grades k–5 scope and sequence your 1 choice for world

Your #1 Choice for World-Class Mathematics!

Deep Math Understanding. Real-World Problem Solvers.

Grades K–5 Scope and Sequence

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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

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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.


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



Compareandorderwholenumbersto10,000,000.

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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NumberandOperations NumberandOperations

SetsandNumbers

Use concrete models to createasetwithagivennumberof objects (upto20).


Use concrete and pictorial modelstocreateasetwith agivennumberof objects (upto1,000).

SetsandNumbers

Groupobjectsandnumbersupto100intensandones.

Groupobjectsandnumbersupto1,000intohundreds,tens,andones.

Groupobjectsintoequalsizedgroups.

Use cardinal and ordinal numbers.

Usecardinalnumbersupto100andordinalnumbersupto10th.



Usenumberstorepresentquantitiesupto20.




Representnumbersto10,000indifferentequivalentforms.


Understand place value conceptsthroughmillions.



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.


CompareandOrder



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.



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NumberandOperations(continued) NumberandOperations(continued)

PlaceValue(continued)

Expressnumbersto100instandardandwordforms.

Expressnumbersto1,000 intermsof placevalue.


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 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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Expressnumbersto100instandardandwordforms.

Expressnumbersto1,000 intermsof placevalue.


Compose and decompose multi-digitnumbers(includingexpandedform).

FractionConcepts

Connect geometric concepts withunitfractions—halves,thirds,andfourths.

FractionConcepts


Recognize,write,name,andillustratemixednumbersandimproperfractions.

Convertfractionstodecimals.

Understand the relationship betweenafractionandawhole.


Findafractionof aset. Relatefractionsanddivisionexpressions.

Compareandorderhalves,thirds,andfourthsusingbarmodels.

Comparefractionsusingmodelsandnumberlines.

Generate equivalent fractions.

Identifyequivalentfractionsthroughtheuseof models,multiplication,division,andnumberlines.



Money Identifyandrelatecoinvalues(penny,nickel,dime,quarter).

Identifyandrelatecoinvalues(penny,nickel,dime,quarter).

Identify$1,$5,$10,and$20bills.

Money Addandsubtractmoney.



Count and make combinationsof coinsandbills.

Comparemoneyamounts. Solvereal-worldproblemsinvolving addition and subtractionof money.

DecimalConcepts

Use the dollar sign and decimalpoint.

DecimalConcepts


Modeldecimalsusingtenthsandhundredths.

Modeldecimalsusingthousandths.

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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


Useratiostosolveproblems.

Findequivalentratios.

Solveproblemswithpercent.

Convertfractionstopercents.

Findapercentof anumber.

WholeNumberComputation:AdditionandSubtraction

Modeljoiningandseparatingsets.

Modeladditionandsubtractionsituations.

Modeladditionandsubtractionwithplacevalue.


Modelregroupinginadditionandsubtractionwithplacevalue.

Use+,-,and=towritenumbersentencesforadditionandsubtractionstories.

Usemodels,numbers,andsymbolsforadditionandsubtractionfactsto20.

Recall addition and subtractionfacts.

Usetheorder,grouping,andzeropropertiestodevelopadditionandsubtractionfactstrategies.

Usedifferentmethodstodevelopfluencyinaddingandsubtractingmulti-digitnumbers.

Addandsubtractupto2-digitnumberswithandwithoutregrouping

Addandsubtractwholenumbersto1,000.


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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.


Convertdecimalstofractions.



Useratiostosolveproblems.


Solveproblemswithpercent.

Convertfractionstopercents.

Findapercentof anumber.


Modeljoiningandseparatingsets.

Modeladditionandsubtractionsituations.

Modeladditionandsubtractionwithplacevalue.


Modelregroupinginadditionandsubtractionwithplacevalue.

Use+,-,and=towritenumbersentencesforadditionandsubtractionstories.

Usemodels,numbers,andsymbolsforadditionandsubtractionfactsto20.

Recall addition and subtractionfacts.

Usetheorder,grouping,andzeropropertiestodevelopadditionandsubtractionfactstrategies.

Usedifferentmethodstodevelopfluencyinaddingandsubtractingmulti-digitnumbers.

Addandsubtractupto2-digitnumberswithandwithoutregrouping



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WholeNumberComputation:AdditionandSubtractionReal-WorldProblems

Represent addition and subtractionstories.

Formulateadditionandsubtractionstories.


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.


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


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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Formulateadditionandsubtractionstories.


Solve addition and subtractionproblemsusingbasicfacts.

Solve multi-digit addition andsubtractionproblems byusingabarmodel.

Solve addition and subtractionproblemswithgreaternumbersbyusing abarmodel.


Countby2sand5supto20.

Countby2s,5s,and10s. Multiplyanddividewith2, 3,4,5,and10.


Multiplyanddividewith6,7,8,and9.

Addingthesamenumbertomultiply.

Represent multiplication as repeatedaddition.

Represent multiplication in differentways.



Represent division as repeatedsubtraction.

Represent division in differentways.

Recallmultiplicationfactsandrelateddivisionfacts.




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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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


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 toaddsubtract,multiply,anddivide.

Use mental math and estimationstrategiestofindsums,differences,products,andquotients.

Use estimation and mental mathtoestimatesums,differences,products,andquotients.

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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


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.





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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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


Findthegreatestcommonfactorandleastcommonmultiple.

Identifyprimeandcompositenumbers.

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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.



Patterns Createandanalyzemultiplication and division patterns.



Countby2sand5s. Skipcountby2s,5s,and10s.

Skipcountby2s,3s,4s,5s,and10s.

Skipcountby6s,7s,8s,and9s.



Findmissingtermsinrepeatingpatterns.



Analyzenumberandcountingpatterns.



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.


NumberTheory


NumberTheory


Findthegreatestcommonfactorandleastcommonmultiple.

Identifyprimeandcompositenumbers.

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Algebra(continued) Alegbra(continued)

FunctionalRelationships

Understand the relationships betweenthenumbersinfactfamilies.

Recognizehowbarmodelsshowrelationshipsbetweennumbersandunknownsinnumbersentences.


Understand the relationshipsbetweenthenumbersinmultiplicationanddivisionfactfamilies.

Understand the relationships betweenthenumbersandsymbolsinformulasforareaandperimeter.

Understand the relationships betweenthenumbersandsymbolsinformulasforsurfaceareaandvolume.

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.


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.


Graphlinearequations.

EqualityandInequality

Understand the meaning of the=signinnumbersentences.

Understandthedifferencebetweenequalityandinequality.

Use and create models that demonstrateequalityorinequality.


Understandequalityandinequality.



Use<,>,and=towritenumbersentences.

Writeandsolveinequalities.

Geometry Geometry

SizeandPosition

Understandbig,middle-sized,andsmall.

Describepositionwithleftandright.

SizeandPosition

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Algebra(continued) Alegbra(continued)


Understand the relationships betweenthenumbersinfactfamilies.

Recognizehowbarmodelsshowrelationshipsbetweennumbersandunknownsinnumbersentences.


Understand the relationshipsbetweenthenumbersinmultiplicationanddivisionfactfamilies.


Understand the relationships betweenthenumbersandsymbolsinformulasforsurfaceareaandvolume.




Expressions/Models



Expressions/Models


Useavarietyof concrete,pictorial,andsymbolicmodelsformultiplicationand division; and addition andsubtractionwithfractionsanddecimals.

Uselettersasvariables.

Simplifyalgebraicexpressions.

Usetheorderof operationsinnumericexpressionswithtwoormoreoperations.



Modeladditionandsubtractionsituationsbywritingadditionandsubtractionnumbersentences.

Modelmultiplicationanddivisionsituationsbywritingmultiplication and division numbersentences.


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.


Determinethevalueof missingquantitiesinnumbersentences.



Graphlinearequations.



Understandthedifferencebetweenequalityandinequality.

Use and create models that demonstrateequalityorinequality.





Use<,>,and=towritenumbersentences.

Writeandsolveinequalities.

Geometry Geometry

SizeandPosition

Understandbig,middle-sized,andsmall.

Describepositionwithleftandright.

SizeandPosition

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Geometry(continued) Geometry(continued)

SizeandPosition(continued)

Describeandcompareobjectsbyposition.

Usepositionalwordstodescribelocation.


LinesandAngles

Identifypartsof linesandcurves.

LinesandAngles

Identifyperpendicularandparallellines.

Drawperpendicularandparallellines.

Workwithanglesonastraightline.

Identifyrightanglesandcompare angles to right angles.

Construct and measure angles.

Workwithanglesatapoint.

Two-DimensionalShapes

Identifysimilaritiesanddifferences.


Nameflatshapesthatmakeupreal-worldobjects.

Identifyreal-worldtwo-dimensionalshapes.

Identify,describe,sort,andclassifytwo-dimensionalshapes.

Identifyanddescribeattributesandpropertiesof two-dimensionalshapes.


Describe,analyze,compare,andclassifytwo-dimensionalshapesbytheirsidesandangles.

Applythepropertiesof squaresandrectangles.

Applythepropertiesof right,isosceles,andequilateraltriangles.

Sortandclassifytwo-dimensionalshapes.


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.


Findtheareaof atriangle.

Three-DimensionalShapes

Nameandsortsolidshapes. Identifyreal-worldthree-dimensionalshapes.


Identifyandclassifyprismsandpyramids.

Understand that three-dimensional shapes are madeupof two-dimensionalshapes.

Identifytwo-dimensionalshapes in three-dimensional shapes.

Identify,describe,sort,andclassifythree-dimensionalshapes.

Identifythesolidthatcanbemadefromanet.

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LinesandAngles


LinesandAngles

Identifyperpendicularandparallellines.

Drawperpendicularandparallellines.

Workwithanglesonastraightline.

Identifyrightanglesandcompare angles to right angles.

Construct and measure angles.

Workwithanglesatapoint.





Identifyreal-worldtwo-dimensionalshapes.


Identifyanddescribeattributesandpropertiesof two-dimensionalshapes.


Describe,analyze,compare,andclassifytwo-dimensionalshapesbytheirsidesandangles.

Applythepropertiesof squaresandrectangles.

Applythepropertiesof right,isosceles,andequilateraltriangles.

Sortandclassifytwo-dimensionalshapes.



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.


Findandcomparetheareaof planefiguresindifferentsquareunits.


Findtheareaof atriangle.


Nameandsortsolidshapes. Identifyreal-worldthree-dimensionalshapes.


Identifyandclassifyprismsandpyramids.

Understand that three-dimensional shapes are madeupof two-dimensionalshapes.

Identifytwo-dimensionalshapes in three-dimensional shapes.

Identify,describe,sort,andclassifythree-dimensionalshapes.

Identifythesolidthatcanbemadefromanet.

20



Three-DimensionalShapes(continued)

Sortandclassifythree-dimensionalshapes.

Identifysurfacesthatslide,stack,androll.


Identifycylinders,spheres,andcones.

Recognizeshapesfromdifferentperspectives.

Describecylinders,spheres,andconesbythenumberof andtypesof faces,andthenumberof edgesandvertices.

Compose and decompose three-dimensionalshapes.

Buildsolidsusingunitcubes.

CongruenceandSymmetry

Develop initial understandingof 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




Sortandclassifythree-dimensionalshapes.



Identifycylinders,spheres,andcones.


Describecylinders,spheres,andconesbythenumberof andtypesof faces,andthenumberof edgesandvertices.

Compose and decompose three-dimensionalshapes.

Buildsolidsusingunitcubes.


Develop initial understandingof congruenceandsymmetry.


Identifysymmetricalfiguresandonelineof symmetry.

Identifylineandrotationalsymmetry.

Solveproblemsinvolvingcongruency.

Relaterotationalsymmetrytoturnsandcongruency.

Transformations Transformations Identifypairsof shapesthatshowaflip,slide,andturn.

Usetransformationstoformtessellations.


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.


Usereferentstoestimatedistance.

22


Measurement(continued) Measurement(continued)

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






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



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





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.


Perimeter Perimeter Measureperimeterof planefigures.

Findtheperimeterof compositefigures.

26



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).


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


Decomposesolidfigurestofindthesurfacearea.

Estimate and measure volumeincubicunits.

DataAnalysis DataAnalysis

ClassifyingandSorting

Understanding similarities anddifferencesinobjectsandshapes.

Sortandclassifygeometricshapes.

Sortandclassifytwo-andthree-dimensional shapes byproperties.



Sortingandclassifyingobjectsusingoneortwoattributes.

Sortingandclassifyingdatainordertomakegraphs.

Collectandorganizedatainpicturegraphs.

Collectandorganizedatainbargraphsandlineplots.

Constructlineplots,stem-and-leaf plots,tables,andlinegraphs.

Representdatainadoublebargraph.

27





Choose the appropriate tool,unit,andstrategytomeasureperimeter.

Solveproblemsinvolvingtheperimeterof squares,rectangles,andcompositefigures.

Estimatetheperimeterof surfacesandobjects.

Area Compare areas using non-standardunits.

Compose and decompose two-dimensionalshapes (foundationforunderstandingarea).


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.




Decomposesolidfigurestofindthesurfacearea.

Estimate and measure volumeincubicunits.

DataAnalysis DataAnalysis


Understanding similarities anddifferencesinobjectsandshapes.

Sortandclassifygeometricshapes.

Sortandclassifytwo-andthree-dimensional shapes byproperties.



Sortingandclassifyingobjectsusingoneortwoattributes.

Sortingandclassifyingdatainordertomakegraphs.

Collectandorganizedatainpicturegraphs.

Collectandorganizedatainbargraphsandlineplots.

Constructlineplots,stem-and-leaf plots,tables,andlinegraphs.


28


DataAnalysis(continued) DataAnalysis(continued)

CollectandOrganizeData

Organizedataforapicturegraph.

Collectandorganizedataindifferentways.



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.


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


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.



Buildskillsinmultiplication,division,fractionconcepts,dataanalysis,andmeasurement through problemsolving.

Build skills in multiplication; division;fractionconcepts,decimals,ratios,andpercents;dataanalysis;and measurement through problemsolving.

29


DataAnalysis(continued) DataAnalysis(continued)


Organizedataforapicturegraph.




RepresentData

Represent data in pictographs.

Represent measurements anddatainpicturegraphs,tallycharts,andbargraphs.


RepresentData



Interpret data in picture graphs,tallycharts,andbargraphs.

Interpretpicturegraphswithscales.


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.



Expresstheprobabilityof aneventasafraction.

Comparetheresultsof anexperimentwiththeoreticalprobability.

Findallpossiblecombinationsbylisting,makingatreediagram,andmultiplying.

ProblemSolving ProblemSolving


Build skills in addition and subtractionthroughproblemsolving.

Buildskillsinaddition,subtraction,andmeasurement through problemsolving.




Buildskillsinmultiplication,division,fractionconcepts,dataanalysis,andmeasurement through problemsolving.

Build skills in multiplication; division;fractionconcepts,decimals,ratios,andpercents;dataanalysis;and measurement through problemsolving.

30


ProblemSolving(continued) ProblemSolving(continued)

SolveReal-WorldProblems

Solvereal-worldproblemsinvolving addition and subtraction.


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.




Use appropriate strategies tosolvereal-worldproblems.

Use appropriate strategies to solvereal-worldproblems.

ApplyandExplainProblemSolving

Solvereal-worldproblems. ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.

ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.





ExploreConcepts

Usemodelstoexplainreasoning.

ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.


ExploreConcepts




ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.





InvestigateMathematicalIdeas

Investigateideaswithtwo-dimensionalshapes.

Furtherinvestigatemathematicalideasbycompleting critical thinking skillsactivities.






Identify,Demonstrate,andExplainMathematicalProof

Demonstratethatonlyafewbigthingsfitintosmallspacesandmanysmallthingsfitintobigspaces.

Exploretransitivitybycomparing lengths and weightsof threedifferentobjects.

Demonstrate the inverse relationshipbetweenthe sizeof aunitandthenumberof units.



Showthatsomefigurescanbeturnedandnotchangeshapeorsize(rotationalsymmetry).

Applytheideathatthesumof anglesonastraightlineis180°.


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.


31










Solvereal-worldproblemsinvolving multiplication; division;conceptswithfractions,decimals,ratios,andpercents;dataanalysis;andmeasurement.






Use appropriate strategies tosolvereal-worldproblems.

Use appropriate strategies to solvereal-worldproblems.


Solvereal-worldproblems. ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.






ExploreConcepts

Usemodelstoexplainreasoning.



ExploreConcepts










Investigateideaswithtwo-dimensionalshapes.








Demonstratethatonlyafewbigthingsfitintosmallspacesandmanysmallthingsfitintobigspaces.

Exploretransitivitybycomparing lengths and weightsof threedifferentobjects.

Demonstrate the inverse relationshipbetweenthe sizeof aunitandthenumberof units.



Showthatsomefigurescanbeturnedandnotchangeshapeorsize(rotationalsymmetry).

Applytheideathatthesumof anglesonastraightlineis180°.


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.


32



Identify,Demonstrate,andExplainMathematicalProof(continued)


Interpretpicturegraphs,tallycharts,andbargraphs.

Interpret picture graphs withscales.


Interpretbargraphswithscales.

Analyzeadatasetbyfindingitsmean,median,mode,andrange.

Comparetheresultsof anexperimenttovalidatetheuseof theoreticalprobability.

Identifyandextendrepeatingshapepatterns.

Identifyandextendgrowingnumberpatternsandrepeatingshapepatterns.


Createandanalyzemultiplication and division patterns.



UseaVarietyofReasoningSkills

Sortandclassifyusingattributes.





Usepropertiesof squaresand rectangles to solve problemsaboutareaandperimeter.

Exploretherelationshipamonglists,treediagrams,and multiplication to calculatecombinations.


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.






CommunicatewithPeers,Teachers,andOthers

Discuss mathematical ideas in paired and small-group activities.

Discuss mathematical ideas inLet’sExploreactivities.






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.






33





Interpretpicturegraphs,tallycharts,andbargraphs.

Interpret picture graphs withscales.


Interpretbargraphswithscales.

Analyzeadatasetbyfindingitsmean,median,mode,andrange.

Comparetheresultsof anexperimenttovalidatetheuseof theoreticalprobability.

Identifyandextendrepeatingshapepatterns.

Identifyandextendgrowingnumberpatternsandrepeatingshapepatterns.






Sortandclassifyusingattributes.





Usepropertiesof squaresand rectangles to solve problemsaboutareaandperimeter.

Exploretherelationshipamonglists,treediagrams,and multiplication to calculatecombinations.


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


Consolidate thinking in independentactivities.








Discuss mathematical ideas in paired and small-group activities.













Share mathematical ideas in paired and small-group activities.







34


Communication(continued) Communication(continued)

ExpressMathematicalIdeas

Expressideasinpairedandsmallgroupactivities.

ExpressideasinMathJournalactivities,usinglessonvocabulary.






Use chapter and lesson vocabularycorrectly.





Connections Connections

RecognizeConnectionsinMathematicalIdeas

Understand the connection betweenquantitiesandwrittennumerals.

Understand the relationship betweencountingandadditionandsubtraction.

Examineandapplytheinverserelationshipbetweenadditionandsubtraction.


Applytheinverserelationshipbetweenmultiplicationanddivision.

Demonstrate that decimal notationisanextensionof thebase-tensystem.

Relatefractionsanddivision.

Understand the relationships amongthenumbersinfactfamilies.

Connect geometric concepts withunitfractions.


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.



UnderstandHowConceptsBuildonOneAnother

Explorerelationshipsamongcounting,ordering,andordinalnumbers.

Learnhowplacevalueconceptsapplytoregrouping in addition and subtraction.

Understandhowpatternscanbedescribedusingnumbers,operations,anddatadisplays.






Connectequivalentfractions,decimals,andpercents.

Recognizetherelationshipbetweenbarmodels,numbersentences,andnumberpatterns.

Useaddition,subtraction,multiplication,anddivisiontoconstructandanalyzegraphs,frequencytables,andlineplots.

Makeconnectionsamongthegreatestcommonfactor,leastcommonmultiple,andoperationswithfractions.

35


Communication(continued) Communication(continued)


Expressideasinpairedandsmallgroupactivities.












Connections Connections


Understand the connection betweenquantitiesandwrittennumerals.

Understand the relationship betweencountingandadditionandsubtraction.

Examineandapplytheinverserelationshipbetweenadditionandsubtraction.


Applytheinverserelationshipbetweenmultiplicationanddivision.

Demonstrate that decimal notationisanextensionof thebase-tensystem.


Understand the relationships amongthenumbersinfactfamilies.

Connect geometric concepts withunitfractions.


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.




Explorerelationshipsamongcounting,ordering,andordinalnumbers.

Learnhowplacevalueconceptsapplytoregrouping in addition and subtraction.

Understandhowpatternscanbedescribedusingnumbers,operations,anddatadisplays.






Connectequivalentfractions,decimals,andpercents.

Recognizetherelationshipbetweenbarmodels,numbersentences,andnumberpatterns.

Useaddition,subtraction,multiplication,anddivisiontoconstructandanalyzegraphs,frequencytables,andlineplots.

Makeconnectionsamongthegreatestcommonfactor,leastcommonmultiple,andoperationswithfractions.

36


Connections(continued) Connections(continued)

SolveReal-WorldProblemsinContextsOutsideofMathematics

Solvereal-worldproblemsinvolvingmoreandless.

Solvereal-worldproblems involvingaddition,subtraction,andmeasurement.

Solvereal-worldproblemsinvolvingaddition,subtraction,multiplication,division,measurement,anddataanalysis.




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 modelstocreateasetwith agivennumberof objects(upto1,000).


Use place value models to read,write,andrepresentnumbersto10,000.



Usenumbersandnumeralsto represent quantities up to20.



Representnumbersindifferentequivalentforms.



Use picture cards to communicate understanding of comparisons(biggerandsmaller).

Usenumberbondstorepresentnumbers.



Usesymbolicnotation(<and>)tocomparenumbers.


Modeldecimalstotenthsandhundredths.



Usethe+,−,and=symbolstorepresentreal-worldadditionandsubtractionsituations.

Usebarmodelstorepresentadditionandsubtractionsituations.

Solve addition and subtractionproblemswithgreaternumbersbyusingabarmodel

Write addition and subtractionnumbersentencesforreal-worldproblemswithfractionsanddecimals.

Exploretheuseof lettersasvariablesinexpressionsandinequalities.


Represent numerical data usingpicturegraphs,tallycharts,andbargraphs.

Represent numerical data usingpicturegraphswithscales,tallycharts,andbargraphs.

Represent multiplication and divisionindifferentways.

Usemodelstoshowrelationshipsbetweenimproperfractionsandmixednumbers.

Convertfractionsanddecimalstopercents.



Useavarietyof representationsformultiplicationanddivision,suchasarrays,areamodels,numberlines,grouping,andsharing.


Representcombinationswithlists,treediagrams,andmultiplication.

37


Connections(continued) Connections(continued)


Solvereal-worldproblemsinvolvingmoreandless.

Solvereal-worldproblems involvingaddition,subtraction,andmeasurement.

Solvereal-worldproblemsinvolvingaddition,subtraction,multiplication,division,measurement,anddataanalysis.




Solvereal-worldproblemsinvolving multiplication; division;fraction,decimal,ratio,andpercentconcepts;dataanalysis;andmeasurement.


Compareexperimentalresultsandtheoreticalprobability.

Representation Representation


Use concrete models to createasetwithagivennumberof objects(upto20).


Use concrete and pictorial modelstocreateasetwith agivennumberof objects(upto1,000).


Use place value models to read,write,andrepresentnumbersto10,000.



Usenumbersandnumeralsto represent quantities up to20.



Representnumbersindifferentequivalentforms.



Use picture cards to communicate understanding of comparisons(biggerandsmaller).

Usenumberbondstorepresentnumbers.



Usesymbolicnotation(<and>)tocomparenumbers.


Modeldecimalstotenthsandhundredths.



Usethe+,−,and=symbolstorepresentreal-worldadditionandsubtractionsituations.

Usebarmodelstorepresentadditionandsubtractionsituations.

Solve addition and subtractionproblemswithgreaternumbersbyusingabarmodel


Exploretheuseof lettersasvariablesinexpressionsandinequalities.


Represent numerical data usingpicturegraphs,tallycharts,andbargraphs.

Represent numerical data usingpicturegraphswithscales,tallycharts,andbargraphs.

Represent multiplication and divisionindifferentways.

Usemodelstoshowrelationshipsbetweenimproperfractionsandmixednumbers.

Convertfractionsanddecimalstopercents.



Useavarietyof representationsformultiplicationanddivision,suchasarrays,areamodels,numberlines,grouping,andsharing.


Representcombinationswithlists,treediagrams,andmultiplication.

38


Representation(continued) Representation(continued)

UseRepresentationstoModel,Organize,andRecord(continued)

Representmultiplicationwithskipcounting,dotpaperarrays,andbarmodels.





Represent division as repeatedsubtractionsentences.

Describeandextendshapepatterns.








Identifyarulefornumberandcountingpatterns.



SelectandApplyRepresentationstoModelProblems

Representquantitieswithobjects,numbercubes,andnumerals.




Useavarietyof modelstorepresentfractionsandequivalentfractions.

Translatebetweenequivalent improper fractionsandmixednumbers.

Translatebetweenfractionsandpercents.




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.


Usereferentstoestimatelength,capacity,andweight.

Measureperimeterandareaincustomaryandmetricunits.

Measurevolumeof arectangularprism.



39




Representmultiplicationwithskipcounting,dotpaperarrays,andbarmodels.





Represent division as repeatedsubtractionsentences.

Describeandextendshapepatterns.








Identifyarulefornumberandcountingpatterns.




Representquantitieswithobjects,numbercubes,andnumerals.




Useavarietyof modelstorepresentfractionsandequivalentfractions.

Translatebetweenequivalent improper fractionsandmixednumbers.

Translatebetweenfractionsandpercents.




Useavarietyof modelsformulti-digit multiplication anddivisionof wholenumbers.

Selectthemostusefulformof thequotient.

Representmultiplicationwithskipcountingandarrays.

Usecustomaryunits(includingfractions)tomeasurelength,weight,andcapacity.

Useavarietyof modelsforadditionandsubtractionof fractionsanddecimals.

Useanettofindthesurfaceareaof aprism.


Showunderstandingof big,middle-sized,small,andsamesize.

Measureandcomparelengthsandweightsusingnon-standardunits.

Usemetricandcustomaryunitstomeasurelength,volume(capacity),weight,andmass.


Usereferentstoestimatelength,capacity,andweight.

Measureperimeterandareaincustomaryandmetricunits.

Measurevolumeof arectangularprism.



40



InterpretPhenomenathroughRepresentations(continued)


Identifyreal-worldtwo-andthree-dimensionalshapes.


Usefrequencytables,bargraphs,picturegraphs,andlineplotstosolveproblems.

Collectdataandorganizeitinatable.


Represent measurements and data in picture graphs andbargraphs.


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.




Usetechnology(virtualmanipulatives and computers)tomodelanddraw.




Usetechnology(virtualmanipulativesandcomputers)tomodelanddraw.

Useacalculatortomodel,compute,andsolveproblems.

41





Identifyreal-worldtwo-andthree-dimensionalshapes.


Usefrequencytables,bargraphs,picturegraphs,andlineplotstosolveproblems.

Collectdataandorganizeitinatable.


Represent measurements and data in picture graphs andbargraphs.


Representdatainbargraphsandpicturegraphs.

Createalinegraphfromdatainatable.

Represent an equation as a graphedline.

Orderanumberof objectsaccordingtolength,height,orweight.

Solveproblemsaboutsharingequallyandmakingequalgroups.

Solvereal-worldproblemsaboutsocialphenomena.


Usemeasuresof centraltendencytodescribetypicalvaluesof datasets(social).

Use one-to-one correspondence.

Useavarietyof modelsforaddingandsubtracting.

Usebarmodelstorepresentaddition,subtraction,multiplication,anddivisionsituations.








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™ is a trademark of Times Publishing Limited. © Houghton Mifflin Harcourt Publishing Company.

All rights reserved. Printed in the U.S.A 01/11 MS9824 Z-1474076

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Math in Focus: Singapore Math by Marshall Cavendish istheU.S.editionofMy Pals are Here! Maths,theworld-classprogrammostwidelyusedinSingaporeclassroomstoday.MarshallCavendishmathprogramshavecontributedtoSingapore’sconsistenttopperformanceininternationalstudiessince1995.

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