MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5...
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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.
EngageNY
Module3.1
Exittickets
Midandendofmoduleassessments
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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
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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.
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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
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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×
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5=40,oneknows40÷5=8)orpropertiesofoperations.BytheendofGrade3,knowfrommemoryallproductsoftwoone‐digitnumbers.
3.OA.8Solvetwo‐stepwordproblemsusingthefouroperations.Representtheseproblemsusingequationswithaletterstandingfortheunknownquantity.Assessthereasonablenessofanswersusingmentalcomputationandestimationstrategiesincluding
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rounding.(Thisstandardislimitedtoproblemsposedwithwholenumbersandhavingwhole‐numberanswers;studentsshouldknowhowtoperformoperationsintheconventionalorderwhentherearenoparenthesestospecifyaparticularorder,i.e.,OrderofOperations.)
3.NBT.1Useplacevalueunderstandingtoroundwholenumberstothenearest10or100.
3.NBT.2Fluentlyaddandsubtract
TimeMeasurementandProblemSolving
MeasuringWeightandLiquidVolumein
RoundingtotheNearestTenandHundred
Relateskip‐countingbyfivesontheclockandtellingtimetoacontinuousmeasurementmodel,thenumberline.
Countbyfivesandonesonthenumberlineasastrategytotelltimetothenearestminuteontheclock.
EngageNY
Module3.2
Exittickets
Midandendofmoduleassessments
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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,
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minutes,e.g.,byrepresentingtheproblemonanumberlinediagram.
3.MD.2Measureandestimateliquidvolumesandmassesofobjectsusingstandardunitsofgrams(g),kilograms(kg),andliters(l).(Excludescompoundunitssuchascm3andfindingthegeometricvolumeofacontainer.)Add,subtract,multiply,ordividetosolveone‐stepwordproblems
involvingmassesorvolumesthataregiveninthe
andmillilitersgiveninthesameunits.
Roundtwo‐andthree‐digitnumberstothenearesttenontheverticalnumberline.
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sameunits,e.g.,byusingdrawings(suchasabeakerwithameasurementscale)torepresenttheproblem.(Excludesmultiplicativecomparisonproblems,i.e.,problemsinvolvingnotionsof“timesasmuch”)
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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
EngageNY
Module3.2
Exittickets
Midandendofmoduleassessments
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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.
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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.
EngageNY
Module3.3
Exittickets
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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.
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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
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×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.
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problemsusingthefouroperations.Representtheseproblemsusingequationswithaletterstandingfortheunknownquantity.Assessthereasonablenessofanswersusingmentalcomputationandestimationstrategiesincludingrounding.(Thisstandardislimitedtoproblemsposedwithwholenumbersandhavingwhole‐numberanswers;studentsshouldknowhowtoperformoperationsintheconventional
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orderwhentherearenoparenthesestospecifyaparticularorder,i.e.,OrderofOperations.)
3.OA.9Identifyarithmeticpatterns(includingpatternsintheadditiontableormultiplicationtable),andexplainthemusingpropertiesofoperations.Forexample,observethat4timesanumberisalwayseven,andexplainwhy4timesanumbercanbedecomposedintotwoequaladdends.
Useplacevalueunderstanding
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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.
EngageNY
Module3.4
Exittickets
Midandendofmoduleassessments
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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
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whole‐numbersidelengthsbytilingit,andshowthattheareaisthesameaswouldbefoundbymultiplyingthesidelengths.
b.Multiplysidelengthstofindareasofrectangleswithwhole‐numbersidelengthsinthecontextofsolvingrealworldandmathematicalproblems,andrepresentwhole‐numberproductsasrectangularareasinmathematicalreasoning.
c.Usetilingtoshowinaconcretecasethattheareaofa
compositefigurestoformrectangles.
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rectanglewithwhole‐numbersidelengthsaandb+cisthesumofa×banda×c.Useareamodelstorepresentthedistributivepropertyinmathematicalreasoning.
d.Recognizeareaasadditive.Findareasofrectilinearfiguresbydecomposingthemintonon‐overlappingrectanglesandaddingtheareasofthenon‐overlappingparts,applyingthistechniquetosolverealworldproblems.