marlboro central school district – k ‐5...

MARLBOROCENTRALSCHOOLDISTRICT–K‐5CURRICULUMMAP2015

Subject:MathematicsGrade:3

Quarter 1

N.Y.S. Performance Indicator

Content/Concepts: What students should know (Unit organizing idea, understanding, or essential question)

Skills (What Students Should Be Able To Do)

Resources

(District

/technology)

Major Assessments

(Tests, projects, etc.)

3.OA.1Interpretproductsofwholenumbers,e.g.,interpret5x7asthetotalnumberofobjectsin5groupsof7objectseach.Forexample,describeacontextinwhichatotalnumberofobjectscanbeexpressedas5x7.

MultiplicationandtheMeaningoftheFactors

DivisionasanUnknownFactorProblem

MultiplicationUsingUnitsof2and3

DivisionUsingUnitsof2and3

MultiplicationandDivisionUsingUnitsof4

DistributivePropertyandProblemSolvingUsingUnitsof2–5and10

MultiplicationandtheMeaningoftheFactors

Understandequalgroupsofasmultiplicationanddivision.

Relatemultiplicationanddivisiontothearraymodel.

Interpretthemeaningoffactors—thesizeofthegrouporthenumberofgroups.

Understandthemeaningoftheunknownasthesizeofthegroupindivision.

Understandthemeaningoftheunknownasthenumberofgroupsindivision.

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3.OA.2Interpretwhole‐numberquotientsofwholenumbers,e.g.,interpret56÷8asthenumberofobjectsineachsharewhen56objectsarepartitionedequallyinto8shares,orasanumberofshareswhen56objectsarepartitionedintoequalsharesof8objectseach.Forexample,describeacontextinwhichanumberofsharesoranumberofgroupscanbeexpressedas56÷8.

3.OA.3Usemultiplication

Interprettheunknownindivisionusingthearraymodel.

MultiplicationUsingUnitsof2and3,4,5,10

Demonstratethecommutativityofmultiplication,andpracticerelatedfactsbyskip‐countingobjectsinarraymodels.

Findrelatedmultiplicationfactsbyaddingandsubtractingequalgroupsinarraymodels.

Modelandapplythedistributivepropertywitharraystodecomposeunitsasastrategytomultiply.

Interpretthequotientasthenumberofgroupsorthenumberofobjectsineachgroupusingunitsof2,3,4,5,10

Skip‐countobjectsinmodelstobuildfluencywith

anddivisionwithin100tosolvewordproblemsinsituationsinvolvingequalgroups,arrays,andmeasurementquantities,e.g.,byusingdrawingsandequationswithasymbolfortheunknownnumbertorepresenttheproblem.

3.OA.4Determinetheunknownwholenumberinamultiplicationordivisionequationrelatingthreewholenumbers.Forexample,determinetheunknownnumberthat

multiplicationfactsusingunitsof2,3,4,5,10.

Relatearraystotapediagramstomodelthecommutativepropertyofmultiplication.

Usethedistributivepropertyasastrategytofindrelatedmultiplicationfacts.

Modeltherelationshipbetweenmultiplicationanddivision.

Solvetwo‐stepwordproblemsinvolvingmultiplicationanddivision,andassessthereasonablenessofanswers.

Solvetwo‐stepwordproblemsinvolvingallfouroperations,andassessthereasonablenessofanswers.

makestheequationtrueineachoftheequations8x?=48,5=_÷3,6x6=?

3.OA.5Applypropertiesofoperationsasstrategiestomultiplyanddivide.(Studentsneednotuseformaltermsfortheseproperties.)Examples:If6×4=24isknown,then4×6=24isalsoknown.(Commutativepropertyofmultiplication.)3×5×2canbefoundby3×5=15,then15×2=30,orby5×2=10,then3×10=30.(Associativepropertyof

multiplication.)Knowingthat8×5=40and8×2=16,onecanfind8×7as8×(5+2)=(8×5)+(8×2)=40+16=56.(Distributiveproperty.)

3.OA.6Understanddivisionasanunknown‐factorproblem.Forexample,find32÷8byfindingthenumberthatmakes32whenmultipliedby8.

3.OA.7Fluentlymultiplyanddividewithin100,usingstrategiessuchastherelationshipbetweenmultiplicationanddivision(e.g.,knowingthat8×

5=40,oneknows40÷5=8)orpropertiesofoperations.BytheendofGrade3,knowfrommemoryallproductsoftwoone‐digitnumbers.

3.OA.8Solvetwo‐stepwordproblemsusingthefouroperations.Representtheseproblemsusingequationswithaletterstandingfortheunknownquantity.Assessthereasonablenessofanswersusingmentalcomputationandestimationstrategiesincluding

rounding.(Thisstandardislimitedtoproblemsposedwithwholenumbersandhavingwhole‐numberanswers;studentsshouldknowhowtoperformoperationsintheconventionalorderwhentherearenoparenthesestospecifyaparticularorder,i.e.,OrderofOperations.)

3.NBT.1Useplacevalueunderstandingtoroundwholenumberstothenearest10or100.

3.NBT.2Fluentlyaddandsubtract

TimeMeasurementandProblemSolving

MeasuringWeightandLiquidVolumein

RoundingtotheNearestTenandHundred

Relateskip‐countingbyfivesontheclockandtellingtimetoacontinuousmeasurementmodel,thenumberline.

Countbyfivesandonesonthenumberlineasastrategytotelltimetothenearestminuteontheclock.

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within1000usingstrategiesandalgorithmsbasedonplacevalue,propertiesofoperations,and/ortherelationshipbetweenadditionandsubtraction.

Solveproblemsinvolvingmeasurementandestimationofintervalsoftime,liquidvolumes,andmassesofobjects.

3.MD.1Tellandwritetimetothenearestminuteandmeasuretimeintervalsinminutes.Solvewordproblemsinvolvingadditionandsubtractionoftimeintervalsin

Two‐andThree‐DigitMeasurementAdditionUsingtheStandardAlgorithm

Two‐andThree‐DigitMeasurementSubtractionUsingtheStandardAlgorithm

Solvewordproblemsinvolvingtimeintervalswithin1hourbycountingbackwardandforwardusingthenumberlineandclock.

Solvewordproblemsinvolvingtimeintervalswithin1hourbyaddingandsubtractingonthenumberline.

Buildanddecomposeakilogramtoreasonaboutthesizeandweightof1kilogram,100grams,10grams,and1gram.

Solveone‐stepwordproblemsinvolvingmetricweightswithin100andestimatetoreasonaboutsolutions.

Estimateandmeasureliquidvolumeinlitersandmillilitersusingtheverticalnumberline.

Solvemixedwordproblemsinvolvingallfouroperationswithgrams,kilograms,liters,

minutes,e.g.,byrepresentingtheproblemonanumberlinediagram.

3.MD.2Measureandestimateliquidvolumesandmassesofobjectsusingstandardunitsofgrams(g),kilograms(kg),andliters(l).(Excludescompoundunitssuchascm3andfindingthegeometricvolumeofacontainer.)Add,subtract,multiply,ordividetosolveone‐stepwordproblems

involvingmassesorvolumesthataregiveninthe

andmillilitersgiveninthesameunits.

Roundtwo‐andthree‐digitnumberstothenearesttenontheverticalnumberline.

sameunits,e.g.,byusingdrawings(suchasabeakerwithameasurementscale)torepresenttheproblem.(Excludesmultiplicativecomparisonproblems,i.e.,problemsinvolvingnotionsof“timesasmuch”)

MARLBOROCENTRALSCHOOLDISTRICT–K‐5CURRICULUMMAP2015

Subject:MathematicsGrade:3rd

Quarter 2

N.Y.S. Performance Indicator

Content/Concepts: What students should know (Unit organizing idea, understanding, or essential question)

Skills (What Students Should Be Able To Do)

Resources

(District /technology)

Major Assessments

(Tests, projects, etc.)

3.NBT.1Useplacevalueunderstandingtoroundwholenumberstothenearest10or100.

3.NBT.2Fluentlyaddandsubtractwithin1000usingstrategiesandalgorithmsbasedonplacevalue,propertiesofoperations,and/ortherelationship

TimeMeasurementandProblemSolving

MeasuringWeightandLiquidVolumeinMetricUnits

RoundingtotheNearestTenandHundred

Two‐andThree‐DigitMeasurementAdditionUsingtheStandardAlgorithm

Two‐andThree‐DigitMeasurementSubtractionUsingtheStandardAlgorithm

Roundtothenearesthundredontheverticalnumberline.Two‐andThree‐DigitMeasurementAdditionUsingtheStandardAlgorithm

Addmeasurementsusingthestandardalgorithmtocomposelargerunitsonce.

Addmeasurementsusingthestandardalgorithmtocomposelargerunitstwice.

Estimatesumsbyroundingandapplytosolvemeasurementwordproblems.

Decomposeoncetosubtractmeasurementsincluding

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betweenadditionandsubtraction.

3.MD.1Tellandwritetimetothenearestminuteandmeasuretimeintervalsinminutes.Solvewordproblemsinvolvingadditionandsubtractionoftimeintervalsinminutes,e.g.,byrepresentingtheproblemonanumberlinediagram.

3.MD.2Measureandestimateliquidvolumesandmassesofobjectsusingstandardunitsofgrams(g),kilograms(kg),andliters(l).Add,subtract,multiply,or

threedigitminuendswithzerosinthetensoronesplace.

Decomposetwicetosubtractmeasurementsincludingthreedigitminuendswithzerosinthetensandonesplaces.

Estimatedifferencesbyroundingandapplytosolvemeasurementwordproblems.

Estimatesumsanddifferencesofmeasurementsbyrounding,andthensolvemixedwordproblems.

dividetosolveone‐stepwordproblemsinvolvingmassesorvolumesthataregiveninthesameunits,e.g.,byusingdrawings(suchasabeakerwithameasurementscale)torepresenttheproblem.

3.OA.3Usemultiplicationanddivisionwithin100tosolvewordproblemsinsituationsinvolvingequalgroups,arrays,andmeasurement

ThePropertiesofMultiplicationandDivision

MultiplicationandDivisionUsingUnitsof6and7

MultiplicationandDivisionUsingUnitsupto8

MultiplicationandDivisionUsingUnitsof9

Studycommutativitytofindknownfactsof6,7,8,and9.

Applythedistributiveandcommutativepropertiestorelatemultiplicationfacts5×n+nto6×nandn×6wherenisthesizeoftheunit.

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quantities,e.g.,byusingdrawingsandequationswithasymbolfortheunknownnumbertorepresenttheproblem

3.OA.4Determinetheunknownwholenumberinamultiplicationordivisionequationrelatingthreewholenumbers.Forexample,determinetheunknownnumberthatmakestheequationtrueineachoftheequations8x?=48,5=___÷3,6x6=?Understandpropertiesofmultiplicationandthe

AnalysisofPatternsandProblemSolvingIncludingUnitsof0and1

MultiplicationofSingle‐DigitFactorsandMultiplesof10

Multiplyanddividewithfamiliarfactsusingalettertorepresenttheunknown.

Countbyunitsof6tomultiplyanddivideusingnumberbondstodecompose.

Countbyunitsof7tomultiplyanddivideusingnumberbondstodecompose.

Usethedistributivepropertyasastrategytomultiplyanddivideusingunitsof6and7.

Interprettheunknowninmultiplicationanddivisiontomodelandsolveproblemsusingunitsof6and7.

Understandthefunctionofparenthesesandapplytosolvingproblems.

Modeltheassociativepropertyasastrategytomultiply.

Usethedistributivepropertyasastrategytomultiplyanddivide.

relationshipbetweenmultiplicationanddivision.

3.OA.5Applypropertiesofoperationsasstrategiestomultiplyanddivide.(Studentsneednotuseformaltermsfortheseproperties.)Examples:If6×4=24isknown,then4×6=24isalsoknown.(Commutativepropertyofmultiplication.)3×5×2canbefoundby3×5=15,then15×2=30,orby5×2=10,then3×10=30.(Associativepropertyofmultiplication.)Knowingthat8

Interprettheunknowninmultiplicationanddivisiontomodelandsolveproblems.

Applythedistributivepropertyandthefact9=10–1asastrategytomultiply.

Identifyandusearithmeticpatternstomultiply.

Interprettheunknowninmultiplicationanddivisiontomodelandsolveproblems.

Reasonaboutandexplainarithmeticpatternsusingunitsof0and1astheyrelatetomultiplicationanddivision.

Solvetwo‐stepwordproblemsinvolvingallfouroperationsandassessthereasonablenessofsolutions.

Multiplybymultiplesof10usingtheplacevaluechart.

Useplacevaluestrategiesandtheassociativepropertyn×(m×10)=(n×m)×10(wherenandmarelessthan

×5=40and8×2=16,onecanfind8×7as8×(5+2)=(8×5)+(8×2)=40+16=56.(Distributiveproperty.)

3.OA.7Fluentlymultiplyanddividewithin100,usingstrategiessuchastherelationshipbetweenmultiplicationanddivision(e.g.,knowingthat8×5=40,oneknows40÷5=8)orpropertiesofoperations.BytheendofGrade3,knowfrommemoryallproductsoftwoone‐digitnumbers.

3.OA.8Solvetwo‐stepword

10)tomultiplybymultiplesof10.

Solvetwo‐stepwordproblemsinvolvingmultiplyingsingle‐digitfactorsandmultiplesof10.

problemsusingthefouroperations.Representtheseproblemsusingequationswithaletterstandingfortheunknownquantity.Assessthereasonablenessofanswersusingmentalcomputationandestimationstrategiesincludingrounding.(Thisstandardislimitedtoproblemsposedwithwholenumbersandhavingwhole‐numberanswers;studentsshouldknowhowtoperformoperationsintheconventional

orderwhentherearenoparenthesestospecifyaparticularorder,i.e.,OrderofOperations.)

3.OA.9Identifyarithmeticpatterns(includingpatternsintheadditiontableormultiplicationtable),andexplainthemusingpropertiesofoperations.Forexample,observethat4timesanumberisalwayseven,andexplainwhy4timesanumbercanbedecomposedintotwoequaladdends.

Useplacevalueunderstanding

andpropertiesofoperationstoperformmulti‐digitarithmetic.(Arangeofalgorithmsmaybeused.)

3.NBT.3Multiplyone‐digitwholenumbersbymultiplesof10intherange10–90(e.g.,9×80,5×60)usingstrategiesbasedonplacevalueandpropertiesofoperations

3.MD.5Recognizeareaasanattributeofplanefiguresandunderstandconceptsofareameasurement.

a.Asquarewithsidelength1unit,called“aunit

FoundationsforUnderstandingArea

ConceptsofAreaMeasurement

ArithmeticPropertiesUsingArea

ApplicationsofAreaUsingSideLengthsofFigures

Understandareaasanattributeofplanefigures.

Decomposeandrecomposeshapestocompareareas.

Modeltilingwithcentimeterandinchunitsquaresasastrategytomeasurearea.

Formrectanglesbytilingwithunitsquarestomakearrays.

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square,”issaidtohave“onesquareunit”ofarea,andcanbeusedtomeasurearea.

b.Aplanefigurewhichcanbecoveredwithoutgapsoroverlapsbynunitsquaresissaidtohaveanareaofnsquareunits.

3.MD.6Measureareasbycountingunitsquares(squarecm,squarem,squarein,squareft,andimprovisedunits).

3.MD.7Relateareatotheoperationsofmultiplicationandaddition.

a.Findtheareaofarectanglewith

Drawrowsandcolumnstodeterminetheareaofarectanglegivenanincompletearray.

Interpretareamodelstoformrectangulararrays.

Findtheareaofarectanglethroughmultiplicationofthesidelengths.

Analyzedifferentrectanglesandreasonabouttheirarea.

Applythedistributivepropertyasastrategytofindthetotalareaofalargerectanglebyaddingtwoproducts.

Demonstratethepossiblewholenumbersidelengthsof

rectangleswithareasof24,36,48,or72squareunitsusingtheassociative

Solvewordproblemsinvolvingarea.

Findareasbydecomposingintorectanglesorcompleting

whole‐numbersidelengthsbytilingit,andshowthattheareaisthesameaswouldbefoundbymultiplyingthesidelengths.

b.Multiplysidelengthstofindareasofrectangleswithwhole‐numbersidelengthsinthecontextofsolvingrealworldandmathematicalproblems,andrepresentwhole‐numberproductsasrectangularareasinmathematicalreasoning.

c.Usetilingtoshowinaconcretecasethattheareaofa

compositefigurestoformrectangles.

rectanglewithwhole‐numbersidelengthsaandb+cisthesumofa×banda×c.Useareamodelstorepresentthedistributivepropertyinmathematicalreasoning.

d.Recognizeareaasadditive.Findareasofrectilinearfiguresbydecomposingthemintonon‐overlappingrectanglesandaddingtheareasofthenon‐overlappingparts,applyingthistechniquetosolverealworldproblems.