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Grade2,Module2:

AdditionandSubtractionofLengthUnitsMission:ExploreLength

WordProblems

TableofContents

WORDPROBLEMS..…………………………………………………………………....…………………………………………………2–6

TopicA:UnderstandConceptsAbouttheRuler..........................................................................2

TopicB:MeasureandEstimateLengthUsingDifferentMeasurementTools............................4

TopicC:MeasureandCompareLengthsUsingDifferentLengthUnits......................................5

TopicD:RelateAdditionandSubtractiontoLength..................................................................6

WORDPROBLEMS

2

TopicA:UnderstandingConceptsAbouttheRulerTopicAbeginswithanexplorationofconceptsabouttheruler.LESSON1ApplicationProblem(8minutes)

Vincentcounts30dimesand87penniesinabowl.Howmanymorepenniesthandimesareinthebowl?

Note:Thiscomparewithdifferenceunknownproblempresentsanopportunitytoworkthroughthecommonmisconceptionthatmoremeansadd.Afterdrawingthetwotapes,askguidingquestionssuchas,“DoesVincenthavemoredimesorpennies?”“DoesVincenthave30pennies?”(Yes!)“Tellmewheretodrawalinetoshow30pennies.”“Thispartofthetaperepresents30pennies.Whatdoesthisotherpartofthepenniestaperepresent?”(Thepartthatismorethanthedimes.)Thiswillhelpstudentsrecognizethattheyarecomparing,notcombining,thequantities.

Thisproblemhasaninterestingcomplexitybecause,thoughtherearemoreofthem,thepenniesareworthless.Askstudents,“CouldyoubuymorewithVincent’spenniesorwithhisdimes?Howdoyouknow?”

NOTESONMULTIPLEMEANSOFEXPRESSION:

Toavoidinhibitingchildren’snaturaldrawingsduringtheRDWprocess,becarefulnottocommunicatethatthetapediagramisthebestor“right”way.Ifadrawingmakessense,itisright.Regularlyguidestudentsthroughthemodelingofaproblemwiththetapesothatthisimportantmodelgraduallyenterstheirtoolkit.

WORDPROBLEMS

3

NOTESONDIFFERENTIATINGTHEAPPLICATIONPROBLEM:

The9ApplicationProblemsofModule2areallcomparisonsituations.§ Lessons1and2:comparewith

differenceunknown§ Lessons3and4:comparewith

biggerunknown§ Lessons5and6:comparewith

smallerunknown§ Lesson7:comparewithsmaller

unknownusingmorethan§ Lesson8:comparewithbigger

unknownusinglessthan§ Lesson9:comparewithbigger

unknownusingshorterthan

ThechallengingsituationtypesinLessons7,8,and9mightbefrustratingifstudentshavenotbeensuccessfulinLessons1–6.ConsidereditingthesituationsinLessons7–9toinsteadrepeatthoseofLessons1–6,returningtothemorechallengingproblemtypesineitherModule3or4afterstudentshavegainedmoreconfidencewiththesimplercomparisonsituations.

LESSON2ApplicationProblem(6minutes)

Withonepush,Brian’stoycartraveled40centimetersacrosstherug.Whenpushedacrossahardwoodfloor,ittraveled95centimeters.Howmanymorecentimetersdidthecartravelonthehardwoodfloorthanacrosstherug?

Note:Thiscomparewithdifferenceunknownproblemgivesstudentsfurtherpracticewithcomparingquantities.Anewcomplexityistocomparelengthmeasurementsratherthannumbersofdiscreteobjects.

LESSON3ApplicationProblem(8minutes)

Jamiehas65flashcards.Harryhas8morecardsthanJamie.HowmanyflashcardsdoesHarryhave?

Note:Thisproblemtype,comparewithbiggerunknown,challengesstudentstomakesenseofthesituationanddeterminetheoperationtosolve.ItfollowsthetwopreviouscomparewithdifferenceunknownApplicationProblemstoalertstudentstoreadandunderstandthesituationinsteadofrelyingonkeywordsthattelltheoperation.Thisproblemexemplifiestheerrorinusingmorethanasakeywordtosubtract,sinceinthissituationstudentssolvebyaddingtheparts.Theproblemcouldberepresentedusingonetape,butsincestudentsarejustbeginningtodocomparisonproblemsatthislevelofsophisticationwithlargernumbers,itmaybewisetodrawonetapetorepresenteachboy’scardsemphasizingthefactofthecomparison.

WORDPROBLEMS

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TopicB:MeasureandEstimateLengthUsingDifferentMeasurementToolsInLesson4,studentsbegintousecentimeterrulers,metersticks,andmetertapestomeasurevariousobjects.LESSON4ApplicationProblem(7minutes)

Calebhas37morepenniesthanRichard.Richardhas40pennies.Joehas25pennies.HowmanypenniesdoesCalebhave?

Note:Thisproblemhastheaddedcomplexityofextraneousinformation,Joe’spennies.Ask,“DoIneedtodrawJoe’spennies?”Dependingontheneedsofstudents,thiscanbeomittedinordertofocusonthecomparewithbiggerunknownproblemwheremorethanisusedtocomparetwoquantities,andadditionisusedtosolve.LESSON5ApplicationProblem(7minutes)

Ethanhas8fewerplayingcardsthanTristan.Tristanhas50playingcards.HowmanyplayingcardsdoesEthanhave?

Note:Thiscomparewithsmallerunknownproblemusesthewordfewer,whichprobablywillsuggestsubtractiontostudents.Thenumberswerepurposelychosensostudentshavetheopportunitytousethetakefromtenstrategytosolve.

WORDPROBLEMS

5

TopicC:MeasureandCompareLengthsUsingDifferentLengthUnitsInTopicC,studentsusedifferentlengthunitstomeasureandcomparelengths.LESSON6ApplicationProblem(7minutes)

Eveis7centimetersshorterthanJoey.Joeyis91centimeterstall.HowtallisEve?

Intoday’slesson,studentsmeasureandcomparelengthsincentimetersandmeters.ThiscomparewithsmallerunknownproblemissimilartotheprobleminLesson5,butheremeasurementunitsareusedwithshorterthanratherthanlessthanorfewerthan.

LESSON7ApplicationProblem(6minutes)

Luigihas9morebooksthanMario.Luigihas52books.HowmanybooksdoesMariohave?

Note:ThiscomparewithsmallerunknownproblemhasthecomplexitythatwesubtracttofindthenumberofbooksMariohas,thoughthereisnoactionoftakingaway,andthewordmoreinthefirstsentencemightsuggestadditiontostudents.Moreandmorethanareoftenmistakenlytaughtaskeywordssignalingeithertoaddorsubtract.Thisapproachdistractsstudentsfromthemoreessentialtaskofconsideringthepart–wholerelationshipswithinaproblemafterrepresentingitwithadrawing.

WORDPROBLEMS

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TopicD:RelateAdditionandSubtractiontoLengthInTopicD,studentsrelateadditionandsubtractiontolength.LESSON8ApplicationProblem(6minutes)

Billthefrogjumped7centimeterslessthanRobinthefrog.Billjumped55centimeters.HowfardidRobinjump?

Note:Thiscomparewithbiggerunknownproblemusesthewordless,whichpresentsanopportunityforstudentstoworkthroughtheeasymistakethatlessorlessthanmeanstosubtract.Askguidingquestionssuchas,whojumpedfarther?This,alongwithatapediagram,helpsstudentsrecognizethatRobinjumpedfartherandhelpsthemdeterminetheoperation,addition.

LESSON9ApplicationProblem(6minutes)

Richard’ssunfloweris9centimetersshorterthanOscar’s.Richard’ssunfloweris75centimeterstall.HowtallisOscar’ssunflower?

ThiscomparewithbiggerunknownproblemissimilartotheprobleminLesson8,butheretheword“shorter”relatestomeasurement.Thisisinanticipationoftoday’sConceptDevelopment,whereinstudentsmeasurelengthsofstringsandusetapediagramstorepresentandcomparelengths.LESSON10Noapplicationproblemforthislesson.