Dr Lee Ngan Hoe • Dr Koay Phong Lee • Charlotte Collars Ong Bee Leng • Tan Cheow Seng

Coursebook3rd edition5B

PrefaceShaping Maths (3rd Edition) is an instructional package written according to the 2013 Ministry of Education, Singapore, primary mathematics syllabus. The package is designed to meet the learning needs of pupils from Primary 1 to 6. The Primary 5 package consists of two Coursebooks, two Activity Books and two Teacher’s Planning Guides.

ApproachShaping Maths (3rd Edition) adopts a thematic approach towards the learning of mathematics in the upper primary levels. These themes reflect various aspects of pupils’ lives and help provide a concrete framework for the mathematical concepts that pupils learn in class. Pupils’ learning is then reinforced through the use of pictures and icons before they are introduced to the formal symbolic mode of mathematical representation. The themes also provide an environment for pupils to experience the interdisciplinary nature of learning.

Continuing research in education has resulted in the introduction of new features in the third edition. Through these features, educators are further equipped with various strategies in addressing teaching and learning needs. These features include hands-on activities, group/pair work and open-ended questions to encourage exploration and in-depth thinking among pupils. This will equip pupils well for the challenges of the 21st century.

Friends of Shaping MathsThe themes of the Coursebook revolve around Aini, Bala, Caili and David. The characters stimulate pupils’ interest and heighten their involvement in the learning process.

FeaturesColourfully illustrated unit openers encourage rich and active pupil participation in learning and connections to everyday life through whole class discussion.

Howmanycopiesdoesthephotocopierprintin1minute? Itprints225copies

forevery5minutes.

Itcanprint90copiesin2minutes.

Arateinvolvestwoquantities.Itisexpressedasonequantityperunitofanotherquantity.

4Rate

AB5B,p75>>Recall4

68

07(M)SMCB5B_04a.indd 68 27/6/16 10:52 am

Caili

Aini

Bala

David

2 Ajugcontainingsomewaterhasatotalmassof4.35kg.Afterpouring

14ofthewater,thetotalmassofthejugandtheremainingwater

is3.45kg.Whatisthemassoftheemptyjug?

3 MrsRitabuys6cartonsofsoyabeanmilk.Eachcartoncontains1.25lofsoyabeanmilk.DoesMrsRitahaveenoughsoyabeanmilktofillup20mugswithacapacityof320mleach?Explain.

Solvethefollowingproblems.Thenestimatetocheckifyouranswersreasonable.

4 16identicalreamsofA4printingpaperarestacked.Theheightofthestackis92.8cm.Whatistheheightofthestackafter5reamsaretakenaway?

5 12.9moffencingisusedforthethreesidesofarectangulargardennexttoawall.Thewidthofthegardenis3.45m.Itcosts$18tocover1m2oflandwithgrass.Whatisthecostofcoveringthisgardenplotwithgrass?

3.45m

6 MrsNerahas15mofcloth.Shewantstosew25cushioncovers.Eachcushioncoverrequires0.56mofcloth.DoesMrsNerahaveenoughclothtosew25suchcushioncovers?Shouldtherebeleftovercloth,howmanymorecushioncoversofthesamesizecanMrsNerasew?

AB5B,p33>>Activity3

39

04(M)SMCB5B_02.indd 39 1/7/16 11:47 am

Studythefollowingfiguresdrawnonasquaregrid.

AB

C

ED

PropertyFigure

A B C D EOnepairofparallelsides ✓

Twopairsofparallelsides ✓ ✓ ✓ ✓

Allanglesarerightangles. ✓ ✓

Oppositesidesareequal. ✓ ✓ ✓ ✓

Allsidesareequal. ✓ ✓

Nameofthefigure Rectangle Trapezium Parallelogram Rhombus Square

Types of Quadrilaterals

AppIt!@www.mceducation.com/sgstudent/sapp5

132 Unit8 Quadrilaterals

12(M)SMCB5B_08a.indd 132 1/7/16 11:48 am

Fun

Mathswith

Plan a Shopping ListWhat to do:

STEP 1 Collectcataloguesorbrochuresfromdepartmentstoresorsupermarkets.

STEP 2 Makealistoftheitemsthatyoucanbuywith$500.Writeareceiptliketheoneshownontheright.

STEP 3 Exchangeyourreceiptwithanotherpair.Use a calculator to check whether your classmates’ entriesarecorrect.

Discount=20%offusualpriceGST=7%afterdiscount

AB 5B, p 73 >> Let’s Find Out

Activityfor2pupils

Whatyouneed:

catalogues or brochures

a piece of paper

calculator

66 Unit3 Percentage

06(M)SMCB5B_03.indd 66 7/11/16 9:39 AM

My Notes

TypesofQuadrilaterals

Figure Property

Square

• Twopairsofparallelsides• Allanglesarerightangles.• Oppositesidesareequal.• Allsidesareequal.

Rectangle• Twopairsofparallelsides• Allanglesarerightangles.• Oppositesidesareequal.

Parallelograma b

cd

• Twopairsofparallelsides• Oppositesidesareequal.• Oppositeanglesareequal. ∠a�∠c ∠b�∠d

Rhombusa

bc

d

• Twopairsofparallelsides• Oppositesidesareequal.• Allsidesareequal.• Oppositeanglesareequal. ∠a�∠c ∠b�∠d

Trapeziuma b

cd

• Onepairofparallelsides• Thesumofapairofangles betweenthetwoparallelsides is180°. ∠a�∠d�180° ∠b�∠c�180°

DrawingQuadrilateralsDifferentquadrilateralscanbedrawnaccordingtothegivenanglesandlengthsusingaruler,protractorandsetsquare.

AB5B,p169>>MyMathsJournal

• Thesumofapairofangles betweenthetwoparallelsides

180°

DifferentquadrilateralscanbedrawnaccordingtotheDifferentquadrilateralscanbedrawnaccordingtothe

AB5B,p169>>MyMathsJournal

DifferentquadrilateralscanbedrawnaccordingtotheDifferentquadrilateralscanbedrawnaccordingtothe

144 Unit8 Quadrilaterals

12(M)SMCB5B_08.indd 144 7/18/16 10:06 AM

Question classification helps teachers spend their time more effectively by using the appropriate questions to get pupils to master the necessary skills.

Prerequisite skills

Reinforcement of current concepts

Higher-order thinking skills/enrichment

App It! helps pupils master concepts learnt through engaging and interative applets.

Fun with Maths engages pupils in interactive maths activities that encourage exploration, discovery and active thinking.

Guiding questions build the habit of checking to understand a problem.

My Notes helps pupils consolidate and recall, and commit to memory key learning concepts.

ReviewC

1 ABandCDarestraightlines.Findtheunknownmarkedangles.

a) b)

66°66°

a

B

A

69° 43°

bB

A

C

D

2 ∠a�∠b�∠c.Find∠c.

bc

a

3 AB,CDandEFarestraightlines.Findtheunknownmarkedangles.

a) b)

53°

eC B

A D

d

68°45°

C E

B

DF

A

c) d)

f

52°67°

B

A

67°67°

g

C

D

B

A

145

13(M)SMCB5B_RevC.indd 145 1/7/16 11:51 am

Activities have been included to provide more individual, pair and group hands-on learning. These, along with the manipulatives required, are highlighted for ease of use.

Review provides a formative assessment of pupils’ understanding and helps to consolidate learning.

NEW!

Thepicturebelowisdrawnonapieceofpaper.Thewholepieceofpaperisdividedinto100squares.

Whatpercentageofthewholepieceofpaperispink?

Whatpercentageofthewholepieceofpaperisgreen?Whatpercentageofthewholepieceofpaperisorange?Whatpercentageofthewholepieceofpaperiscoloured?

ActivityGroup

Lookforexampleswherepercentagesareusedaroundyouanddiscusstheirusagewiththeclass.

Percent

4outof100is4%.

50 Unit3 Percentage

06(M)SMCB5B_03.indd 50 1/7/16 11:50 am

Sections with this icon involve the use of calculators.

2 FourOperationsofDecimals 33 • AdditionandSubtraction 34 • MultiplicationandDivision 36 • SolvingWordProblems 38

ReviewA 45

4 Rate 68 • Rate 69 • SolvingWordProblems 72

CONTENTS1 Decimals 2

• MultiplyingbyTens,Hundredsand Thousands 3 • DividingbyTens,Hundredsand Thousands 14 • ConversionofMeasures 2 1 • SolvingWordProblems 28

3 Percentage 49 • Percent 50 • ExpressingFractionsasPercentages 55 • PercentageofaQuantity 6 1

5 Average 83

ReviewB 92

6 Angles 96 • FindingUnknownAngles 97

8 Quadrilaterals 130 • TypesofQuadrilaterals 132 • Parallelograms,RhombusesandTrapeziums 135 • DrawingQuadrilaterals 140

ReviewC 145

7 Triangles 108 • TypesofTriangles 109 • SumoftheAnglesofaTriangle 113 • AnglesinaTriangle 117 • DrawingTriangles 121

What is the value of 0.1 10?What is the value of 0.01 10?

AB 5B, p 1 >> Recall 1

How many paper clips do you need to measure half of the ribbon? How do you write this as a fraction of the total number of paper clips? How do you write this fraction as a decimal?

How many beads do you need to measure 10 paper clips? How many beads do you need to measure 2 paper clips? How do you write this as a fraction of the total number of beads? How do you write this fraction as a decimal?

1Decimals

110 of the ribbon

22

Multiplying by Tens, Hundreds and Thousands

10 thousandths 1 hundredth

10 hundredths 1 tenth

10 tenths 1 one

3 tenths 10 30 tenths 3 ones

1

100.1

0.1

0.1

1

1

0.3 10 3

3 hundredths 10 30 hundredths 3 tenths

100.01

0.01

0.01

0.1

0.1

0.1

0.03 10 0.3

3 thousandths 10 30 thousandths

hundredths

100.010.001

0.001

0.001 0.01

0.01

0.003 10

3

1 Multiply.

a) 0.2 10 b) 0.5 10 c) 0.7 10 d) 0.04 10 e) 0.06 10 f ) 0.09 10 g) 0.002 10 h) 0.004 10 i ) 0.008 10 j ) 0.009 × 10

2 Multiply.

a) 0.54 10

Ones Tenths Hundredths

5 45 4

When a decimal is multiplied by 10, its decimal point moves 1 place to the right.

Given number Multiply by Product

0.3 10 0.3 × 10 = 3

0.03 10 0.03 × 10 = 0.3

0.003 10 0.003 × 10 = 0.03

4 hundredths 10 4 tenths5 tenths 10 5 ones

4 Unit 1 Decimals

b) 2.45 10

Tens Ones Tenths Hundredths

2 4 52 4 5

3 Multiply.

a) 0.123 10

b) 3.456 10

4 Multiply.

a) 0.17 10 b) 0.029 10 c) 0.304 10 d) 1.08 10 e) 4.35 10 f ) 6.732 10 g) 9.2 10 h) 19.57 10 i ) 7.001 10 j ) 4.083 × 10

5 hundredths 10 5 tenths4 tenths 10 4 ones2 ones 10 2 tens

0.123

3.456

5

1.26 4 5.04

0.84 2 1.68

1

5 a) Multiply 0.84 by 20.

b) Multiply 1.26 by 40.

6 Multiply.

a) 0.6 30 b) 0.09 40 c ) 0.17 50 d) 0.002 60

7 Multiply.

a) 1.2 20 b) 3.06 30 c) 1.29 80 d) 1.57 90 e) 1.053 40 f) 1.418 70

AB 5B, p 3 >> Activity 1

Method 11.26 40 1.26 4 10

10

Method 21.26 40 1.26 10 4

4

Method 10.84 20 0.84 2 10

10

Method 20.84 20 0.84 10 2

2

6 Unit 1 Decimals

8 a) Multiply 0.4 by 100.

10

10

10

10

0.1

0.1

0.1

0.1

100

0.4 100

b) Multiply 0.04 by 100.

1

1

1

1

0.01

0.01

0.01

0.01

100

0.04 100

c) Multiply 0.004 by 100.

0.001

0.001

0.001

0.001

0.1

0.1

0.1

0.1

100

0.004 100

d) Multiply.

0.4 100

0.04 100

0.004 100

0.40 1000.04 1000.004 100

7

0.127

9 Multiply.

a) 0.3 100 b) 0.5 100 c) 0.8 100 d) 0.05 100 e) 0.06 100 f) 0.07 100 g) 0.009 100 h) 0.008 100 i) 0.007 100

10 Multiply.

a) 0.16 100

Tens Ones Tenths Hundredths

1 61 6

b) 1.73 100

c) 0.127 100

Tens Ones Tenths Hundredths Thousandths

1 2 71 2 7

d) 2.814 100

0.16

When a decimal is multiplied by 100, its decimal point moves 2 places to the right.

Given number Multiply by Product

0.40 100 40

0.04 100 4

0.004 100 0.4

8 Unit 1 Decimals

11 Multiply.

a) 0.28 100 b) 0.036 100 c) 0.412 100 d) 5.13 100 e) 6.431 100 f ) 9.6 100 g) 45.12 100 h) 5.701 100

12 a) Multiply 0.75 by 300. 0.75 300 0.75 3 100

100

b) Multiply 1.63 by 400. 1.63 400 1.63 4 100

100

c) Multiply 3.45 by 600. 3.45 600 3.45 6 100

100

13 Multiply.

a) 0.4 400 b) 0.05 300 c) 0.18 500 d) 0.003 600 e) 1.7 200 f ) 3.04 300 g) 1.87 800 h) 21.3 600 i ) 4.225 400 j ) 6.804 500

AB 5B, p 5 >> Activity 2

Another method:0.75 100 3

3

Another method:1.63 100 4

4

Another method:3.45 100 6

6

9

14 Multiply 0.8 by 1000.

0.1 0.1

0.1 0.1

0.1 0.1

0.1 0.1

1000

100

100

100

100

100

100

100

100

0.8 1000

15 a) Multiply 0.5 by 1000. 0.5 1000 0.5 10 100

100

b) Multiply 0.05 by 1000. 0.05 1000 0.05 10 100

100

c) Multiply 0.005 by 1000. 0.005 1000 0.005 10 100

100

d) Multiply.

0.5 1000

0.05 1000

0.005 1000

0.5000.0500.005

10 Unit 1 Decimals

2.130

0.241

16 Multiply.

a) 0.4 1000 b) 0.7 1000 c) 0.9 1000 d) 0.03 1000 e) 0.06 1000 f ) 0.08 1000 g) 0.002 1000 h) 0.004 1000 i ) 0.007 1000

17 Multiply.

a) 0.241 1000

Hundreds Tens Ones Tenths Hundredths Thousandths

2 4 12 4 1

b) 2.13 1000

Thousands Hundreds Tens Ones Tenths Hundredths

2 1 32 1 3 0

c) 0.374 1000

d) 5.803 1000

When a decimal is multiplied by 1000, its decimal point moves 3 places to the right.

Given number Multiply by Product

0.500 1000 500

0.050 1000 50

0.005 1000 5

11

18 Multiply.

a) 0.74 1000 b) 0.061 1000 c) 0.442 1000 d) 4.62 1000 e) 5.39 1000 f ) 3.518 1000 g) 7.8 1000 h) 64.4 1000 i ) 6.504 1000 j ) 30.08 1000

19 a) Multiply 0.23 by 3000. 0.23 3000 0.23 3 1000

1000

b) Multiply 4.312 by 4000. 4.312 4000 4.312 1000 4

4

c) Multiply 3.125 by 8000. 3.125 8000 3.125 1000 8

8

20 Multiply.

a) 0.3 4000 b) 0.04 2000 c) 0.15 3000 d) 0.005 5000 e) 1.8 6000 f ) 3.07 3000 g) 2.76 7000 h) 24.7 8000 i ) 2.321 9000 j ) 70.6 8000

0.23 1000 3

4.312 1000 4312

12 Unit 1 Decimals

I wonder how many places the decimal point would move to the right when the decimal is multiplied by 1 million!

21 What are the missing numbers?

a) b)

10 100

10008.4

10 100

10007.23

c) d)

10 100

100014.7

10 100

10004.836

22 What are the missing numbers?

a) b)

100 10

10006.09

100 10

100087.1

c) d)

100 10

10000.023

100 10

100020.009

AB 5B, p 7 >> Activity 3

13

4 tenths 40 hundredths

Dividing by Tens, Hundreds and Thousands

4 ones 40 tenths4 10 4.0 10 40 tenths 10 4 tenths 0.4

1

1

1

1

0.1

0.1

0.1

0.1

10

0.4 10 0.40 10 40 hundredths 10 4 hundredths 0.04

0.01

0.01

0.01

0.01

0.1

0.1

0.1

0.1

10

0.04 10 0.040 10 40 thousandths 10 4 thousandths

0.001

0.001

0.001

0.001

0.01

0.01

0.01

0.01

10

4 hundredths 40 thousandths

14 Unit 1 Decimals

1 Divide.

a) 2 10 b) 5 10 c) 9 10 d) 0.2 10 e) 0.5 10 f) 0.9 10 g) 0.02 10 h) 0.05 10 i) 0.09 10

2 Divide.

a) 1.6 10

Ones Tenths Hundredths

1 61 6

b) 0.25 10

Ones Tenths Hundredths Thousandths

0 2 50 2 5

c) 1.82 10

d) 14.5 10

1 one 10 1 tenth6 tenths 10 6 hundredths

2 tenths 10 2 hundredths5 hundredths 10 5 thousandths

When a number is divided by 10, its decimal point moves 1 place to the left.

Given number Divide by Answer

4 10 0.4

0.4 10 0.040.04 10 0.004

15

3 Divide.

a) 0.13 10 b) 0.48 10 c) 0.56 10 d) 6.4 10 e) 7.3 10 f) 8.91 10 g) 15.23 10 h) 32 10 i) 208 10

4 a) Divide 2.46 by 20. 2.46 20 2.46 2 10

10

b) Divide 1.64 by 40. 1.64 40 1.64 4 10

10

5 Divide.

a) 0.51 30 b) 4.5 90 c) 18.5 50 d) 24.8 80 e) 8 40 f) 56 70

AB 5B, p 9 >> Activity 4

6 Divide 12.4 by 100.

12.4 100

Tens Ones Tenths Hundredths Thousandths

1 2 41 2 4

12.4 1001 ten 100 1 tenth2 ones 100 2 hundredths4 tenths 100 4 thousandths

2.46 2 1.23

1.64 4 0.41

16 Unit 1 Decimals

7 Divide 3 by 100.

3 100

Ones Tenths Hundredths

30 3

8 Divide 0.8 by 100.

0.8 100

Ones Tenths Hundredths Thousandths

0 80 0 8

When a decimal is divided by 100, its decimal point moves 2 places to the left.

Given number Divide by Answer

12.4 100 0.124

03.0 100 0.03

00.8 100 0.008

9 Divide.

a) 0.2 100 b) 0.6 100 c) 0.9 100 d) 4 100 e) 7 100 f) 1.8 100 g) 4.4 100 h) 78.9 100 i) 124.6 100

03.0 1003 ones 100 3 hundredths

00.8 1008 tenths 100 8 thousandths

17

10 a) Divide 6.9 by 300. 6.9 300 6.9 3 100

100

b) Divide 14.5 by 500. 14.5 500 14.5 5 100

100

11 Divide.

a) 0.2 200 b) 5.2 400 c) 8.4 700 d) 1.6 800 e) 3.5 500 f ) 12.3 300 g) 16.8 800 h) 27.9 900 i ) 785 500 j ) 576 400

AB 5B, p 11 >> Activity 5

12 Divide 3 by 1000.

3 1000

14.5 5 2.9

003.0

6.9 3 2.3

18 Unit 1 Decimals

012.013 Divide 12 by 1000.

12 1000

14 Divide 432 by 1000.

432 1000

When a decimal is divided by 1000, its decimal point moves 3 places to the left.

Given number Divide by Answer

003.0 1000 0.003

012.0 1000 0.012

432.0 1000 0.432

15 Divide.

a) 4 1000 b) 36 1000 c ) 26 1000 d) 114 1000 e) 231 1000 f ) 3050 1000

16 Divide 8 by 2000. 8 2000 8 2 1000

1000

8 2 4

432.0

19

17 Divide 564 by 4000. 564 4000 564 4 1000

1000

18 Divide.

a) 4 4000 b) 18 3000 c ) 48 2000 d) 55 5000 e) 160 4000 f ) 357 7000 g) 644 4000 h) 816 8000 i ) 1224 6000 j ) 2092 4000

19 What are the missing numbers?

a) b)

10 10

10028.9

10 10

10057.9

c) d)

10 100

1000706

10 100

10002841

e) f )

100 10

10007046

100 10

1000462

564 4 141

AB 5B, pp 13 & 15 >> Activities 6 & 7

20 Unit 1 Decimals

Recall these measurements.

Length1 m 100 cm1 km 1000 m

Volume1 l 1000 ml

Mass1 kg 1000 g

Time1 h 60 min

Bala came in first in a high jump event. He cleared a height of 1.4 m. What is this height in centimetres?

1.4 m 1.4 × 100 140 cm

The height is 140 cm.

After the high jump event, Bala drank 300 ml of water. What was the amount of water that Bala drank in litres?

300 ml 300 1000 0.3 l

Bala drank 0.3 l.

14.6mmConversion of Measures

A metre is greater than a centimetre.1 m 100 cmTo convert to a smaller unit, multiply.

A millilitre is smaller than a litre.1000 ml 1 lTo convert to a larger unit, divide.

21

To convert metres to centimetres, multiply by 100.

1 What are the missing numbers?

350 ml

1000 ml

0.1 l0.2 l0.3 l

1 l

l

l

1000 ml

ml

ml

ml

Compare the amounts of water. What do you notice?

ml l

l is less than ml.

2 What are the missing measurements?

0

00.15 m 1 m

50 cm 100 cm

m

cm

3 a) Express 0.85 m in centimetres. 0.85 m 0.85 100

cm

22 Unit 1 Decimals

b) Express 2.75 m in centimetres. 2.75 m 2.75 100

cm

4 a) Express 0.5 km in metres. 0.5 km 0.5 1000

m

b) Express 3.15 l in millilitres. 3.15 l 3.15 1000

ml

c) Express 2.73 kg in grams. 2.73 kg 2.73 1000

g

5 Find the equivalent measures.

a) 0.35 m cm b) 0.125 km m

c ) 2.95 m cm d) 3.85 km m

e) 0.55 l ml f ) 0.825 kg g

g) 3.45 l ml h) 5.2 kg g

To convert kilometres to metres, multiply by 1000.

3.150

2.75

2.730

23

6 a) Express 2.25 m in metres and centimetres. 2.25 m 2 m 0.25 m

2 m cm

b) Express 5.238 kg in kilograms and grams. 5.238 kg 5 kg 0.238 kg

5 kg g

7 Find the equivalent measures.

a) 2.8 m m cm

b) 3.12 m m cm

c) 3.28 km km m

d) 4.025 km km m

e) 2.2 l l ml

f) 5.225 l l ml

g) 4.8 kg kg g

h) 8.75 kg kg g

1 m 100 cm

0.25 m cm

1 kg 1000 g

0.238 kg g

24 Unit 1 Decimals

To convert centimetres to metres, divide by 100.

To convert grams to kilograms, divide by 1000.

330.0

8 a) Express 245 cm in metres. 245 cm 245 100

m

b) Express 525 g in kilograms. 525 g 525 1000

kg

c) Express 330 ml in litres. 330 ml 330 1000

l

9 Find the equivalent measures.

a) 32 cm m b) 450 m km

c) 475 ml l d) 75 g kg

10 a) Express 2 m 42 cm in metres. 2 m 42 cm 2 m 0.42 m

m

b) Express 5 l 125 ml in litres.

5 l 125 ml 5 l l

l125 ml l

42 cm 42 100 0.42 m

25

11 Find the equivalent measures.

a) 3 m 5 cm m

b) 4 m 18 cm m

c) 6 kg 258 g kg

d) 3 l 375 ml l

e) 5 km 438 m km

f) 6 km 300 m km

g) 7 kg 25 g kg

h) 4 l 50 ml l

AB 5B, p 17 >> Activity 8

12 a) Express 325 cm in metres.

Method 2325 cm 325 100

m325.0

25 cm 25 100 0.25 m

Method 1325 cm 300 cm 25 cm 3 m 0.25 m

m

26 Unit 1 Decimals

b) Express 2405 m in kilometres.

13 Find the equivalent measures.

a) 828 cm m b) 3470 m km

c ) 1246 ml l d) 6080 g kg

e) 2009 cm m f ) 4100 ml l

14 A large rock sits at the top of Bukit Timah Hill. The height and the location of the hill are carved on the rock.

a) What is the height of Bukit Timah Hill in metres? b) What is the height of Bukit Timah Hill in centimetres? c) Which unit of measurement is more appropriate? Explain.

App It! @ www.mceducation.com/sgstudent/sapp5 AB 5B, p 19 >> Activity 9

405 m 405 1000 0.405 km

Method 12405 m 2000 m 405 m 2 km 0.405 km

km

Method 22405 m 2405 1000

km2405.0

27

Solving Word Problems

The mass of a sheet of paper is 5 g. There are 500 such sheets of paper in a ream. a) What is the mass of the ream of paper in kilograms?b) Mr Tan uses half a ream of paper to print his report. WhatisthemassofMrTan’sreport?

a)First, find the mass of the ream of paper in grams. Then convert grams to kilograms.1000 g 1 kg

Method 1

500 5 2500 The mass of 500 sheets of paper is 2500 g.

2500 g 2500 1000 2.5 kgThe mass of the ream of paper is 2.5 kg.

Method 2

5 g 5 1000 0.005 kgThe mass of a sheet of paper is 0.005 kg.

500 0.005 2.5The mass of the ream of paper is 2.5 kg.

First, find the mass of a sheet of paper in kilograms. 1000 g 1 kg Then find the mass of the ream of paper.

b) 2.5 2 1.25 ThemassofMrTan’sreportis1.25kg. 1.25 kg is lighter

than 2 kg and heavier than 1 kg.

28 Unit 1 Decimals

1 Jamie ran 1.98 km and Bala ran 1800 m. Who ran the shorter distance? How many kilometres shorter?

2 A jug contains 2.4 l of water. It can fill 20 identical glasses to the brim. How many millilitres of water are there in each glass?

3 Mr Koh jogged 8 laps around a 400-m track. What distance did Mr Koh jog? Give your answer in kilometres.

4 A rectangular hall is 24.68 m long and 20 m wide. Find its floor area.

5 The mass of 20 identical tins of sardines is 8.5 kg. What is the mass of 2 such tins of sardines? Give your answer in kilograms.

6 An apple costs $0.45. A mango costs 3 times as much as an apple. Find the cost of 10 such mangoes.

7 A train route from Station A to Station B is 24.45 km. Each return trip is from Station A to Station B, and back to Station A. A train driver completes 30 return trips. Find the total distance travelled by the train.

8 4.5 kg of white sugar are mixed with 5 times as much brown sugar. The mixture is packed equally into 10 packets. How many kilograms of mixture does each packet contain?

AB 5B, p 21 >> Activity 10

29

Fun

Mathswith

1 1

9

29

39

49

Patterns in DecimalsWhat to do:

What you need:

calculator

30 Unit 1 Decimals

a) Describe the pattern that you observe.

b) Express 59 and 6

9 as decimals without using a calculator.

c) Use a calculator to check your answers.

d) Express 79 and 8

9 as decimals without using a calculator.

e) What do you think the calculator would show for 99?

2 Investigate the patterns observed when you express the elevenths as decimals.

111

211

311

411

a) Describe the pattern that you observe.

b) Express 511 and 6

11 as decimals without using a calculator.

c) Use a calculator to check your answers.

3 Investigate the patterns observed when you express the sevenths as decimals.

AB 5B, p 25 >> Let's Find Out

31

My Notes

AB 5B, p 26 >> My Maths Journal

Multiplying by Tens, Hundreds and ThousandsWhen a number is multiplied by 10, its decimal point moves 1 place to the right.When a number is multiplied by 100, its decimal point moves 2 places to the right.When a number is multiplied by 1000, its decimal point moves 3 places to the right.

Dividing by Tens, Hundreds and ThousandsWhen a number is divided by 10, its decimal point moves 1 place to the left.When a number is divided by 100, its decimal point moves 2 places to the left.When a number is divided by 1000, its decimal point moves 3 places to the left.

Conversion of Measures

A B

100 cm0 cm 200 cm1 m0 m 2 m

0.25 kg 250 g

Length1 m 100 cm1 km 1000 mMass1 kg 1000 gVolume1 l 1000 mlTime1 h 60 min

Examples:

2000 ml

1800 ml

1600 ml

1400 ml

1200 ml

1000 ml

800 ml

600 ml

400 ml

200 ml

1.5 l 1500 ml

32 Unit 1 Decimals