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COURSEBOOK3rd Edition6B
Dr Lee Ngan Hoe • Dr Koay Phong Lee • Charlotte Collars Ong Bee Leng • Tan Cheow Seng
t
CanIuseallthese24cubestomakeabigcube?Explain.
Mycuboidis3unitslongand2unitswide.
Volume�3�2�
�24cubicunits
Whatwillbetheheightofmycuboid?
Use24unitcubestobuildacuboidthatisdifferentfromthecuboidsbuiltbyAini,BalaandCaili.Findthelength,breadthandheightofyourcuboid.
ActivityGroup
18 Unit2 Volume
AB6B,p21>>Recall2
03(M)SMCB6B_U2.indd 18 4/7/17 3:54 pm
2Volume
Aini,BalaandCailieachuse24unitcubestobuildacuboid.
Mycuboidis4unitslong,2unitswideand3units high.Thevolumeofmycuboidis4�2�3�24cubicunits.
3units
2units
4units
2units
4units
Mycuboidis4unitslongand3unitswide.
Volume�4�3� �24cubicunitsTheheightofmycuboidis units.
17
03(M)SMCB6B_U2.indd 17 4/7/17 3:54 pm
DavidBala
Caili
Aini
PrefaceShapingMaths (3rdEdition) isan instructionalpackagewrittenaccordingtothe2013MinistryofEducation,Singapore,primarymathematicssyllabus.Thepackage isdesignedtomeetthelearningneedsofpupilsfromPrimary1to6.ThePrimary6package consists of twoCoursebooks, twoActivity Booksandtwo Teacher’s Planning Guides.
ApproachShapingMaths(3rdEdition)adoptsathematicapproachtowardsthelearningofmathematicsintheupperprimarylevels.Thesethemesreflectvariousaspectsof pupils’ lives and help provide a concrete framework for the mathematical concepts that pupils learn in class. Pupils’ learning is then reinforced through theuseofpicturesandiconsbeforetheyareintroducedtotheformalsymbolicmodeofmathematicalrepresentation.Thethemesalsoprovideanenvironmentforpupilstoexperiencetheinterdisciplinarynatureoflearning.
Continuing research in education has resulted in the introduction of newfeatures in the third edition. Through these features, educators are furtherequippedwithvariousstrategies inaddressing teachingand learningneeds.These features includehands-onactivities,group/pairworkandopen-endedquestionstoencourageexplorationandin-depththinkingamongpupils.Thiswillequippupilswellforthechallengesofthe21stcentury.
FriendsofShapingMathsThe themes of the Coursebook revolve around Aini, Bala, Caili and David.The characters stimulate pupils’ interest and heighten their involvement in the learningprocess.
FeaturesColourfully illustrated unit openers encourage rich and active pupilparticipationinlearningandconnectionstoeverydaylifethroughwholeclassdiscussion.
12 TownUandTownVwere450kmapart.MrAhmaddrovefromTownUtoTown Vataconstantspeedof75km/h.Atthesametime,MrAbduldrovefromTownVtoTownUataconstantspeedof90km/h.Howfarapartweretheyafter1h?
TownU
450km
MrAhmad75km/h,1h
MrAbdul90km/h,1h?
TownV
13 AcarandalorrystartedtravellingatthesametimefromTownRtoTownS.
WhenthecararrivedinTownS,thelorryhadonlytravelled35ofthejourney.
Thelorryneeded45minmoretocompletethejourney.Thelorrytravelledataconstantspeedof60km/h.Findthedistancebetweenthetwotowns.
TownR
Lorry60km/h
Car
?
45min
TownS
14 TownPandTownQwere472 12kmapart.MotoristXleftTownPforTownQat
10 45,travellingataconstantspeedof65km/h.Atthesametime,MotoristYleftTownQforTownP,travellingataconstantspeedof70km/h.Bothmotoriststookthesameroute.Whattimedidtheypasseachother?
TownP
47212km
MotoristX65km/h
MotoristY70km/h
TownQ
Totaldistancecoveredbybothmotoristsin1h� km
Totaltimetakentocover472 12km� h
hafter1045is .
Theypassedeachotherat .
141414 Unit1 Speed AB6B,p15>>Activity5
02(M)SMCB6B_U1 2pf.indd 14 12/6/17 5:41 PM
1 Joharicycledataconstantspeedof200m/min.Howfardidhecyclein45 min?Giveyouranswerinmetres.
2 MrTancompletedajourneyin6hatanaveragespeedof50km/h.MrYucompletedthesamejourneyatanaveragespeedof75km/h.HowmuchlesstimedidMrYuspendthanMrTantocompletethejourney?
3 MrsJonestook5htotravelfromTownPtoTownQ.Shetook2htocoverthefirsthalfofherjourneyatanaveragespeedof100km/h.Findheraveragespeedforthesecondhalfofthejourney.
ReviewA
4 Muthu and his brother Raju take the same route to school. Muthu’s constant walking speed is 30 m/min faster than Raju’s. When Muthu reaches their school in 12 min,
Rajuhasonlywalked23ofthedistance.Findthedistancebetweentheirhouseand
theschool.
Raju Muthu
12min
House School
5 MrsFoostartedherjourneyat7a.m.anddroveataconstantspeedof55km/h.2 h later, Mrs Chen started her journey from the same starting point as Mrs Foo and took 2 h to catch up with Mrs Foo. What was Mrs Chen’s constant driving speed?
35
04(M)SMCB6B_Review A 1pf.indd 35 8/6/17 4:18 PM
Joharicycledataconstantspeedof200m/min.Howfardidhecyclein45 min?Giveyouranswerinmetres.
MrTancompletedajourneyin6hatanaveragespeedof50km/h.MrYucompletedthesamejourneyatanaveragespeedof75km/h.HowmuchlesstimedidMrYuspendthanMrTantocompletethejourney?
MrsJonestook5htotravelfromTownPtoTownQ.Shetook2htocoverthefirsthalfofherjourneyatanaveragespeedof100km/h.Findheraveragespeedforthesecondhalfofthejourney.
Muthu and his brother Raju take the same route to school. Muthu’s constant walking speed is 30 m/min faster than Raju’s. When Muthu reaches their school in 12 min,
PartAForeachquestion,fouroptionsaregiven.Oneofthemisthecorrectanswer.Foreachquestion,fouroptionsaregiven.Oneofthemisthecorrectanswer.
3 Findtheremainderwhen8348isdividedby5.
( 1) 1 (2) 2
(3) 3 (4) 8
2 Express1.005asamixednumberinitssimplestform.
( 1) 1 120
(2) 1 5100
(3) 1 1200
(4) 1 51000
3 Thefigureismadeupofeight1-cmsquares.Whatisitsperimeter?
( 1) 16cm (2) 20cm
(3) 24cm (4) 32cm
4 Arectangulartankmeasures60cmby40cmby30cm.Howmuchwateris
neededtofillthetankto45ofitscapacity?
( 1) 14.4l (2) 57.6l
(3) 72l (4) 90l75
Revision
08(M)SMCB6B_Revision 1pf.indd 75 8/6/17 10:15 PM
MySummaryhelpspupilstoconsolidatetheirlearningattheendoftheyear.Italsoservesasaquickrevisionguideforpupils.
Questionclassificationhelpsteachersspendtheirtimemoreeffectivelybyusingtheappropriatequestionsto getpupilstomasterthenecessaryskills.
Reinforcementofcurrentconcepts
Higher-orderthinkingskills/enrichment
Reinforcementofcurrentconcepts Reinforcementofcurrentconcepts Reinforcementofcurrentconcepts
Higher-orderthinkingskills/enrichment Higher-orderthinkingskills/enrichment Higher-orderthinkingskills/enrichment Higher-orderthinkingskills/enrichment Higher-orderthinkingskills/enrichment Higher-orderthinkingskills/enrichment Higher-orderthinkingskills/enrichment Higher-orderthinkingskills/enrichment
Distancetravelled�Speed�Timetaken
Aini,Caili,BalaandDavidboughtsomegifts.Nametheshapesofthesolidsthattheybought.
Apuzzlecube Aboxofcookies
Abarofchocolate Atinofbiscuits
ThegiftthatIboughtformymotherhad2triangularfaces.CanyouguesswhatIboughtforher?
1 Belowaredrawingsofpyramids.
A B C
face
base base base
a) Howmanyfacesdoeseachpyramidhave?
b) Whatistheshapeofeachfaceofeachsolid?
c) Drawapyramidwithatriangularbaseonapieceofpaper.
Apuzzlecube
54 Unit4 SolidFigures
06(M)SMCB6B_U4 1pf.indd 54 8/6/17 5:15 PM
Guidingquestionsbuildthehabitofcheckingtounderstandaproblem.
Fun
Mathswith
4 x 100 m RelayWhat to do: STEP Selectyourteammembersandwritetheirnamesinthef irstcolumnofatablesuchasbelow.
Example:
Teammembers Distance(m) Timetaken(s) Speed�Distance
Time(m/s)
100m
100m
100m
100m
STEP Gotoarunningtrack.
STEP Eachmemberruns100m.
STEP Recordthetimetakenbyeachmember.Findtheaveragerunningspeedofeachmember.
Whoisthefastestrunnerintheteam?
Comparetheaveragerunningspeedsofyourteammemberswiththoseoftheotherteams.Predicttheteamthatwillwinthe4×100mrelay.Explainyourprediction.
Whatyouneed: stopwatch
Activityfor4pupils
15
AB 6B, p 19 >> Let’s Find Out
02(M)SMCB6B_U1 2pf.indd 15 12/6/17 5:42 PM
STEP Selectyourteammembersandwritetheirnamesinthef irstcolumnofatableSelectyourteammembersandwritetheirnamesinthef irstcolumnofatablesuchasbelow.suchasbelow.
Example:
Teammembers Distance(m) Timetaken(s) Speed�Distance
Time(m/s)
100m
100m
100m
100m
STEP Gotoarunningtrack. Gotoarunningtrack. Gotoarunningtrack.
STEP Eachmemberruns100m.Eachmemberruns100m.
STEP Recordthetimetakenbyeachmember.Recordthetimetakenbyeachmember.Findtheaveragerunningspeedofeachmember.Findtheaveragerunningspeedofeachmember.
Whoisthefastestrunnerintheteam?
Comparetheaveragerunningspeedsofyourteammemberswiththoseoftheotherteams.Predicttheteamthatwillwinthe4×100mrelay.Explainyourprediction.
15
AB 6B, p 19 >> Let’s Find Out
AB6B,p90>>MyMathsJournal
My Notes
Nameofsolid Drawing
Cube
Cuboid
Prism
Cylinder
Pyramid
Cone
Nets
Dottedlinesrepresentthehiddenedges.
DrawingsofSolidFigures
AB6B,p90>>MyMathsJournal
Anetisaaflatshapethatcanbefoldedtoformasolidsuchasacube.
Asolidcanhavemorethanonenet.
acube
67
06(M)SMCB6B_U4 1pf.indd 67 8/6/17 5:15 PM
FunwithMathsengagespupilsininteractivemathsactivitiesthatencourageexploration,discoveryandactivethinking.
MyNoteshelpspupilsconsolidateandrecall,andcommittomemorykeylearningconcepts.
t
Cubes and Cuboids
a) Buildthreecuboids.Use641-cmcubestobuildeachcuboid.Thenfindthemissingnumbersinthetablebelow.
Cuboid Length
(cm)Breadth(cm)
Height(cm)
Basearea(cm2)
Volume(cm3)
A 2 4 64
B 2 16 64
C 2 4 8 64
Volumeofacuboid�Length�Breadth�Height
Length� VolumeBreadth�Height
Height� VolumeLength�Breadth
� VolumeBasearea
A
?2cm
4cm
B
2cm?
16cm
C
2cm
4cm
?
ActivityGroup
Breadth� VolumeLength�Height
19
03(M)SMCB6B_U2 1pf.indd 19 8/6/17 2:08 PM
Sectionswiththisiconinvolvetheuseofcalculators.
speed is 30 m/min faster than Raju’s. When Muthu reaches their school in 12 min,
Rajuhasonlywalked
theschool.
5 MrsFoostartedherjourneyat7a.m.anddroveataconstantspeedof55km/h. MrsFoostartedherjourneyat7a.m.anddroveataconstantspeedof55km/h.2 h later, Mrs Chen started her journey from the same starting point as Mrs Foo and took 2 h to catch up with Mrs Foo. What was Mrs Chen’s constant driving speed?
speed is 30 m/min faster than Raju’s. When Muthu reaches their school in 12 min,
Rajuhasonlywalked
theschool.
MrsFoostartedherjourneyat7a.m.anddroveataconstantspeedof55km/h.2 h later, Mrs Chen started her journey from the same starting point as Mrs Foo and took 2 h to catch up with Mrs Foo. What was Mrs Chen’s constant driving speed?
( 1) 1 ( 1) 1 ( 1) 1 ( 1) 1 ( 1) 1 120
(2) 1 5100
(3) 1 1200
(4) 1 51000
3 Thefigureismadeupofeight1-cmsquares.Whatisitsperimeter? Thefigureismadeupofeight1-cmsquares.Whatisitsperimeter?
( 1) 16cm (2) 20cm
(3) 24cm (4) 32cm
4 Arectangulartankmeasures60cmby40cmby30cm.Howmuchwateris Arectangulartankmeasures60cmby40cmby30cm.Howmuchwateris
neededtofillthetankto45ofitscapacity?ofitscapacity?
( 1) 14.4l (2) 57.6l
(3) 72l (4) 90l
NumberNotationandPlaceValue• We can write a number as a product of two or more factors.
product factors
12 � 2 � 2 � 3
• 29 � 20 � 29 � 2 � 10 � 58 × 10 � 580
• We use ‘≈’ to represent ‘approximately equal to’.
•
NumberRoundedto
thenearestten thenearesthundred
thenearestthousand
32 561 32 560 32 600 33 000
thenearestwholenumber
1decimalplace
2decimalplaces
14.285 14 14.3 14.29
14.643 15 14.6 14.64
• Number Operation Answer
32 × 10 320
32 × 100 3200
32 × 1000 32 000
0.003 × 10 0.03
0.003 × 100 0.3
0.003 × 1000 3
MySummaryNumberNotationandPlaceValue• We can write a number as a product of two or more factors.NumberNotationandPlaceValue• We can write a number as a product of two or more factors.NumberNotationandPlaceValue• We can write a number as a product of two or more factors.NumberNotationandPlaceValue• We can write a number as a product of two or more factors.NumberNotationandPlaceValue• We can write a number as a product of two or more factors.
888888 MySummary
09(M)SMCB6B_Summary 2pf.indd 88 13/6/17 3:59 PM
Activitieshavebeenincludedtoprovidemoreindividual,pairandgrouphands-onlearning.These,alongwiththemanipulativesrequired,arehighlightedforeaseofuse.
ReviewandRevisionprovideaformativeassessment of pupils’ understandingandhelptoconsolidatelearning.
NEW!
CONTENTS
ReviewB 68 Revision 75 MySummary 88
1 Speed 2 • Speed 4 • AverageSpeed 6 • SolvingWordProblems 9
2 Volume 17 • CubesandCuboids 19 • SolvingWordProblems 25
3 PieCharts 41 • ReadingPieCharts 42
ReviewA 35
4 SolidFigures 52 • DrawingsofSolidFigures 53 • Nets 57
1Speed
I reached the finish line before Caili. I am faster than Caili.
David is behind me. He is slower than I am.
Who took the shortest time to complete the walk?
22
Bala walked faster. He took a shorter time to walk 250 m.In 1 min, Bala walked 50 m and Caili walked 41.7 m.Bala‘s walking speed was 50 m per minute.Caili‘s walking speed was 41.7 m per minute.
Speed tells us how fast the children walked. It is the distance travelled per unit of time.
Did David walk more than 41 m in 1 min? Explain.
Speed is the distance travelled per unit of time.Speed Distance travelled Time taken
In the 2016 Olympics,• gold medalist Usain Bolt of Jamaica ran 100 m in 9.81 s.• Elaine Thompson of Jamaica ran 100 m in 10.71 s.• Matej Toth of Slovakia walked 50 km in 3 h 40 min 58 s.• Joseph Schooling of Singapore swam the 100 m butterfly in 50.39 s.
Who can run faster, Usain Bolt or Elaine Thompson? How do you know? Do you think Usain Bolt can run 200 m in 19.62 s? Explain.
Know?
Did You
I walked 250 m in 6 min.I walked 250 m in 5 min.
3
AB 6B, p 1 >> Recall 1
Speed
The taxi travelled at 60 kilometres per hour.We write 60 kilometres per hour as 60 km/h.
At this speed, how far would it travel in 2 h? km
At this speed, how far would it travel in 12 h? km
At this speed, how far would it travel in 2 12 h? km
At this speed, how long would the taxi take to cover 180 km? h
At this speed, how long would it take to cover 120 km? h
At this speed, how long would it take to cover 90 km? h
Bala and Caili shared a taxi home after the fun walk.The speedometer showed how fast the taxi was travelling.
SMCB6B_U1_1
Distance travelled Speed Time taken
Time taken Distance Speed
4 Unit 1 Speed
1 The figure below shows the maximum speed of each car.
Car A81 km/h
Car C90 km/h
Car B74 km/h
Car D89 km/h
Arrange the cars from the slowest to the fastest. Explain.
2 Read the speed shown on each speedometer.
010
20
30
40
5060
70 80 90100
110
120
130
140
160
km/h
1500
1020
30
40
5060
70 80 90100
110
120
130
140
160
km/h
1500
1020
30
40
5060
70 80 90100
110
120
130
140
160
km/h
150
Car X
010
20
30
40
5060
70 80 90100
110
120
130
140
160
km/h
1500
1020
30
40
5060
70 80 90100
110
120
130
140
160
km/h
1500
1020
30
40
5060
70 80 90100
110
120
130
140
160
km/h
150
Car Y
010
20
30
40
5060
70 80 90100
110
120
130
140
160
km/h
1500
1020
30
40
5060
70 80 90100
110
120
130
140
160
km/h
1500
1020
30
40
5060
70 80 90100
110
120
130
140
160
km/h
150
Car Z
a) Which car is travelling the fastest?
b) Explain the speedometer reading of Car X.
c) Car Y travelled at this speed for 12 h. How far did it travel at this speed?
3 David‘s toy robot walked 240 cm in 5 s. What was its speed?
4 After ascending, an aeroplane travels a distance of 1800 km at a speed of 900 km/h before descending. Find the time it takes to travel at this speed.
We can calculate speed, distance and time using the following:
DS T
5 A toy train is moving at 70 cm/s. At this speed, what is the distance it will cover in 5 s?
AB 6B, p 5 >> Activity 1
5
Average Speed
12 s 150 m 1 s ? m
Osman swims 50 m in 2 min.
Does Osman swim at the same speed throughout? Explain.
Osman swims a total of 50 m in 2 min.
He swims an average of m in 1 min.
His average speed is m/min.
Average speed Total distance travelled Total time taken
1 Roderick cycled 72 km in 3 h. What was his average cycling speed in km/h?
2 A remote-controlled car covers 150 m in 12 s. Find its average speed in m/s.
150 12
Its average speed is m/s.
6 Unit 1 Speed
