you will need - · pdf fileyou will need • fraction strips (blm 10) • hundredths...

OPEN-ENDED

You will need•materialsfor

modellingdecimals(e.g.,HundredthsGrids(BLM8)orbasetenblocks)

Pathway 1Dividing Whole Numbers by Decimals

Takumaisusingcansthathold0.❚❚Ltopourwaterintoacontainerthatholds❚L.

• Decidehowmanylitresthecansandthecontainercanhold.Recordthenumbersbelow.

• Estimatethenumberofcansneededtofillthecontainer.Explainhowyouestimated.

• Howmanyfullandpartialcans(asadecimal)areneededtofillthecontainer?Showyourworkandcheckthatyouranswermakessense.

Eachcanholds0. L. Thecontainerholds L.

estimatednumberofcans:about________cans

numberoffullandpartialcans:________cans

• Youcanmodelthedivisionofawholenumberbyadecimalusingahundredthsgrid,basetenblocks(wherethelargecubeisthewhole),oranumberline.

Remember

Copyright © 2012 by Nelson Education Ltd.56

Leaps and BoundsDividingWholeNumbersbyDecimals,Pathway1

Leap SR 7-8_Topic 4.indd 56 2/25/12 2:52 PM

• Repeat2moretimes.Usedifferentdigitseachtime.








Leaps and Bounds DividingWholeNumbersbyDecimals,Pathway1


GuiDEDPathway 1

You will need•FractionStrips

(BLM10)•HundredthsGrids

(BLM8)•basetenblocks•playcoins

Shahercreatedafootprintthatwas0.09mlong.Shewantedtoknowhowmanyfootprintswouldfitalonga5mwall.Sheknewsheneededtodivide5by0.09.

Youcanusevariousstrategiestodivide5by0.09.

• Youshouldestimatefirsttomakesureyouranswermakessense.

0.09isalmost1tenthand5is50tenths.50tenths41tenthis50,soabout50footprintswillfit.

• Youcandivide5by0.09byrenamingbothmeasurementssoyoucandividebyawholenumberinsteadofadecimal.

5m5500cmand0.09m59cm.So,dividing500by9isthesameasdividing5by0.09.

93555495,so50049555R5.Aremainderof5,whenyoudivideby9,is59.

Thisfractionstripmodelshowsthat59isabout12,or0.5.

So5m40.09misabout55.5footprints.

• Youcandivide5by0.09bymodellingwithhundredthsgrids.

Eachgridrepresents1wholemetre,so5gridsrepresent5m.Youcanshadesetsof9smallsquares,or9hundredths(0.09),andthencountthenumberofsetsof9inthe5grids.

LEAP 7/8 SR

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11 11 11 11 11

That’s55setsof0.09with0.05leftover.0.05ofa0.09cmfootprintisabouthalf.

That’s55footprintsandabouthalfafootprint,or55.5.LEAP 7/8 SR

0-176351531

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19

12

12

59

19

19

19

19

19

19

19

19

Dividing Whole Numbers by Decimals

• Youcandividewhenyouwanttoknowhowmanytimesonethingfitsintoanother.

Remember


DividingWholeNumbersbyDecimals,Pathway1 Leaps and Bounds


• Abouthowmany0.10mfootprintswouldfitalongthewall?Whydoesyouranswermakesense?

Try These 1. Howdoeseachmodelshowthecalculation?

a) 340.556

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b) 240.455

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c) 240.2510

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1st pass

d) 440.4510

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4.00 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6

• Basetenblockscanbeusedtomodeldecimals.Ifthelargecubeisthewhole,or1,thenaflatis0.1,arodis0.01,andasmallcubeis0.001.

Remember


DividingWholeNumbersbyDecimals,Pathway1Leaps and Bounds


2. Explainorshowhowtomodeleachcalculation.Writethequotient.

a) 240.255________ c) 140.225 ________

b) 340.65________ d) 440.75 ________

3. Estimateeachquotient.Explainhowyoucouldcheckyourestimateusingamodel.

a) 140.33isabout________.

b) 240.41isabout________.

c) 340.8isabout________.

d) 540.7isabout________.


DividingWholeNumbersbyDecimals,Pathway1 Leaps and Bounds


4. Circlethegreaterquotient.Explainhowyouknowitisgreater.

a) 440.8or440.7

b) 540.23or440.23

5. Astickis0.3mlong.Howmanystickstallissomeonewithaheightof2m?Showyourthinking.

6. Youdivideawholenumberbyadecimal,andthequotientisabout7.Whatnumbersmightyouhavedivided?

________4________isabout7.

7. DoyouagreewithAaron?Showorexplainwhy.

8. Usethefactthat640.4515tohelpyoucalculateeachquotient.Explainyourreasoning.

a) 1240.45________

b) 640.85________

9. Whymightyourename4as40tenthstocalculate440.8?

2 4 0.4 5 4 4 0.8

Itisusefultothinkofdivisionashowmanyofonethingfitsintoanother,whendividingbydecimalsorbyfractions.

FYI


DividingWholeNumbersbyDecimals,Pathway1Leaps and Bounds


OPEN-ENDED


modellingdecimals(e.g.,TenthsGrids(BLM9),HundredthsGrids(BLM8),ThousandthsGrids(BLM7),basetenblocks,ormoney)

Pathway 2Dividing Decimals by Whole Numbers

• Towriteadecimalto the nearest hundredth,decidewhichnumberintheform❚.❚❚thedecimalisclosestto.

e.g.,5.128iscloseto5.13.

• Onewaytocheckaquotientisbymultiplying.e.g.,If124354,then433512.

Remember

Theareaofacityneedstobedividedintoequal-sizedzonesforgarbageandrecyclingcollection.

Part A

• Decideontheareaofthecity.Recordtheareaintheblanksbelow.

• Decideonanumberofzonesbetween3and9.

• Estimatetheareaofeachzone.

• Determinetheactualareaofeachzoneto the nearest hundredthandshowyourwork.Thencheckyouranswer.

areaofcity: . km2 numberofzones:________

estimatedareaofeachzone:about________km2

actualareaofeachzone:________km2


Leaps and BoundsDividingDecimalsbyWholeNumbers,Pathway2


Part B

• RepeatPartA,butuseanareathatisnottoocloseinsizeandexpressitasadecimalhundredth.Useadifferentnumberofzones.




Part C

• RepeatPartA,butuseanareathatisnottoocloseinsizeandexpressitasadecimalthousandth.Useadifferentnumberofzones.Determinetheactualareato the nearest thousandth.




LB56SR

ISBN: 0-17-635153-1FNCO Dave McKay Illustration

T04-F12-LB78SR

dhmPass 2nd passApprovedNot Approved


Leaps and Bounds DividingDecimalsbyWholeNumbers,Pathway2


GuiDEDPathway 2


modellingdecimals(e.g.,TenthsGrids(BLM9),HundredthsGrids(BLM8),ThousandthsGrids(BLM7),basetenblocks,orplaymoney)

Rihannaneedstodividea4.12m2pieceofpaperinto6equalsectionsforhergrouptoshare.Howbigwilleachsectionbe?

Youcanusedifferentstrategiestodivide4.12m2by6tosolvetheproblem.

• Ifyouestimatethequotientof4.1246first,youcanusetheestimatetodecideifyouractualanswerisreasonable.

4.1246ismorethan34650.5.

Soeachstudentwillgetasectionthatisabitbiggerthan0.5m2.

• Todeterminetheactualquotientof4.1246,youcanusehundredthsgridstomodel4.12andshareitequallyamong6students.

LEAP 7/8 SR

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2nd pass

Thereare412squares,or412hundredths,toshare.

41246568R4,whichmeansthereare68hundredths(0.68)ineachshareand4squares,or4hundredths,leftover.

Ifthe4leftoversquares,orhundredths,aresharedamongthe6students,eachgetsalmost1moresquareorhundredth,whichisabout0.09.So4.1246isabout0.69.

Eachpersoninthegroupwillgetabout0.69m2ofpaper.

Ryanhada9.346mlongstripofpapertoshareequallyamong8students.Howlongwilleachstudent’ssharebe?

• Youcanestimateeachstudent’sshare.

9.34648ismorethan84851,soeachstudentwillgetastripthatisabitlongerthan1m.

Dividing Decimals by Whole Numbers

• Whenyoudivide,youshareanamountequallyintoequalgroups,exceptforany“remainder,”orleftoveramount.

Remember




• Todeterminetheactualquotientof9.34648,youcanrenamethedecimalasawholenumber,andthenrenamethequotient.

Since1m51000mm,then9.346m59346mm.

93464851168R2Aremainderof2whendividingby8isnotevenhalf.

Since934648isabout1168,then9.34648isabout1.168.

Eachstudentwillgetastripofabout1.168m.

Try These 1. Explainhoweachmodelshowseachcalculation.

a) 3.6643

LEAP 7/8 SR

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b) 3.4848

LEAP 7/8 SR

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2nd pass

c) 1.23646

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2. Estimateeachquotient.

a) 5.13244isabout________.

b) 13.45848isabout________.

c) 9.1245isabout________.

d) 11.0443isabout________.


Remember




3. Explainorshowhowtomodeleachcalculation.Writethequotient.

a) 5.2445________ b) 3.72465________

4. Eachpartbelowisaboutadifferentwaytocalculate3.844.

a) Howdoyouknow3.844isabitlessthan1?

b) 3.844538tenths44,and38tenths445912tenths.

Howdoyouknowthequotientof3.844is0.95?

c) Whymightyouthinkof3.8as$3.80tohelpyousolve3.844?

5. Calculate.Showyourthinking.

a) 5.13435________ c) 10.48445 ________

b) 10.52425________ d) 9.48465 ________




6. Marcocalculated3.12342bycalculating312342.Whatdoesheneedtoremembertodo?Why?

7. Acardrove228.3kmin3h.Howfardiditgoeachhour,onaverage?

________________

8. Adecimaldividedbyawholenumberis3.41.Whatnumberscouldhavebeendivided?Write2possiblesolutions.

________4________53.41

________4________53.41

9. If4.26Lofjuiceissharedamong6people,eachgets0.71L.Use4.264650.71tohelpyoufigureouteachsharebelow.Explainyourreasoning.

a) 10.26L465________ b) 4.26L435________

10. Createaproblemthatyoucouldsolvebydividing5.2by4.

11. Usethedigits2,3,4,8,and9intheblanks.

a) Createthegreatestpossiblequotient.

. 4 5________

b) Createtheleastpossiblequotient.

. 4 5________

LB56SR


T04-F18-LB78SR

dhmPass 4th passApprovedNot Approved

Whenyouaredividingbyawholenumber,itmakessensetothinkofdivisionassharing.

FYI




OPEN-ENDED


modellingdecimals(e.g.,TenthsGrids(BLM9),HundredthsGrids(BLM8),ThousandthsGrids(BLM7),basetenblocks,ormoney)

Pathway 3Multiplying with Decimals

Estelleboughtbetween3and9packagesofmeatthatallhadthesamemass.

Part A

• Decideonanumberofpackagesofmeat.

• Decideonamasslessthan5kgintheform❚.❚kgforeachpackage.Recordthemassbelow.Donotusea0intheblanks.

• Figureoutthetotalmass.Showyourwork.

• Estimatetocheckyouranswer.Showhowyouestimated.

• Repeatwithanothernumberofpackagesandmass.

numberofpackages:______

massofeach: . kg

totalmass:___________kg

estimate:about___________kg


massofeach: . kg



• Youcanmultiplytocalculatethetotalamountwhenallthegroupsareequal.

• Youcanmodelmultiplicationusinggrids,basetenblocks,ormoney.

Remember


Leaps and BoundsMultiplyingwithDecimals,Pathway3


Part B

• RepeatPartA,butuseadifferentnumberofpackagesandamassintheform❚.❚❚thatislessthan5kg.


massofeach: . kg




massofeach: . kg



Part C

• RepeatPartA,butuseadifferentnumberofpackagesandamassintheform❚.❚❚❚thatislessthan5kg.


massofeach: . kg




massofeach: . kg




Leaps and Bounds MultiplyingwithDecimals,Pathway3


GuiDED


modellingdecimals(e.g.,TenthsGrids(BLM9),HundredthsGrids(BLM8),ThousandthsGrids(BLM7),basetenblocks,orplaymoney)

Pathway 3

Vincentusedatrundlewheeltomeasurethedistancefromhometoschool.Itwas2255m,whichis2.255km.Howfardoesheridehisbikeeachdayifhebikestoandfromschooltwiceaday?

Thereareseveralstrategiesyoucanusetomultiply432.255.

• Youcanestimate.

432.255isabitmorethan432.Sothedistanceisabout8km.

• Youcanmodel432.255usingbasetenblocks.

2.255is8largecubes,8flats,20rods,and20smallcubes.

LEAP 7/8 SR

0-176351531

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T04-F22-LB78SR.ai

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D. Loates

4th pass

Youcantradeblocks,startingfromthethousandths(smallcubes),tofigureouttheproductof432.255.

LEAP 7/8 SR

0-176351531

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T04-F23-LB78SR.ai

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D. Loates

4th pass

432.25559.02

Sothedistanceis9.02km.

• Youcanmultiply432.255byrenamingthedecimalsoyoucanworkwithawholenumberinstead.

2.25552255thousandths432255thousandths59020thousandths,or9.020432.25559.02

SoVincentrides9.02kmeachday.

Multiplying with Decimals


Remember

• Thisstrategyislikeignoringthedecimalpoint,multiplyingthedecimallikeawholenumber,andthenestimatingtodecidewheretoputthedecimalpoint.

Remember




• Youcanmultiply432.255inparts.

2.25552ones12tenths15hundredths15thousands

432.25558ones18tenths120hundredths120thousandths

Youcantradeasyouwouldwithbasetenblocks:

Ones Tenths Hundredths Thousandths

8 8 20 20

9 2

8ones18tenths120hundredths120thousandths59ones12hundredths59.02

432.255km59.02km

Try These 1. Explainhoweachmodelshowseachcalculation.

a) 230.23

LEAP 7/8 SR

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T04-F24-LB78SR.ai

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D. Loates

2nd pass

b) 332.135

LEAP 7/8 SR

0-176351531

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T04-F25-LB78SR.ai

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D. Loates

4th pass

2. Explainorshowhowtomodeleachcalculation.Writetheproduct.

a) 531.45________________ b) 632.1035 ________________




3. Estimateeachproduct.

a) 533.105isabout________.

b) 932.412isabout________.

c) 632.046isabout________.

d) 738.23isabout________.

4. Salmanfiguredout731.361bymultiplying731361.Whatdoeshehavetoremembertodo?Why?

5. Circlethegreaterproductineachpair.Howdoyouknowitisgreater?Iftheproductsareequal,circlebothandexplainhowyouknowtheyareequal.

a) 430.823or430.83

b) 432.28or831.14

6. Gurmeetlaidsix0.235mwoodenstripsendtoend.Whatisthetotallength?Showyourthinking.

7. Supposeyouhad$8.24inyourleftpocketand3timesasmuchinyourrightpocket.Howmuchisinyourrightpocket?Showyourthinking.




8. Ifyouweretodriveanaverageof78.2km/hfor8h,howfarwouldyouget?Showyourwork.

9. Createaproblemthatyoucouldsolvebymultiplying631.4.

10. a) DoyouagreewithLim’sstrategy?Why?

b) Whywouldthatbeagoodstrategyformultiplying?

11. Usethedigits2,3,4,8,and9intheblanks.

a) Createthegreatestpossibleproduct.

. 3 5________________

b) Createtheleastpossibleproduct.

. 3 5________________

12. Completethissentence:

Youusuallymultiplywhen

To multiply 5 3 4.248, I would multiply 10 3 2.124 instead.

• Km/hisashortformforkilometresperhour.e.g.,78.2km/hmeansyoudrive78.2kmin1hour.

Remember

Multiplicationisalwaysaboutthetotalamountofsomeequalgroups,nomatterwhattypesofnumbersyouaremultiplying—decimals,fractions,orwholenumbers.

FYI




OPEN-ENDED


modellingdecimals(e.g.,PlaceValueCharts(toThousandths)(BLM6),ThousandthsGrids(BLM7),orbasetenblocks)

Pathway 4

IngridandJavieruseddifferenttoolstomeasurethelengthandwidthofarectangularroom.Ingridmeasuredthewidthtothenearestthousandthofametre(thenearestmillimetre).Javier’stoolwaslessprecise,sohemeasuredthelengthonlytothenearesthundredthofametre(thenearestcentimetre).

0 1 2 3 4 5 6 7

0 1 2 3 4 5 6 7

LB56SR


T04-F27-LB78SR

dhmPass Second Pass 111024ApprovedNot Approved

Part A

• Chooseawidthcloseto7.5mintheform7.❚❚❚m.

• Choosealengthabitlongerthan13mintheform13.❚❚m.

• Whatistheperimeteroftheroom?Showyourwork.

• Howmuchlongeristhelengththanthewidth?Showyourwork.

width:7. m length:13. m

Whatistheperimeter?________m

Howmuchlongeristhelengththanthewidth?________m

Adding and Subtracting Decimals

• Theperimeterofarectangleisthesumofthe2lengthsand2widths.

Remember


Leaps and BoundsAddingandSubtractingDecimals,Pathway4


Part B

• RepeatPartAtwiceusingdifferentwidthsandlengths.







LB56SR


T04-F28-LB78SR

dhmPass Second Pass 111024ApprovedNot Approved


Leaps and Bounds AddingandSubtractingDecimals,Pathway4


GuiDEDPathway 4


modellingdecimals(e.g.,PlaceValueCharts(toThousandths)(BLM6),ThousandthsGrids(BLM7),orbasetenblocks)

Jennifer’sfamilyistakingatripfromSurrey,BritishColumbia,toLaval,Québec,andthentoHalifax,NovaScotia.

LEAP 7/8 SR0-176351531

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T04-F29-LB56SR.ai

VISUTronX

D. Loates

4th pass

Laval

Surrey Halifax

from Surrey to Laval 4518.169 kmfrom Laval to Halifax 1249.74 kmfrom Laval to Fredericton 821.098 km

Fredericton

Adding Decimals

TofigureouthowfartheywilldrivefromSurreytoHalifax,youcanadd4518.16911249.74.

• Youcanestimatethesum.

4518.16911249.74isabout45001125055750km.

• Youcanadd4518.16911249.74byaddingthewholenumberpartsandthenusingagridtoaddthedecimalparts.

Addthewholenumbers:45181124955767

Addthedecimals,0.16910.74,usingathousandthsgrid:

0.169is1tenth16hundredths19thousandths,whichis1column16squares19smallrectangles.

0.74is7tenths14hundredths,whichis7columns14squares.

Altogether,that’s8columns110squares19smallrectangles,or9columns19smallrectangles,whichis9tenths19thousandths,or0.909.

Combinethewholenumberanddecimalsums:576710.90955767.909km

LEAP 7/8 SR

0-176351531

FN

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T04-F30-LB78SR.ai

VISUTronX

D. Loates

2nd pass

0.169 0.74

Adding and Subtracting Decimals




• Youcanadd4518.16911249.74byaddinginsteps.

Addthewholenumbers: 45181124955767

Thinkof0.169inparts: 0.16950.110.0610.009

Add0.16910.74insteps: 0.7410.150.84 0.8410.0650.90 0.9010.00950.909

Addthewholenumberanddecimal: 576710.90955767.909km

Subtracting Decimals

IfJennifer’sfamilywenttoFrederictoninsteadofHalifax,thedistancewouldbeless.Tofigureouthowmuchless,youcancalculate1249.742821.098.

• Youcanestimatethedifference.

1249.742821.098isabout120028005400.

• Youcancalculate1249.742821.098byaddingupfrom821.098to1249.74insteps.

LEAP 7/8 SR

0-176351531

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T04-F31-LB78SR.ai

VISUTronX

D. Loates

2nd pass

821.098821.1

0.002 0.9 78 349.74

822 900 1249.74

Toadd349.7417810.0910.002,youcanadd3491785427andthenadd0.7410.910.00250.092.That’s428.642altogether.

ThedistancetoFrederictonwouldbe428.642kmless.

• Youcanalsocalculate1249.742821.098usingwholenumbers,byrenamingthemeasurementunitsused.

1249.74km2821.098km51249740m2821098m5428642m5428.642km

• Youcanalsosubtractusingaplacevaluechartandregrouping.

Thousands Hundreds Tens Ones Tenths Hundredths Thousandths

1–

122

842

91

67

0

349

1008

4 2 8 6 4 2

Withoutaplacevaluechart,thesubtractionlookslikethis:

Thedistancewouldbe428.642kmless.

126310

1249.7402 8 21.098

4 28.642




Try These 1. Estimateeachsum.

a) 42.8137.192isabout____________.

b) 510.8162.49isabout____________.

c) 311.4147.922isabout____________.

d) 511.811204.38isabout____________.

2. Estimateeachdifference.

a) 42.8237.192isabout____________.

b) 510.8262.49isabout____________.

c) 311.4247.922isabout____________.

d) 1204.382511.8isabout____________.

3. Whycanyouignorethedecimalpartsofthenumberstoestimate14.298127.123,butnottoestimate0.31210.947?

4. Sketchamodelordescribeastrategytocalculate.

a) 4.12613.85________ b) 15.123.8725 ________

5. HowcouldyouhavepredictedthethousandthsdigitineachanswerinQuestion4?




6. UsethePartsofaYearcharttohelpyou.

a) Whatpartofayearis37days?Showyourwork.Explainwhyyouranswermakessense.

b) Whatpartofayearis29days?Howdoyouknow?

7. a) Whymightsomeonethinkitiseasytoadd4.2310.006?

b) Whymightsomeonethinkitiseasytosubtract4.23623.0?

8. Write2possiblesolutionsforeachsituation.

a) Thesumof2decimalsis5.123.

________________1________________55.123

________________1________________55.123

b) Thedifferencebetween2decimalsis3.923.

________________2________________53.923

________________2________________53.923

9. a) Usethedigits1to9tocreatethegreatestpossibledifference.

. 2 . 5______________

b) Usethedigits1to9tocreatetheleastpossibledifference.

. 2 . 5______________

It’s easy to add 4.23 1 0.006 and easy to subtract 4.236 2 3.0.

Addingandsubtractingarecloselyrelated.Yousometimesuseoneoperationtohelpyouwiththeother.Forexample,toadd2.3410.99,youcanaddtoomuch,2.3411,andthensubtract0.01tocompensate.

FYI

Parts of a Year

Estimated part of a

year

1day 0.003

1week 0.019

1month(30days) 0.08




you will need - · pdf fileyou will need • fraction strips (blm 10) • hundredths...

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