5 d 40 : 55 : 15

: 7 : :

: 3

Chapter 7 Ratio 11/7/16 6:29 pm

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02_(M)MPaHTB5A_Preface.indd 3

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CONTENTS

1 Whole Numbers

Lesson 1 Numbers to 10 Million

6

7

2 Operations of Whole Numbers

16

3 Fractions and Mixed Numbers

53

4 Multiplication of Whole Numbers, Fractions and Mixed Numbers

70

Lesson Lesson Lesson Lesson

1 Multiplying by 10, 100, 1000 and Their Multiples 2 Dividing by 10, 100, 1000 and Their Multiples 3 Order of Operations 4 Solving Word Problems

Lesson 1 Fractions and Division Lesson 2 Addition of Mixed Numbers Lesson 3 Subtraction of Mixed Numbers

Lesson 1 Product of a Fraction and a Whole Number Lesson 2 Product of Two Fractions Lesson 3 Product of a Mixed Number and a Whole Number

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17 27 35 41

54 60 63

71 74 81

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5 Fractions: Word Problems 6

Lesson 1 Solving Word Problems Area of a Triangle Lesson 1 Area of a Triangle Lesson 2 Composite Figures

86

87

102 103 110

7 Ratio

118

8 Volume of Cubes and Cuboids

146

Lesson Lesson Lesson Lesson

Lesson Lesson Lesson Lesson

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1 Finding Ratios 2 Equivalent Ratios 3 Comparing Three Quantities 4 Solving Word Problems

1 Volume of a Solid 2 Drawing Cubes and Cuboids 3 Volume of a Cube and a Cuboid 4 Volume of a Liquid

119 124 128 131

147 151 159 164

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Chapter

1

Whole Numbers

In the 1980s, your grandfather bought a 3-bedroom condominium for $450 000. How much does a 3-bedroom condominium cost now?

Type

Floor Area (m2)

Price ($)

2-bedroom

70

1 170 000

3-bedroom

93

1 209 000

4-bedroom

123

1 599 000

5-bedroom

150

2 080 000

How do I read $1 209 000?

dea I g i B

n Lesso

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1

Numbers to 10 Million

The next two place values after ten thousands are hundred thousands and millions.

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Lesson

1

Numbers to 10 Million

Reading and writing 6-digit numbers Before you learn ... There are 147 853 people in a queue. Use

1 000 000

100 000

10 000

1000

100

10

1

to count aloud

and show the number of people in the queue. Recall Count in thousands. 1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

10 000

10 000, 20 000, 30 000, 40 000, 50 000, 60 000, 70 000, 80 000, 90 000, 100 000

10 thousands 5 1 ten thousand L

N

EAR 1A

Count in ten thousands.

10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000

10 ten thousands 5 1 hundred thousand

1 ten thousand 5 10 thousands 10 ten thousands 5 100 thousands So, 1 hundred thousand 5 100 thousands.

L

N

EAR 1B

100 000

Count in hundred thousands. 100 000

100 000

100 000

100 000

100 000

100 000

100 000

100 000

100 000

100 000

10 hundred thousands 5 1 million

1 hundred thousand 5 100 thousands 10 hundred thousands 5 1000 thousands So, 1000 thousands 5 1 million.

1 000 000

100 000, 200 000, 300 000, 400 000, 500 000, 600 000, 700 000, 800 000, 900 000, 1 000 000

Lesson 1 Numbers to 10 Million

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L

N

EAR 1C

Count using

1 000 000

100 000

10 000

1000

100

10

1

.

100 000

10 000

1000

100

100

10

1

100 000

10 000

1000

100

100

10

1

100 000

10 000

1000

100

100

1

1000

100

100

1

100 000

1

100

100 000

Hundred Ten Thousands Hundreds Thousands Thousands 5

3

4

five hundred and thirty-four thousand

8

9

Tens

Ones

2

6

stands for stands for stands for stands for stands for stands for 4 thousands 9 hundreds 2 tens 5 hundred 3 ten 6 ones thousands thousands 4000 900 20 6 500 000 30 000

1

534 926

nine hundred and twenty-six

five hundred and thirty-four thousand, nine hundred and twenty-six

Chapter 1 Whole Numbers

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TRY

1A Write in numerals and in words. 100 000

10 000 10 000

1000

100

100

10

100 000

10 000 10 000

1000

100

100

10

100 000

10 000

1000

100

100

100 000

10 000

100

100

100 000

10 000

100

1

Numerals:

Words: TRY

1B Write in figures. a

six hundred and seventy-three thousand, nine hundred and eleven

b

five hundred and eighteen thousand and four

c

two hundred thousand, one hundred and six

TRY

1C Write in words.

a

320 176

b

438 830

c

906 095

TRY

1D Find the missing numbers.

a

234 156 5 234 000 1

b

318 205 5

1 205

c

482 000 1

5 482 670

d

1 780 5 600 780 Lesson 1 Numbers to 10 Million

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Reading and writing 7-digit numbers Before you learn ... Mr Krishnan donated $10 000 000 to a charity. Use

1 000 000

100 000

10 000

1000

100

10

1

to count

aloud and show the amount of money he donated. L

N

EAR 1A

Count in millions. 1 000 000

1 000 000

1 000 000

1 000 000

1 000 000

1 000 000

1 000 000

1 000 000

1 000 000

10 000 000 ten millions

1 000 000

1 000 000, 2 000 000, 3 000 000, 4 000 000, 5 000 000, 6 000 000, 7 000 000, 8 000 000, 9 000 000, 10 000 000 L

N

EAR 1B

Count using

100 000

10 000

1000

100

10

1

.

1 000 000

100 000

10 000 10 000

1000

100

100

10

1 000 000

100 000

10 000

1000

100

100

10

1 000 000

100 000

10 000

100

10

100 000

10 000

100

10

10 000

100

10

Millions 3

1 000 000

Hundred Ten Thousands Hundreds Thousands Thousands 4

6

2

7

1

Tens

Ones

5

1

stands for stands for stands for stands for stands for stands stands 3 millions 4 hundred 6 ten 2 thousands 7 hundreds for for 3 000 000 thousands thousands 2000 700 5 tens 1 one 400 000 60 000 50 1

3 462 751

three million seven hundred and fifty-one four hundred and sixty-two thousand

10

three million, four hundred and sixty-two thousand, seven hundred and fifty-one

Chapter 1 Whole Numbers

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R LEA N

Read and write large numbers.

Hands-On Activity

Work in groups.

1 Use

1 000 000

100 000

10 000

1000

100

10

to show 458 712.

1

2 Write in words.

Example

3 Switch roles. Repeat a

543 201

1 and 2 with these numbers.

b

c 1 645 027

359 490

d

2 000 546

TRY

1A Write in figures and in words. 10 000 10 000

100

10

1

100 000

10 000 10 000

100

10

1

100 000

10 000 10 000

100

1

100 000

10 000 10 000

100

1

100 000

10 000

1 000 000

100 000

1 000 000

1 000 000

100 000

1

Figures:

Words:

Lesson 1 Numbers to 10 Million

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TRY

1B Write in figures.

a

three million, five hundred and sixty-seven thousand and forty-five

b

four million, six hundred and five thousand, three hundred and seventy-nine

c

six million, three hundred and twenty-one thousand, five hundred and four

TRY

1C Write in words.

a

1 234 567

b

8 090 909

c

2 653 870

TRY

1D Find the missing numbers.

a

2 300 598 5 2 000 000 1

b

4 216 350 5

1 216 000 1 350

c

5 000 000 1

1 946 5 5 081 946

d

9 000 000 1

1 20 5 9 106 020

Maths Sharing

12

1 598

Find examples of numbers in the millions from the Internet and develop a sense of the size of 1 million.

1 Search the Internet for the seating capacity of the Singapore Indoor Stadium. Imagine that a new indoor stadium with a seating capacity of 1 000 000 will be built. How many times as large as the Singapore Indoor Stadium will the new indoor stadium be? Discuss.

Chapter 1 Whole Numbers

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2 Look up the Internet for three different examples of numbers in millions up to 10 million.

Example The population of Singapore was 5 076 700 in 2010.

Discuss. Workbook A: Practice 1, pages 5–6

Chapter 1 Review 1 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

5 380 170

3 Find the missing numbers.

a

578 312 5 578 000 1

b

4 623 180 5

c

d

1 623 000 1 180

1 608 5 210 608 9 000 000 1 408 000 1

5 9 408 326 Workbook A: Chapter 1 Review, page 7 Maths Journal, page 8

Chapter 1 Whole Numbers

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Big Idealues after

Chapter Wrap-Up

o place va usands The next tw undred tho h re a s d n ten thousa s. and million

Whole Numbers Reading and Writing 6-digit Numbers Reading Hundred Ten Thousands Hundreds Thousands Thousands 6

3

4

0

six hundred and thirty-four thousand

Tens

Ones

5

8

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 and Writing 7-digit Numbers Reading Millions 4 four million

Hundred Ten Thousands Hundreds Tens Thousands Thousands 1

5 one hundred and fifty-two thousand

2

0

8

Ones 0

eighty

four million, one hundred and fifty-two thousand and eighty Writing In numerals or figures: 4 152 080 In words: four million, one hundred and fifty-two thousand and eighty

14

Chapter 1 Whole Numbers

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Put On Your Thinking Cap!

1 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 1 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

F ind the smallest number of 99s that must be added to get a 1 in the ones place.

c

ithout multiplying 99 by 45, explain how you can find the sum of W 45 ninety-nines.

Workbook A: Put On Your Thinking Cap! pages 9–10

Chapter 1 Whole Numbers

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