grade level/course: lesson/unit plan name: …...figure out the cost of 2 tickets ($14) and then add...

of 29 MCC@WCCUSD (WCCUSD) 11/10/15

GradeLevel/Course:7Lesson/UnitPlanName:IdentifyingProportionalandNonproportionalRelationshipsinTablesandinGraphsRationale/LessonAbstract:Thislessonfocusesonstudentsexaminingthecharacteristicsofproportionalrelationshipsanddeterminingwhenandwhytwoquantitiesareactuallyinaproportionalrelationship.Timeframe:2classperiodswithapossible1classextensionCommonCoreStandard(s):7.RP.2Recognizeandrepresentproportionalrelationshipsbetweenquantities.a.Decidewhethertwoquantitiesareinaproportionalrelationship,e.g.,bytestingforequivalentratiosinatableorgraphingonacoordinateplaneandobservingwhetherthegraphisastraightlinethroughtheorigin.MathematicalPractices:MP.1…studentssolveproblemsinvolvingratiosandratesanddiscusshowtheysolvedthem.MP.3Studentsconstructargumentswithverbalorwrittenexplanationsaccompaniedbymodels,graphs,andtables.Theyfurtherrefinetheirmathematicalcommunicationskillsthroughmathematicaldiscussionsinwhichtheycriticallyevaluatetheirownthinkingandthethinkingofotherstudents.Studentsshouldbeencouragedtoanswerquestionssuchasthese:“Howdidyougetthat?”“Whyisthistrue?”“Doesthatalwayswork?”MP.4Proportionalrelationshipspresentopportunitiesformodeling.Forexample,formodelingpurposes,thenumberofpeoplewholiveinanapartmentbuildingmightbetakenasproportionaltothenumberofstoriesinthebuilding.Studentsshouldbeencouragedtoanswerquestionssuchas,“Whataresomewaystorepresentthequantities?”or“Howmightithelptocreateatable,chart,orgraph?”

Lessons: 1 CoverPage2–7 Day1:IdentifyingProportionalRelationshipsinTables(Lesson)8–15 Day2:IdentifyingProportionalRelationshipsinGraphs(Lesson)16–17 Day3:IdentifyingProportionalRelationshipsinGraphsandTables(GroupActivity)Handouts:18–20 Day1:IdentifyingProportionalRelationshipsinTables(Handout) 21 Day1:IdentifyingProportionalRelationshipsinTables(ExitTicket) 22–23 Day2:IdentifyingProportionalRelationshipsinGraphs(Handout)24 Day2:IdentifyingProportionalRelationshipsinGraphs(ExitTicket)25 Day2:IdentifyingProportionalRelationshipsinGraphs(CoordinatePlane)26–28 Day3:QuestionPrompts29 Day3:GalleryWalkHandout


Day1:IdentifyingProportionalRelationshipsinTablesInstructionalResources/Materials:Pencil,paper,handoutPriorKnowledge:Simplifyingratios,proportionalrelationshipsActivity/Lesson(20-25minutes):StudentswillworkoncompletingtablesforExample1independently(5minutes).Studentswillthencollaboratewithapartner(ifseatedinpairs)ortheirgrouptodiscusstheresultsoftheirtablesandworkoneachofthefollow-upquestionstogether(10minutes).Groupnorm:nostudentisallowedtoproceedtothenextquestionuntileveryonehaswrittendownananswertothecurrentquestion.Lastly,studentswillsharetheirsolutionswiththewholeclass(5-10minutes).Thereareoftentimesmultiplewaysthataproblemmayhavebeencompletedorexplained,sotheteachershouldcirculateduringthegroupworktimetoselectstudentswhohavedifferingapproachestopresenttotheclass.EXAMPLE1:RunningtheRaceYouhavedecidedtojoinalongdistancerunningteam.Therearetwoteamsthatyoucanjoin.TeamArunsataconstantrateof3milesperhour.TeamBruns4milesthefirsthourandthen2milesperhourafterthat.Yourtask:Completethetableforeachteamshowingthedistancesthatwouldberunfortimesof1,2,3,4,5,and6hours.Usingyourtables,answerthequestionsthatfollow.1)Forwhichteamisdistanceproportionaltotime?Explainyourreasoning.

TeamAsincealltheratioscomparingdistancetotimeareequivalent.Theequivalentratiois3.Everymeasureoftimecanbemultipliedby3togivethecorrespondingmeasuresofdistance.

TeamATime(hrs) Distance(miles)

1 32 63 94 125 156 18

TeamBTime(hrs) Distance(miles)

1 42 63 84 105 126 14


2)Explainhowyouknowthedistancefortheotherteamisnotproportionaltotime?

TheratiosarenotequivalentforTeamB.Theratiosare4,3,8/3,2.5,12/5,and14/6(7/3).Everymeasureoftimecannotbemultipliedbyaconstanttogiveeachcorrespondingmeasureofdistance.

3)Ifthemembersontheteamranfor10hours,howfarwouldeachmemberrunoneachteam? TeamA=30miles TeamB=22miles4)Iftheracewere3mileslong,whichteamwouldwin?Explain. TeamBwouldwinbecausemoredistancewascoveredinlesstime.5)Iftheracewere7mileslong,whichteamwouldwin?Explain. TeamAwouldwinbecausemoredistancewascoveredinlesstime.Example1Takeaway:Twoquantitiesareproportionaliftheyhaveaconstantratioorunitrate.Forrelationshipsinwhichtheratioisnotconstant,thetwoquantitiesarenonproportional.

EXAMPLE2(5minutes):Andrewearns$18perhourmowinglawns.Istheamountofmoneyheearnsproportionaltothenumberofhourshespendsmowing?Completethetableandprovideanexplanationofyourreasoning.Promptingquestionsfromteacher:•Whatdoyouneedtofind?Whethertheamountofmoneyheearnsisproportionaltothe

numberofhourshespendsmowing.•HowwouldyourepresenttheamountofmoneyAndrewearnsperhourasaunitratio?

$181 hour

•Howwouldyoudeterminehowmuchhemakesforeachnumberofhoursworked?

Multiplythenumberofhoursworkedby$18.Oraddanadditional$18foreachhourworked.

Earnings($) 18 36 54 72Time(h) 1 2 3 4


•Whatwillyouneedtodotodetermineiftherelationshipisproportional? Writetherelationshipbetweentheamountheearnedandhoursworkedasaratioin simplestformforeachnumberofhoursworked

amount earnednumber of hours

→181

or 18 362

or 18 543

or 18 724

or 18

•Arethetwoquantitiesproportional?Justifyyourthinking.

Alloftheratiosbetweenthetwoquantitiescanbesimplifiedto18.Theamountofmoneyheearnsisproportionaltothenumberofhourshespendsmowing.EXAMPLE3(5minutes):TicketServantcharges$7perbaseballgameticketplusa$3processingfeeperorder.Isthecostofanorderproportionaltothenumberofticketsordered?Completethetableandprovideanexplanationforyourreasoning.Promptingquestionsfromteacher:•Whatdoyouneedtofind?Ifthecostofanorderisproportionaltothenumberoftickets.

•Howwouldyourepresentthecostoforderingoneticketasaunitratio? $101 ticket

•Howwouldyoudeterminethecostoforderingtwotickets?

Figureoutthecostof2tickets($14)andthenaddthe$3processingfee.Oradd$7tothetotalcostoforderingoneticket.

•Whatwillyouneedtodotodetermineiftherelationshipisproportional? Writetherelationshipbetweenthecostandnumberofticketsasaratioinsimplestform foreachnumberoftickets.

cost of ordertickets ordered

→101

or 10 172

or 8.5 243

or 8 314

or 7.75

•Arethetwoquantitiesproportional?Justifyyourthinking.

Sincetheratiosofthetwoquantitiesarenotthesame,thecostofanorderisnotproportionaltothenumberofticketsordered.

Cost($) 10 17 24 31TicketsOrdered 1 2 3 4


YOUTRY1(7minutes):ThetablesshownbelowrepresentthenumberofpagesMiguelandKarleereadovertime.Writedownatleastthreeobservationsyoucanmakeaboutthetwotables(hint:proportionaland/ornonproportionalrelationshipsshouldbeincludedinatleasttwooftheobservations).Providejustificationforyourobservations.

•AlloftheratiosbetweenMiguel’squantitiesare 25soMiguel’sreadingraterepresentsa

proportionalrelationship.

pagesminutes

→25

410

or 25

615

or 25

•TheratiosbetweenKarlee’squantitiesarenotthesamesoKarlee’sreadingratedoesnot representaproportionalrelationship.

pagesminutes

→35

410

or 25

715

•MiguelandKarleereadthesameamountofpagesafter10minutes.•KarleereadmorepagesthanMiguelafter15minutes.ExtensionquestionsforYouTry1:a)HowmanypagesdoyouthinkMiguelwillhavereadafter20minutes?Howdoyouknow? Miguelwilllikelyread8pagesafter20minutesbasedonhisreadingrateof2pages every5minutes.b)HowmanypagesdoyouthinkKarleewillhavereadafter20minutes?Howdoyouknow? Itisimpossibletodeterminehowmanypagesshewillhavereadbasedonthe

informationgiven.c)WhyisitmoredifficulttodeterminehowmanypagesKarleewillread? Becauseherreadingrateisnotconstant.

PagesMiguelRead 2 4 6Time(min) 5 10 15

PagesKarleeRead 3 4 7Time(min) 5 10 15


YOUTRY2(7minutes):ThetablesshownbelowrepresenttheamountofmoneyearnedperhourforJohnandJackie.

Question1:Whichsituationrepresentsaproportionalrelationshipbetweenthehoursworkedandtheamountearned?Providejustificationforeachofthetables.TheratiosbetweenJohn’squantitiesarenotthesamesoJohn’searningratedoesnot representaproportionalrelationship.

earnings ($)hours (h)

→121

or 12 202

or 10 313

AlloftheratiosbetweenJackie’squantitiesare12soJackie’searningraterepresentsa proportionalrelationship.

earnings ($)hours (h)

→121

or 12 242

or 12 363

or 12

Question2:Howmuchwouldeachearniftheyworkedafourthhour?BecauseJohn’searningrateisnotconstant,wecannotdeterminehowmuchhewouldmake afterfourhoursofwork.Jackiewouldmake$48.Closingquestion:Howdoesknowingwhethertwoquantitiesareproportionalhelpanswerquestionsaboutthequantities?Forexample,ifweknow1cup=8oz,whatdoesthatallowustodo? Understandingtherelationshipcanallowyoutofindmissingquantities.Fortheabove example,onecupcanbesubstitutedfor8ouncesorviceversa.

John’sEarnings($) 12 20 31Time(h) 1 2 3

Jackie’sEarnings($) 12 24 36Time(h) 1 2 3


EXITTICKET(5minutes):Sararanlapsaroundagym.Hertimesareshowninthetablebelow.Sarathinksthenumberoflapsisproportionaltothetimebecausethenumberoflapsalwaysincreasesby2.Isshecorrect?Providejustificationforyouranswer.

Itisnotproportionalbecausetheratiooflapstotimeisnotconsistent.

number of lapstime (min)

→32

or 1.5 53

74

or 1.75 95

or 1.8

Time(min) 2 3 4 5Laps 3 5 7 9


Day2:IdentifyingProportionalRelationshipsinGraphsInstructionalResources/Materials:Pencil,paper,ruler,handoutPriorKnowledge:Thecoordinateplane,plottingpoints,quadrants,orderedpairs,x-axis,y-axis,origin,determiningproportionalrelationshipsintables.Activity/Lesson:Openingactivity(10minutes):Agroup(orpair)ofstudentswillreceiveallfourhalfsheetsoftablesandgraphs.Foreachproblem,studentswilldeterminewhetherthetwoquantitiesinthetablerepresentaproportionalrelationship.Whentheyarefinished,theyaretosetasidetheproblemsforthetimebeing.STUDENTSDONOTGRAPHTHEINFORMATIONFROMTHETABLES…YET.TheCoordinatePlaneReview(5-7minutes):Teachershouldprojectacoordinateplane(doccamorcomputer)andhavestudentshelplabelthevariouspartsofthegrid(thefourquadrants,theaxes).Somequestionstodiscuss:•Whatisanorderedpair? Apairofnumbers,suchas(1,3)usedtolocateorgraphpointsonacoordinategrid.•Whatistheoriginandwhereisitlocated? Thepointwherethexandyaxisintersect,atorderedpair(0,0).•Whenweareplottingapoint,wheredowecountfrom? Theorigin,(0,0).•Whyareweonlyfocusingonquadrant1? Allofthevaluesarepositive.Sincewearemeasuringorcountingquantities(numberof videogamesrentedandcost),thenumbersinourratioswillpositive.Showstudentshowtoplotthepoint(1,3)andlabelthex-andy-coordinate.•Howwouldweplotthepoint,(2,5)? Fromtheorigin,wego2totherightonthex-axisandthenup5onthey-axis.Aftergraphingthepoints(1,3)and(2,5),connectthetwopointsonthecoordinateplane.•Howwouldyoudescribethegraph? Thepointsformastraightline.


StudentsshouldlocatetheirpilesoftablesandrefertoExample1(videogameexample).FromaTabletoGraph–Examples1and2(5-10minutes):EXAMPLE1:Aswimmingpooliscurrentlyfilledwithonegallonofwater.Agardenhoseisusedtofillthepoolataconstantrate.Fromtheinformationfromthetable,determinewhetherthenumberofgallonsisproportionaltothenumberofminutes.

Istherelationshipproportionalornonproportional?Providejustificationforyourreasoning.Itisnotproportionalbecausetheratioofcosttogamesisnotconsistent.

number of gallonstime (min)

→31

or 3 52

or 2.5 73

94

or 2.25

FillingtheSwimmingPoolTime

(Minutes)NumberofGallons

1 32 53 74 9


Teachershouldmodelhowtographtheinformationshowninthetable.•Beforeyoucangraph,whatdoyouneedtoknow? Theorderedpairs.•Howcanyoufindtheorderedpairs? Usethetable.•Whatwillthex-valuesrepresent? Thetimeinminutes.•Whatwillthey-valuesrepresent? Thenumberofgallonsinthepool.•Howdoweplotthefirstratiopair?

Iftherelationshipis1:3,where1represents1minuteand3isthenumberofgallons,thenfromthefirstpoint,wego1totherightonthex-axisandthenup3onthey-axis.

•Howdoweplotthesecondratiopair?

Iftherelationshipis2:5,where2represents2minutesand5isthenumberofgallons,thenfromthefirstpoint,wego2totherightonthex-axisandthenup5onthey-axis.

Studentsshouldgraphtherestofthepoints(3,7)and(4,9).


EXAMPLE2:TheslowestmammalonEarthisthetreesloth.Itmovesataspeedof6feetperminute.Completethetable,determinewhetherthenumberoffeettheslothmovesisproportionaltothenumberofminutesitmoves,andexplainyourreasoning.

Istherelationshipproportionalornonproportional?Providejustificationforyourreasoning.

Atthispoint,ifstudentsarecomfortablegraphing(inpairsoringroups),theyshouldgraphExample2.Ifthemajorityofthestudentsarenotcomfortableyet,theteachershouldgraphthepointsforExample2withthem.

Time(min) 1 2 3 4Distance(ft) 6 12 18 24

Itisproportionalbecausetheratiobetweenthedistanceandtimeisalways6.


ComparingtheGraphs–Examples1and2(7minutes):HavestudentscompareExamples1and2sidebyside.Havethestudentsmakeobservationsaboutthetwographs(Example1-nonproportionalrelationshipandExample2-proportionalrelationship)andrecordthestatementssidebyside.(Usingadoccam,whiteboard,orposter.)•Whataresomesimilaritiesbetweenthetwoexamples? Bothhavepointsthatlieonastraightline.•Whataresomedifferencesbetweenthetwoexamples? ThelineforExample1doesnotgothroughtheorigin,butthelineforExample2does.•Whyarethelinesstraight? Foreveryincreaseof1onthex-axis,thereisanincreaseofthesameamount

onthey-axis.•Inexample1,areweabletoinferhowmuchafifthgamewouldcost? Yes,thecostofeachrentalgoesupby$2foreachrental(afterthefirstrental)so5 gameswouldcost$11.•Inexample2,canweinferhowfartheslothwouldwalkafterfiveminutes? Yes,theslothwalks6ftperminuteaccordingtothetablesoafterfiveminutes,the slothwouldwalk30feet.•Whatcanweinferaboutgraphsoftwoquantitiesthatareproportionaltoeachother? Thegraphwillbeastraightlinethatgoesthroughtheorigin.•Basedonthesetwographs,whatcommonerrormightastudentmakewhendeciding whetheragraphofthequantitiesrepresentsaproportionalrelationship?

Astudentmightbelievethatbothgraphsshowaproportionalrelationshipbecausethepointslieonastraightline,butthelineofagraphthatrepresentsaproportionalrelationshipmustalsogothroughtheorigin.

ProportionalRelationship(Ex.2)•pointsallfallonastraightline•linegoesthroughtheorigin

NonproportionalRelationship(Ex.1)

•pointsallfallonastraightline•linedoesn’tgothroughtheorigin


MakingPredictions–Examples3and4(10minutes):BeforestudentsgraphtheinformationfromthetableinExample3,theteachersshouldaskthefollowingquestions.•ForExample3,doesthetablerepresentaproportionalrelationship? Yes.•Ifwegraphtheinformationfromthetable,whatcanyoupredictaboutthegraph?

Shareyourthoughtswithaneighbor. Thepointswilllieonastraightlineandwillgothroughtheorigin.EXAMPLE3:Aparticularbrandoffruitcupshas70caloriesin1serving,210caloriesin3servings,and350caloriesin5servings.Completethetable,determinewhetherthe

relationshipbetweenthetwoquantitiesareproportional,andexplainyourreasoning.

•Wasyourpredictioncorrect? Yes,thepointslieonastraightlineandthelinegoesthroughtheorigin.•Areweabletoinferhowmanycalories6servingsmighthave? Yes.Thereare70caloriesperserving,so6servingswouldhave420calories.

CaloriesinFruitCupsServings Calories

1 703 2105 350

Istherelationshipproportionalornonproportional?Providejustificationforyourreasoning.Itisproportionalbecausealloftheratiosarethesame.


BeforestudentsgraphtheinformationfromthetableinExample4,theteachersshouldaskthefollowingquestions.•ForExample4,doesthetablerepresentaproportionalrelationship? No.•Ifwegraphtheinformationfromthetable,whatcanyoupredictaboutthegraph? Shareyourthoughtswithaneighbor. Thepointswilllieonastraightlineandwillnotgothroughtheorigin.EXAMPLE4:Thetableshowsthenumberofcaloriesanathleteburnedperminuteofexercise.Usethetabletodeterminewhetherthenumberofcaloriesburnedisproportionaltothenumberofminutes.

•Wasyourpredictioncorrect? No,thepointsdonotlieonastraightline,butthepointsgothroughtheorigin.•Areweabletoinferhowmanycaloriestheathletemightburnafter4minutes? No.Theratiosofcaloriestominutesarenotequal.•Ifweweretodrawalinethroughthepoints,wouldwebeabletoextendtheline? No.Becausetheratiosarenotequal,wecannotaccuratelypredictwherethenextpoint wouldbe.

CaloriesBurnedNumberofMinutes

NumberofCalories

0 01 42 83 15

Istherelationshipproportionalornonproportional?Providejustificationforyourreasoning.Itisnotproportionalbecausetheratioofcalories

burnedtotimeisnotconsistent.


•Arethereanyconclusionswecanmakeaboutthegraphsoftwoquantitiesthatare proportionaltoeachother? Whentwoproportionalquantitiesaregraphedonacoordinateplane,thegraphis representedbyastraightlinethroughtheorigin.•Basedonallfourgraphs,whatcommonerrorsmightastudentmakewhendeciding whetheragraphofthequantitiesrepresentsaproportionalrelationship?

Pointsthatlieonastraightlinedoesnotnecessarilymeanthegraphrepresentsaproportionalrelationship.Thegraphmustalsogothroughtheorigin.Inaddition,agraphcouldgothroughtheorigin,butthepointsmustbeastraightlineinorderforthequantitiestobeinaproportionalrelationship.

EXITTICKET(5minutes):Whichvideogameplayer(s)representsaproportionalrelationshipbetweenthetimeandthenumberoflevelspassed?Providejustificationforeachofthethreegraphs. Morgan’sgraphisastraightlinethroughtheoriginandthereforerepresentsa proportionalrelationship. Renee’sgraphisnotastraightlinesotherelationshipbetweentimeandlevelspassedis

notproportional.Bob’sgraphisastraightline,butdoesnotpassthroughtheoriginsoitdoesnotrepresentaproportionalrelationship.


Day3(Extension):IdentifyingProportionalRelationships–GroupActivityInstructionalResources/Materials:Pencils,posterpaper,scratchpaper,graphpaper,ruler,post-its,envelopeswiththeproblemandratiosinside.PriorKnowledge:ContentfromLessons1and2.Activity/Lesson:ThisisanextensionofLessons1and2.Studentswillbeworkingingroupstocreatetablesandgraphtheinformationinthetablestoidentifywhetherornotthetwoquantitiesrepresentedareproportionaltoeachother.Openingactivity(10minutes):Intheirgroups(ofthreeorfourstudents),handoutthematerialsneededforthisactivity.

• Havethegroupstakeoutthecontentsoftheenvelopeandstatetheproblem• Havethegroupsarrangetheratios“inorder”,createatable,andgraphtheinformation• Studentsshouldusemultiplemethodstoshowwhetherthequantitiesrepresentedin

theenvelopeareproportionaltoeachotherornot• Dividetheposterpaperintofourquadrants(mightbeeasiesttojusthavestudentsfold

theposterpaperintoquarters)• Labelasfollows:Quadrant1–Table;Quadrant2–Problem;Quadrant3–Graph;

Quadrant4–ProportionalorNot,ExplainWorkingCollaboratively(15minutes):Studentswillhave15minutestodiscusstheproblemandrecordtheirresponsesontotheposterpaper.Teachershouldcirculateandpraisestudentswhoareworkingcollaboratively,dialoguingaboutthemathassociatedwiththeproblem,engagedintheconversation,makingpostersthatclearlypresenttheirfindings(visuallyappealing).Havestudentsplacetheirfinishedpostersaroundtheclassroom.Feelfreetodesignatewhereeachgroupputsuptheirposter(teachercouldputupsignsaroundtheclassroomforeachgroup).GalleryWalk(15minutes–3minutesperposter):Haveeachgroupofstudentsstartatadifferentposter(onegroupperposterifpossible).Theyhave3minutestowriteanythoughtsonpost-itsandstickthemtotheposters.HavestudentsanswerthequestionsontheirGalleryWalkHandout.Teachershouldletstudentsknowwhentomoveontothenextposter.


Closing(10minutes):

• Whyisitbeneficialtomakeposterswithotherstudents?Whynotsimplydothisactivityonyourown?

Wecantalkabouttheproblemwithothersandlearnfromourconversationabouttheproblem.Somestudentsmightcomeupwithsomethingwehadn’tthoughtof.We’reabletoshareinformationwiththeothers.

• Whatdoesitmeanforadisplaytobebothvisuallyappealingandinformative?

Thereader/viewershouldbeabletofinddataandresultsfairlyquickly.Lookingatandreadingthepostershouldbesomewhatenjoyable(easytounderstand).

• Howmuchtimedidyourgroupspendonthecontentofyourposterversusthetime

spentmakingthepostervisuallyappealing?Whichismoreimportant?They’rebothimportant.It’simportantfortheinformationtobeaccurate,butit’salsoimportantforotherstoseehowwedeterminedouranswer.Iftheydon’tunderstandourthoughtprocessfromourposter,wedidn’tdoagoodjobofpresentingtheinformation.


IdentifyingProportionalRelationshipsinTables Name:________________________7.RP.2aDecidewhethertwoquantitiesareina Date:____________________ proportionalrelationships Period:______EXAMPLE1:RunningtheRaceYouhavedecidedtojoinalongdistancerunningteam.Therearetwoteamsthatyoucanjoin.TeamArunsataconstantrateof3milesperhour.TeamBruns4milesthefirsthourandthen2milesperhourafterthat.Yourtask:Completethetableforeachteamshowingthedistancesthatwouldberunfortimesof1,2,3,4,5,and6hours.Usingyourtables,answerthequestionsthatfollow.a)Forwhichteamisdistanceproportionaltotime?Explainyourreasoning.b)Explainhowyouknowthedistancefortheotherteamisnotproportionaltotime?c)Ifthemembersontheteamranfor10hours,howfarwouldeachmemberrunoneachteam?d)Iftheracewere3mileslong,whichteamwouldwin?Explain.e)Iftheracewere7mileslong,whichteamwouldwin?Explain.

TeamATime(hrs) Distance(miles)

1 32 3 4 5 6

TeamBTime(hrs) Distance(miles)

1 42 3 4 5 6


YOUTRY1:ThetablesshownbelowrepresentthenumberofpagesMiguelandKarleereadovertime.Writedownatleastthreeobservationsyoucanmakeaboutthetwotables(hint:proportionaland/ornonproportionalrelationshipsshouldbeincludedinatleasttwooftheobservations).Providejustificationforyourobservations.

Earnings($) Time(h)

Cost($) TicketsOrdered

PagesMiguelRead 2 4 6Time(min) 5 10 15

PagesKarleeRead 3 4 7Time(min) 5 10 15

EXAMPLE2:Andrewearns$18perhourmowinglawns.Istheamountofmoneyheearnsproportionaltothenumberofhourshespendsmowing?Completethetableandprovideanexplanationofyourreasoning.

EXAMPLE3:TicketServantcharges$7perbaseballgameticketplusa$3processingfeeperorder.Isthecostofanorderproportionaltothenumberofticketsordered?Completethetableandprovideanexplanationforyourreasoning.


YOUTRY1:ExtensionQuestionsa)HowmanypagesdoyouthinkMiguelwillhavereadafter20minutes?Howdoyouknow?b)HowmanypagesdoyouthinkKarleewillhavereadafter20minutes?Howdoyouknow?c)WhyisitmoredifficulttodeterminehowmanypagesKarleewillread?YOUTRY2:ThetablesshownbelowrepresenttheamountofmoneyearnedperhourforJohnandJackie.

Question1:Whichsituationrepresentsaproportionalrelationshipbetweenthehoursworkedandtheamountearned?Providejustificationforeachofthetables.Question2:Howmuchwouldeachearniftheyworkedafourthhour?Closingquestion:Howdoesknowingwhethertwoquantitiesareproportionalhelpanswerquestionsaboutthequantities?Forexample,ifweknow1cup=8oz,whatdoesthatallowustodo?

John’sEarnings($) 12 20 31Time(h) 1 2 3

Jackie’sEarnings($) 12 24 36Time(h) 1 2 3


Time(min) 2 3 4 5Laps 3 5 7 9

Time(min) 2 3 4 5Laps 3 5 7 9

Time(min) 2 3 4 5Laps 3 5 7 9

Time(min) 2 3 4 5Laps 3 5 7 9

EXITTICKET:Sararanlapsaroundagym.Hertimesareshowninthetablebelow.Sarathinksthenumberoflapsisproportionaltothetimebecausethenumberoflapsalwaysincreasesby2.Isshecorrect?Providejustificationforyouranswer.





EXAMPLE2:TheslowestmammalonEarthisthetreesloth.Itmovesataspeedof6feetperminute.Completethetable,determinewhetherthenumberoffeettheslothmovesisproportionaltothenumberofminutesitmoves,andexplainyourreasoning.

FillingtheSwimmingPoolTime

(Minutes)NumberofGallons

1 32 53 74 9

Time(min) 1 2 3 4Distance(ft) 6


EXAMPLE1:Aswimmingpooliscurrentlyfilledwithonegallonofwater.Agardenhoseisusedtofillthepoolataconstantrate.Fromtheinformationfromthetable,determinewhetherthenumberofgallonsisproportionaltothenumberofminutes.



EXAMPLE3:Aparticularbrandoffruitcupshas70caloriesin1serving,210caloriesin3servings,and350caloriesin5servings.Completethetable,determinewhethertherelationshipbetweenthetwoquantitiesareproportional,andexplainyourreasoning.

EXAMPLE4:Thetableshowsthenumberofcaloriesanathleteburnedperminuteofexercise.Usethetabletodeterminewhetherthenumberofcaloriesburnedisproportionaltothenumberofminutes.

CaloriesinFruitCupsServings Calories

1

CaloriesBurnedNumberofMinutes

NumberofCalories

0 01 42 83 15




EXITTICKET:Whichvideogameplayer(s)representsaproportionalrelationshipbetweenthetimeandthenumberoflevelspassed?Providejustificationforeachofthethreegraphs.





•Whatisanorderedpair? •Whatistheoriginandwhereisitlocated? •Whenweareplottingapoint,wheredowecountfrom?•Whyareweonlyfocusingonquadrant1? Plotthepoint(1,3)andlabelthex-andy-coordinate.•Howwouldweplotthepoint,(2,5)?Aftergraphingthepoints(1,3)and(2,5),graphalinethatgoesthroughthetwopoints.•Howwouldyoudescribethegraph?


Lesson3QuestionPrompts:Cutoutthequestionpromptsandratiosandplaceinalabeledenvelopeforeachgroup.

Group1

Alocalfrozenyogurtshopisknownfortheirmonstersundaes.Theratiosrepresentthenumberoftoppingstototalcost.Createa

table,thengraphandexplainifthequantitiesareproportionaltoeachotherornot.

Group2

Theschoollibraryreceivesmoneyforeverybooksoldattheschool’sbookfair.Theratiosrepresentthenumberofbookssoldtothe

amountofmoneythelibraryreceives.Createatable,thengraphandexplainifthequantities

areproportionaltoeachotherornot.

4to0 6:3 1to5 2to10

86

Thetotalcostofa10-toppingsundae

is$9.

Thelibraryreceived$15forselling

3books.4:20

12to12 5:25

Group3

Yourunclejustboughtahybridcarandwantstotakeyouandyoursiblingscamping.Theratiosrepresentthenumberofgallons

remainingtohoursofdriving.Createatable,thengraphandexplainifthequantitiesare

proportionaltoeachotherornot.

Group4

ForaScienceproject,Elidecidedtostudycoloniesofmold.Heobservedapieceofbreadthatwasmoldingforanumberofdays.Theratiosrepresentthenumberofdayspassedtocoloniesofmoldonthebread.Createatable,thengraphandexplainifthequantitiesare


8to0

After1hourofdriving,thereare6gallonsofgasleftin

thetank.

1to1 2to4

4:4 2to7 3:9416

08

Twenty-fivecolonieswerefoundonthe

5thday.


Group5

Frankpurchasedapre-paidcellphoneplan.TheratiosrepresentFrank’scosttominutes

used.Createatable,thengraphandexplainifthequantitiesareproportionaltoeachother

ornot.

Group6

Alocalfrozenyogurtshopisknownfortheirmonstersundaes.Theratiosrepresentthenumberoftoppingstototalcost.Createa

table,thengraphandexplainifthequantitiesareproportionaltoeachotherornot.

0:0 $1.50for3minutes 4to0 6:3

3to6 6:1286

Thetotalcostofa10-toppingsundae

is$9.

$10for20minutes 12to12

Group7

Theschoollibraryreceivesmoneyforeverybooksoldattheschool’sbookfair.Theratiosrepresentthenumberofbookssoldtothe

amountofmoneythelibraryreceives.Createatable,thengraphandexplainifthequantities

areproportionaltoeachotherornot.

Group8

Yourunclejustboughtahybridcarandwantstotakeyouandyoursiblingscamping.Theratiosrepresentthenumberofgallons

remainingtohoursofdriving.Createatable,thengraphandexplainifthequantitiesare


1to5 2to10 8to0After1hourofdriving,thereare6gallonsofgasleftinthetank.

Thelibraryreceived$15forselling

3books.4:20 4:4 2to7

5:25 08


Group9

ForaScienceproject,Elidecidedtostudy

coloniesofmold.Heobservedapieceofbreadthatwasmoldingforanumberofdays.Theratiosrepresentthenumberofdayspassedtocoloniesofmoldonthebread.Createatable,thengraphandexplainifthequantitiesare


Group10

Frankpurchasedapre-paidcellphoneplan.TheratiosrepresentFrank’scosttominutes

used.Createatablethen,graphandexplainifthequantitiesareproportionaltoeachother

ornot.

1to1 2to4 0:0 $1.50for3minutes

3:9416

3to6 6:12

Twenty-fivecolonieswerefoundonthe

5thday. $10for20minutes


GalleryWalkQuestions Name:________________________7.RP.2aDecidewhethertwoquantitiesareina Date:____________________ proportionalrelationships Period:______Asyouwalkaroundwithyourgroups,carefullyobserveeachposter,andwritedownanythoughtsorcommentsonpost-itsandstickthemtotheposter(outoftheway,ifpossible).Answerthefollowingquestionsbelow.A)Whichgroupshavegraphsandtablesthatrepresentproportionalrelationshipsandwhichdidnot?

ProportionalRelationship NonproportionalRelationshipB)Whatarethecharacteristicsoftheproblemsthatrepresentproportionalrelationships?

C)Forthegraphsrepresentingproportionalrelationships,whatdoes(0,0)meaninthecontextofthegivensituation?

D)Whenyoufindthegroupthathasthesameproblemasyours,doyounoticeanydifferencesbetweentheirposterandyours?E)Asyouobserveotherposters,doyounoticeanycommonmistakes?Howmighttheybefixed?F)Wasthereagroup(ortwo)thatstoodoutbyrepresentingtheirproblemsandfindingsinanexceptionalclearandvisuallyappealingway?

grade level/course: lesson/unit plan name: …...figure out the cost of 2 tickets ($14) and then add...

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