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MFM1P

Unit1:ProportionalReasoningMathwithsheppard.weebly.com

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Unit1:ProportionalReasoning

Day Date Topic LearningGoal Homework

1.1 Sept7 RepresentingRatios*MulletActivity

Howtorepresentratiosinvariouscontexts.

Homework1.1

1.2 Sept8 EquivalentRatios Howtoreduceratiosanddetermineequivalentratios.

Homework1.2

1.3 Sept9 RatiosQuizUnderstandingRates

Howtocalculateunitrate.

Homework1.3

1.4 Sept12 ComparingRates Howtocalculateunitrateanddeterminethebetterbuy.

Homework1.4

1.5 Sept13 RatesQuizProportionalReasoning

Part1

Howtosetupaproportiontosolveforagivenquantity.

Homework1.5

1.6 Sept14 ProportionalReasoningPart2

Howtosetupaproportionandsolvebymultiplicationrelationships.

Homework1.6

1.7 Sept15 ProportionsQuizProblemSolvingwith

Proportions

Howtosetupaproportiontosolveforagivenquantity.

Homework1.7

1.8 Sept16 SolvingPercentProblems Howuseproportionstosolvepercentproblems.

Homework1.8

1.9 Sept19 TipsandTaxes Howtouseproportionstocalculatetipsandtaxes.

Homework1.9

1.10 Sept20 PercentQuizDiscountsandSalePrices

Howtouseproportionstocalculatediscountsandsaleprices.

Homework1.10

1.R Sept21 UnitReview

Sept22 Unit1Test

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MFM1P–Unit1:ProportionalReasoning–Lesson2 Date:______________Learninggoal:howtoreduceratiosanddetermineequivalentratios.

EquivalentRatios

ACTIVITY-RATIOGRIDS

i. Shadethegridontherightsothattheratioofshadedsquarestototalsquaresisthesameastheratiointhegridontheleft.

ii. Writetheratiosofshadedsquarestothewholenumberofsquaresbesideeachgrid.iii. Showtheratioin3ways

1a.

1b.

2a.

2b.

3a.

3b.

Recall:Aratioisacomparisonoftwoquantitieswiththesameunits.

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LESSONEx.Thereare4soccerballsforevery2basketballs,theratioofsoccertobasketballsis4:2Question:Howmanybasketballsforevery2soccerballs?Let’smakeamodel:

Butitcouldalsobedescribedas8:4,sinceforevery8soccerballs,therewouldbe4basketballs.

Thefirsttermisdoublethesecondinbothcases,sotheseareequivalent(equal).Ifwemultiplythetwotermsbythesameamount,wewillhaveanequivalentratio.Example1:Whichoftheseratiosareequivalentratios? a)2:5and2:3 b)2:5and4:10 c)4:10and6:15

SCALEFACTORS

Therearetwowaystodetermineequivalentratios.

MethodA

Multiplyeachterminaratiobythesamenumber.eg.8:10=

MethodB

Divideeachterminaratiobyacommonfactor.eg.8:10=

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Example2:Determineanequivalentratio.ShowyourscalefactorByMultiplying ByDividing

a) 2:3=

a)30:50=

b) 4:3=

b)21:7=

Example4:Findthemissingnumbertomakeeachpairofratiosequivalent. a)5:6=____:24 b)12:36=8:_____Example5:Youmake5cupsofpunchbymixing3cupsofcranberryjuicewith2cupsofapplejuice.Howmuchcranberryjuiceandhowmuchapplejuicedoyouneedtomakefourtimestheoriginalrecipe?REDUCINGRATIOSTOLOWESTTERMSExpressthenumberofcirclestosquareasaratio.Reducetolowesttermsifpossible.

Writethefollowingratiosusingeitherdoubledotorfractionalnotation.Reduceifneeded. a.18poundsto12pounds b.5daysto31days Writeeachratioasafractioninlowestterms,ifpossible a.12to4 b.35:25 c.60to180

d.15 e.7:4 f.8 20 28

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Homework1.2:EquivalentRatios1. Writeeachratioasaratioinlowestterms. a.2to4 b.3to12 c.35:7 d.15 e.7:4 f.8 20 28 h.18 g.6:18 12 i.24to96 2. Writeeachratiousingrationotation,thenreducetolowesttermsifpossible.

a)$2comparedto$8.b)Inaclass,14of30studentsaregirls.

c)Theratioof$46to$23d)Theratioof21daysto28dayse)Inaclass,thereare32chairsand8tables.

3. Findthemissingtermineachpairofequivalentratios. a)7:9=49:_____ b)7:13=77:______ c)45:36=______:12 d)30:48=______:8 e)72:84=______:7 f)121:88=______:84. Bobneedstomix2cupsoforangejuiceconcentratewith3.5cupsofwatertomakeorangejuice.Bobhas

6cupsofconcentrate.Howmuchwaterwillheneed?

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5. Usethedataaboutwinsandlossesonschoolteamstoanswerthequestions.

a)Writetheratioofwinstolossesforeachsport.Reducetolowestterms.

c) Whichsportshaveequivalentwin–lossratios?

6. Trevoristrainingforaduathlon,whichisaracethatconsistsofrunningandcycling.Thecyclinglegislongerthantherunninglegoftherace,sowhileTrevortrains,herideshisbikemorethanheruns.Duringtraining,Trevorruns4milesforevery14milesherideshisbike.

a)Identifytheratioassociatedwiththisproblem:

b)Oneweek,Trevorrodehisbikefor84miles.HowmuchdidherunduringthatweekaccordingtoTrevor’strainingschedule?

c)WhenTrevorcompletedallofhistrainingfortheduathlon,theratiooftotalnumberofmilesherantototalnumberofmileshecycledwas80:280.IsthispossibleaccordingtoTrevor’strainingschedule?Explainwhyorwhynot.

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7. Theratioofsheeptochickensis5:8.a)Whatistheratioofchickenstosheep? b)Whatisthefractionofsheeptoanimals?

8. a)Simplifyeachratio(reducetolowestterms)b) Whichratiosineachpairareequivalent?

a)12:15 and 48:60 b) 3:2 and 25:16

c)3:4 and 15:18 d) 625:125 and 180:36

1.2Answers1.a)1:2b)1:4c)5:1d)3:4e)7:4f)2:7g)1:3h)3:2i)1:42.a)2:8=1:4b)14:30=7:15c)46:23=2:1d)21:28=3:4e)32:8=4:13.a)63b)143c)15d)5e)6f)114.14cupsofwater5.a)Hockey3:2Volleyball2:1Baseball:3:2b)HockeyandBaseball6.a)4:14=run:bikeb)24c)yes

7.a)8:5b)5:138.a)4:5equivalentb)notequivalentc)notequivalentd)5:1equivalent

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MFM1P–Unit1:ProportionalReasoning–Lesson3 Date:______________Learninggoal:howtocalculateunitrate.

UnderstandingRates

RATERate:Acomparisonoftwoquantitieswithdifferentunits.

Example: .390390hrmihourspermiles →

Herearesomerates:

• Chrisdrove107milesintwohours.• Orangesareonsalefor$1.49for12.• Ginaearns$4.75perhourforbaby-sitting.• Thereare500sheetsononerollofpapertowels.

State3examplesofratesthatyouknow.WHENWRITINGRATES,YOUMUSTALWAYSSHOWTHE_______________OFMEASUREMENTS.Example1:Writeeachrateasafractioninthelowestterms. a)132patientsto8doctors. b)72lettersin4minutes. c)90textsfrom2students. d)$525for25people.UNITRATE

UnitRate:Arateinwhichthesecondquantityis1.

Example: .130

.390390

hrmi

hrmihourspermiles =→

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CalculatingUnitRatesWorkedexample:Geraldpays$90for6yogaclasses.Whatisthecostperclass?

Example2:Acruiseshiptravels200milesin50minutes.Howfardoestheshiptravelperminute?

Example3:Findtheunitrate.Showyourwork.

a) 90eggsfrom15chickens. b)780kmin12hoursUNITPRICEUnitPrice:Aunitrateusedtocomparecostperitem.

Example:boxboxes

boxesper175.3$

650.22$650.22$ =→

Example4:Thecostof2cartonsofmilkis$5.50.Whatistheunitprice?

ProblemSolvingwithUnitRatesYoucansolverateproblemsbyusingaunitrateorbyusingequivalentrates.a)Sarahhastwowirelessproviderstochoosefrom.Super-Celloffers250baseminutesfor$24.99amonth.Easy-Phonehasaplanthatincludes325baseminutesfor$34.99amonth.Whichischeaper?b)AtownineastTexasreceived10inchesofrainin4days.Ifitkeptrainingatthisratefora31-daymonth,howmuchraindidthetownreceive?

UNITPRICE=COSTdividedbyAMOUNT

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Homework1.3:UnderstandingRates1. Determineifthefollowingareexamplesofrates,unitrates,orunitprice.

a) priceofwheatis$2for3Kgb) 50persecondc) acargoes100milesin1.5hourd) priceofpetrolis$5pergallon.e) $2.00for5muffinsf) acargoes60milesin1hourg) priceofcornis$2perounceh) 6busestotransportagroupof300people

2. Describethedifferencebetweenarate,aunitrate,andaunitprice.Useexampleswithyourdescriptions.

3. Give2examplesofratesthatareusedineverydaylife.Writetheunitsforeachofyourrates.4. Writeeachrateasafractioninthelowestterms.Besuretoincludeyourincludes. a)72pillsfor36cats. b)90mileson3gallons. 5. Writeeachofthefollowingratesasaunitrate. a) 3Tbsp b)135pitches 2tsp 45strikes c) 128miles d)2250pencils 4hours 18boxes6. Determinetheunitrateineachsituation. a)200milesin15hours. b)42booksfor12students.

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c)Anorcaswims110kmin2h. d)Cathyplants45daffodilsin30min.

e)Thecruisingspeedofabluewhaleallowsittotravel193kmin10h.

7. Lindsayhasscored15goalsin10lacrossegamesthisseason.

a)Whatisherunitrateofscoring?

b)HowmanygoalsmightLindsayscorein36games?Whatassumptionsdoyoumake?

8. Ginaearns$78.00forworking6h.Asadmakes$192.50afterworking14h.Determineeachperson’sunit

rateofpay.Whohasagreaterhourlyrateofpay?9. MoniqueworkedasacleanerattheCalgaryStampedeandExhibition.Shewaspaid$84foran8-hday.

a)WhatwasMonique’shourlyrateofpay?

b)HowmuchwouldMoniqueearnfor35hofwork?**FINDHOURLYRATEFIRST

10. Whichisabetterbuy?Showyourwork.

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30ouncesofvinegarfor$2.99 OR 48ouncesofvinegarforcost$4.09.1.3Answers1.a)Rateb)unitratec)rated)unitpricee)ratef)unitrateg)unitpriceh)rate2.rate=acomparisonbetweentwoquantities,unitrate=arateperone,unitprice=thepriceperone3.answersmayvary4.a)2pills/1catb)30miles/1gallon5.a)1.5tbsp/tspb)3pitches/strikec)32miles/hoursd)125pencils/boxes6.a)13.3miles/hoursb)3.5books/studentc)55km/hd)1.5daf/mine)19.3km/hf)6times/hours7.a)1.5goals/gameb)54goals 8.$13and$13.75,Asad9.a)$10.50/hb)$367.5010.48ounces

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MFM1P–Unit1:ProportionalReasoning–Lesson4 Date:______________Learninggoal:howtocalculateunitrateanddeterminethebetterbuy.

ComparingRates

Example1:Shanaisatthegrocerystorecomparingtwobrandsofjuice.BrandAcosts$3.84fora16-ouncebottle.BrandBcosts$4.50fora25-ouncebottle.Tocomparethecosts,Shanamustcomparepricesforequalamountsofjuice.Howcanshedothis?

Example2:Mariahislookingforapart-timejob.Shewantstowork15haweek.Shehasbeenofferedthreepositions.

DayCampCounsellor Cashier LibraryAssistant

$7.50perhour $25.00for3h $44.00for5h

a)Whichjobpaysthemost? b)Forthejobinparta,howmuchwillMariahearninoneweek?

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Example3:Twostoresareadvertisingspecialsonapples.

Applesaresoldindividually.Howmuchlesswould30applescostatStoreBthanatStoreA?

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Homework1.4:ComparingRates

1. Writeaunitrateforeachstatement.Besuretoincludeyourincludes. a)$399earnedin3weeks b)680kmtravelledin8h

c)12bottlesofjuicefor$3.49 d)3cansofsoupfor$0.99

e)200milesin15hours. f)85feetin20seconds. g)42booksfor12students. h)39childrenfrom13families.

2. Thegrocerystoreadvertisesthefollowing. a)Determinetheunitrateforeachpackagein$/mL. b)Whichpackageisthebestbuy?Explainyourchoice.

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3. Thetableshowsthepriceofdifferent-sizedpackagesofmixednuts.

a)Determinetheunitrateforeachpackagein$/kg. b)Whichpackageisthebestbuy?Explainyourchoice.

4. Mr.Gomeztravelled525kmin6h. a)AssumeMr.Gomeztravelledthesamedistanceeachhour.Whatisthisdistanceperhour?

b)Atthisrate,howlongwillittakeMr.Gomeztotravel700km?

5. Whichisthegreatestaveragespeed?(Hint:Comparetheunitrates)

i)60kmin3h ii)68kmin4h iii)70kmin5h

6. LakelseLake,BC,hadthemostsnowforonedayinCanada,whichwas118.1cm.Assumethesnowfellataconstantrate.Howmuchsnowfellin1h?

1.4ComparingRates1.a)$133/weekb)85km/hc)$0.29/botd)$0.33/cane)13.3mi/hf)4.25ft/secg)3.5books/studenth)3children/family2.a)A$0.0053/mlB0.00478/mlC0.00465/mlb)C

3.a)1-$0.0073/g2-$0.00618/g3-$0.0069/gb)24a)87.5km/hb)8hours5.4.92cm/h6.b)A$3.61/kgB$2.21/kg-Bisthebetterbuy

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MFM1P–Unit1:ProportionalReasoning–Lesson5 Date:______________Learninggoal:howtosetupaproportiontosolveforagivenquantity.

ProportionalReasoningPart1

Vocab:Aproportion=anequationthatshows2ratiosorratesareequalWARMUP:Ex.1TheSuarezfamilypaid$15.75for3movietickets.Howmuchwouldtheyhavepaidfor12tickets?Decideonastrategytosolve.Sharewithapartner&copyanothertypeofstrategytosolve.MyStrategy: AnotherStrategy:Ex.2AtSidekicksleadershipcamp,thecampersaredividedintogroups.Eachgrouphas16campersand2cabins.Howmanycabinsareneededfor64campers?Fillinthechartwiththedifferentstrategies

STRATEGIES#1CreatingEquivalentRatios

#2FindingUnitRates

Reflect:Whenwouldyouuseeachstrategy?Ex.3:Justintakeshispulseandcounts18heartbeatsin15seconds.Whatisherheartrateinbeatsperminute?Hint:thereare_____sec.inevery1minute.

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Ex.4:SamworksinPeterborough.Eachweek,hetravels125kmforworkandusesapproximately13Lofgasoline.Whatishiscar’srateoffuelconsumptioninlitersper100km?Findunitratetosolve.

Ex.5:Atthemovietheatre,65studentticketsweresoldforoneshow.Theratioofadultticketssoldtostudentticketssoldwas3:5.Howmanyadultticketsweresold?*setupproportiontosolve

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Homework1.5:ProportionalReasoningPart11. Determinethemissingvaluetomakeeachrateequivalent.Includetheunits.

***Showscalefactor

a) b) c)

2. Determinethemissingvaluetomakeeachrateequivalent.Includetheunits.

a) $486students

=?

1student=

?15students

b) $135900MB

=?

1MB=

?160MB

3. Foreachofthefollowingquestions,setupaproportion,findtheunitrate,thensolve.

a) Seanbuys8DVDsfor$120.EachDVDcoststhesameamount.i)Howmuchdoes1DVDcost? ii)Howmuchdo13DVDscost?

b) Loraworksfor4daysandearns$224.Atthisrate:i) Howmuchdoessheearnin1day? ii)Howmuchdoessheearnin11days?

4. Amachinecanbind1000booksin8min.

a)Howmanybookscanthemachinebindin1h?*thereare___minin1hour

b)Howlongwillittaketobind7250books?Explain.

60km3h

=?6h

$34cans

=$15?

178beats2min

=?

1min

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5. Therecommendedseedingonapackageofgrassseedis200gper9m2.Careyspread150gover6.5m2.Isthismorethan,equalto,orlessthantherecommendedseeding?

6. LoChoiwantstobuyadozendoughnuts.Shehasacoupon.Thisweek,thedoughnutsareonsalefor$3.99adozen.IfLoChoiusesthecoupon,eachdoughnutis$0.35.ShouldLoChoiusethecoupon?Justifyyouranswer.

7. Twocarstravelalongahighwayatthesamespeed.CarAtravels20kmin12min.HowlongwillittakeCar

Btotravel50km?8. Asoccerteamplayed28gamesandwon4outofevery7games.Therewerenotiedgames.

a)Howmanygamesdidtheylose?b)Whatwastheteam’swin–lossratioinlowestterms.c)Ifthistrendcontinues,howmanylosseswouldyouexpecttheteamtohaveoncetheyhavewon20games?

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9. Alexmakesnecklacesusingcolouredbeads.Theratioofbluebeadstoredbeadsis3:4andtheratioofredbeadstoyellowbeadsis4:1.IfAlexwouldliketomakeanecklacewith56beads,howmanyofeachcolourwouldsheneed?

1.5Answers1.a)120kmb)20cansc)89beats 2.a)$8/student,$120/15studentsb)$0.15/MB,$24/MB3.a)$15/DVDb)$195 4.a)7500b)58min 5.morethanrecommended6.salepriceischeaper 7.30mins 8.a)12gamesb)4:3c)15losses9.21blue28red7yellow

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MFM1P–Unit1:ProportionalReasoning–Lesson6 Date:______________Learninggoal:howtosetupaproportionandsolvebymultiplicationrelationships.

ProportionalReasoningPart2

Solveeachproportionbymultiplicationrelationships:

a) Isthereanotherwaytosolve?Let’strya)

b)

Whyisitdifficulttosolvethefollowingusingmultiplicationrelationships:

c)

d) d)

Howcouldwesolvetheseequations?(Show2ways)

k1

142=

4218

7=

a

1025

12=

u645

=d 98

6 r=

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Example1:Solveeachwordproblemusingaproportiona)Arecipefor8peoplecallsfor3cupsofflour.Howmuchflourwouldbeneededfor12people?b)Abreakfastcerealcontainscorn,wheat,andriceintheratioof3to4to2.Ifaboxofcerealcontains225gofcorn,howmuchricedoesitcontain?c)Mayaworksasapharmacist.Therecommendeddosageoffluvaccinefora15kgchildis0.2ml.Determinewhatdosagesheshouldgivea36kgchildiftheratioremainsthesame.

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Homework1.6:ProportionalReasoningPart2

1. Solveforeachunknown.Showyourwork.

a)6:8=n:12 b)2=8 c)4:n=6:9 7nd)n=11 e)3=2 f)0.4=12 63 n5 1.5n

Solvebyusingaproportion.Roundanswerstothenearesttenth(onedecimal)ifnecessary.Answereachquestionwithasentence.

2. Youjog3.6milesin30minutes.Atthatrate,howlongwillittakeyoutojog4.8miles?3. Youearn$33in8hours.Atthatrate,howmuchwouldyouearnin5hours?4. Ifonegallonofpaintcovers825sq.ft.,howmuchpaintisneededtocover2640sq.ft.?

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5. Amapscaledesignates1inch=50miles.Ifthedistancebetweentwotownsonthemapis2.75inches,howmanymilesmustyoudrivetogofromthefirsttowntothesecond?

6. Atanautomotiverepairshop,3.5hoflabourcosts$311.50.Whatisthelabourchargefora5-hjob?Howcouldyoucheckyouranswer?

7. Yougetsixpiecesofguminapackagethatcosts$0.87.

a)Ifyoucouldbuyapackagewiththreepiecesofgum,howmuchwoulditcost?

b)Howmuchwouldyoupayforapackageofeight?

1.6Answers1.a)9b)28c)6d)22e)7.5f)45 2.40minutes 3.$20.63 4.3.2gallons 5.137.5miles6.$519.17 7.a)$0.44b)$1.16

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MFM1P–Unit1:ProportionalReasoning–Lesson7 Date:______________Learninggoal:howtosetupaproportiontosolveforagivenquantity.

ProportionalReasoningProblemSolving

MINDSON.GUMMYBEARS!Act1:Howmanyregularbearsequalonesuperbear?Anumbertoolow:_____ Toohigh:______ Myguess:______Howmanyminibearswouldequalonesuperbear?Act2:Whatinformationdoweneed?Act3:AnswerExtension:Ifyouwantedtoeatthemostgummyfortheleastmoney,shouldyoubuyregularbearsorminibears?Whatwouldbeafairpriceforasuperbear?____________________--------------------------------------------------------------------------------------------------------------------------------Example:Abagoffertilizercontainsnitrogentophosphorustopotassiuminaratioof20:10:5.Thebagcontains3.6kgofphosphorus.Whatisthetotalmassofnitrogenandpotassium?

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Assignment1.7:ProblemSolvingWithProportions

1. Inthefirstyearofafundraisingcampaign,donationsarecollectedatarateof$700eachdayfor8days.Inthesecondyear,thedailyratedoublesandthecampaignis3dayslonger.Howmuchmoneyisraisedinthesecondyear?

2. Youonlyneedfourcolouredmarkers.Thesmallestpackageavailablehassixmarkersinitandcosts$9.00.

Onepackagehasbeenopenedandcontainsonlyfivemarkers.Youaskthesalesclerkhowmuchitwouldcost.Whatwouldthecostofthisdamagedpackagebe?Justifyyouranswer.

3. Thetablebelowshowsthecostofwaterforthreecustomers.Theyeachpaythe

samecostperlitre.Frankpays$36.12forwateratthesamerate.Determinethenumberoflitresofwaterthathepurchases.Showyourwork.

4. Aclassisgoingonafieldtriptoalocationthatis85kmfromtheschool.Fuelfor

thebuscosts$1.09/L.Thebususes35Loffuelforevery100km.Findthecostoffuelforthebustotaketheclassonthefieldtripandbacktotheschool.

5. Foracertaintypeoframp,theratiooftheheightoftheramptothehorizontallengthoftherampneeds

tobe1:4.Aramphasbeendesignedtobe26minhorizontallengthwithaheightof7m.Wouldthisrampbesafe?Showyourworkandjustifyyouranswer.

6. Clarenceworksatvet’soffice.Heneedstogiveadoseofmedicinetoa24kgdog.Therecommendeddosage

foradogthatweights10kgis25ml.DeterminethedoseClarenceshouldgivetothe24kgdogiftherateremainsthesame.Showyourwork.

7. LisaandMarioexercisedatthegymtogether.Lisaburned120caloriesin8minutes.Marioburned49

caloriesin210seconds.Iftheybothkeptworkingoutatthesamepace,whichofthetwowillburnmorecaloriesfor1hourandhowmanymore?Showyourwork.

1.7Solutions1.$19252.$7.50($1.50percrayon) 3.42000L4.$64.86 5.Yes(heightislessthan4timesasbigaslength)6.60mL7.Lisa,60caloriesmore

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MFM1P–Unit1:ProportionalReasoning–Lesson8 Date:______________Learninggoal:howuseproportionstosolvepercentproblems.

SolvingPercentProblems

Example1:Onaparticularday,8%ofallofthepeopleinaschoolbuildingareadults.Ifthereare2325peopleintheschool,howmanyadultsarethere?Example2:Supposeaschoolhas720students.Atleast60%arerequiredtoparticipateinafund-raiserbeforeasponsoringcompanywillhelpwithaschoolevent.Howmanystudentsareneeded? Example3:Vincescored82.5%onamathtest.Johnhad15outof18onthesametest.Whodidbetter?Howdoyouknow?

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Example4:Studentcouncilestimatesthat85%ofthegrade9studentsatJohnF.Rossaregoingtothedance.

a)Whatpercentageofstudentsarenotgoingtothedance?

b)Ifthereare462grade9students,howmanyaregoingtothedance?

c)Ifonethirdofthegrade9studentsgoingtothedanceboughttheirticketsatthedoor,howmanyticketsdotheyneedforgrade9satthedoor?

Example5:Ethanhad$550inthebank.Hetookout$50tospendonapresent. a)Whatpercentofhismoneyisstillinthebank? b)Howmuchcouldhehavetakenoutifhewantedtomakesurethat70%wasstillinthebank?

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Homework1.8:SolvingPercentProblems

1. Therewere288spectatorsatthefootballgame.75%werecheeringforthehometeam.

a)Howmanyspectatorswerecheeringforthehometeam?Explain.

b)Approximately40%ofthespectatorswerestudents.Howmanyspectatorswereadults?

2. TheIncredibleChocolateChipCompanyhasdiscoveredthat36outof400chocolatechipcookiesdonot

containenoughchocolatechips.Whatpercentofthechocolatechipcookiesdonothaveenoughchips?3. Hersheyisinakennelwith15catsand35dogs.40%ofthepetsarescaredofthunderstorms(eek!).With

theincomingstorm,howmanypetswillneedsomecalmingmeasurestoeasetheiranxiety?4. Mrs.Sheppardgavea$5.00tiptoawaitressforservingamealcosting$27.00.Whatpercentofthebill

washertip? 5. IntheCentralCityGrandPrix,outof30carsthatstartedtherace,12ofthemfinished.Whatpercentof

thecarsfinishedtherace?Whatpercentdidnotfinishtherace?

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6. Ericearned60pointsonhislasttest.Iftherewere75possiblepoints,whatwashispercentgrade?7. Inavolleyballgame,Carolineservedtheballoverthenet16outof20times.Whatpercentdidshenot

makeherserveoverthenet? 8. Restaurantetiquettedictatesthatyoushouldleavea15%tipfortheserveriftheserviceisacceptable.If

thatisthecase,howmuchshouldyoutipifyourtotalis$36.00? 9. In2014,20%of200studentsvotedtoprotestabanonjunkfood.In2015,30%of100studentsvotedto

protestthesameban.Howmanymoremembersvotedtoprotestthebanin2014thanin2015? 1.8Answers1.a)216peopleb)115people 2.9% 3.20pets 4.14%5.80% 6.87.5%7.20% 8.$5.40 9.10more

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MFM1P–Unit1:ProportionalReasoning–Lesson9 Date:______________Learninggoal:howtocalculatetipsandtaxes.

TipsandTaxes

WARMUP:TakeacoupleminutestodiscusswhatyouknowabouttippingatarestaurantWhataresomethingstoconsiderwhendeterminingtheamounttotipaserver?Example1:Thegeneralguidelineis20%forexcellentservice,and15%foraminimumtip.Ifamealcosts$45.29,whatwouldbethetipforexcellentservice?EASYWAYTOCALCULATETIPS“ONTHEFLY”….MentalMath:10%ofanythingiseasytofigureoutinyourheadbecauseyoujustmovethedecimaltotheleftoneplace.Youcandouble10%tofind20%. ie.10%of$55.00is5.50,so20%is$11.00.Example2:Calculateeachamountwithoutacalculator.

10%of$34=________ 20%of$43=_________ 10%of$16=________ 20%of$36=_________

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CALCULATINGTAXESTaxisEXTRAAMOUNTYOUHAVETOPAYonmostitemsthatyoupurchase:clothes,gifts,foodfromarestaurant,etc.InOntario,wepay_______________________________________(HST)onmanyofourpurchases.OncurrentrateofHSTis________,whichmeansthatyoupayanextra$______intaxforeach100dollarsthatyouspend. Wheredoourtaxesgo? Whatitemsdon’tgettaxed?Example3:Supposeanitemcosts$89andyouhavetopayHST. a)EstimatetheHSTontheitem.*hint:thinkofourshortcut b)CalculatetheHSTonthatitem. c)Howmuchisthetotalcostincludingthetax?Example4:Calculatethetax(13%HST)onanewTVthatcost$457.

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TAXES–SHORTCUT SydneycalculatedtheHSTforanitemmultiplyingby0.13.Whydoesthatmakesense? NoahcalculatedthefinalpriceforanitemincludingHSTbymultiplyingby1.13.Whydoesthatmakesense? Example5:Useyourshort-cutstrategytodeterminethefinalpriceofthefollowingitemsincludingHST. a)Anewtruckthatcosts$32000 b)Acandlethatcosts$8.50 Example6:Tierneygoestothemovietheatreandhas$20tospendontreats.

• Softdrink$2.29• Chocolatebars$1.69• Popcorn$3.49

Shebuystwosoftdrinks,achocolatebarandpopcorn.Shealsopays13%tax.HowmuchchangeshouldTierneyreceivefromher$20?Showyourwork.

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Homework1.9:TipsandTaxes

1. TheAndersonswenttodinneratSwissChalet.Iftheirdinnercost$42.95andtheylefta15%

tipfortheirserver,howmuchdidtheyleaveasatip?2. TheKerwoodswentouttoeatatMontana’s.Ifthebillwas$58.65andtheygavetheirserver

a15%tip,howmuchdidtheypayaltogether?

3. MarkandhisthreefriendsateoutatApplebee’s.Theirbilltotalled$52.35.Iftheyleftthe

servera20%tip,howmuchwouldeachpersonpaysplittingthebillevenly?

4. VickymadesomepurchasesattheSunflowerMarket.Sheboughtstrawberriesfor$3.50,

carrotsfor$2.25andabouquetofflowersfor$9.95.Ifsalestaxis13%,whatisherfinalbill?

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5. Youhavea$20giftcardfromabookstorethatyouusetobuytwobooksfor$18.49.The

salestaxis5.75%.Willyourgiftcardcoverthecost?Explain.6. Rickbought3shirtsfor$18each,2pairofsocksfor$3.99apair,andapairofpantsfor

$45.00.HowmuchdidhepayincludingHST?

1.9Answers1.$6.44 2.67.453.$15.71totalforeachperson4.$17.74 5.Yes,itwillcost$19.55 6.$120.89

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MFM1P–Unit1:ProportionalReasoning–Lesson10 Date:______________Learninggoal:howtouseproportionstocalculatediscountsandsaleprices.

DiscountsandSalePrices

Mostflyersthatyoulookatalwayshavesales.Explainthedifferencebetweenthefollowingwords RegularPrice Discount SalePrice LOOKINGATDISCOUNTSSometimesdiscountsaregivenasadollaramountoffandothertimesitisgivenasapercentageoftheprice.Whichofthefollowingdealsisbetter?

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Calculatingthediscountà

Example1:Anphonethatregularlysellsfor$280isonsalefor25%off.Whatistheamountofdiscount?

Example2:HDTVsareonsalefor25%off.Whatisthediscountonatelevisionthatnormallycosts$885?CalculatingSalePriceà Example3:Ajacketwasregularlypricedat$159.99.Itwasmarkeddownby30%.Method#1:Calculatethediscount,thensubtract Method#2:Determinesaletofindthesaleprice percentageandcalculatethesalepriceExample4:Avideogameisdiscountedby30%.Itsregularpriceis$89.99.

a)Calculatethesalepriceofthevideogamebeforetaxes.

b)Calculatethesalepriceofthevideogameincludingtaxes(13%).

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Homework1.10:DiscountsandSalePrice

1. HowmuchwillJordonsaveonthepriceofacomputerlistedat$989.98ifitisdiscountedby30%?

2. Inadepartmentstore,a$40dressismarked,"Save25%."Whatisthediscount?Whatisthe

salepriceofthedress?3. Abicyclehasaregularpriceof$175.Itisonsalefor20%off.Determinethetotalcost,

including13%tax?Showyourwork.

4. Avideostoreoffersthesechoices.

• ChoiceA:30%offeachDVDwithregularprice$25.00• ChoiceB:BuytwoDVDsfor$40.00.Whichisthebetterdealforthecustomer?Justify

youranswer.

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5.Margaretmanagesasecond-handclothingstoreinLangley,BC.Thestoreadvertisesthatifyoubuy3items,youwillget15%offthemostexpensiveitem,20%offthesecondmostexpensive,and30%offthecheapestitem.Youchoosethreeitemscosting$10.00,$25.00,and$12.00.Howmuchwillyoupayforthethreeitems?6.Susanbuysatennisracketfromastore.

•Thetennisracket’soriginalpriceis$75.•Alltennisracketsareonsalefor25%offtheoriginalprice.•Thetennisrackethasascratch,soshereceivesanadditional10%offthesaleprice.

HowmuchdoesSusanpayforhertennisracket,including13%tax?Showyourwork.

1.10Answers1.$296.99 2.Discount$10,saleprice$303. 3.Discount$35,saleprice$140,taxes18.20total$158.20 4.ChoiceAisbetter5.$21.25+$9.60+$7=$37.85 6.$57.20