grades k–5 scope and sequence your 1 choice for world
TRANSCRIPT
Your #1 Choice for World-Class Mathematics!
Deep Math Understanding. Real-World Problem Solvers.
Grades K–5 Scope and Sequence
2
Math in Focus™: Singapore Math by Marshall Cavendish is the U.S. Edition of Singapore’s most widely used program.
Grade K
Grade 3
Grade 1
Grade 4
Grade 2
Grade 5
3
Concept and skill development through hands-on instruction and practice
Key Differences and Distinguishing Characteristics
• basicfacts• placevalue• mentalmath• geometryconcepts
• fractions• decimals
• ratios• modeldrawing
• expressions,equations,andinequalities
Scope and Sequence Grades K–5
Articulated SequenceMath in Focusanswersthecallforacoherentsequenceof topicsgivingstudentstimetomasterfoundationaltopics, sothatlittlerepetitionisrequiredthenextyear.Thus,eachgradelevelcoversfewertopicsbutinmoredepth,andyouwon’tfindalltopicsineverygradelevel.
• “Missingtopics” Whenatopicappearstobe“missing,”youcanbeassuredthatitisfoundineitheranearlierorlatergradelevel.ForexampleyouwillfindcalendarconceptsinGradesKand1,butnotrepeatedinGrade2.
• Moreadvanced Asaresultof notrepeatingtopicsyearafteryear,studentswhouseMath in Focus willadvancefasterthanstudentsinotherprograms.Asaresult, youmayfindtopicsthatseemtobe“tooadvanced.”However,youwillfindyourstudentseasilyabletohandlethechallengeaslongastheyhavehadtheappropriatepreliminaryinstruction.
Developmental ContinuumKindergarten Grades1–2 Grades3–5
Preparation for AlgebraMath in Focusanswersthecalltopreparestudentsforalgebra.AsrecommendedbytheNationalMathPanel,theMath in Focussequenceof topicsemphasizes:
• Numbersense,basicfacts,andcomputation Anearlyunderstandingof compositionanddecompositionof numbersisdevelopedintandemwithmasteryof basic factsandcomputationalgorithmsinGradesK–2.
• Fractionsandproportionalreasoning Significanttimeisallocatedforin-depthworkwithfractionsinGrades3–5.
• Problemsolving Challengingproblemsolvingisbuilt intoeachchapterineverygradelevel.
Foundationalconceptsthroughsongs,rhymes,andhands-onactivities
Emphasisonproblemsolving,skillconsolidation,andadeepunderstandinginpreparationforalgebra
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Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
NumberandOperations NumberandOperations
SetsandNumbers
Use concrete models to createasetwithagivennumberof objects (upto20).
Use concrete and pictorial modelstocreateasetwithagivennumberof objects(upto100).
Use concrete and pictorial modelstocreateasetwith agivennumberof objects (upto1,000).
SetsandNumbers
Groupobjectsandnumbersupto100intensandones.
Groupobjectsandnumbersupto1,000intohundreds,tens,andones.
Groupobjectsintoequalsizedgroups.
Use cardinal and ordinal numbers.
Usecardinalnumbersupto100andordinalnumbersupto10th.
Explorenegativenumbersincontext.
NumberRepresentation
Usenumberstorepresentquantitiesupto20.
Usenumberbondstorepresentnumbercombinations.
Use place value models to create equivalent representationsof numbers.
NumberRepresentation
Representnumbersto10,000indifferentequivalentforms.
Representnumbersto100,000invariouscontexts.
Understand place value conceptsthroughmillions.
Representnumbersto100onanumberline.
Representnumbersto1,000onanumberline.
Count Countupto20objectsinaset.
Countto100. Countto1,000. Count Countto10,000.
Countonandbackto20. Countby1s,2s,5s,and10sforwardandbackwardto100.
Countbymultiplesof ones,tens,andhundreds.
Countbyhundredsandthousands.
Countbythousandsandtenthousands.
Countbyhundredthousandsandmillions.
Countin2sand5sup to20.
CompareandOrder
Compare and order sets and numbersupto20.
Compareandorderwholenumbersto100.
Compareandorderwholenumbersto1,000.
CompareandOrder
Compareandorderwholenumbersto10,000.
Compareandorderwholenumbersto100,000.
Compareandorderwholenumbersto10,000,000.
Compare and order using the terms fewer,more,andless.
Compare and order using the terms same,more,fewer,greater than,less than,equal to,greatest,andleast.
Use<,>,and=tocomparewholenumbers.
PlaceValue Use place value models and place value charts to representnumbersto100.
Usebase-tenmodelsand place value charts to representnumbersto1,000.
PlaceValue Use place value models to read,write,andrepresentnumbersto10,000.
Expressnumbersto100,000instandard,expanded,andwordforms.
Expressnumbersto10,000,000invariousforms.
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Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
NumberandOperations NumberandOperations
SetsandNumbers
Use concrete models to createasetwithagivennumberof objects (upto20).
Use concrete and pictorial modelstocreateasetwithagivennumberof objects(upto100).
Use concrete and pictorial modelstocreateasetwith agivennumberof objects (upto1,000).
SetsandNumbers
Groupobjectsandnumbersupto100intensandones.
Groupobjectsandnumbersupto1,000intohundreds,tens,andones.
Groupobjectsintoequalsizedgroups.
Use cardinal and ordinal numbers.
Usecardinalnumbersupto100andordinalnumbersupto10th.
Explorenegativenumbersincontext.
NumberRepresentation
Usenumberstorepresentquantitiesupto20.
Usenumberbondstorepresentnumbercombinations.
Use place value models to create equivalent representationsof numbers.
NumberRepresentation
Representnumbersto10,000indifferentequivalentforms.
Representnumbersto100,000invariouscontexts.
Understand place value conceptsthroughmillions.
Representnumbersto100onanumberline.
Representnumbersto1,000onanumberline.
Count Countupto20objectsinaset.
Countto100. Countto1,000. Count Countto10,000.
Countonandbackto20. Countby1s,2s,5s,and10sforwardandbackwardto100.
Countbymultiplesof ones,tens,andhundreds.
Countbyhundredsandthousands.
Countbythousandsandtenthousands.
Countbyhundredthousandsandmillions.
Countin2sand5sup to20.
CompareandOrder
Compare and order sets and numbersupto20.
Compareandorderwholenumbersto100.
Compareandorderwholenumbersto1,000.
CompareandOrder
Compareandorderwholenumbersto10,000.
Compareandorderwholenumbersto100,000.
Compareandorderwholenumbersto10,000,000.
Compare and order using the terms fewer,more,andless.
Compare and order using the terms same,more,fewer,greater than,less than,equal to,greatest,andleast.
Use<,>,and=tocomparewholenumbers.
PlaceValue Use place value models and place value charts to representnumbersto100.
Usebase-tenmodelsand place value charts to representnumbersto1,000.
PlaceValue Use place value models to read,write,andrepresentnumbersto10,000.
Expressnumbersto100,000instandard,expanded,andwordforms.
Expressnumbersto10,000,000invariousforms.
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Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
NumberandOperations(continued) NumberandOperations(continued)
PlaceValue(continued)
Expressnumbersto100instandardandwordforms.
Expressnumbersto1,000 intermsof placevalue.
PlaceValue(continued)
Compose and decompose multi-digitnumbers(includingexpandedform).
FractionConcepts
Connect geometric concepts withunitfractions—halves,thirds,andfourths.
FractionConcepts
Understand the meanings andusesof fractionsincludingfractionof aset.
Recognize,write,name,andillustratemixednumbersandimproperfractions.
Convertfractionstodecimals.
Understand the relationship betweenafractionandawhole.
Understandthatthesizeof afractionalpartisrelativetothesizeof thewhole.
Findafractionof aset. Relatefractionsanddivisionexpressions.
Compareandorderhalves,thirds,andfourthsusingbarmodels.
Comparefractionsusingmodelsandnumberlines.
Generate equivalent fractions.
Identifyequivalentfractionsthroughtheuseof models,multiplication,division,andnumberlines.
Convertamongmixednumbersandimproperfractions.
Addandsubtractlikefractions.
Money Identifyandrelatecoinvalues(penny,nickel,dime,quarter).
Identifyandrelatecoinvalues(penny,nickel,dime,quarter).
Identify$1,$5,$10,and$20bills.
Money Addandsubtractmoney.
Count and make coin combinations.
Count and make coin combinations.
Count and make combinationsof coinsandbills.
Comparemoneyamounts. Solvereal-worldproblemsinvolving addition and subtractionof money.
DecimalConcepts
Use the dollar sign and decimalpoint.
DecimalConcepts
Use the dollar sign and decimalpointinmoneyamounts.
Modeldecimalsusingtenthsandhundredths.
Modeldecimalsusingthousandths.
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Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
NumberandOperations(continued) NumberandOperations(continued)
PlaceValue(continued)
Expressnumbersto100instandardandwordforms.
Expressnumbersto1,000 intermsof placevalue.
PlaceValue(continued)
Compose and decompose multi-digitnumbers(includingexpandedform).
FractionConcepts
Connect geometric concepts withunitfractions—halves,thirds,andfourths.
FractionConcepts
Understand the meanings andusesof fractionsincludingfractionof aset.
Recognize,write,name,andillustratemixednumbersandimproperfractions.
Convertfractionstodecimals.
Understand the relationship betweenafractionandawhole.
Understandthatthesizeof afractionalpartisrelativetothesizeof thewhole.
Findafractionof aset. Relatefractionsanddivisionexpressions.
Compareandorderhalves,thirds,andfourthsusingbarmodels.
Comparefractionsusingmodelsandnumberlines.
Generate equivalent fractions.
Identifyequivalentfractionsthroughtheuseof models,multiplication,division,andnumberlines.
Convertamongmixednumbersandimproperfractions.
Addandsubtractlikefractions.
Money Identifyandrelatecoinvalues(penny,nickel,dime,quarter).
Identifyandrelatecoinvalues(penny,nickel,dime,quarter).
Identify$1,$5,$10,and$20bills.
Money Addandsubtractmoney.
Count and make coin combinations.
Count and make coin combinations.
Count and make combinationsof coinsandbills.
Comparemoneyamounts. Solvereal-worldproblemsinvolving addition and subtractionof money.
DecimalConcepts
Use the dollar sign and decimalpoint.
DecimalConcepts
Use the dollar sign and decimalpointinmoneyamounts.
Modeldecimalsusingtenthsandhundredths.
Modeldecimalsusingthousandths.
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Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
NumberandOperations(continued) NumberandOperations(continued)
DecimalConcepts(continued)
DecimalConcepts(continued)
Understand decimal notation through hundredthsasanextensionof thebase-tensystem.
Understand place value concepts through thousandths.
Readandwritedecimalsthat are greater than or lessthan1.
Compare and order decimals.
Identifyequivalent decimals.
Connectequivalentfractionsanddecimals.
Convertdecimalstofractions.
Ratio,Proportion,andPercent
Ratio,Proportion,andPercent
Useratiostosolveproblems.
Findequivalentratios.
Solveproblemswithpercent.
Convertfractionstopercents.
Findapercentof anumber.
WholeNumberComputation:AdditionandSubtraction
Modeljoiningandseparatingsets.
Modeladditionandsubtractionsituations.
Modeladditionandsubtractionwithplacevalue.
WholeNumberComputation:AdditionandSubtraction
Modelregroupinginadditionandsubtractionwithplacevalue.
Use+,-,and=towritenumbersentencesforadditionandsubtractionstories.
Usemodels,numbers,andsymbolsforadditionandsubtractionfactsto20.
Recall addition and subtractionfacts.
Usetheorder,grouping,andzeropropertiestodevelopadditionandsubtractionfactstrategies.
Usedifferentmethodstodevelopfluencyinaddingandsubtractingmulti-digitnumbers.
Addandsubtractupto2-digitnumberswithandwithoutregrouping
Addandsubtractwholenumbersto1,000.
Addandsubtractwholenumbersto10,000.
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Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
NumberandOperations(continued) NumberandOperations(continued)
DecimalConcepts(continued)
DecimalConcepts(continued)
Understand decimal notation through hundredthsasanextensionof thebase-tensystem.
Understand place value concepts through thousandths.
Readandwritedecimalsthat are greater than or lessthan1.
Compare and order decimals.
Identifyequivalent decimals.
Connectequivalentfractionsanddecimals.
Convertdecimalstofractions.
Ratio,Proportion,andPercent
Ratio,Proportion,andPercent
Useratiostosolveproblems.
Findequivalentratios.
Solveproblemswithpercent.
Convertfractionstopercents.
Findapercentof anumber.
WholeNumberComputation:AdditionandSubtraction
Modeljoiningandseparatingsets.
Modeladditionandsubtractionsituations.
Modeladditionandsubtractionwithplacevalue.
WholeNumberComputation:AdditionandSubtraction
Modelregroupinginadditionandsubtractionwithplacevalue.
Use+,-,and=towritenumbersentencesforadditionandsubtractionstories.
Usemodels,numbers,andsymbolsforadditionandsubtractionfactsto20.
Recall addition and subtractionfacts.
Usetheorder,grouping,andzeropropertiestodevelopadditionandsubtractionfactstrategies.
Usedifferentmethodstodevelopfluencyinaddingandsubtractingmulti-digitnumbers.
Addandsubtractupto2-digitnumberswithandwithoutregrouping
Addandsubtractwholenumbersto1,000.
Addandsubtractwholenumbersto10,000.
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Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
NumberandOperations(continued) NumberandOperations(continued)
WholeNumberComputation:AdditionandSubtractionReal-WorldProblems
Represent addition and subtractionstories.
Formulateadditionandsubtractionstories.
WholeNumberComputation:AdditionandSubtractionReal-WorldProblems
Solve addition and subtractionproblemsusingbasicfacts.
Solve multi-digit addition andsubtractionproblems byusingabarmodel.
Solve addition and subtractionproblemswithgreaternumbersbyusing abarmodel.
WholeNumberComputation:MultiplicationandDivisionConcepts
Countby2sand5supto20.
Countby2s,5s,and10s. Multiplyanddividewith2, 3,4,5,and10.
WholeNumberComputation:MultiplicationandDivisionConcepts
Multiplyanddividewith6,7,8,and9.
Addingthesamenumbertomultiply.
Represent multiplication as repeatedaddition.
Represent multiplication in differentways.
Applyunderstandingof modelsformultiplicationanddivision.
Representsharingequallyandmakingequalgroups.
Represent division as repeatedsubtraction.
Represent division in differentways.
Recallmultiplicationfactsandrelateddivisionfacts.
Usethe×,÷,and=symbolsto represent multiplication anddivisionsituations.
WholeNumberComputation:MultiplicationandDivisionAlgorithms
WholeNumberComputation:MultiplicationandDivisionAlgorithms
Multiply1s,10s,and100swithandwithoutregrouping.
Developfluencyinmultiplyingmulti-digitnumbers.
Multiplymulti-digitnumbers.
Use addition and multiplication properties tomultiply.
Divide10sand1swithand withoutregrouping,noremainder.
Dividebya1-digitnumber,witharemainder.
Findquotientsinvolvingmulti-digitdividends.
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Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
NumberandOperations(continued) NumberandOperations(continued)
WholeNumberComputation:AdditionandSubtractionReal-WorldProblems
Represent addition and subtractionstories.
Formulateadditionandsubtractionstories.
WholeNumberComputation:AdditionandSubtractionReal-WorldProblems
Solve addition and subtractionproblemsusingbasicfacts.
Solve multi-digit addition andsubtractionproblems byusingabarmodel.
Solve addition and subtractionproblemswithgreaternumbersbyusing abarmodel.
WholeNumberComputation:MultiplicationandDivisionConcepts
Countby2sand5supto20.
Countby2s,5s,and10s. Multiplyanddividewith2, 3,4,5,and10.
WholeNumberComputation:MultiplicationandDivisionConcepts
Multiplyanddividewith6,7,8,and9.
Addingthesamenumbertomultiply.
Represent multiplication as repeatedaddition.
Represent multiplication in differentways.
Applyunderstandingof modelsformultiplicationanddivision.
Representsharingequallyandmakingequalgroups.
Represent division as repeatedsubtraction.
Represent division in differentways.
Recallmultiplicationfactsandrelateddivisionfacts.
Usethe×,÷,and=symbolsto represent multiplication anddivisionsituations.
WholeNumberComputation:MultiplicationandDivisionAlgorithms
WholeNumberComputation:MultiplicationandDivisionAlgorithms
Multiply1s,10s,and100swithandwithoutregrouping.
Developfluencyinmultiplyingmulti-digitnumbers.
Multiplymulti-digitnumbers.
Use addition and multiplication properties tomultiply.
Divide10sand1swithand withoutregrouping,noremainder.
Dividebya1-digitnumber,witharemainder.
Findquotientsinvolvingmulti-digitdividends.
12
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
NumberandOperations(continued) NumberandOperations(continued)
WholeNumberComputation:MultiplicationandDivisionReal-WorldProblems
Usebarmodelstorepresentmultiplication and division situations.
WholeNumberComputation:MultiplicationandDivisionReal-WorldProblems
Usebarmodelstorepresentmultiplication and division situations.
Solve multiplication and divisionfactproblems.
Solveone-andtwo-stepmultiplication and division problems.
Solve multi-digit multiplication and division problems.
Solve multiplication and divisionproblems.
Selectthemostusefulformof thequotientandinterprettheremainder.
FractionComputation
Addandsubtractlikefractions(halves,thirds,fourths).
FractionComputation
Addandsubtractlikefractions.
Addandsubtractunlikefractions.
Addandsubtractunlikefractionsandmixednumbers.
Multiplyproperfractions,improperfractions,mixednumbers,andwholenumbers.
Dividefractionsbywholenumbers.
Solvewordproblemswithaddition,subtraction,multiplication,anddivision of fractions.
DecimalComputation
Addandsubtractmoney. Solve addition and subtractionmoneyproblems.
DecimalComputation
Addandsubtractmoneyamounts.
Addandsubtractdecimals. Addandsubtractdecimals.
Multiplyanddividedecimalsbywholenumbers.
Solveproblemswithadditionandsubtractionof decimals.
Solveproblemswithmultiplication and division of decimals.
EstimationandMentalMath
Use mental math strategies toaddandsubtract.
Use mental math strategies toaddandsubtract.
EstimationandMentalMath
Use mental math strategies toaddsubtract,multiply,anddivide.
Use mental math and estimationstrategiestofindsums,differences,products,andquotients.
Use estimation and mental mathtoestimatesums,differences,products,andquotients.
13
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
NumberandOperations(continued) NumberandOperations(continued)
WholeNumberComputation:MultiplicationandDivisionReal-WorldProblems
Usebarmodelstorepresentmultiplication and division situations.
WholeNumberComputation:MultiplicationandDivisionReal-WorldProblems
Usebarmodelstorepresentmultiplication and division situations.
Solve multiplication and divisionfactproblems.
Solveone-andtwo-stepmultiplication and division problems.
Solve multi-digit multiplication and division problems.
Solve multiplication and divisionproblems.
Selectthemostusefulformof thequotientandinterprettheremainder.
FractionComputation
Addandsubtractlikefractions(halves,thirds,fourths).
FractionComputation
Addandsubtractlikefractions.
Addandsubtractunlikefractions.
Addandsubtractunlikefractionsandmixednumbers.
Multiplyproperfractions,improperfractions,mixednumbers,andwholenumbers.
Dividefractionsbywholenumbers.
Solvewordproblemswithaddition,subtraction,multiplication,anddivision of fractions.
DecimalComputation
Addandsubtractmoney. Solve addition and subtractionmoneyproblems.
DecimalComputation
Addandsubtractmoneyamounts.
Addandsubtractdecimals. Addandsubtractdecimals.
Multiplyanddividedecimalsbywholenumbers.
Solveproblemswithadditionandsubtractionof decimals.
Solveproblemswithmultiplication and division of decimals.
EstimationandMentalMath
Use mental math strategies toaddandsubtract.
Use mental math strategies toaddandsubtract.
EstimationandMentalMath
Use mental math strategies toaddsubtract,multiply,anddivide.
Use mental math and estimationstrategiestofindsums,differences,products,andquotients.
Use estimation and mental mathtoestimatesums,differences,products,andquotients.
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Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
NumberandOperations(continued) NumberandOperations(continued)
EstimationandMentalMath(continued)
EstimationandMentalMath(continued)
Decidewhetheranestimateorexactanswerisneeded.
Estimatequantitybyusingreferents.
Round to the nearest ten to estimate sums and differences.
Usefront-endestimationand rounding to estimate sumsanddifferences.
Use estimation in determiningrelativesizes of amountsordistances.
Estimate sums and differenceswithfractions anddecimals.
Roundandestimatewithdecimals.
Estimate products and quotientswithdecimals.
Algebra Algebra
Patterns Describeandextendrepeatingshapepatterns.
Identify,describe,andextendtwo-andthree-dimensionalshapepatterns.
Describe,extend,andcreatetwo-dimensionalshapepatterns.
Patterns Createandanalyzemultiplication and division patterns.
Identify,describe,andextendnumericandnon-numericpatterns.
Identify,describe,andextendnumeric patterns involving alloperations.
Countby2sand5s. Skipcountby2s,5s,and10s.
Skipcountby2s,3s,4s,5s,and10s.
Skipcountby6s,7s,8s,and9s.
Describearuleforsortingobjects.
Identifyaruleforsortingobjects.
Findmissingtermsinrepeatingpatterns.
Identifyandextendgrowingandrepeatingpatterns.
Identifyrulesfornumberpatterns.
Analyzenumberandcountingpatterns.
Usearuletodescribeasequenceof numbersorobjects.
Findrulestocompletenumberpatterns.
Findmissingtermsingrowingandrepeatingpatterns.
Findmissingtermsintablepatterns.
Properties Identify0astheidentityelementforadditionandsubtraction.
Understand that addition andsubtractionareinverseoperations.
Properties Understand that multiplication and division arerelated.
Represent division as the inverseof multiplication.
Use the Associative and CommutativePropertiesof Addition.
Applypropertiesof addition. Createandanalyzemultiplication and division patterns.
UsetheDistributivePropertyasamultiplicationstrategy.
Model,define,andexplainpropertiesof multiplication.
NumberTheory
Identifyoddandevennumbers.
NumberTheory
Identifyoddandevennumbers.
Findthegreatestcommonfactorandleastcommonmultiple.
Identifyprimeandcompositenumbers.
15
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
NumberandOperations(continued) NumberandOperations(continued)
EstimationandMentalMath(continued)
EstimationandMentalMath(continued)
Decidewhetheranestimateorexactanswerisneeded.
Estimatequantitybyusingreferents.
Round to the nearest ten to estimate sums and differences.
Usefront-endestimationand rounding to estimate sumsanddifferences.
Use estimation in determiningrelativesizes of amountsordistances.
Estimate sums and differenceswithfractions anddecimals.
Roundandestimatewithdecimals.
Estimate products and quotientswithdecimals.
Algebra Algebra
Patterns Describeandextendrepeatingshapepatterns.
Identify,describe,andextendtwo-andthree-dimensionalshapepatterns.
Describe,extend,andcreatetwo-dimensionalshapepatterns.
Patterns Createandanalyzemultiplication and division patterns.
Identify,describe,andextendnumericandnon-numericpatterns.
Identify,describe,andextendnumeric patterns involving alloperations.
Countby2sand5s. Skipcountby2s,5s,and10s.
Skipcountby2s,3s,4s,5s,and10s.
Skipcountby6s,7s,8s,and9s.
Describearuleforsortingobjects.
Identifyaruleforsortingobjects.
Findmissingtermsinrepeatingpatterns.
Identifyandextendgrowingandrepeatingpatterns.
Identifyrulesfornumberpatterns.
Analyzenumberandcountingpatterns.
Usearuletodescribeasequenceof numbersorobjects.
Findrulestocompletenumberpatterns.
Findmissingtermsingrowingandrepeatingpatterns.
Findmissingtermsintablepatterns.
Properties Identify0astheidentityelementforadditionandsubtraction.
Understand that addition andsubtractionareinverseoperations.
Properties Understand that multiplication and division arerelated.
Represent division as the inverseof multiplication.
Use the Associative and CommutativePropertiesof Addition.
Applypropertiesof addition. Createandanalyzemultiplication and division patterns.
UsetheDistributivePropertyasamultiplicationstrategy.
Model,define,andexplainpropertiesof multiplication.
NumberTheory
Identifyoddandevennumbers.
NumberTheory
Identifyoddandevennumbers.
Findthegreatestcommonfactorandleastcommonmultiple.
Identifyprimeandcompositenumbers.
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Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Algebra(continued) Alegbra(continued)
FunctionalRelationships
Understand the relationships betweenthenumbersinfactfamilies.
Recognizehowbarmodelsshowrelationshipsbetweennumbersandunknownsinnumbersentences.
FunctionalRelationships
Understand the relationshipsbetweenthenumbersinmultiplicationanddivisionfactfamilies.
Understand the relationships betweenthenumbersandsymbolsinformulasforareaandperimeter.
Understand the relationships betweenthenumbersandsymbolsinformulasforsurfaceareaandvolume.
Describenumberrelationshipsincontext.
Describenumberrelationshipsincontext.
Describenumberrelationshipsincontext.
Expressions/Models
Useavarietyof concrete,pictorial,andsymbolicmodelsforadditionandsubtraction.
Useavarietyof concrete,pictorial,andsymbolicmodelsforaddition,subtraction,multiplication,anddivision.
Expressions/Models
Useavarietyof concrete,pictorial,andsymbolicmodelsformulti-digitaddition,subtraction,multiplication,anddivision.
Useavarietyof concrete,pictorial,andsymbolicmodelsformultiplicationand division; and addition andsubtractionwithfractionsanddecimals.
Uselettersasvariables.
Simplifyalgebraicexpressions.
Usetheorderof operationsinnumericexpressionswithtwoormoreoperations.
NumberSentencesandEquations
Modeladditionandsubtractionstorieswithadditionandsubtractionnumbersentences.
Modeladditionandsubtractionsituationsbywritingadditionandsubtractionnumbersentences.
Modelmultiplicationanddivisionsituationsbywritingmultiplication and division numbersentences.
NumberSentencesandEquations
Write multiplication and divisionnumbersentences.
Writeandsolvenumbersentencesforone-,two-,andthree-stepreal-worldproblems.
Writeandsolvenumbersentencesandequationsforone-andtwo-stepreal-worldproblems.
Usebarmodelsandnumbersentences to represent real-worldproblems.
Writeandsolvenumbersentencesforone-andtwo-stepreal-worldproblems.
Usebarmodelsandnumbersentencesforone-,two-,andthree-stepreal-worldproblems.
Writeandsolveequations.
Determinethevalueof missingquantitiesinnumbersentences.
Determine the missing parts (quantitiesorsymbols)innumbersentences.
Determine the missing parts (quantitiesorsymbols)innumbersentences.
Graphlinearequations.
EqualityandInequality
Understand the meaning of the=signinnumbersentences.
Understandthedifferencebetweenequalityandinequality.
Use and create models that demonstrateequalityorinequality.
EqualityandInequality
Understandequalityandinequality.
Understandequalityandinequality.
Understandequalityandinequality.
Use<,>,and=towritenumbersentences.
Writeandsolveinequalities.
Geometry Geometry
SizeandPosition
Understandbig,middle-sized,andsmall.
Describepositionwithleftandright.
SizeandPosition
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Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Algebra(continued) Alegbra(continued)
FunctionalRelationships
Understand the relationships betweenthenumbersinfactfamilies.
Recognizehowbarmodelsshowrelationshipsbetweennumbersandunknownsinnumbersentences.
FunctionalRelationships
Understand the relationshipsbetweenthenumbersinmultiplicationanddivisionfactfamilies.
Understand the relationships betweenthenumbersandsymbolsinformulasforareaandperimeter.
Understand the relationships betweenthenumbersandsymbolsinformulasforsurfaceareaandvolume.
Describenumberrelationshipsincontext.
Describenumberrelationshipsincontext.
Describenumberrelationshipsincontext.
Expressions/Models
Useavarietyof concrete,pictorial,andsymbolicmodelsforadditionandsubtraction.
Useavarietyof concrete,pictorial,andsymbolicmodelsforaddition,subtraction,multiplication,anddivision.
Expressions/Models
Useavarietyof concrete,pictorial,andsymbolicmodelsformulti-digitaddition,subtraction,multiplication,anddivision.
Useavarietyof concrete,pictorial,andsymbolicmodelsformultiplicationand division; and addition andsubtractionwithfractionsanddecimals.
Uselettersasvariables.
Simplifyalgebraicexpressions.
Usetheorderof operationsinnumericexpressionswithtwoormoreoperations.
NumberSentencesandEquations
Modeladditionandsubtractionstorieswithadditionandsubtractionnumbersentences.
Modeladditionandsubtractionsituationsbywritingadditionandsubtractionnumbersentences.
Modelmultiplicationanddivisionsituationsbywritingmultiplication and division numbersentences.
NumberSentencesandEquations
Write multiplication and divisionnumbersentences.
Writeandsolvenumbersentencesforone-,two-,andthree-stepreal-worldproblems.
Writeandsolvenumbersentencesandequationsforone-andtwo-stepreal-worldproblems.
Usebarmodelsandnumbersentences to represent real-worldproblems.
Writeandsolvenumbersentencesforone-andtwo-stepreal-worldproblems.
Usebarmodelsandnumbersentencesforone-,two-,andthree-stepreal-worldproblems.
Writeandsolveequations.
Determinethevalueof missingquantitiesinnumbersentences.
Determine the missing parts (quantitiesorsymbols)innumbersentences.
Determine the missing parts (quantitiesorsymbols)innumbersentences.
Graphlinearequations.
EqualityandInequality
Understand the meaning of the=signinnumbersentences.
Understandthedifferencebetweenequalityandinequality.
Use and create models that demonstrateequalityorinequality.
EqualityandInequality
Understandequalityandinequality.
Understandequalityandinequality.
Understandequalityandinequality.
Use<,>,and=towritenumbersentences.
Writeandsolveinequalities.
Geometry Geometry
SizeandPosition
Understandbig,middle-sized,andsmall.
Describepositionwithleftandright.
SizeandPosition
18
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Geometry(continued) Geometry(continued)
SizeandPosition(continued)
Describeandcompareobjectsbyposition.
Usepositionalwordstodescribelocation.
SizeandPosition(continued)
LinesandAngles
Identifypartsof linesandcurves.
LinesandAngles
Identifyperpendicularandparallellines.
Drawperpendicularandparallellines.
Workwithanglesonastraightline.
Identifyrightanglesandcompare angles to right angles.
Construct and measure angles.
Workwithanglesatapoint.
Two-DimensionalShapes
Identifysimilaritiesanddifferences.
Two-DimensionalShapes
Nameflatshapesthatmakeupreal-worldobjects.
Identifyreal-worldtwo-dimensionalshapes.
Identify,describe,sort,andclassifytwo-dimensionalshapes.
Identifyanddescribeattributesandpropertiesof two-dimensionalshapes.
Identify,describe,sort,andclassifytwo-dimensionalshapes.
Describe,analyze,compare,andclassifytwo-dimensionalshapesbytheirsidesandangles.
Applythepropertiesof squaresandrectangles.
Applythepropertiesof right,isosceles,andequilateraltriangles.
Sortandclassifytwo-dimensionalshapes.
Identifypartsof linesandcurves.
Classifyandsortpolygonsandquadrilateralsbyattributesandproperties.
Findunknownanglemeasures and side lengths of squaresandrectangles.
Applythesumof theanglemeasuresof atriangle.
Makeflatshapepictures. Compose and decompose two-dimensionalshapes.
Compose and decompose two-dimensionalshapes.
Investigate composing anddecomposingtwo-dimensionalshapes.
Identifyfiguresthatformtessellations.
Applythepropertiesof aparallelogram,rhombus,andtrapezoid.
Useattributesandproperties to solve problems.
Demonstrate that the sum of anytwosidelengthsof a triangle is greater than the lengthof thethirdside.
Compare areas using non-standardunits.
Developfoundationsforunderstandingarea.
Findandcomparetheareaof planefiguresindifferentsquareunits.
Understand the relationships betweenthenumbersandsymbolsinformulasforareaandperimeter.
Findtheareaof atriangle.
Three-DimensionalShapes
Nameandsortsolidshapes. Identifyreal-worldthree-dimensionalshapes.
Three-DimensionalShapes
Identifyandclassifyprismsandpyramids.
Understand that three-dimensional shapes are madeupof two-dimensionalshapes.
Identifytwo-dimensionalshapes in three-dimensional shapes.
Identify,describe,sort,andclassifythree-dimensionalshapes.
Identifythesolidthatcanbemadefromanet.
19
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Geometry(continued) Geometry(continued)
SizeandPosition(continued)
Describeandcompareobjectsbyposition.
Usepositionalwordstodescribelocation.
SizeandPosition(continued)
LinesandAngles
Identifypartsof linesandcurves.
LinesandAngles
Identifyperpendicularandparallellines.
Drawperpendicularandparallellines.
Workwithanglesonastraightline.
Identifyrightanglesandcompare angles to right angles.
Construct and measure angles.
Workwithanglesatapoint.
Two-DimensionalShapes
Identifysimilaritiesanddifferences.
Two-DimensionalShapes
Nameflatshapesthatmakeupreal-worldobjects.
Identifyreal-worldtwo-dimensionalshapes.
Identify,describe,sort,andclassifytwo-dimensionalshapes.
Identifyanddescribeattributesandpropertiesof two-dimensionalshapes.
Identify,describe,sort,andclassifytwo-dimensionalshapes.
Describe,analyze,compare,andclassifytwo-dimensionalshapesbytheirsidesandangles.
Applythepropertiesof squaresandrectangles.
Applythepropertiesof right,isosceles,andequilateraltriangles.
Sortandclassifytwo-dimensionalshapes.
Identifypartsof linesandcurves.
Classifyandsortpolygonsandquadrilateralsbyattributesandproperties.
Findunknownanglemeasures and side lengths of squaresandrectangles.
Applythesumof theanglemeasuresof atriangle.
Makeflatshapepictures. Compose and decompose two-dimensionalshapes.
Compose and decompose two-dimensionalshapes.
Investigate composing anddecomposingtwo-dimensionalshapes.
Identifyfiguresthatformtessellations.
Applythepropertiesof aparallelogram,rhombus,andtrapezoid.
Useattributesandproperties to solve problems.
Demonstrate that the sum of anytwosidelengthsof a triangle is greater than the lengthof thethirdside.
Compare areas using non-standardunits.
Developfoundationsforunderstandingarea.
Findandcomparetheareaof planefiguresindifferentsquareunits.
Understand the relationships betweenthenumbersandsymbolsinformulasforareaandperimeter.
Findtheareaof atriangle.
Three-DimensionalShapes
Nameandsortsolidshapes. Identifyreal-worldthree-dimensionalshapes.
Three-DimensionalShapes
Identifyandclassifyprismsandpyramids.
Understand that three-dimensional shapes are madeupof two-dimensionalshapes.
Identifytwo-dimensionalshapes in three-dimensional shapes.
Identify,describe,sort,andclassifythree-dimensionalshapes.
Identifythesolidthatcanbemadefromanet.
20
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Geometry(continued) Geometry(continued)
Three-DimensionalShapes(continued)
Sortandclassifythree-dimensionalshapes.
Identifysurfacesthatslide,stack,androll.
Three-DimensionalShapes(continued)
Identifycylinders,spheres,andcones.
Recognizeshapesfromdifferentperspectives.
Describecylinders,spheres,andconesbythenumberof andtypesof faces,andthenumberof edgesandvertices.
Compose and decompose three-dimensionalshapes.
Buildsolidsusingunitcubes.
CongruenceandSymmetry
Develop initial understandingof congruenceandsymmetry.
CongruenceandSymmetry
Identifysymmetricalfiguresandonelineof symmetry.
Identifylineandrotationalsymmetry.
Solveproblemsinvolvingcongruency.
Relaterotationalsymmetrytoturnsandcongruency.
Transformations Transformations Identifypairsof shapesthatshowaflip,slide,andturn.
Usetransformationstoformtessellations.
Demonstratethatfiguresandtheirflip,slide,andturnimagesarecongruent.
CoordinateGeometry
CoordinateGeometry
Develop coordinate readinesswithtablesandlinegraphs.
Plotpointsonacoordinategrid.
Measurement Measurement
LengthandDistance
Compare lengths and heights using non-standard units.
Comparetwolengthsbycomparingeachwithathirdlength(transitivity).
Demonstrate linear measure asaniterationof units.
LengthandDistance
Select appropriate units and tools to estimate and measurelength.
Compare and order lengths (long,short,longest,shortest).
Use a start line to measure length.
Userulerstomeasurelength. Usemetersticks,12-inchrulers,andyardstickstomeasurelength.
Developabackgroundformeasurement using non-standardunits.
Measurelengths,using non-standardunits.
Measurelengthsinmeters,centimeters,feet,andinches.
Measurelengthtothenearesthalf inchandinch.
Explaintheneedforequal-lengthunitstomeasure.
Usereferentstoestimatedistance.
21
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Geometry(continued) Geometry(continued)
Three-DimensionalShapes(continued)
Sortandclassifythree-dimensionalshapes.
Identifysurfacesthatslide,stack,androll.
Three-DimensionalShapes(continued)
Identifycylinders,spheres,andcones.
Recognizeshapesfromdifferentperspectives.
Describecylinders,spheres,andconesbythenumberof andtypesof faces,andthenumberof edgesandvertices.
Compose and decompose three-dimensionalshapes.
Buildsolidsusingunitcubes.
CongruenceandSymmetry
Develop initial understandingof congruenceandsymmetry.
CongruenceandSymmetry
Identifysymmetricalfiguresandonelineof symmetry.
Identifylineandrotationalsymmetry.
Solveproblemsinvolvingcongruency.
Relaterotationalsymmetrytoturnsandcongruency.
Transformations Transformations Identifypairsof shapesthatshowaflip,slide,andturn.
Usetransformationstoformtessellations.
Demonstratethatfiguresandtheirflip,slide,andturnimagesarecongruent.
CoordinateGeometry
CoordinateGeometry
Develop coordinate readinesswithtablesandlinegraphs.
Plotpointsonacoordinategrid.
Measurement Measurement
LengthandDistance
Compare lengths and heights using non-standard units.
Comparetwolengthsbycomparingeachwithathirdlength(transitivity).
Demonstrate linear measure asaniterationof units.
LengthandDistance
Select appropriate units and tools to estimate and measurelength.
Compare and order lengths (long,short,longest,shortest).
Use a start line to measure length.
Userulerstomeasurelength. Usemetersticks,12-inchrulers,andyardstickstomeasurelength.
Developabackgroundformeasurement using non-standardunits.
Measurelengths,using non-standardunits.
Measurelengthsinmeters,centimeters,feet,andinches.
Measurelengthtothenearesthalf inchandinch.
Explaintheneedforequal-lengthunitstomeasure.
Usereferentstoestimatedistance.
22
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Measurement(continued) Measurement(continued)
LengthandDistance(continued)
Explaintheneedforequal-lengthunitstomeasure.
LengthandDistance(continued)
Count length units in groups of 10sand1s.
Compare and measure lengthsusingcustomary andmetricunits.
Estimate and measure length,distance,andheightinmeters,centimeters,andkilometers.
Compare measurements madeusingdifferentunits.
Demonstrate partitioning andtransitivityinrelation tolength.
Convert among metric units of length.
Understand the inverse relationshipbetweenthesizeof aunitandthenumberof units.
Solveproblemsinvolvingestimating,measuring,andcomputinglength.
Solveone-andtwo-stepreal-worldproblemsinmeasurement.
Weight/Mass Orderobjectsbyweight. Compare and measure weightsusingnon-standardunits.
Compare and measure masses.
Weight/Mass Select appropriate units and tools to estimate and measureweight.
Compareweightsusingnon-standardunits.
Comparetwomassesbycomparingeachwithathirdmass(transitivity).
Usereferentstoestimateweight.
Estimateandfindmasses of objects.
Solveweightproblems. Solvemassproblems. Convertamongunitsof mass.
Capacity/Volume
Compare capacities using non-standardunits.
Measurevolume(capacity) inliters.
Capacity/Volume
Select appropriate tools and units to estimate and measure volume and capacity.
Solvevolumeproblems. Determine the volume and capacityof acontainer.
Relatetheunitsof customarycapacitytooneanother.
Usereferentstoestimatecapacity.
23
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Measurement(continued) Measurement(continued)
LengthandDistance(continued)
Explaintheneedforequal-lengthunitstomeasure.
LengthandDistance(continued)
Count length units in groups of 10sand1s.
Compare and measure lengthsusingcustomary andmetricunits.
Estimate and measure length,distance,andheightinmeters,centimeters,andkilometers.
Compare measurements madeusingdifferentunits.
Demonstrate partitioning andtransitivityinrelation tolength.
Convert among metric units of length.
Understand the inverse relationshipbetweenthesizeof aunitandthenumberof units.
Solveproblemsinvolvingestimating,measuring,andcomputinglength.
Solveone-andtwo-stepreal-worldproblemsinmeasurement.
Weight/Mass Orderobjectsbyweight. Compare and measure weightsusingnon-standardunits.
Compare and measure masses.
Weight/Mass Select appropriate units and tools to estimate and measureweight.
Compareweightsusingnon-standardunits.
Comparetwomassesbycomparingeachwithathirdmass(transitivity).
Usereferentstoestimateweight.
Estimateandfindmasses of objects.
Solveweightproblems. Solvemassproblems. Convertamongunitsof mass.
Capacity/Volume
Compare capacities using non-standardunits.
Measurevolume(capacity) inliters.
Capacity/Volume
Select appropriate tools and units to estimate and measure volume and capacity.
Solvevolumeproblems. Determine the volume and capacityof acontainer.
Relatetheunitsof customarycapacitytooneanother.
Usereferentstoestimatecapacity.
24
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Measurement(continued) Measurement(continued)
Capacity/Volume(continued)
Capacity/Volume(continued)
Estimate and measure capacityinlitersandmilliliters.
Convert among metric units of capacity.
Time Nameandorderthedaysof theweekandthemonthsof theyear.
Readacalendartoidentifythedaysof theweek,months,andseasonsof theyear.
Time
Recognizethecorrectwaytowritethedate.
UseA.M.andP.M.towritetime.
Readtimeonadigitalclock.
Telltimetothehourandhalf hour.
Telltimetofiveminutes. Convertbetweenhoursandminutes.
Comparedurationsof events.
Findelapsedtime. Determineelapsedtime.
Addandsubtractunitsof time.
Temperature Temperature ReadaFahrenheitthermometer.
Choose the appropriate tool and unit to measure temperature.
Usereferentstoestimatetemperature.
Angles Angles Compare angles to right angles.
Estimate and measure angleswithaprotractor.
Applytheideathatthesumof anglesonastraightline is180°.
Classifyanglesbyanglemeasure.
Applytheideathatverticalanglesareequalinmeasure.
Relate1/4-,1/2-,3/4-,andfullturnstothenumberof rightangles.
Applytheideathatthesumof anglesatapointis360°.
Perimeter Perimeter Measureperimeterof planefigures.
Findtheperimeterof compositefigures.
25
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Measurement(continued) Measurement(continued)
Capacity/Volume(continued)
Capacity/Volume(continued)
Estimate and measure capacityinlitersandmilliliters.
Convert among metric units of capacity.
Time Nameandorderthedaysof theweekandthemonthsof theyear.
Readacalendartoidentifythedaysof theweek,months,andseasonsof theyear.
Time
Recognizethecorrectwaytowritethedate.
UseA.M.andP.M.towritetime.
Readtimeonadigitalclock.
Telltimetothehourandhalf hour.
Telltimetofiveminutes. Convertbetweenhoursandminutes.
Comparedurationsof events.
Findelapsedtime. Determineelapsedtime.
Addandsubtractunitsof time.
Temperature Temperature ReadaFahrenheitthermometer.
Choose the appropriate tool and unit to measure temperature.
Usereferentstoestimatetemperature.
Angles Angles Compare angles to right angles.
Estimate and measure angleswithaprotractor.
Applytheideathatthesumof anglesonastraightline is180°.
Classifyanglesbyanglemeasure.
Applytheideathatverticalanglesareequalinmeasure.
Relate1/4-,1/2-,3/4-,andfullturnstothenumberof rightangles.
Applytheideathatthesumof anglesatapointis360°.
Perimeter Perimeter Measureperimeterof planefigures.
Findtheperimeterof compositefigures.
26
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Measurement(continued) Measurement(continued)
Perimeter(continued)
Perimeter(continued)
Choose the appropriate tool,unit,andstrategytomeasureperimeter.
Solveproblemsinvolvingtheperimeterof squares,rectangles,andcompositefigures.
Estimatetheperimeterof surfacesandobjects.
Area Compare areas using non-standardunits.
Compose and decompose two-dimensionalshapes (foundationforunderstandingarea).
Developfoundationsforunderstandingarea.
Area Findandcomparetheareaof planefiguresindifferentsquareunits.
Explainareaasanattributeof two-dimensionalfigures.
Makedifferentplanefigureswiththesamearea.
Connect area measure totheareamodelformultiplication; use it to justifytheformulafortheareaof arectangle.
Findtheareaof triangles.
Estimateareaof smallandlargesurfaces.
Estimate and measure area insquareunits.
Compare the area and perimeterof twoplanefigures.
Selectappropriateunits,strategies,andtoolstosolveareaproblems.
Findtheareaof rectanglesandcompositefigures.
Explaintherelationshipsamongareaformulasof differentpolygons.
SurfaceAreaandVolume
SurfaceAreaandVolume
Decomposesolidfigurestofindthesurfacearea.
Estimate and measure volumeincubicunits.
DataAnalysis DataAnalysis
ClassifyingandSorting
Understanding similarities anddifferencesinobjectsandshapes.
Sortandclassifygeometricshapes.
Sortandclassifytwo-andthree-dimensional shapes byproperties.
ClassifyingandSorting
Classifyandsortpolygonsandquadrilateralsbyattributesandproperties.
Sortingandclassifyingobjectsusingoneortwoattributes.
Sortingandclassifyingdatainordertomakegraphs.
Collectandorganizedatainpicturegraphs.
Collectandorganizedatainbargraphsandlineplots.
Constructlineplots,stem-and-leaf plots,tables,andlinegraphs.
Representdatainadoublebargraph.
27
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Measurement(continued) Measurement(continued)
Perimeter(continued)
Perimeter(continued)
Choose the appropriate tool,unit,andstrategytomeasureperimeter.
Solveproblemsinvolvingtheperimeterof squares,rectangles,andcompositefigures.
Estimatetheperimeterof surfacesandobjects.
Area Compare areas using non-standardunits.
Compose and decompose two-dimensionalshapes (foundationforunderstandingarea).
Developfoundationsforunderstandingarea.
Area Findandcomparetheareaof planefiguresindifferentsquareunits.
Explainareaasanattributeof two-dimensionalfigures.
Makedifferentplanefigureswiththesamearea.
Connect area measure totheareamodelformultiplication; use it to justifytheformulafortheareaof arectangle.
Findtheareaof triangles.
Estimateareaof smallandlargesurfaces.
Estimate and measure area insquareunits.
Compare the area and perimeterof twoplanefigures.
Selectappropriateunits,strategies,andtoolstosolveareaproblems.
Findtheareaof rectanglesandcompositefigures.
Explaintherelationshipsamongareaformulasof differentpolygons.
SurfaceAreaandVolume
SurfaceAreaandVolume
Decomposesolidfigurestofindthesurfacearea.
Estimate and measure volumeincubicunits.
DataAnalysis DataAnalysis
ClassifyingandSorting
Understanding similarities anddifferencesinobjectsandshapes.
Sortandclassifygeometricshapes.
Sortandclassifytwo-andthree-dimensional shapes byproperties.
ClassifyingandSorting
Classifyandsortpolygonsandquadrilateralsbyattributesandproperties.
Sortingandclassifyingobjectsusingoneortwoattributes.
Sortingandclassifyingdatainordertomakegraphs.
Collectandorganizedatainpicturegraphs.
Collectandorganizedatainbargraphsandlineplots.
Constructlineplots,stem-and-leaf plots,tables,andlinegraphs.
Representdatainadoublebargraph.
28
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
DataAnalysis(continued) DataAnalysis(continued)
CollectandOrganizeData
Organizedataforapicturegraph.
Collectandorganizedataindifferentways.
Collectandorganizedataindifferentways.
CollectandOrganizeData
RepresentData
Represent data in pictographs.
Represent measurements anddatainpicturegraphs,tallycharts,andbargraphs.
Represent data in picture graphs.
RepresentData
Interpret/AnalyzeData
Interpretdataintallychartsandpictographs.
Interpret data in picture graphs,tallycharts,andbargraphs.
Interpretpicturegraphswithscales.
Interpret/AnalyzeData
Interpretpictureandbargraphswithscales.
Interprettallycharts,bargraphs,picturegraphs,tables,andlinegraphs.
Readbargraphswithscales. Analyzedatainadoublebargraph.
Solveproblemsinvolvingdata.
Solvereal-worldproblemsusingpicturegraphs.
Usefrequencytables,bargraphs,picturegraphs,andlineplotstosolvereal-worldproblems.
Findthemean(average),median,mode,andrangeof adataset.
Probability Probability
Outcomes Outcomes Decidewhetheranoutcomeiscertain,morelikely,equallylikely,lesslikely,orimpossible.
Determineexperimentalprobabilityof anoutcome.
ExpressingProbability
ExpressingProbability
Expresstheprobabilityof aneventasafraction.
Comparetheresultsof anexperimentwiththeoreticalprobability.
Findallpossiblecombinationsbylisting,makingatreediagram,andmultiplying.
ProblemSolving ProblemSolving
BuildSkillsThroughProblemSolving
Build skills in addition and subtractionthroughproblemsolving.
Buildskillsinaddition,subtraction,andmeasurement through problemsolving.
Buildskillsinaddition,subtraction,multiplication,division,andmeasurementthroughproblemsolving.
BuildSkillsThroughProblemSolving
Buildskillsinaddition,subtraction,multiplication,division,andmeasurementthroughproblemsolving.
Buildskillsinmultiplication,division,fractionconcepts,dataanalysis,andmeasurement through problemsolving.
Build skills in multiplication; division;fractionconcepts,decimals,ratios,andpercents;dataanalysis;and measurement through problemsolving.
29
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
DataAnalysis(continued) DataAnalysis(continued)
CollectandOrganizeData
Organizedataforapicturegraph.
Collectandorganizedataindifferentways.
Collectandorganizedataindifferentways.
CollectandOrganizeData
RepresentData
Represent data in pictographs.
Represent measurements anddatainpicturegraphs,tallycharts,andbargraphs.
Represent data in picture graphs.
RepresentData
Interpret/AnalyzeData
Interpretdataintallychartsandpictographs.
Interpret data in picture graphs,tallycharts,andbargraphs.
Interpretpicturegraphswithscales.
Interpret/AnalyzeData
Interpretpictureandbargraphswithscales.
Interprettallycharts,bargraphs,picturegraphs,tables,andlinegraphs.
Readbargraphswithscales. Analyzedatainadoublebargraph.
Solveproblemsinvolvingdata.
Solvereal-worldproblemsusingpicturegraphs.
Usefrequencytables,bargraphs,picturegraphs,andlineplotstosolvereal-worldproblems.
Findthemean(average),median,mode,andrangeof adataset.
Probability Probability
Outcomes Outcomes Decidewhetheranoutcomeiscertain,morelikely,equallylikely,lesslikely,orimpossible.
Determineexperimentalprobabilityof anoutcome.
ExpressingProbability
ExpressingProbability
Expresstheprobabilityof aneventasafraction.
Comparetheresultsof anexperimentwiththeoreticalprobability.
Findallpossiblecombinationsbylisting,makingatreediagram,andmultiplying.
ProblemSolving ProblemSolving
BuildSkillsThroughProblemSolving
Build skills in addition and subtractionthroughproblemsolving.
Buildskillsinaddition,subtraction,andmeasurement through problemsolving.
Buildskillsinaddition,subtraction,multiplication,division,andmeasurementthroughproblemsolving.
BuildSkillsThroughProblemSolving
Buildskillsinaddition,subtraction,multiplication,division,andmeasurementthroughproblemsolving.
Buildskillsinmultiplication,division,fractionconcepts,dataanalysis,andmeasurement through problemsolving.
Build skills in multiplication; division;fractionconcepts,decimals,ratios,andpercents;dataanalysis;and measurement through problemsolving.
30
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
ProblemSolving(continued) ProblemSolving(continued)
SolveReal-WorldProblems
Solvereal-worldproblemsinvolving addition and subtraction.
Solvereal-worldproblemsinvolving addition and subtraction.
Solvereal-worldproblemsinvolvingaddition,subtraction,multiplication,division,andmeasurement.
SolveReal-WorldProblems
Solvereal-worldproblemsinvolvingaddition,subtraction,multiplication,division,andmeasurement.
Solvereal-worldproblemsinvolvingmultiplication,division,fractionconcepts,dataanalysis,andmeasurement.
Solvereal-worldproblemsinvolving multiplication; division;conceptswithfractions,decimals,ratios,andpercents;dataanalysis;andmeasurement.
UseAppropriateStrategiesandThinkingSkillstoSolveProblems
ApplyproblemsolvingstrategiesinPutonYourThinkingCap!andProblemSolvingactivities.
ApplyproblemsolvingstrategiesinPutonYourThinkingCap!andProblemSolvingactivities.
UseAppropriateStrategiesandThinkingSkillstoSolveProblems
ApplyproblemsolvingstrategiesinPutonYourThinkingCap!andProblemSolvingactivities.
Use appropriate strategies tosolvereal-worldproblems.
Use appropriate strategies to solvereal-worldproblems.
ApplyandExplainProblemSolving
Solvereal-worldproblems. ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
ApplyandExplainProblemSolving
ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
ExploreConcepts
Usemodelstoexplainreasoning.
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
ExploreConcepts
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
InvestigateMathematicalIdeas
Investigateideaswithtwo-dimensionalshapes.
Furtherinvestigatemathematicalideasbycompleting critical thinking skillsactivities.
Furtherinvestigatemathematicalideasbycompleting critical thinking skillsactivities.
InvestigateMathematicalIdeas
Furtherinvestigatemathematicalideasbycompleting critical thinking skillsactivities.
Furtherinvestigatemathematicalideasbycompleting critical thinking skillsactivities.
Furtherinvestigatemathematicalideasbycompleting critical thinking skillsactivities.
Identify,Demonstrate,andExplainMathematicalProof
Demonstratethatonlyafewbigthingsfitintosmallspacesandmanysmallthingsfitintobigspaces.
Exploretransitivitybycomparing lengths and weightsof threedifferentobjects.
Demonstrate the inverse relationshipbetweenthe sizeof aunitandthenumberof units.
Identify,Demonstrate,andExplainMathematicalProof
Demonstratethatfiguresandtheirflip,slide,andturnimagesarecongruent.
Showthatsomefigurescanbeturnedandnotchangeshapeorsize(rotationalsymmetry).
Applytheideathatthesumof anglesonastraightlineis180°.
Applytheideathatthesumof anglesatapointis360°.
Describe,sort,andclassifytwo-andthree-dimensionalshapes.
Identifyanddescribeattributesandpropertiesof two-andthree-dimensionalshapes.
Identify,describe,sort,andclassifytwo-andthree-dimensionalshapes.
Identifypairsof shapesthatshowaflip,slide,andturn.
Usepropertiesof squaresand rectangles to solve problems.
Explaintherelationshipsamongareaformulasof differentpolygons.
31
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
ProblemSolving(continued) ProblemSolving(continued)
SolveReal-WorldProblems
Solvereal-worldproblemsinvolving addition and subtraction.
Solvereal-worldproblemsinvolving addition and subtraction.
Solvereal-worldproblemsinvolvingaddition,subtraction,multiplication,division,andmeasurement.
SolveReal-WorldProblems
Solvereal-worldproblemsinvolvingaddition,subtraction,multiplication,division,andmeasurement.
Solvereal-worldproblemsinvolvingmultiplication,division,fractionconcepts,dataanalysis,andmeasurement.
Solvereal-worldproblemsinvolving multiplication; division;conceptswithfractions,decimals,ratios,andpercents;dataanalysis;andmeasurement.
UseAppropriateStrategiesandThinkingSkillstoSolveProblems
ApplyproblemsolvingstrategiesinPutonYourThinkingCap!andProblemSolvingactivities.
ApplyproblemsolvingstrategiesinPutonYourThinkingCap!andProblemSolvingactivities.
UseAppropriateStrategiesandThinkingSkillstoSolveProblems
ApplyproblemsolvingstrategiesinPutonYourThinkingCap!andProblemSolvingactivities.
Use appropriate strategies tosolvereal-worldproblems.
Use appropriate strategies to solvereal-worldproblems.
ApplyandExplainProblemSolving
Solvereal-worldproblems. ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
ApplyandExplainProblemSolving
ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
ExploreConcepts
Usemodelstoexplainreasoning.
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
ExploreConcepts
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
InvestigateMathematicalIdeas
Investigateideaswithtwo-dimensionalshapes.
Furtherinvestigatemathematicalideasbycompleting critical thinking skillsactivities.
Furtherinvestigatemathematicalideasbycompleting critical thinking skillsactivities.
InvestigateMathematicalIdeas
Furtherinvestigatemathematicalideasbycompleting critical thinking skillsactivities.
Furtherinvestigatemathematicalideasbycompleting critical thinking skillsactivities.
Furtherinvestigatemathematicalideasbycompleting critical thinking skillsactivities.
Identify,Demonstrate,andExplainMathematicalProof
Demonstratethatonlyafewbigthingsfitintosmallspacesandmanysmallthingsfitintobigspaces.
Exploretransitivitybycomparing lengths and weightsof threedifferentobjects.
Demonstrate the inverse relationshipbetweenthe sizeof aunitandthenumberof units.
Identify,Demonstrate,andExplainMathematicalProof
Demonstratethatfiguresandtheirflip,slide,andturnimagesarecongruent.
Showthatsomefigurescanbeturnedandnotchangeshapeorsize(rotationalsymmetry).
Applytheideathatthesumof anglesonastraightlineis180°.
Applytheideathatthesumof anglesatapointis360°.
Describe,sort,andclassifytwo-andthree-dimensionalshapes.
Identifyanddescribeattributesandpropertiesof two-andthree-dimensionalshapes.
Identify,describe,sort,andclassifytwo-andthree-dimensionalshapes.
Identifypairsof shapesthatshowaflip,slide,andturn.
Usepropertiesof squaresand rectangles to solve problems.
Explaintherelationshipsamongareaformulasof differentpolygons.
32
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
ProblemSolving(continued) ProblemSolving(continued)
Identify,Demonstrate,andExplainMathematicalProof(continued)
Interpretdataintallychartsandpictographs.
Interpretpicturegraphs,tallycharts,andbargraphs.
Interpret picture graphs withscales.
Identify,Demonstrate,andExplainMathematicalProof(continued)
Interpretbargraphswithscales.
Analyzeadatasetbyfindingitsmean,median,mode,andrange.
Comparetheresultsof anexperimenttovalidatetheuseof theoreticalprobability.
Identifyandextendrepeatingshapepatterns.
Identifyandextendgrowingnumberpatternsandrepeatingshapepatterns.
Identifyrulesfornumberpatterns.
Createandanalyzemultiplication and division patterns.
Identify,describe,andextendnumericandnon-numericpatterns.
Identify,describe,andextendnumeric patterns involving alloperations.
UseaVarietyofReasoningSkills
Sortandclassifyusingattributes.
Recognizeshapesfromdifferentperspectives.
Identifysurfacesthatslide,stack,androll.
UseaVarietyofReasoningSkills
Model,define,andexplainpropertiesof multiplication.
Usepropertiesof squaresand rectangles to solve problemsaboutareaandperimeter.
Exploretherelationshipamonglists,treediagrams,and multiplication to calculatecombinations.
Identifysimilaritiesanddifferences.
Use the Commutative and Associativeproperties,and10sand1stosolvetwo-digitadditionandsubtractionproblems.
Exploretheinverserelationshipbetweenadditionandsubtraction.
Exploretheinverserelationshipbetweenmultiplicationanddivision.
Usepropertiesof multiplication (including theDistributiveProperty)inestimationandmentalmath.
Use estimation to check reasonableness.
Use estimation to checkreasonableness(whole-numberaddition,subtraction,multiplicationanddivision).
Communication Communication
ConsolidateMathematicalThinking
Consolidate thinking in independentactivities.
PresentmathematicalthinkingthroughMathJournalactivities.
PresentmathematicalthinkingthroughMathJournalactivities.
ConsolidateMathematicalThinking
PresentmathematicalthinkingthroughMathJournalactivities.
PresentmathematicalthinkingthroughMathJournalactivities.
PresentmathematicalthinkingthroughMathJournalactivities.
CommunicatewithPeers,Teachers,andOthers
Discuss mathematical ideas in paired and small-group activities.
Discuss mathematical ideas inLet’sExploreactivities.
Discuss mathematical ideas inLet’sExploreactivities.
CommunicatewithPeers,Teachers,andOthers
Discuss mathematical ideas inLet’sExploreactivities.
Discuss mathematical ideas inLet’sExploreactivities.
Discuss mathematical ideas inLet’sExploreactivities.
Work together in pairs or groupsinLet’sExplore,Games,andotheractivities.
Work together in pairs or groupsinLet’sExplore,Games,andotheractivities.
Work together in pairs or groupsinLet’sExplore,Games,andotheractivities.
Work together in pairs or groupsinLet’sExplore,Games,andotheractivities.
Work together in pairs or groupsinLet’sExplore,Games,andotheractivities.
ShareMathematicalThinking
Share mathematical ideas in paired and small-group activities.
Share mathematical ideas withothersduringLet’sExploreandHands-Onactivities.
Share mathematical ideas withothersduringLet’sExploreandHands-Onactivities.
ShareMathematicalThinking
Share mathematical ideas withothersduringLet’sExploreandHands-Onactivities.
Share mathematical ideas withothersduringLet’sExploreandHands-Onactivities.
Share mathematical ideas withothersduringLet’sExploreandHands-Onactivities.
33
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
ProblemSolving(continued) ProblemSolving(continued)
Identify,Demonstrate,andExplainMathematicalProof(continued)
Interpretdataintallychartsandpictographs.
Interpretpicturegraphs,tallycharts,andbargraphs.
Interpret picture graphs withscales.
Identify,Demonstrate,andExplainMathematicalProof(continued)
Interpretbargraphswithscales.
Analyzeadatasetbyfindingitsmean,median,mode,andrange.
Comparetheresultsof anexperimenttovalidatetheuseof theoreticalprobability.
Identifyandextendrepeatingshapepatterns.
Identifyandextendgrowingnumberpatternsandrepeatingshapepatterns.
Identifyrulesfornumberpatterns.
Createandanalyzemultiplication and division patterns.
Identify,describe,andextendnumericandnon-numericpatterns.
Identify,describe,andextendnumeric patterns involving alloperations.
UseaVarietyofReasoningSkills
Sortandclassifyusingattributes.
Recognizeshapesfromdifferentperspectives.
Identifysurfacesthatslide,stack,androll.
UseaVarietyofReasoningSkills
Model,define,andexplainpropertiesof multiplication.
Usepropertiesof squaresand rectangles to solve problemsaboutareaandperimeter.
Exploretherelationshipamonglists,treediagrams,and multiplication to calculatecombinations.
Identifysimilaritiesanddifferences.
Use the Commutative and Associativeproperties,and10sand1stosolvetwo-digitadditionandsubtractionproblems.
Exploretheinverserelationshipbetweenadditionandsubtraction.
Exploretheinverserelationshipbetweenmultiplicationanddivision.
Usepropertiesof multiplication (including theDistributiveProperty)inestimationandmentalmath.
Use estimation to check reasonableness.
Use estimation to checkreasonableness(whole-numberaddition,subtraction,multiplicationanddivision).
Communication Communication
ConsolidateMathematicalThinking
Consolidate thinking in independentactivities.
PresentmathematicalthinkingthroughMathJournalactivities.
PresentmathematicalthinkingthroughMathJournalactivities.
ConsolidateMathematicalThinking
PresentmathematicalthinkingthroughMathJournalactivities.
PresentmathematicalthinkingthroughMathJournalactivities.
PresentmathematicalthinkingthroughMathJournalactivities.
CommunicatewithPeers,Teachers,andOthers
Discuss mathematical ideas in paired and small-group activities.
Discuss mathematical ideas inLet’sExploreactivities.
Discuss mathematical ideas inLet’sExploreactivities.
CommunicatewithPeers,Teachers,andOthers
Discuss mathematical ideas inLet’sExploreactivities.
Discuss mathematical ideas inLet’sExploreactivities.
Discuss mathematical ideas inLet’sExploreactivities.
Work together in pairs or groupsinLet’sExplore,Games,andotheractivities.
Work together in pairs or groupsinLet’sExplore,Games,andotheractivities.
Work together in pairs or groupsinLet’sExplore,Games,andotheractivities.
Work together in pairs or groupsinLet’sExplore,Games,andotheractivities.
Work together in pairs or groupsinLet’sExplore,Games,andotheractivities.
ShareMathematicalThinking
Share mathematical ideas in paired and small-group activities.
Share mathematical ideas withothersduringLet’sExploreandHands-Onactivities.
Share mathematical ideas withothersduringLet’sExploreandHands-Onactivities.
ShareMathematicalThinking
Share mathematical ideas withothersduringLet’sExploreandHands-Onactivities.
Share mathematical ideas withothersduringLet’sExploreandHands-Onactivities.
Share mathematical ideas withothersduringLet’sExploreandHands-Onactivities.
34
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Communication(continued) Communication(continued)
ExpressMathematicalIdeas
Expressideasinpairedandsmallgroupactivities.
ExpressideasinMathJournalactivities,usinglessonvocabulary.
ExpressideasinMathJournalactivities,usinglessonvocabulary.
ExpressMathematicalIdeas
ExpressideasinMathJournalactivities,usinglessonvocabulary.
ExpressideasinMathJournalactivities,usinglessonvocabulary.
ExpressideasinMathJournalactivities,usinglessonvocabulary.
Use chapter and lesson vocabularycorrectly.
Use chapter and lesson vocabularycorrectly.
Use chapter and lesson vocabularycorrectly.
Use chapter and lesson vocabularycorrectly.
Use chapter and lesson vocabularycorrectly.
Connections Connections
RecognizeConnectionsinMathematicalIdeas
Understand the connection betweenquantitiesandwrittennumerals.
Understand the relationship betweencountingandadditionandsubtraction.
Examineandapplytheinverserelationshipbetweenadditionandsubtraction.
RecognizeConnectionsinMathematicalIdeas
Applytheinverserelationshipbetweenmultiplicationanddivision.
Demonstrate that decimal notationisanextensionof thebase-tensystem.
Relatefractionsanddivision.
Understand the relationships amongthenumbersinfactfamilies.
Connect geometric concepts withunitfractions.
Understandthatthesizeof afractionalpartisrelativetothesizeof thewhole.
Examinetherelationshipbetweenfractionsanddecimals.
Understand the connection amongfractions,decimals,ratios,andpercentsaswaystorepresentpartsof awhole.
Connect addition and multiplication (repeated addition).
Connectsubtractionand division (repeated subtraction).
Connecttheunitsof customarycapacitytooneanother.
Makeconnectionsamongmultiplication,division,factors,andmultiples.
Examinetherelationshipsbetweenthree-dimensionalfiguresandthetwo-dimensionalfiguresthatformthem.
Recognizeandapplydifferentstrategiesforaddingandsubtracting one-andtwo-digitnumbers.
Recognizeandapplydifferentstrategiesformultiplication and division facts.
Understand the relationshipsbetweenthenumbersinmultiplication-divisionfactfamilies.
Convertamongmixednumbersandimproperfractions.
Relatefractionsanddivision.
UnderstandHowConceptsBuildonOneAnother
Explorerelationshipsamongcounting,ordering,andordinalnumbers.
Learnhowplacevalueconceptsapplytoregrouping in addition and subtraction.
Understandhowpatternscanbedescribedusingnumbers,operations,anddatadisplays.
UnderstandHowConceptsBuildonOneAnother
Understand the meanings andusesof fractionsincludingfractionof aset.
Describenumberrelationshipsincontext.
Explaintherelationshipsamongareaformulasof differentpolygons.
Connectequivalentfractionsanddecimals.
Connectequivalentfractions,decimals,andpercents.
Recognizetherelationshipbetweenbarmodels,numbersentences,andnumberpatterns.
Useaddition,subtraction,multiplication,anddivisiontoconstructandanalyzegraphs,frequencytables,andlineplots.
Makeconnectionsamongthegreatestcommonfactor,leastcommonmultiple,andoperationswithfractions.
35
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Communication(continued) Communication(continued)
ExpressMathematicalIdeas
Expressideasinpairedandsmallgroupactivities.
ExpressideasinMathJournalactivities,usinglessonvocabulary.
ExpressideasinMathJournalactivities,usinglessonvocabulary.
ExpressMathematicalIdeas
ExpressideasinMathJournalactivities,usinglessonvocabulary.
ExpressideasinMathJournalactivities,usinglessonvocabulary.
ExpressideasinMathJournalactivities,usinglessonvocabulary.
Use chapter and lesson vocabularycorrectly.
Use chapter and lesson vocabularycorrectly.
Use chapter and lesson vocabularycorrectly.
Use chapter and lesson vocabularycorrectly.
Use chapter and lesson vocabularycorrectly.
Connections Connections
RecognizeConnectionsinMathematicalIdeas
Understand the connection betweenquantitiesandwrittennumerals.
Understand the relationship betweencountingandadditionandsubtraction.
Examineandapplytheinverserelationshipbetweenadditionandsubtraction.
RecognizeConnectionsinMathematicalIdeas
Applytheinverserelationshipbetweenmultiplicationanddivision.
Demonstrate that decimal notationisanextensionof thebase-tensystem.
Relatefractionsanddivision.
Understand the relationships amongthenumbersinfactfamilies.
Connect geometric concepts withunitfractions.
Understandthatthesizeof afractionalpartisrelativetothesizeof thewhole.
Examinetherelationshipbetweenfractionsanddecimals.
Understand the connection amongfractions,decimals,ratios,andpercentsaswaystorepresentpartsof awhole.
Connect addition and multiplication (repeated addition).
Connectsubtractionand division (repeated subtraction).
Connecttheunitsof customarycapacitytooneanother.
Makeconnectionsamongmultiplication,division,factors,andmultiples.
Examinetherelationshipsbetweenthree-dimensionalfiguresandthetwo-dimensionalfiguresthatformthem.
Recognizeandapplydifferentstrategiesforaddingandsubtracting one-andtwo-digitnumbers.
Recognizeandapplydifferentstrategiesformultiplication and division facts.
Understand the relationshipsbetweenthenumbersinmultiplication-divisionfactfamilies.
Convertamongmixednumbersandimproperfractions.
Relatefractionsanddivision.
UnderstandHowConceptsBuildonOneAnother
Explorerelationshipsamongcounting,ordering,andordinalnumbers.
Learnhowplacevalueconceptsapplytoregrouping in addition and subtraction.
Understandhowpatternscanbedescribedusingnumbers,operations,anddatadisplays.
UnderstandHowConceptsBuildonOneAnother
Understand the meanings andusesof fractionsincludingfractionof aset.
Describenumberrelationshipsincontext.
Explaintherelationshipsamongareaformulasof differentpolygons.
Connectequivalentfractionsanddecimals.
Connectequivalentfractions,decimals,andpercents.
Recognizetherelationshipbetweenbarmodels,numbersentences,andnumberpatterns.
Useaddition,subtraction,multiplication,anddivisiontoconstructandanalyzegraphs,frequencytables,andlineplots.
Makeconnectionsamongthegreatestcommonfactor,leastcommonmultiple,andoperationswithfractions.
36
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Connections(continued) Connections(continued)
SolveReal-WorldProblemsinContextsOutsideofMathematics
Solvereal-worldproblemsinvolvingmoreandless.
Solvereal-worldproblems involvingaddition,subtraction,andmeasurement.
Solvereal-worldproblemsinvolvingaddition,subtraction,multiplication,division,measurement,anddataanalysis.
SolveReal-WorldProblemsinContextsOutsideofMathematics
Solvereal-worldproblemsinvolvingaddition,subtraction,multiplication,division,andmeasurement.
Solvereal-worldproblemsinvolvingmultiplication,division,fractionconcepts,dataanalysis,andmeasurement.
Solvereal-worldproblemsinvolving multiplication; division;fraction,decimal,ratio,andpercentconcepts;dataanalysis;andmeasurement.
Solvereal-worldproblemsrelatedtomoney.
Compareexperimentalresultsandtheoreticalprobability.
Representation Representation
UseRepresentationstoModel,Organize,andRecord
Use concrete models to createasetwithagivennumberof objects(upto20).
Use concrete and pictorial modelstocreateasetwithagivennumberof objects(upto100).
Use concrete and pictorial modelstocreateasetwith agivennumberof objects(upto1,000).
UseRepresentationstoModel,Organize,andRecord
Use place value models to read,write,andrepresentnumbersto10,000.
Representnumbersto100,000invariouscontexts.
Explorenegativenumbersincontext.
Usenumbersandnumeralsto represent quantities up to20.
Representnumbersto100onanumberline.
Representnumbersto1,000onanumberline.
Representnumbersindifferentequivalentforms.
Expressnumbersto100,000instandard,expanded,andwordforms.
Expressnumbersto10,000,000invariousforms.
Use picture cards to communicate understanding of comparisons(biggerandsmaller).
Usenumberbondstorepresentnumbers.
Understand the meaning of the=signinnumbersentences.
Understandequalityandinequality.
Usesymbolicnotation(<and>)tocomparenumbers.
Use the dollar sign and decimalpointinmoneyamounts.
Modeldecimalstotenthsandhundredths.
Findequivalentratios.
Modeladditionandsubtractionstorieswithadditionandsubtractionnumbersentences.
Usethe+,−,and=symbolstorepresentreal-worldadditionandsubtractionsituations.
Usebarmodelstorepresentadditionandsubtractionsituations.
Solve addition and subtractionproblemswithgreaternumbersbyusingabarmodel
Write addition and subtractionnumbersentencesforreal-worldproblemswithfractionsanddecimals.
Exploretheuseof lettersasvariablesinexpressionsandinequalities.
Represent addition and subtractionstories.
Represent numerical data usingpicturegraphs,tallycharts,andbargraphs.
Represent numerical data usingpicturegraphswithscales,tallycharts,andbargraphs.
Represent multiplication and divisionindifferentways.
Usemodelstoshowrelationshipsbetweenimproperfractionsandmixednumbers.
Convertfractionsanddecimalstopercents.
Representsharingequallyandmakingequalgroups.
Usethe×,÷,and=symbolsto represent multiplication anddivisionsituations.
Useavarietyof representationsformultiplicationanddivision,suchasarrays,areamodels,numberlines,grouping,andsharing.
Applyunderstandingof modelsformultiplicationanddivision.
Representcombinationswithlists,treediagrams,andmultiplication.
37
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Connections(continued) Connections(continued)
SolveReal-WorldProblemsinContextsOutsideofMathematics
Solvereal-worldproblemsinvolvingmoreandless.
Solvereal-worldproblems involvingaddition,subtraction,andmeasurement.
Solvereal-worldproblemsinvolvingaddition,subtraction,multiplication,division,measurement,anddataanalysis.
SolveReal-WorldProblemsinContextsOutsideofMathematics
Solvereal-worldproblemsinvolvingaddition,subtraction,multiplication,division,andmeasurement.
Solvereal-worldproblemsinvolvingmultiplication,division,fractionconcepts,dataanalysis,andmeasurement.
Solvereal-worldproblemsinvolving multiplication; division;fraction,decimal,ratio,andpercentconcepts;dataanalysis;andmeasurement.
Solvereal-worldproblemsrelatedtomoney.
Compareexperimentalresultsandtheoreticalprobability.
Representation Representation
UseRepresentationstoModel,Organize,andRecord
Use concrete models to createasetwithagivennumberof objects(upto20).
Use concrete and pictorial modelstocreateasetwithagivennumberof objects(upto100).
Use concrete and pictorial modelstocreateasetwith agivennumberof objects(upto1,000).
UseRepresentationstoModel,Organize,andRecord
Use place value models to read,write,andrepresentnumbersto10,000.
Representnumbersto100,000invariouscontexts.
Explorenegativenumbersincontext.
Usenumbersandnumeralsto represent quantities up to20.
Representnumbersto100onanumberline.
Representnumbersto1,000onanumberline.
Representnumbersindifferentequivalentforms.
Expressnumbersto100,000instandard,expanded,andwordforms.
Expressnumbersto10,000,000invariousforms.
Use picture cards to communicate understanding of comparisons(biggerandsmaller).
Usenumberbondstorepresentnumbers.
Understand the meaning of the=signinnumbersentences.
Understandequalityandinequality.
Usesymbolicnotation(<and>)tocomparenumbers.
Use the dollar sign and decimalpointinmoneyamounts.
Modeldecimalstotenthsandhundredths.
Findequivalentratios.
Modeladditionandsubtractionstorieswithadditionandsubtractionnumbersentences.
Usethe+,−,and=symbolstorepresentreal-worldadditionandsubtractionsituations.
Usebarmodelstorepresentadditionandsubtractionsituations.
Solve addition and subtractionproblemswithgreaternumbersbyusingabarmodel
Write addition and subtractionnumbersentencesforreal-worldproblemswithfractionsanddecimals.
Exploretheuseof lettersasvariablesinexpressionsandinequalities.
Represent addition and subtractionstories.
Represent numerical data usingpicturegraphs,tallycharts,andbargraphs.
Represent numerical data usingpicturegraphswithscales,tallycharts,andbargraphs.
Represent multiplication and divisionindifferentways.
Usemodelstoshowrelationshipsbetweenimproperfractionsandmixednumbers.
Convertfractionsanddecimalstopercents.
Representsharingequallyandmakingequalgroups.
Usethe×,÷,and=symbolsto represent multiplication anddivisionsituations.
Useavarietyof representationsformultiplicationanddivision,suchasarrays,areamodels,numberlines,grouping,andsharing.
Applyunderstandingof modelsformultiplicationanddivision.
Representcombinationswithlists,treediagrams,andmultiplication.
38
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Representation(continued) Representation(continued)
UseRepresentationstoModel,Organize,andRecord(continued)
Representmultiplicationwithskipcounting,dotpaperarrays,andbarmodels.
UseRepresentationstoModel,Organize,andRecord(continued)
Determine the missing parts (quantitiesorsymbols)innumbersentences.
Write addition and subtractionnumbersentencesforreal-worldproblemswithfractionsanddecimals.
Writeandsolveequations.
Represent division as repeatedsubtractionsentences.
Describeandextendshapepatterns.
Identify,describe,andextendtwo-andthree-dimensionalshapepatterns.
Describe,extend,andcreatetwo-dimensionalshapepatterns.
Createandanalyzemultiplication and division patterns.
Describearuleforsortingobjects.
Identifyaruleforsortingobjects.
Identifyandextendgrowingandrepeatingpatterns.
Identifyrulesfornumberpatterns.
Identifyarulefornumberandcountingpatterns.
Usearuletodescribeasequenceof numbersorobjects.
Findrulestocompletenumberpatterns.
SelectandApplyRepresentationstoModelProblems
Representquantitieswithobjects,numbercubes,andnumerals.
Usenumberbondstorepresentnumbercombinations.
Use place value models to create equivalent representationsof numbers.
SelectandApplyRepresentationstoModelProblems
Useavarietyof modelstorepresentfractionsandequivalentfractions.
Translatebetweenequivalent improper fractionsandmixednumbers.
Translatebetweenfractionsandpercents.
Useavarietyof concrete,pictorial,andsymbolicmodelsforadditionandsubtraction.
Useavarietyof concrete,pictorial,andsymbolicmodelsforaddition,subtraction,multiplication,anddivision.
Useavarietyof concrete,pictorial,andsymbolicmodelsformulti-digitaddition,subtraction,multiplication,anddivision.
Useavarietyof modelsformulti-digit multiplication anddivisionof wholenumbers.
Selectthemostusefulformof thequotient.
Representmultiplicationwithskipcountingandarrays.
Usecustomaryunits(includingfractions)tomeasurelength,weight,andcapacity.
Useavarietyof modelsforadditionandsubtractionof fractionsanddecimals.
Useanettofindthesurfaceareaof aprism.
InterpretPhenomenathroughRepresentations
Showunderstandingof big,middle-sized,small,andsamesize.
Measureandcomparelengthsandweightsusingnon-standardunits.
Usemetricandcustomaryunitstomeasurelength,volume(capacity),weight,andmass.
InterpretPhenomenathroughRepresentations
Usereferentstoestimatelength,capacity,andweight.
Measureperimeterandareaincustomaryandmetricunits.
Measurevolumeof arectangularprism.
Describeandcompareobjectsbyposition.
Usepositionalwordstodescribelocation.
39
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Representation(continued) Representation(continued)
UseRepresentationstoModel,Organize,andRecord(continued)
Representmultiplicationwithskipcounting,dotpaperarrays,andbarmodels.
UseRepresentationstoModel,Organize,andRecord(continued)
Determine the missing parts (quantitiesorsymbols)innumbersentences.
Write addition and subtractionnumbersentencesforreal-worldproblemswithfractionsanddecimals.
Writeandsolveequations.
Represent division as repeatedsubtractionsentences.
Describeandextendshapepatterns.
Identify,describe,andextendtwo-andthree-dimensionalshapepatterns.
Describe,extend,andcreatetwo-dimensionalshapepatterns.
Createandanalyzemultiplication and division patterns.
Describearuleforsortingobjects.
Identifyaruleforsortingobjects.
Identifyandextendgrowingandrepeatingpatterns.
Identifyrulesfornumberpatterns.
Identifyarulefornumberandcountingpatterns.
Usearuletodescribeasequenceof numbersorobjects.
Findrulestocompletenumberpatterns.
SelectandApplyRepresentationstoModelProblems
Representquantitieswithobjects,numbercubes,andnumerals.
Usenumberbondstorepresentnumbercombinations.
Use place value models to create equivalent representationsof numbers.
SelectandApplyRepresentationstoModelProblems
Useavarietyof modelstorepresentfractionsandequivalentfractions.
Translatebetweenequivalent improper fractionsandmixednumbers.
Translatebetweenfractionsandpercents.
Useavarietyof concrete,pictorial,andsymbolicmodelsforadditionandsubtraction.
Useavarietyof concrete,pictorial,andsymbolicmodelsforaddition,subtraction,multiplication,anddivision.
Useavarietyof concrete,pictorial,andsymbolicmodelsformulti-digitaddition,subtraction,multiplication,anddivision.
Useavarietyof modelsformulti-digit multiplication anddivisionof wholenumbers.
Selectthemostusefulformof thequotient.
Representmultiplicationwithskipcountingandarrays.
Usecustomaryunits(includingfractions)tomeasurelength,weight,andcapacity.
Useavarietyof modelsforadditionandsubtractionof fractionsanddecimals.
Useanettofindthesurfaceareaof aprism.
InterpretPhenomenathroughRepresentations
Showunderstandingof big,middle-sized,small,andsamesize.
Measureandcomparelengthsandweightsusingnon-standardunits.
Usemetricandcustomaryunitstomeasurelength,volume(capacity),weight,andmass.
InterpretPhenomenathroughRepresentations
Usereferentstoestimatelength,capacity,andweight.
Measureperimeterandareaincustomaryandmetricunits.
Measurevolumeof arectangularprism.
Describeandcompareobjectsbyposition.
Usepositionalwordstodescribelocation.
40
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Representation(continued) Representation(continued)
InterpretPhenomenathroughRepresentations(continued)
Nameflatshapesthatmakeupreal-worldobjects.
Identifyreal-worldtwo-andthree-dimensionalshapes.
InterpretPhenomenathroughRepresentations(continued)
Usefrequencytables,bargraphs,picturegraphs,andlineplotstosolveproblems.
Collectdataandorganizeitinatable.
Representdatainadoublebargraph.
Represent measurements and data in picture graphs andbargraphs.
Represent data in picture graphs.
Representdatainbargraphsandpicturegraphs.
Createalinegraphfromdatainatable.
Represent an equation as a graphedline.
Orderanumberof objectsaccordingtolength,height,orweight.
Solveproblemsaboutsharingequallyandmakingequalgroups.
Solvereal-worldproblemsaboutsocialphenomena.
Solvereal-worldproblemsinvolvingsocialsituations.
Usemeasuresof centraltendencytodescribetypicalvaluesof datasets(social).
Use one-to-one correspondence.
Useavarietyof modelsforaddingandsubtracting.
Usebarmodelstorepresentaddition,subtraction,multiplication,anddivisionsituations.
Solvereal-worldproblemsrelatedtomoney.
Solvereal-worldproblemsinvolvingmultiplication,division,fractionconcepts,dataanalysis,andmeasurement.
Solvereal-worldproblemsinvolvingsocialsituations.
Usetechnology(virtualmanipulatives and computers)tomodelanddraw.
Usetechnology(virtualmanipulatives and computers)tomodelanddraw.
Usetechnology(virtualmanipulatives and computers)tomodelanddraw.
Usetechnology(virtualmanipulatives and computers)tomodelanddraw.
Usetechnology(virtualmanipulativesandcomputers)tomodelanddraw.
Useacalculatortomodel,compute,andsolveproblems.
41
Kindergarten Grade1 Grade2 Grade3 Grade4 Grade5
Representation(continued) Representation(continued)
InterpretPhenomenathroughRepresentations(continued)
Nameflatshapesthatmakeupreal-worldobjects.
Identifyreal-worldtwo-andthree-dimensionalshapes.
InterpretPhenomenathroughRepresentations(continued)
Usefrequencytables,bargraphs,picturegraphs,andlineplotstosolveproblems.
Collectdataandorganizeitinatable.
Representdatainadoublebargraph.
Represent measurements and data in picture graphs andbargraphs.
Represent data in picture graphs.
Representdatainbargraphsandpicturegraphs.
Createalinegraphfromdatainatable.
Represent an equation as a graphedline.
Orderanumberof objectsaccordingtolength,height,orweight.
Solveproblemsaboutsharingequallyandmakingequalgroups.
Solvereal-worldproblemsaboutsocialphenomena.
Solvereal-worldproblemsinvolvingsocialsituations.
Usemeasuresof centraltendencytodescribetypicalvaluesof datasets(social).
Use one-to-one correspondence.
Useavarietyof modelsforaddingandsubtracting.
Usebarmodelstorepresentaddition,subtraction,multiplication,anddivisionsituations.
Solvereal-worldproblemsrelatedtomoney.
Solvereal-worldproblemsinvolvingmultiplication,division,fractionconcepts,dataanalysis,andmeasurement.
Solvereal-worldproblemsinvolvingsocialsituations.
Usetechnology(virtualmanipulatives and computers)tomodelanddraw.
Usetechnology(virtualmanipulatives and computers)tomodelanddraw.
Usetechnology(virtualmanipulatives and computers)tomodelanddraw.
Usetechnology(virtualmanipulatives and computers)tomodelanddraw.
Usetechnology(virtualmanipulativesandcomputers)tomodelanddraw.
Useacalculatortomodel,compute,andsolveproblems.
42
Aligned with National and International Research Recommendations
NationalMathAdvisoryPanel
“Useshouldbemadeof whatisclearlyknownfromrigorousresearchabouthowchildrenlearn,especiallybyrecognizingthemutually-reinforcingbenefitsof conceptualunderstanding,proceduralfluency,andautomatic(i.e.,quickandeffortless)recallof facts.”
—Foundations for Success,2008
Math in Focusaddresses fewer topics in greater depth
at each level.
• Knowledgeisbuiltcarefullyandthoroughlywithbothmulti-page lessons and multi-daylessons.
• Timeisbuiltintotheprogramtodevelopunderstandingwithhands-on activitieswithmanipulatives,aswellasextensive skills practice.
Math in Focusdevelops concepts and skills in tandem.
• Manipulativesandvisualrepresentationsprovideaconceptualbackbone.
• Skills are connected to concepts through visual representations.
• Extensiveproblemsolvingmerges conceptual understanding with computational skills.
NationalCouncilof Teachersof Mathematics
“Acurriculumismorethanacollectionof activities:it
mustbecoherent,focusedonimportantmathematics,
andwellarticulatedacrossthegrades.”
—Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics,2006
Focus and Depth Interlocking Concepts and Skills
1 Ways to Add . . . . . . . . . . . . . . . . . . . . . 42
Learn Addbycountingon•Countto findhowmanymore•Addusing numberbonds
Hands-On Activities Count on to addusingconnectingcubes•Useten framestoadd(CommutativeProperty)
Game CardFun!
Let’s Practice and Practice and Apply WorkbookA:Practice1 . . . . . . . . . . . . 46–47
Let’s Practice and Practice and Apply WorkbookA:Practice2 . . . . . . . . . . . . 50–51
Grade1,Chapter3,Lesson1
Skill Building
Concept Building
the WHY
the HOW
43
Aligned with National and International Research Recommendations
SingaporeMinistryof Education
“Mathematicalproblemsolvingiscentraltomathematicslearning.Itinvolvestheacquisitionandapplicationof mathematicsconceptsandskillsinawiderangeof situations,includingnon-routine, open-ended,andreal-worldproblems.”
—Mathematics Syllabus: Primary,2006
BarModel: a visual representationof awordproblem(Grade2)
Math in Focususes a scaffolded approach to solving word
problems, focusing on model drawing to build success and confidence.
• Thevisualrepresentationof wordproblemsleadstosymbolicsolutionsof rich and complex problems.
• Studentsdrawonpriorknowledge,aswellasrecentlyacquiredconceptsandskills,astheycombineproblem solving strategies with critical thinking skills.
Emphasis on Problem Solving
NationalResearchCouncil
“Opportunitiesshouldinvolveconnectingsymbolicrepresentationsandoperationswithphysicalorpictorialrepresentations,aswellastranslatingbetweenvarioussymbolicrepresentations.”
—Adding It Up: Helping Children Learn Mathematics,2001
Math in Focususes clear and engaging visuals that present
concepts and model solutions.
• Minimal textandsimple,directvisualsallowallstudents,regardlessof languageskills,tofocusonthemathlesson.
• Theuseof model drawingsofferavisualrepresentationof wordproblems,leadingtosymbolicsolutionsof richandcomplexproblems.
• Consistentuseof theconcrete–pictorial–abstract pedagogyrepeatedly“models”themodel-drawingproblemsolvingstrategy.
NumberBonds: a visual forcomposinganddecomposingnumbers(Grade1)
Clear Visuals and Use of Models
104
6
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Math in Focus: Singapore Math by Marshall Cavendish istheU.S.editionofMy Pals are Here! Maths,theworld-classprogrammostwidelyusedinSingaporeclassroomstoday.MarshallCavendishmathprogramshavecontributedtoSingapore’sconsistenttopperformanceininternationalstudiessince1995.