marlboro central school district – k ‐5 …...math understand equal groups of as multiplication...

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MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 CURRICULUM MAP 2015 Subject: Mathematics Grade: 3 Quarter 1 N.Y.S. Performance Indicator Content/Concepts: What students should know Skills (What Students Should Be Able To Do) Resources Major Assessments 3.OA.1 Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7. 3.OA.2 Interpret whole‐number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 Multiplication and the Meaning of the Factors Division as an Unknown Factor Problem Multiplication Using Units of 2 and 3 Division Using Units of 2 and 3 Multiplication and Division Using Units of 4 Distributive Property and Problem Solving Using Units of 2–5 and 10 Multiplication and the Meaning of the Factors: Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the meaning of factors—the size of the group or the number of groups Engage NY:Module1 Math Manipulatives Kit Flashcards Websites Exit Tickets Mid and End‐of‐ Module Assessments

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Page 1: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

MARLBOROCENTRALSCHOOLDISTRICT–K‐5CURRICULUMMAP2015

Subject:MathematicsGrade:3

Quarter 1

N.Y.S. Performance Indicator

Content/Concepts: What students should know

Skills (What Students Should Be Able To Do)

Resources

Major Assessments

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

3.OA.2Interpretwhole‐numberquotientsofwholenumbers,e.g.,interpret56÷8asthenumberofobjectsineachsharewhen56

MultiplicationandtheMeaningoftheFactors

DivisionasanUnknownFactorProblem

MultiplicationUsingUnitsof2and3

DivisionUsingUnitsof2and3

MultiplicationandDivisionUsingUnitsof4

DistributivePropertyandProblemSolvingUsingUnitsof2–5and10

MultiplicationandtheMeaningoftheFactors:

Understandequalgroupsofasmultiplicationanddivision

Relatemultiplicationanddivisiontothearraymodel

Interpretthemeaningoffactors—thesizeofthegrouporthenumberofgroups

EngageNY:Module1

MathManipulativesKit

Flashcards

Websites

ExitTickets

MidandEnd‐of‐ModuleAssessments

Page 2: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

objectsarepartitionedequallyinto8shares,orasanumberofshareswhen56objectsarepartitionedintoequalsharesof8objectseach.Forexample,describeacontextinwhichanumberofsharesoranumberofgroupscanbeexpressedas56÷8.

3.OA.3Usemultiplicationanddivisionwithin100tosolvewordproblemsinsituationsinvolvingequalgroups,arrays,andmeasurementquantities,e.g.,byusingdrawingsandequationswithasymbolfortheunknownnumbertorepresenttheproblem.

DivisionasanUnknownFactorProblem:

Understandthemeaningoftheunknownasthesizeofthegroupindivision

Understandthemeaningoftheunknownasthenumberofgroupsindivision

Interprettheunknownindivisionusingthearraymodel

AnalyzeArraystoMultiplyUsingUnitsof2and3:

Demonstratethecommutativityofmultiplication,andpracticerelatedfactsbyskip‐countingobjectsinarraymodels

Findrelatedmultiplicationfactsbyaddingandsubtractingequal

Page 3: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

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

3.OA.5Applypropertiesofoperationsasstrategiestomultiplyanddivide.(Studentsneednotuseformaltermsfortheseproperties.)Examples:If6×4=24isknown,then4×6=24isalsoknown.(Commutativepropertyofmultiplication)3×5×2canbefoundby3×

groupsinarraymodels

Modelandapplythedistributivepropertywitharraystodecomposeunitsasastrategytomultiply

DivisionUsingUnitsof2and3:

Modeldivisionastheunknownfactorinmultiplicationusingarraysandtapediagrams

Interpretthequotientasthenumberofgroupsorthenumberofobjectsineachgroupusingunitsof2,3,4,5,10

Skip‐countobjectsinmodelstobuildfluencywithmultiplicationfactsusingunitsof2,3,4,5,10

Page 4: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

5=15,then15×2=30,orby5×2=10,then3×10=30(Associativepropertyofmultiplication).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)or

Relatearraystotapediagramstomodelthecommutativepropertyofmultiplication

Usethedistributivepropertyasastrategytofindrelatedmultiplicationfacts

Modeltherelationshipbetweenmultiplicationanddivision

DistributivePropertyandProblemSolvingUsingUnitsof2‐5and10:

Applythedistributivepropertytodecomposeunits

Solvetwo‐stepwordproblemsinvolvingmultiplicationanddivision,andassessthereasonablenessofanswers

Page 5: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

propertiesofoperations.BytheendofGrade3,knowfrommemoryallproductsoftwoone‐digitnumbers.

3.OA.8Solvetwo‐stepwordproblemsusingthefouroperations.Representtheseproblemsusingequationswithaletterstandingfortheunknownquantity.Assessthereasonablenessofanswersusingmentalcomputationandestimationstrategiesincludingrounding.(Thisstandardislimitedtoproblemsposedwithwholenumbersandhavingwhole‐numberanswers;studentsshouldknowhowtoperformoperationsintheconventional

Solvetwo‐stepwordproblemsinvolvingallfouroperations,andassessthereasonablenessofanswers

Page 6: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

orderwhentherearenoparenthesestospecifyaparticularorder,i.e.,OrderofOperations.).

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

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

TimeMeasurementandProblemSolving

MeasuringWeightandLiquidVolumeinMetricUnits

TimeMeasurementandProblemSolving:

Relateskip‐countingbyfivesontheclockandtellingtimetoacontinuousmeasurementmodel,thenumberline

Countbyfivesandonesonthenumberlineasastrategytotelltimetothenearestminuteontheclock

Solvewordproblemsinvolvingtimeintervalswithin1hourbycountingbackwardandforwardusingthenumberlineandclock

EngageNY:Module2

BrainPopJr.

Flocabulary

MathManipulativesKit

Balancescale

Digitalscale

Platformscale

1kgricebags

Variouslitercontainers

Flashcards

Websites

Exittickets

MidandEnd‐of‐ModuleAssessments

Page 7: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

thataregiveninthesameunits,e.g.,byusingdrawings(suchasabeakerwithameasurementscale)torepresenttheproblem.

Solvewordproblemsinvolvingtimeintervalswithin1hourbyaddingandsubtractingonthenumberline

MeasuringWeightandLiquidVolumeinMetricUnits:

Buildanddecomposeakilogramtoreasonaboutthesizeandweightof1kilogram,100grams,10grams,and1gram

Solveone‐stepwordproblemsinvolvingmetricweightswithin100andestimatetoreasonaboutsolutions

Decomposealitertoreasonaboutthesizeof1liter,100milliliters,10milliliters,and1milliliter

Page 8: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

Estimateandmeasureliquidvolumeinlitersandmillilitersusingtheverticalnumberline

Solvemixedwordproblemsinvolvingallfouroperationswithgrams,kilograms,liters,andmillilitersgiveninthesameunits

Page 9: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

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/orthe

RoundingtotheNearestTenandHundred

Two‐andThree‐DigitMeasurementAdditionUsingtheStandardAlgorithm

Two‐andThree‐DigitMeasurementSubtractionUsingtheStandardAlgorithm

RoundingtotheNearestTenandHundred:

Roundtwo‐digitmeasurementstothenearesttenontheverticalnumberline

Roundtwoandthree‐digitnumberstothenearesttenontheverticalnumberline

Roundtothenearesthundredontheverticalnumberline

Two‐and‐ThreeDigitMeasurementAddition

EngageNY:Module2

MathManipulativesKit

Flashcards

Websites

Exittickets

MidandEnd‐of‐ModuleAssessments

Page 10: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

relationshipbetweenadditionandsubtraction.

UsingtheStandardAlgorithm:

Addmeasurementsusingthestandardalgorithmtocomposelargerunitsonce

Addmeasurementsusingthestandardalgorithmtocomposelargerunitstwice

Estimatesumsbyroundingandapplytosolvemeasurementwordproblems

Two‐andThree‐DigitMeasurementSubtractionUsingtheStandardAlgorithm:

Decomposeoncetosubtractmeasurementsincludingthreedigitminuendswithzerosinthetensoronesplace

Decomposetwicetosubtractmeasurements

Page 11: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

includingthreedigitminuendswithzerosinthetensandonesplaces

Estimatedifferencesbyroundingandapplytosolvemeasurementwordproblems

Estimatesumsanddifferencesofmeasurementsbyrounding,andthensolvemixedwordproblems

3.OA.3Usemultiplicationanddivisionwithin100tosolvewordproblemsinsituationsinvolvingequalgroups,arrays,andmeasurementquantities,e.g.,byusingdrawingsandequationswitha

ThePropertiesofMultiplicationandDivision

MultiplicationandDivisionUsingUnitsof6and7

MultiplicationandDivisionUsingUnitsupto8

MultiplicationandDivisionUsingUnitsof9

AnalysisofPatternsandProblemSolvingIncludingUnitsof0and1

Studycommutativitytofindknownfactsof6,7,8,and9.

Applythedistributiveandcommutativepropertiestorelatemultiplicationfacts5×n+nto6×nandn×6wherenisthesizeoftheunit.

Multiplyanddividewithfamiliarfactsusingalettertorepresenttheunknown.

Countbyunitsof6tomultiplyanddivideusingnumberbondstodecompose.

EngageNY

Module3.3

Exittickets

Midandendofmoduleassessments

Page 12: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

symbolfortheunknownnumbertorepresenttheproblem

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

MultiplicationofSingle‐DigitFactorsandMultiplesof10

Countbyunitsof7tomultiplyanddivideusingnumberbondstodecompose.

Usethedistributivepropertyasastrategytomultiplyanddivideusingunitsof6and7.

Interprettheunknowninmultiplicationanddivisiontomodelandsolveproblemsusingunitsof6and7.

Understandthefunctionofparenthesesandapplytosolvingproblems.

Modeltheassociativepropertyasastrategytomultiply.

Usethedistributivepropertyasastrategytomultiplyanddivide.

Interprettheunknowninmultiplicationanddivisiontomodelandsolveproblems.

Applythedistributivepropertyandthefact9=10–1asastrategytomultiply.

Page 13: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

multiplicationanddivision.

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

Identifyandusearithmeticpatternstomultiply.

Interprettheunknowninmultiplicationanddivisiontomodelandsolveproblems.

Reasonaboutandexplainarithmeticpatternsusingunitsof0and1astheyrelatetomultiplicationanddivision.

Solvetwo‐stepwordproblemsinvolvingallfouroperationsandassessthereasonablenessofsolutions.

Multiplybymultiplesof10usingtheplacevaluechart.

Useplacevaluestrategiesandtheassociativepropertyn×(m×10)=(n×m)×10(wherenandmarelessthan10)tomultiplybymultiplesof10.

Solvetwo‐stepwordproblemsinvolvingmultiplyingsingle‐digitfactorsandmultiplesof10.

Page 14: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

×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.

Page 15: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

3.OA.8Solvetwo‐stepwordproblemsusingthefouroperations.Representtheseproblemsusingequationswithaletterstandingfortheunknownquantity.Assessthereasonablenessofanswersusingmentalcomputationandestimationstrategiesincludingrounding.(Thisstandardislimitedtoproblemsposedwithwholenumbersandhavingwhole‐numberanswers;studentsshouldknowhowtoperform

Page 16: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

operationsintheconventionalorderwhentherearenoparenthesestospecifyaparticularorder,i.e.,OrderofOperations.)

3.OA.9Identifyarithmeticpatterns(includingpatternsintheadditiontableormultiplicationtable),andexplainthemusingpropertiesofoperations.Forexample,observethat4timesanumberisalwayseven,andexplainwhy4timesanumbercanbedecomposedinto

Page 17: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

twoequaladdends.

Useplacevalueunderstandingandpropertiesofoperationstoperformmulti‐digitarithmetic.(Arangeofalgorithmsmaybeused.)

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

3.MD.5Recognizeareaasanattributeofplanefiguresandunderstand

FoundationsforUnderstandingArea

ConceptsofAreaMeasurement

Understandareaasanattributeofplanefigures.

Decomposeandrecomposeshapestocompareareas.

EngageNY

Module3.4

Exittickets

Midandendofmoduleassessments

Page 18: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

conceptsofareameasurement.

a.Asquarewithsidelength1unit,called“aunitsquare,”issaidtohave“onesquareunit”ofarea,andcanbeusedtomeasurearea.

b.Aplanefigurewhichcanbecoveredwithoutgapsoroverlapsbynunitsquaresissaidtohaveanareaofnsquareunits.

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

ArithmeticPropertiesUsingArea

ApplicationsofAreaUsingSideLengthsofFigures

Modeltilingwithcentimeterandinchunitsquaresasastrategytomeasurearea.

Formrectanglesbytilingwithunitsquarestomakearrays.

Drawrowsandcolumnstodeterminetheareaofarectanglegivenanincompletearray.

Interpretareamodelstoformrectangulararrays.

Findtheareaofarectanglethroughmultiplicationofthesidelengths.

Analyzedifferentrectanglesandreasonabouttheirarea.

Applythedistributivepropertyasastrategytofindthetotalareaofalargerectanglebyaddingtwoproducts.

Demonstratethepossiblewholenumbersidelengthsof

Page 19: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

3.MD.7Relateareatotheoperationsofmultiplicationandaddition.

a.Findtheareaofarectanglewithwhole‐numbersidelengthsbytilingit,andshowthattheareaisthesameaswouldbefoundbymultiplyingthesidelengths.

b.Multiplysidelengthstofindareasofrectangleswithwhole‐numbersidelengthsinthecontextofsolvingrealworldandmathematicalproblems,andrepresentwhole‐numberproducts

rectangleswithareasof24,36,48,or72squareunitsusingtheassociative

Solvewordproblemsinvolvingarea.

Findareasbydecomposingintorectanglesorcompletingcompositefigurestoformrectangles.

Page 20: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

asrectangularareasinmathematicalreasoning.

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

d.Recognizeareaasadditive.Findareasofrectilinearfiguresbydecomposingthemintonon‐overlappingrectanglesand

Page 21: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

addingtheareasofthenon‐overlappingparts,applyingthistechniquetosolverealworldproblems.

Page 22: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

MARLBOROCENTRALSCHOOLDISTRICT–K‐5CURRICULUMMAP2015

Subject:MathematicsGrade:3

Quarter 3

N.Y.S. Performance Indicator

Content/Concept: What students should know

Skills (What Students Should Be Able To Do)

Resources Major Assessments

3.NF.1Understandafraction1/basthequantityformedby1partwhenawholeispartitionedintobequalparts;understandafractiona/basthequantityformedbyapartsofsize1/b. 3.NF.2Understandafractionasanumberonthenumberline;representfractionsonanumberlinediagram.a.Representafraction1/bonanumberlinediagrambydefiningtheintervalfrom0to1asthewholeandpartitioningitintobequalparts.Recognizethateachparthassize1/bandthattheendpointofthepartbasedat0locatesthenumber1/bonthenumberline.

PartitioningaWholeintoEqualParts

UnitFractionsandTheirRelationtotheWhole

ComparingUnitFractionsandSpecifyingtheWhole

FractionsontheNumberLine

EquivalentFractions

Comparison,Order,andSizeofFractions

PartitioningaWholeintoEqualParts:

Specifyandpartitionawholeintoequalparts,identifyingandcountingunitfractionsusingconcretemodels

Specifyandpartitionawholeintoequalparts,identifyingandcountingunitfractionsbyfoldingfractionstrips

Specifyandpartitionawholeintoequalparts,identifyingandcountingunitfractionsbydrawingpictorialareamodels

Representandidentifyfractionalpartsofdifferentwholes

UnitFractionsandTheirRelationtotheWhole:

EngageNY:Module5

MathManipulativesKit

Fractionsstrips

Flashcards

Websites

Exittickets

MidandEnd‐of‐ModuleAssessments

Page 23: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

b.Representafractiona/bonanumberlinediagrambymarkingoffalengths1/bfrom0.Recognizethattheresultingintervalhassizea/bandthatitsendpointlocatesthenumbera/bonthenumberline. 3.NF.3Explainequivalenceoffractionsinspecialcases,andcomparefractionsbyreasoningabouttheirsize.a. Understandtwofractionsasequivalent(equal)iftheyarethesamesize,orthesamepointonanumberline.

b. Recognizeandgeneratesimpleequivalentfractions,e.g.,1/2=2/4,4/6=2/3.Explainwhythefractionsareequivalent,e.g.,byusingavisualfractionmodel.

c. Expresswholenumbersasfractions,andrecognizefractionsthatareequivalenttowholenumbers.Examples:Express3intheformof3=3/1;recognizethat6/1=6;locate4/4and1atthesamepointofanumberlinediagram.

Partitionawholeintoequalpartsanddefinetheequalpartstoidentifytheunitfractionnumerically

Buildnon‐unitfractionslessthanonewholefromunitfractions

Identifyandrepresentshadedandnon‐shadedpartsofonewholeasfractions

Representpartsofonewholeasfractionswithnumberbonds

Buildandwritefractionsgreaterthanonewholeusingunitfractions

ComparingUnitFractionsandSpecifyingtheWhole:

Compareunitfractionsbyreasoningabouttheirsizeusingfractionstrips

Compareunitfractionswithdifferent‐sizedmodelsrepresentingthewhole

Specifythecorrespondingwholewhenpresentedwithoneequalpart

Identifyashadedfractionalpartindifferentwaysdependingonthedesignationofthewhole

Page 24: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

d. Comparetwofractionswiththesamenumeratororthesamedenominatorbyreasoningabouttheirsize.Recognizethatcomparisonsarevalidonlywhenthetwofractionsrefertothesamewhole.Recordtheresultsofcomparisonswiththesymbols>,=,or<,andjustifytheconclusions,e.g.,byusingavisualfractionmodel.

3.G.2Partitionshapesintopartswithequalareas.Expresstheareaofeachpartasaunitfractionofthewhole.Forexample,partitionashapeinto4partswithequalarea,anddescribetheareaofeachpartas1/4oftheareaoftheshape.

FractionsontheNumberLine:

Placeunitfractionsonanumberlinewithendpoints0and1

Placeanyfractiononanumberlinewithendpoints0and1

Placewholenumberfractionsandfractionsbetweenwholenumbersonthenumberline

Practiceplacingvariousfractionsonthenumberline

Comparefractionsandwholenumbersonthenumberlinebyreasoningabouttheirdistancefrom0

Understanddistanceandpositiononthenumberlineasstrategiesforcomparingfractions

EquivalentFractions:

Recognizeandshowthatequivalentfractionshavethesamesize,thoughnotnecessarilythesameshape

Recognizeandshowthatequivalentfractionsrefertothesamepointonthenumberline

Generatesimpleequivalentfractionsbyusingvisual

Page 25: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

fractionmodelsandthenumberline

Expresswholenumbersasfractionsandrecognizeequivalencewithdifferentunits

Expresswholenumberfractionsonthenumberlinewhentheunitintervalis1

Decomposewholenumberfractionsgreaterthan1usingwholenumberequivalencewithvariousmodels

Explainequivalencebymanipulatingunitsandreasoningabouttheirsize

Comparison,Order,andSizeofFractions:

Comparefractionswiththesamenumeratorpictorially

Comparefractionswiththesamenumeratorusing<,>,or=,anduseamodeltoreasonabouttheirsize

Partitionvariouswholespreciselyintoequalpartsusinganumberlinemethod

Page 26: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

3.MD.3Drawascaledpicturegraphandascaledbargraphtorepresentadatasetwithseveralcategories.Solveone‐andtwo‐step“howmanymore”and“howmanyless”problemsusinginformationpresentedinscaledbargraphs.Forexample,drawabargraphinwhicheachsquareinthebargraphmightrepresent5pets.

GenerateandAnalyzeCategoricalData

GenerateandAnalyzeCategoricalData:

Generateandorganizedata Rotatetapediagrams

vertically Createscaledbargraphs Solveone‐andtwo‐step

problemsinvolvinggraphs

EngageNY:Module6

MathManipulativesKit

Flashcards

Websites

Exittickets

MidandEnd‐of‐ModuleAssessments

Page 27: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

MARLBOROCENTRALSCHOOLDISTRICT–K‐5CURRICULUMMAP2015

Subject:MathematicsGrade:3

Quarter 4

N.Y.S. Performance Indicator

Content/Concept: What students should know

Skills (What Students Should Be Able To Do)

Resources

Major Assessments

3.MD.4Generatemeasurementdatabymeasuringlengthsusingrulersmarkedwithhalvesandfourthsofaninch.Showthedatabymakingalineplot,wherethehorizontalscaleismarkedoffinappropriateunits—wholenumbers,halves,orquarters.

GenerateandAnalyzeMeasurementData

GenerateandAnalyzeMeasurementData:

Createrulerwith1‐inch,1/2inch,and1/4inchintervals,andgeneratemeasurementdata

Interpretmeasurementdatafromvariouslineplots

Representmeasurementdatawithlineplots

Analyzedatatoproblemsolve

EngageNY:Module6

MathManipulativesKit

Flashcards

Websites

Exittickets

MidandEnd‐of‐ModuleAssessments

3.OA.8Solvetwo‐stepwordproblemsusingthefouroperations.Representtheseproblemsusingequationswithaletterstandingfortheunknownquantity.Assessthereasonablenessofanswersusingmentalcomputationandestimationstrategiesincludingrounding.(This

SolvingWordProblems

AttributesofTwo‐DimensionalFigures

ProblemSolvingwithPerimeter

RecordingPerimeterandAreaDataonLinePlots

SolvingWordProblems: Solvewordproblemsin

variedcontextsusingalettertorepresenttheunknown

Shareandcritiquepeersolutionstrategiestovariedwordproblems

EngageNY:Module7

MathManipulativesKit

Variouscircularobjects

Yarn

Exittickets

MidandEnd‐of‐ModuleAssessments

Page 28: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

standardislimitedtoproblemsposedwithwholenumbersandhavingwhole‐numberanswers;studentsshouldknowhowtoperformoperationsintheconventionalorderwhentherearenoparenthesestospecifyaparticularorder[OrderofOperations]).3.MD.4Generatemeasurementdatabymeasuringlengthsusingrulersmarkedwithhalvesandfourthsofaninch.Showthedatabymakingalineplot,wherethehorizontalscaleismarkedoffinappropriateunits—wholenumbers,halves,orquarters. 3.MD.8Solverealworldandmathematicalproblemsinvolvingperimetersofpolygons,includingfindingtheperimetergiventhesidelengths,findinganunknownsidelength,andexhibitingrectangleswiththesameperimeteranddifferentareasorwiththesameareaanddifferentperimeters.

ProblemSolvingwithPerimeterandArea

AttributesofTwo‐DimensionalFigures

Compareandclassifyquadrilaterals

Compareandclassifyotherpolygons

Drawpolygonswithspecifiedattributestosolveproblems

Reasonaboutcomposinganddecomposingpolygonsusingtetrominoes

Createatangrampuzzleandobserverelationshipsamongtheshapes

Reasonaboutcomposinganddecomposingpolygonsusingtangrams

ProblemSolvingwithPerimeter:

Decomposequadrilateralstounderstandperimeterastheboundaryofashape

Tessellatetounderstandperimeterastheboundaryofashape

Measuresidelengthsinwholenumberunitstodeterminetheperimeterofpolygons

Rulers

Flashcards

Websites

Page 29: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

3.G.1Understandthatshapesindifferentcategories(e.g.,rhombuses,rectangles,andothers)mayshareattributes(e.g.,havingfoursides),andthatthesharedattributescandefinealargercategory(e.g.,quadrilaterals).Recognizerhombuses,rectangles,andsquaresasexamplesofquadrilaterals,anddrawexamplesofquadrilateralsthatdonotbelongtoanyofthesesubcategories.

Exploreperimeterasanattributeofplanefiguresandsolveproblems

Determinetheperimeterofregularpolygonsandrectangleswhenwholenumbermeasurementsaremissing

Solvewordproblemstodetermineperimeterwithgivensidelengths

Usestringtomeasuretheperimeterofvariouscirclestothenearestquarterinch

Useallfouroperationstosolveproblemsinvolvingperimeterandmissingmeasurements

RecordingPerimeterandAreaDataonLinePlots:

Constructrectanglesfromagivennumberofunitsquaresanddeterminetheperimeters

Usealineplottorecordthenumberofrectanglesconstructedfromagivennumberofunitsquares

Constructrectangleswithagivenperimeterusingunitsquaresanddeterminetheirareas

Page 30: MARLBORO CENTRAL SCHOOL DISTRICT – K ‐5 …...Math Understand equal groups of as multiplication and division Relate multiplication and division to the array model Interpret the

Usealineplottorecordthenumberofrectanglesconstructed

ProblemSolvingwithPerimeterandArea

Solveavarietyofwordproblemswithperimeter

Solveavarietyofwordproblemsinvolvingareaandperimeter