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Maths 5A3rd Edition

Pupil’s Book

Dr Fong Ho Kheong • Gan Kee Soon • Chelvi Ramakrishnan

•AP

PRO

VE

DBY MINISTRY OF EDUCATIO

N•

for use from 2017–2021

(M)MPaHTB5A_TP.indd 3 11/7/16 6:33 pm

PrefaceMy 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:

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

Workbook A:Put On Your Thinking Cap!pages 83–84Review 2, pages 85–88

Put On Your Thinking Cap!Put On Your Thinking Cap!

1 Annacycledfromschooltohome.Shestoppedbythepostoffice,thenwentbacktothemalltobuylunch.Shethenheadedhomefromthemall.Use the following clues to find how far Anna’s home is from her school.

School Mall Postoffice Home • The post office is 2 25 km from Anna’s school. • The mall is 1 1

10kmfromthepostoffice. • Anna’s home is 2 310kmfromthemall.

2 Rehnaspent 15 of her money on 8 pencils and 2 markers. The cost of each

markeristwicethecostofeachpencil.Sheboughtsomemoremarkerswith58ofherremainingmoney.HowmanymarkersdidRehnabuyaltogether?

3 Andreahasaboxofcoins.Shewrotedownthenumberofcoinsshehasbutspilledherdrinkoverherpaper.

Coin Number of Coins20¢

950¢

However,sheknowsthat 310 of her coins are 50¢ and the rest are 20¢ coins. Also, she has more than 50 but fewer than 100 coins. Howmanycoinsdoesshehave?

Chapter 5 Fractions:WordProblems 10108_(M)MPaHTB5A_05.indd 101

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Big Idea

The area of a triang

le is given by

half the product of

a base and the

corresponding heig

ht.

Any side of a triangle can be its base.

The height is perpendicular to the base.

Example

C

AB

Z base

height

Base and Height

The area of a triangle is half the area of a rectangle with the same ‘base’ and

‘height’ or 12 3 base 3 height.

F

E

G

D2 cm

4 cm

Area of triangle DEF

5 12 3 Area of rectangle DEFG

5 12 3 EF 3 DE

5 12 3 base 3 height

5 12 3 4 3 2

5 4 cm2

Finding the Area

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

4 cm

3 cm

8 cm

A

B

CD

E

Area of figure ABCDE5 Area of rectangle

BCDE 1 Area of triangle ABE

Area of rectangle BCDE5 8 3 4 5 32 cm2

Area of triangle ABE

5 12 3 8 3 3

5 12 cm2

Area of the figure5 32 1 125 44 cm2

Composite Figures

Area of a Triangle

Chapter Wrap-UpChapter Wrap-Up

Chapter 6 Area of a Triangle116

09_(M)MPaHTB5A_06.indd 116

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

NEW!

TRY

1A Multiply213by3.E

xpressyouranswerasamixednumber.

Then,checkyouranswerusingacalculator.

2 1333

213335

TRY

1B Multiply.Expressyouranswerinitssimplestform.

a 356325 b 432355

c 134385 d 2835275

e 2593165 f 1237 9105

Workbook A:Practice 3, pages 55–56

Maths SharingExpressamixednumberasaproduct.

Themodelshows4 12.

a Expressthismixednumberasaproductofanothermixednumberanda

wholenumber.

4 125 32

b Usethesamemethodtofindthemissingmixednumberbelow.

8 145 32

Sharewithyourpartnerhowyoufoundthe

missingmixednumbers.

Chapter 4 MultiplicationofWholeNumbers,FractionsandMixedNumbers

82


14/7/16 9:13 am

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

NEW!

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

02_(M)MPaHTB5A_Preface.indd 2 18/8/16 9:32 am

Lesson

3 Order of Operations

Order of operations

L

EARN

1 Forthefollowingproblems,AllyandJoesolvedthemdifferently.Whoiscorrect? a Nelliehad10stickers.Shegaveaway4andbought5more.HowmanystickersdidNelliehaveintheend? 1024155?

Ally’s solution:102456615511Nelliehad11stickersintheend.

Joe’s solution:41559102951Nelliehad1stickerintheend.

Use tochecktheanswer.

givenaway bought 102415 5615 511

Nelliehad11stickersintheend.

AllyandJoeworkedoutthevalueoftheexpression81204422.Ally’s answer was 5. Joe’s answer was 11.Whoseansweriscorrect?Explain.

Before you learn ...

Lesson 3 Order of Operations 35

(M)MPaHTB5A_02.indd 35

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1

Theratioofthenumberofredcapstothenumberofblackcaps

is : .

Theratioofthenumberofblackcapstothenumberofredcaps

is : .

2 Findthemissingnumbers.

a A

B

b A

B

A:B5 : A:B5 :

3 Expresseachratioinitssimplestform.

a 9:65 b 8:20:165


a 7:8521:

b 42:495 :7

c 4:3:7520: :

d 40:55:155 : :3

Chapter 7 ReviewChapter 7 Review

Chapter 7 Ratio142


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NEW!Assess understanding when pupils apply concepts learnt in Review.

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.

NEW!Multiplication of Whole Numbers, Fractions

and Mixed Numbers

This recipe serves 1. How can

I f ind the amount of each

ingredient for 3 servings?

4Chapter

1 ProductofaFractionand

aWholeNumber

2 ProductofTwoFractions

3 ProductofaMixedNumber

andaWholeNumber

Lessons

Big Idea

Whole numbers,

fractions and mixed

numbers can be

multiplied in any

combination.


11/7/16 5:07 pm

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.

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

NEW!For the Teacher:

Solvewordproblems.hands-On activity

LearN

Workingroups.Station 1 1 Readthewordproblem.Drawamodelfortheproblem. example

Aretailersold5vacuumcleaners.2ofthevacuumcleanerscost$659eachandtheotherscost$478each.Howmuchmoneydidtheretailermakefromthesaleofthe5vacuumcleaners?

$659

?

$478

2 Estimatetheanswer.3 Usethemodeltosolvetheproblem.4 Comparetheanswersin 2 and 3 tocheckforreasonableness.5 Switchroles.Repeat 1 to 4 withtheseproblems. a Marybought24boxesofbeads.Eachboxcontained245beads.

Therewere2184redbeadsandtherestwerebluebeads.Sheusedallthebluebeadstomake42bracelets.Howmanybluebeadswereusedforeachbracelet?

b Farahbaked72cupcakesand55muffins.Shesold22cupcakes.Shethenpackedtheremainingcupcakesequallyinto5boxes.Shegaveaway2boxesofcupcakes.Howmanycupcakesdidshehaveleft?

Chapter 2 OperationsofWholeNumbers44


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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.

02_(M)MPaHTB5A_Preface.indd 3 18/8/16 9:32 am

CONTENTS1 WholeNumbers 6

Lesson1 Numbersto10Million 7

2 OperationsofWholeNumbers 16Lesson1 Multiplyingby10,100,1000andTheirMultiples 17

Lesson2 Dividingby10,100,1000andTheirMultiples 27 Lesson3 OrderofOperations 35 Lesson4 SolvingWordProblems 41

3 FractionsandMixedNumbers 53 Lesson1 FractionsandDivision 54 Lesson2 AdditionofMixedNumbers 60 Lesson3 SubtractionofMixedNumbers 63

4 MultiplicationofWholeNumbers,FractionsandMixedNumbers 70

Lesson1 ProductofaFractionandaWholeNumber 71 Lesson2 ProductofTwoFractions 74

Lesson3 ProductofaMixedNumberand aWholeNumber 81

03_(M)MPaHTB5A_Contents.indd 2 19/7/16 7:44 am

5 Fractions:WordProblems 86 Lesson1 SolvingWordProblems 87 6 AreaofaTriangle 102 Lesson1 AreaofaTriangle 103 Lesson2 CompositeFigures 110

7 Ratio 118 Lesson1 FindingRatios 119 Lesson2 EquivalentRatios 124 Lesson3 ComparingThreeQuantities 128 Lesson4 SolvingWordProblems 131

8 VolumeofCubesandCuboids 146 Lesson1 VolumeofaSolid 147 Lesson2 DrawingCubesandCuboids 151 Lesson3 VolumeofaCubeandaCuboid 159 Lesson4 VolumeofaLiquid 164

03_(M)MPaHTB5A_Contents.indd 3 19/7/16 7:44 am

Whole Numbers1Chapter

1 Numbersto10MillionLessonthe next two place values after ten thousands are hundred thousands and millions.

Big Idea

Type FloorArea(m2) Price($)2-bedroom 70 11700003-bedroom 93 12090004-bedroom 123 15990005-bedroom 150 2080000

How do I read $1 209 000?

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

04_(M)MPaHTB5A_01.indd 6 15/7/16 2:25 pm

Lesson

1 Numbers to 10 Million

Reading and writing 6-digit numbers

Recall

Count in thousands.

1000100010001000 1000100010001000 10001000 10 000

10 thousands 5 1 ten thousand

L

EARN

1A Count in ten thousands.

10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 100 000

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

EARN

1B Count in hundred thousands.

1 000 000100 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.

There are 147 853 people in a queue. Use 11001000

10 000100 000

1 000 00010 to count aloud

and show the number of people in the queue.


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

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 7

04_(M)MPaHTB5A_01.indd 7 25/8/16 1:33 pm

LearN

1C Countusing 11001000

10 000100 000

1 000 00010 .

100 000

100 000

100 000

100 000

100 000

10 000

10 000

10 000

1000

1000

1000

1000

100

100

100

100

100

100

100

100

100

10

10

1

1

1

1

1 1

hundredthousands

ten thousands thousands hundreds tens Ones

5 3 4 9 2 6

standsfor5 hundred thousands500000

standsfor3 ten

thousands30000

standsfor4 thousands

4000

standsfor9 hundreds

900

standsfor2 tens20

standsfor6 ones

6

534926

fivehundredandthirty-fourthousand ninehundredandtwenty-six

fivehundredandthirty-fourthousand,ninehundredandtwenty-six

Chapter 1 Whole Numbers8

04_(M)MPaHTB5A_01.indd 8 15/7/16 2:25 pm

trY

1a Writeinnumeralsandinwords.

100 000

100 000

100 000

100 000

100 000

10 000

10 000

10 000

10 000

10 000

10 000

10 000

1000

1000

1000

100

100

100

100

100

100

100

100

100

10

10 1

Numerals:

Words:

trY

1B Writeinfigures.

a sixhundredandseventy-threethousand,ninehundredandeleven

b fivehundredandeighteenthousandandfour

c twohundredthousand,onehundredandsix

trY

1C Writeinwords.

a 320176

b 438830

c 906095

trY

1D Findthemissingnumbers.

a 23415652340001

b 3182055 1205

c 4820001 5482670

d 17805600780


04_(M)MPaHTB5A_01.indd 9 15/7/16 2:25 pm

reading and writing 7-digit numbers L

earN

1a Countinmillions.

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 1 000 000

10000000tenmillions

L

earN

1B Countusing 11001000

10 000100 000

1 000 00010 .

1 000 000

1 000 000

1 000 000

100 000

100 000

100 000

100 000

10 000

10 000

10 000

10 000

10 000 10 000

1000

1000

100

100

100

100

100

100

100

10

10

10

10

10 1

Millions hundredthousands


3 4 6 2 7 5 1

standsfor3 millions3000000

standsfor4 hundred thousands400000

standsfor6 ten

thousands60000

standsfor2 thousands

2000

standsfor7 hundreds

700

standsfor

5 tens50

standsfor

1 one1

threemillion sevenhundredandfifty-one3462751

fourhundredandsixty-twothousand threemillion,fourhundredandsixty-twothousand,

sevenhundredandfifty-one

MrKrishnandonated$10000000toacharity.Use 11001000

10 000100 000

1 000 00010 tocount

aloudandshowtheamountofmoneyhedonated.


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


04_(M)MPaHTB5A_01.indd 10 15/7/16 2:25 pm

Readandwritelargenumbers.hands-On activity L

earN

Workingroups.

1 Use 11001000

10 000100 000

1 000 00010 toshow458712.

2 Writeinwords.

example

3 Switchroles.Repeat 1 and 2 withthesenumbers.

a 543201 b 359490 c 1645027 d 2000546

trY

1a Writeinfiguresandinwords.

1 000 000

1 000 000

1 000 000

10

10

100

100

100

100

100 000

100 000

100 000

100 000

100 000 100 000

10 000

10 000

10 000

10 000

10 000

10 000

10 000

10 000

10 000

1

1

1

1

1

Figures:

Words:


04_(M)MPaHTB5A_01.indd 11 15/7/16 2:25 pm

trY

1B Writeinfigures.

a threemillion,fivehundredandsixty-seventhousandandforty-five

b fourmillion,sixhundredandfivethousand,threehundredand seventy-nine

c sixmillion,threehundredandtwenty-onethousand,fivehundredand four

trY

1C Writeinwords.

a 1234567

b 8090909

c 2653870

trY

1D Findthemissingnumbers.

a 2300598520000001 1598

b 42163505 12160001350

c 50000001 194655081946

d 90000001 12059106020

Maths Sharing FindexamplesofnumbersinthemillionsfromtheInternetanddevelopasenseofthesizeof1million.

1 SearchtheInternetfortheseatingcapacityoftheSingaporeIndoorStadium. Imaginethatanewindoorstadiumwithaseatingcapacityof1000000

willbebuilt. HowmanytimesaslargeastheSingaporeIndoorStadiumwillthenew

indoorstadiumbe? Discuss.


04_(M)MPaHTB5A_01.indd 12 15/7/16 2:25 pm

1 Writeinnumerals.

a threehundredandseventy-sixthousand,twohundredandfourteen

b sevenmillion,fourhundredandfiftythousand,ninehundredand eighty-six

2 Writeinwords.

a 872649

b 5380170


a 57831255780001

b 46231805 16230001180

c 16085210608

d 900000014080001 59408326

2 LookuptheInternetforthreedifferentexamplesofnumbersinmillionsupto10million.

example ThepopulationofSingaporewas5076700in2010.

Discuss.

Workbook a:Chapter 1 review, page 7Maths Journal, page 8

Workbook a:practice 1, pages 5–6

Chapter 1 reviewChapter 1 review

Chapter 1 Whole Numbers 13

04_(M)MPaHTB5A_01.indd 13 15/7/16 2:25 pm

reading

hundredthousands


6 3 4 0 5 8

sixhundredandthirty-fourthousand fifty-eight

sixhundredandthirty-fourthousandandfifty-eight

WritingIn numerals or figures:634058In words:sixhundredandthirty-fourthousandandfifty-eight

reading and Writing 6-digit Numbers

Whole Numbers

reading

onehundredandfifty-twothousand

eightyfourmillion

Millions hundredthousands


4 1 5 2 0 8 0

fourmillion,onehundredandfifty-twothousandandeighty

WritingIn numerals or figures:4152080In words:fourmillion,onehundredandfifty-twothousandandeighty

reading and Writing 7-digit Numbers

Big IdeaThenexttwop

lacevaluesafter

tenthousandsarehundredt

housands

andmillions.

Chapter Wrap-UpChapter Wrap-Up


04_(M)MPaHTB5A_01.indd 14 15/7/16 2:25 pm

Workbook a:put On Your thinking Cap!pages 9–10

put On Your thinking Cap!put On Your thinking Cap!

1 Carinawantstosolvea7-digitsecretcodetoasafe. UsethecluestohelpCarinasolvethesecretcode.

• Allsevendigitsaredifferent. • Thedigitinthetenthousandsplaceis5. • Thedigitinthethousandsplaceistwicethedigitinthe

hundredthousandsplace. • Thedigitintheonesplaceis2morethanthedigitinthemillionsplace. • Thedigitinthemillionsplaceis8lessthanthedigitinthe

hundredsplace. • Thedigitinthemillionsplaceis1lessthanthedigitinthetensplace.

Whatisthesecretcode?

2 a Withoutaddingthe99stogether,findthevalueofeachofthefollowing.

i 99+99

ii 99+99+99+99+99+99 Whatisthevalueofthedigitintheonesplaceineachcase?

b Findthesmallestnumberof99sthatmustbeaddedtogeta1intheonesplace.

c Withoutmultiplying99by45,explainhowyoucanfindthesumof45ninety-nines.

Chapter 1 Whole Numbers 15

04_(M)MPaHTB5A_01.indd 15 15/7/16 2:25 pm

maths 5a · 2 rehna spent 1 5 of her money on 8 pencils and 2 markers. the cost of each marker is...

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