math in focus scope and sequence

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

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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 Focusanswersthecallforacoherentsequenceoftopics

givingstudentstimetomasterfoundationaltopics,

sothatlittlerepetitionisrequiredthenextyear.Thus,eachgrade

levelcoversfewertopicsbutinmoredepth,andyouwon’tfindall

topicsineverygradelevel.

• “Missingtopics” Whenatopicappearstobe“missing,”youcan

beassuredthatitisfoundineitheranearlierorlatergradelevel.

ForexampleyouwillfindcalendarconceptsinGradesKand1,but

notrepeatedinGrade2.

• Moreadvanced Asaresultofnotrepeatingtopicsyearafteryear,studentswhouseMath in Focus willadvancefasterthanstudentsin

otherprograms.Asaresult,

youmayfindtopicsthatseemtobe“tooadvanced.”However,you

willfindyourstudentseasilyabletohandlethechallengeaslongas

theyhavehadtheappropriatepreliminaryinstruction.

Developmental Continuum

Kindergarten Grades 1–2 Grades 3–5

Preparation for AlgebraMath in Focusanswersthecalltopreparestudentsforalgebra.

AsrecommendedbytheNationalMathPanel,theMath in Focus

sequenceoftopicsemphasizes:

• Number sense, basic facts, and computation Anearlyunderstandingofcompositionanddecompositionofnumbersis

developedintandemwithmasteryofbasic

factsandcomputationalgorithmsinGradesK–2.

• Fractions and proportional reasoning Significanttimeis

allocatedforin-depthworkwithfractionsinGrades3–5.

• Problem solving Challengingproblemsolvingisbuilt

intoeachchapterineverygradelevel.

Foundationalconceptsthroughsongs,rhymes,andhands-onactivities

Emphasisonproblemsolving,skillconsolidation,andadeepunderstandinginpreparationforalgebra

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Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5

Number and Operations Number and Operations

Sets and Numbers

Use concrete models to create asetwithagivennumberofobjects (upto20).

Use concrete and pictorial modelstocreateasetwithagivennumberofobjects(upto100).

Use concrete and pictorial modelstocreateasetwith agivennumberofobjects (upto1,000).

Sets and Numbers

Groupobjectsandnumbersupto100intensandones.

Groupobjectsandnumbersupto1,000intohundreds,tens,andones.

Groupobjectsintoequalsizedgroups.

Use cardinal and ordinal numbers.

Usecardinalnumbersupto100andordinalnumbersupto10th.

Explorenegativenumbers incontext.

Number Representation

Usenumberstorepresentquantitiesupto20.

Usenumberbondstorepresentnumbercombinations.

Use place value models to create equivalentrepresentationsofnumbers.


Representnumbersto10,000indifferentequivalentforms.

Representnumbersto100,000invariouscontexts.

Understand place value conceptsthroughmillions.

Representnumbersto100onanumberline.

Representnumbersto1,000onanumberline.

Count Countupto20objectsinaset. Countto100. Countto1,000. Count Countto10,000.

Countonandbackto20. Countby1s,2s,5s,and10sforwardandbackwardto100.

Countbymultiplesofones,tens,andhundreds.

Countbyhundredsandthousands.

Countbythousandsandtenthousands.

Countbyhundredthousandsandmillions.

Countin2sand5sup to20.

Compare and Order

Compare and order sets and numbersupto20.

Compareandorderwholenumbersto100.

Compareandorderwholenumbersto1,000.

Compare and Order



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.

Place Value Use place value models and place value charts to represent numbersto100.

Usebase-tenmodelsand place value charts to represent numbersto1,000.

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

Expressnumbersto100,000instandard,expanded,andwordforms.

Expressnumbersto10,000,000invariousforms.

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Number and Operations Number and Operations

Sets and Numbers

Use concrete models to create asetwithagivennumberofobjects (upto20).


Use concrete and pictorial modelstocreateasetwith agivennumberofobjects (upto1,000).

Sets and Numbers

Groupobjectsandnumbersupto100intensandones.

Groupobjectsandnumbersupto1,000intohundreds,tens,andones.

Groupobjectsintoequalsizedgroups.

Use cardinal and ordinal numbers.

Usecardinalnumbersupto100andordinalnumbersupto10th.

Explorenegativenumbers incontext.


Usenumberstorepresentquantitiesupto20.




Representnumbersto10,000indifferentequivalentforms.


Understand place value conceptsthroughmillions.



Count Countupto20objectsinaset. Countto100. Countto1,000. Count Countto10,000.

Countonandbackto20. Countby1s,2s,5s,and10sforwardandbackwardto100.

Countbymultiplesofones,tens,andhundreds.

Countbyhundredsandthousands.

Countbythousandsandtenthousands.

Countbyhundredthousandsandmillions.

Countin2sand5sup to20.

Compare and Order

Compare and order sets and numbersupto20.

Compareandorderwholenumbersto100.


Compare and Order



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.

Place Value Use place value models and place value charts to represent numbersto100.

Usebase-tenmodelsand place value charts to represent numbersto1,000.

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



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Number and Operations (continued) Number and Operations (continued)

Place Value (continued)

Expressnumbersto100instandardandwordforms.

Expressnumbersto1,000 intermsofplacevalue.


Compose and decompose multi-digitnumbers(includingexpandedform).

Fraction Concepts

Connect geometric concepts withunitfractions—halves,thirds,andfourths.

Fraction Concepts

Understand the meanings andusesoffractionsincludingfractionofaset.

Recognize,write,name,andillustratemixednumbersandimproperfractions.

Convertfractionstodecimals.

Understand the relationship betweenafractionandawhole.

Understandthatthesizeofafractionalpartisrelativetothesizeofthewhole.

Findafractionofaset. Relatefractionsand divisionexpressions.

Compareandorderhalves,thirds,andfourthsusing barmodels.

Comparefractionsusingmodelsandnumberlines.

Generateequivalentfractions.

Identifyequivalentfractionsthroughtheuseofmodels,multiplication,division,andnumberlines.

Convertamongmixednumbersand improperfractions.

Addandsubtractlikefractions.

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

Identifyandrelatecoinvalues(penny,nickel,dime,quarter).

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

Money Addandsubtractmoney.

Count and make coincombinations.


Countandmakecombinationsofcoinsandbills.

Comparemoneyamounts. Solvereal-worldproblemsinvolving addition and subtractionofmoney.

Decimal Concepts

Use the dollar sign and decimalpoint.

Decimal Concepts

Use the dollar sign and decimal pointinmoneyamounts.

Modeldecimalsusingtenthsandhundredths.

Modeldecimals usingthousandths.

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Expressnumbersto100instandardandwordforms.

Expressnumbersto1,000 intermsofplacevalue.


Compose and decompose multi-digitnumbers(includingexpandedform).

Fraction Concepts

Connect geometric concepts withunitfractions—halves,thirds,andfourths.

Fraction Concepts


Recognize,write,name,andillustratemixednumbersandimproperfractions.

Convertfractionstodecimals.

Understand the relationship betweenafractionandawhole.


Findafractionofaset. Relatefractionsand divisionexpressions.

Compareandorderhalves,thirds,andfourthsusing barmodels.

Comparefractionsusingmodelsandnumberlines.

Generateequivalentfractions.

Identifyequivalentfractionsthroughtheuseofmodels,multiplication,division,andnumberlines.

Convertamongmixednumbersand improperfractions.

Addandsubtractlikefractions.

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

Identifyandrelatecoinvalues(penny,nickel,dime,quarter).

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

Money Addandsubtractmoney.



Countandmakecombinationsofcoinsandbills.

Comparemoneyamounts. Solvereal-worldproblemsinvolving addition and subtractionofmoney.

Decimal Concepts

Use the dollar sign and decimalpoint.

Decimal Concepts


Modeldecimalsusingtenthsandhundredths.

Modeldecimals usingthousandths.

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Decimal Concepts (continued)


Understand decimal notation through hundredths as an extensionofthebase-tensystem.

Understand place value conceptsthroughthousandths.

Readandwritedecimalsthatare greater than or lessthan1.

Compareandorderdecimals.

Identifyequivalent decimals.

Connectequivalentfractionsanddecimals.

Convertdecimalstofractions.

Ratio, Proportion, and Percent


Useratiostosolveproblems.

Findequivalentratios.

Solveproblemswithpercent.

Convertfractionstopercents.

Findapercentofanumber.

Whole Number Computation: Addition and Subtraction

Modeljoiningandseparatingsets.

Modeladditionandsubtractionsituations.

Modeladditionandsubtractionwithplacevalue.


Modelregroupinginadditionandsubtractionwithplacevalue.

Use+,-,and=towritenumbersentencesforadditionandsubtractionstories.

Usemodels,numbers,andsymbolsforadditionandsubtractionfactsto20.

Recalladditionandsubtractionfacts.

Usetheorder,grouping,andzeropropertiestodevelopadditionandsubtractionfactstrategies.

Use different methods to developfluencyinaddingandsubtractingmulti-digitnumbers.

Addandsubtractupto2-digitnumberswithandwithoutregrouping

Addandsubtractwholenumbersto1,000.


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Understand decimal notation through hundredths as an extensionofthebase-tensystem.

Understand place value conceptsthroughthousandths.

Readandwritedecimalsthatare greater than or lessthan1.

Compareandorderdecimals.

Identifyequivalent decimals.


Convertdecimalstofractions.



Useratiostosolveproblems.


Solveproblemswithpercent.

Convertfractionstopercents.

Findapercentofanumber.


Modeljoiningandseparatingsets.

Modeladditionandsubtractionsituations.

Modeladditionandsubtractionwithplacevalue.


Modelregroupinginadditionandsubtractionwithplacevalue.

Use+,-,and=towritenumbersentencesforadditionandsubtractionstories.

Usemodels,numbers,andsymbolsforadditionandsubtractionfactsto20.

Recalladditionandsubtractionfacts.

Usetheorder,grouping,andzeropropertiestodevelopadditionandsubtractionfactstrategies.

Use different methods to developfluencyinaddingandsubtractingmulti-digitnumbers.

Addandsubtractupto2-digitnumberswithandwithoutregrouping



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Whole Number Computation: Addition and Subtraction Real-World Problems

Represent addition and subtractionstories.

Formulate addition and subtractionstories.


Solveadditionandsubtractionproblemsusingbasicfacts.

Solve multi-digit addition andsubtractionproblems byusingabarmodel.

Solveadditionandsubtractionproblemswithgreaternumbersbyusing abarmodel.

Whole Number Computation: Multiplication and Division Concepts

Countby2sand5supto20. Countby2s,5s,and10s. Multiplyanddividewith2, 3,4,5,and10.


Multiplyanddividewith6,7,8,and9.

Addingthesamenumbertomultiply.

Represent multiplication as repeatedaddition.

Represent multiplication in differentways.

Applyunderstandingofmodelsformultiplicationanddivision.

Representsharingequallyandmakingequalgroups.

Represent division as repeated subtraction.

Represent division in different ways.

Recallmultiplicationfactsandrelateddivisionfacts.

Usethe×,÷,and=symbolstorepresent multiplication and divisionsituations.

Whole Number Computation: Multiplication and Division Al-gorithms


Multiply1s,10s,and100swithandwithoutregrouping.

Developfluencyinmultiplyingmulti-digitnumbers.

Multiplymulti-digitnumbers.

Use addition and multiplication properties tomultiply.

Divide10sand1swithand withoutregrouping,noremainder.

Dividebya1-digitnumber,witharemainder.

Find quotients involving multi-digitdividends.

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Formulate addition and subtractionstories.


Solveadditionandsubtractionproblemsusingbasicfacts.

Solve multi-digit addition andsubtractionproblems byusingabarmodel.

Solveadditionandsubtractionproblemswithgreaternumbersbyusing 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 repeated subtraction.

Represent division in different ways.

Recallmultiplicationfactsandrelateddivisionfacts.




Multiply1s,10s,and100swithandwithoutregrouping.

Developfluencyinmultiplyingmulti-digitnumbers.

Multiplymulti-digitnumbers.

Use addition and multiplication properties tomultiply.

Divide10sand1swithand withoutregrouping,noremainder.

Dividebya1-digitnumber,witharemainder.

Find quotients involving multi-digitdividends.

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Whole Number Computation: Multiplication and Division Real-World Problems

Usebarmodelstorepresentmultiplication and division situations.



Solve multiplication and division factproblems.

Solveone-andtwo-stepmultiplication and division problems.

Solve multi-digit multiplication anddivisionproblems.

Solve multiplication and division problems.

Selectthemostusefulformofthe quotient and interpret the remainder.

Fraction Computation

Addandsubtractlikefractions(halves,thirds,fourths).


Addandsubtractlikefractions. Addandsubtractunlikefractions.

Addandsubtractunlikefractionsandmixednumbers.

Multiplyproperfractions,improperfractions,mixednumbers,andwholenumbers.

Dividefractionsbywholenumbers.

Solvewordproblemswithaddition,subtraction,multiplication,anddivision offractions.

Decimal Computation

Addandsubtractmoney. Solveadditionandsubtractionmoneyproblems.

Decimal Computation

Addandsubtractmoneyamounts.

Addandsubtractdecimals. Addandsubtractdecimals.

Multiplyanddividedecimalsbywholenumbers.

Solveproblemswithadditionandsubtractionofdecimals.

Solveproblemswithmultiplication and division ofdecimals.

Estimation and Mental Math

Use mental math strategies to addandsubtract.



Use mental math strategies toaddsubtract,multiply,anddivide.

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

Use estimation and mental math toestimatesums,differences,products,andquotients.

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Solve multiplication and division factproblems.

Solveone-andtwo-stepmultiplication and division problems.

Solve multi-digit multiplication anddivisionproblems.

Solve multiplication and division problems.

Selectthemostusefulformofthe quotient and interpret the remainder.


Addandsubtractlikefractions(halves,thirds,fourths).


Addandsubtractlikefractions. Addandsubtractunlikefractions.

Addandsubtractunlikefractionsandmixednumbers.

Multiplyproperfractions,improperfractions,mixednumbers,andwholenumbers.

Dividefractionsbywholenumbers.

Solvewordproblemswithaddition,subtraction,multiplication,anddivision offractions.

Decimal Computation

Addandsubtractmoney. Solveadditionandsubtractionmoneyproblems.

Decimal Computation

Addandsubtractmoneyamounts.

Addandsubtractdecimals. Addandsubtractdecimals.

Multiplyanddividedecimalsbywholenumbers.

Solveproblemswithadditionandsubtractionofdecimals.

Solveproblemswithmultiplication and division ofdecimals.





Use mental math strategies toaddsubtract,multiply,anddivide.

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

Use estimation and mental math toestimatesums,differences,products,andquotients.

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Estimation and Mental Math (continued)


Decidewhetheranestimateorexactanswerisneeded.

Estimatequantitybyusingreferents.

Round to the nearest ten to estimatesumsanddifferences.

Usefront-endestimationandrounding to estimate sums and differences.

Use estimation in determining relativesizes ofamountsordistances.

Estimate sums and differences withfractions anddecimals.

Roundandestimatewithdecimals.

Estimate products and quotients withdecimals.

Algebra Algebra

Patterns Describeandextendrepeatingshapepatterns.

Identify,describe,andextendtwo-andthree-dimensionalshapepatterns.

Describe,extend,andcreatetwo-dimensionalshapepatterns.

Patterns Createandanalyzemultiplication and division patterns.

Identify,describe,andextendnumeric and non-numeric patterns.

Identify,describe,andextendnumeric patterns involving alloperations.

Countby2sand5s. Skipcountby2s,5s,and10s. Skipcountby2s,3s,4s,5s,and10s.

Skipcountby6s,7s,8s,and9s.

Describearuleforsortingobjects.

Identifyaruleforsortingobjects.

Find missing terms in repeating patterns.

Identifyandextendgrowingandrepeatingpatterns.

Identifyrulesfornumberpatterns.

Analyzenumberandcountingpatterns.

Usearuletodescribeasequenceofnumbersorobjects.

Findrulestocompletenumberpatterns.

Findmissingtermsingrowingandrepeatingpatterns.

Findmissingtermsintablepatterns.

Properties Identify0astheidentityelementforadditionandsubtraction.

Understand that addition andsubtractionareinverseoperations.

Properties Understand that multiplication anddivisionarerelated.

Represent division as the inverseofmultiplication.

Use the Associative and CommutativePropertiesofAddition.

Applypropertiesofaddition. Createandanalyzemultiplication and division patterns.

UsetheDistributivePropertyasamultiplicationstrategy.

Model,define,andexplainpropertiesofmultiplication.

Number Theory

Identifyoddandevennumbers.

Number Theory


Find the greatest common factorandleastcommonmultiple.

Identifyprimeandcompositenumbers.

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Decidewhetheranestimateorexactanswerisneeded.

Estimatequantitybyusingreferents.

Round to the nearest ten to estimatesumsanddifferences.

Usefront-endestimationandrounding to estimate sums and differences.

Use estimation in determining relativesizes ofamountsordistances.

Estimate sums and differences withfractions anddecimals.

Roundandestimatewithdecimals.

Estimate products and quotients withdecimals.

Algebra Algebra

Patterns Describeandextendrepeatingshapepatterns.



Patterns Createandanalyzemultiplication and division patterns.



Countby2sand5s. Skipcountby2s,5s,and10s. Skipcountby2s,3s,4s,5s,and10s.

Skipcountby6s,7s,8s,and9s.



Find missing terms in repeating patterns.



Analyzenumberandcountingpatterns.



Findmissingtermsingrowingandrepeatingpatterns.

Findmissingtermsintablepatterns.

Properties Identify0astheidentityelementforadditionandsubtraction.

Understand that addition andsubtractionareinverseoperations.

Properties Understand that multiplication anddivisionarerelated.

Represent division as the inverseofmultiplication.

Use the Associative and CommutativePropertiesofAddition.

Applypropertiesofaddition. Createandanalyzemultiplication and division patterns.

UsetheDistributivePropertyasamultiplicationstrategy.


Number Theory


Number Theory


Find the greatest common factorandleastcommonmultiple.

Identifyprimeandcompositenumbers.

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Algebra (continued) Alegbra (continued)

Functional Relationships

Understand the relationships betweenthenumbersinfactfamilies.

Recognizehowbarmodelsshowrelationshipsbetweennumbersandunknownsinnumbersentences.


Understand the relationships betweenthenumbersinmultiplicationanddivisionfactfamilies.

Understand the relationships betweenthenumbersandsymbolsinformulasforareaandperimeter.

Understand the relationships betweenthenumbersandsymbolsinformulasforsurfaceareaandvolume.

Describenumberrelationshipsincontext.



Expressions/Models

Useavarietyofconcrete,pictorial,andsymbolicmodelsforadditionandsubtraction.

Useavarietyofconcrete,pictorial,andsymbolicmodelsforaddition,subtraction,multiplication,anddivision.

Expressions/Models

Useavarietyofconcrete,pictorial,andsymbolicmodelsformulti-digitaddition,subtraction,multiplication,anddivision.

Useavarietyofconcrete,pictorial,andsymbolicmodelsformultiplicationanddivision;andadditionandsubtractionwithfractionsanddecimals.

Uselettersasvariables.

Simplifyalgebraicexpressions.

Usetheorderofoperationsinnumericexpressionswithtwoormoreoperations.

Number Sentences and Equations

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.

Determinethevalueofmissingquantitiesinnumbersentences.

Determine the missing parts (quantitiesorsymbols)innumbersentences.


Graphlinearequations.

Equality and In-equality

Understandthemeaningofthe=signinnumbersentences.

Understand the difference betweenequalityandinequality.

Use and create models that demonstrateequalityorinequality.


Understandequalityandinequality.



Use<,>,and=towritenumbersentences.

Writeandsolveinequalities.

Geometry Geometry

Size and Position

Understandbig,middle-sized,andsmall.

Describepositionwithleftandright.

Size and Position

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Algebra (continued) Alegbra (continued)


Understand the relationships betweenthenumbersinfactfamilies.

Recognizehowbarmodelsshowrelationshipsbetweennumbersandunknownsinnumbersentences.


Understand the relationships betweenthenumbersinmultiplicationanddivisionfactfamilies.


Understand the relationships betweenthenumbersandsymbolsinformulasforsurfaceareaandvolume.




Expressions/Models



Expressions/Models


Useavarietyofconcrete,pictorial,andsymbolicmodelsformultiplicationanddivision;andadditionandsubtractionwithfractionsanddecimals.

Uselettersasvariables.

Simplifyalgebraicexpressions.

Usetheorderofoperationsinnumericexpressionswithtwoormoreoperations.



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.


Determinethevalueofmissingquantitiesinnumbersentences.



Graphlinearequations.



Understand the difference betweenequalityandinequality.

Use and create models that demonstrateequalityorinequality.





Use<,>,and=towritenumbersentences.

Writeandsolveinequalities.

Geometry Geometry

Size and Position

Understandbig,middle-sized,andsmall.

Describepositionwithleftandright.

Size and Position

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Geometry (continued) Geometry (continued)

Size and Position (continued)

Describeandcompareobjectsbyposition.

Usepositionalwordstodescribelocation.


Lines and Angles

Identifypartsoflinesandcurves.

Lines and Angles

Identifyperpendicularandparallellines.

Drawperpendicularandparallellines.

Workwithanglesonastraightline.

Identifyrightanglesandcompare angles to right angles.

Constructandmeasureangles. Workwithanglesatapoint.

Two- Dimensional Shapes

Identifysimilaritiesanddifferences.


Nameflatshapesthatmakeupreal-worldobjects.

Identifyreal-worldtwo-dimensionalshapes.

Identify,describe,sort,andclassifytwo-dimensionalshapes.

Identifyanddescribeattributesandpropertiesoftwo-dimensionalshapes.


Describe,analyze,compare,andclassifytwo-dimensionalshapesbytheirsidesandangles.

Applythepropertiesofsquaresandrectangles.

Applythepropertiesofright,isosceles,andequilateraltriangles.

Sortandclassifytwo-dimensionalshapes.


Classifyandsortpolygonsandquadrilateralsbyattributesandproperties.

Findunknownanglemeasuresandsidelengthsofsquaresandrectangles.

Applythesumoftheanglemeasuresofatriangle.

Makeflatshapepictures. Composeanddecomposetwo-dimensionalshapes.

Composeanddecomposetwo-dimensionalshapes.

Investigate composing and decomposingtwo-dimensionalshapes.

Identifyfiguresthatformtessellations.

Applythepropertiesofaparallelogram,rhombus,andtrapezoid.

Useattributesandpropertiestosolveproblems.

Demonstratethatthesumofanytwosidelengthsofatriangleisgreaterthanthelengthofthethirdside.

Compare areas using non-standardunits.

Developfoundationsforunderstandingarea.

Find and compare the area ofplanefiguresindifferentsquareunits.


Findtheareaofatriangle.

Three- Dimensional Shapes

Nameandsortsolidshapes. Identifyreal-worldthree-dimensionalshapes.


Identifyandclassifyprismsandpyramids.

Understand that three-dimensional shapes are made upoftwo-dimensionalshapes.

Identifytwo-dimensionalshapes in three-dimensional shapes.

Identify,describe,sort,andclassifythree-dimensionalshapes.

Identifythesolidthatcanbemadefromanet.

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Lines and Angles


Lines and Angles

Identifyperpendicularandparallellines.

Drawperpendicularandparallellines.

Workwithanglesonastraightline.

Identifyrightanglesandcompare angles to right angles.

Constructandmeasureangles. Workwithanglesatapoint.





Identifyreal-worldtwo-dimensionalshapes.


Identifyanddescribeattributesandpropertiesoftwo-dimensionalshapes.


Describe,analyze,compare,andclassifytwo-dimensionalshapesbytheirsidesandangles.

Applythepropertiesofsquaresandrectangles.

Applythepropertiesofright,isosceles,andequilateraltriangles.

Sortandclassifytwo-dimensionalshapes.



Findunknownanglemeasuresandsidelengthsofsquaresandrectangles.

Applythesumoftheanglemeasuresofatriangle.

Makeflatshapepictures. Composeanddecomposetwo-dimensionalshapes.

Composeanddecomposetwo-dimensionalshapes.

Investigate composing and decomposingtwo-dimensionalshapes.

Identifyfiguresthatformtessellations.

Applythepropertiesofaparallelogram,rhombus,andtrapezoid.

Useattributesandpropertiestosolveproblems.

Demonstratethatthesumofanytwosidelengthsofatriangleisgreaterthanthelengthofthethirdside.

Compare areas using non-standardunits.


Find and compare the area ofplanefiguresindifferentsquareunits.


Findtheareaofatriangle.


Nameandsortsolidshapes. Identifyreal-worldthree-dimensionalshapes.


Identifyandclassifyprismsandpyramids.

Understand that three-dimensional shapes are made upoftwo-dimensionalshapes.

Identifytwo-dimensionalshapes in three-dimensional shapes.

Identify,describe,sort,andclassifythree-dimensionalshapes.

Identifythesolidthatcanbemadefromanet.

20



Three- Dimensional Shapes (continued)

Sortandclassifythree-dimensionalshapes.

Identifysurfacesthatslide,stack,androll.


Identifycylinders,spheres,andcones.

Recognizeshapesfromdifferentperspectives.

Describecylinders,spheres,andconesbythenumberofandtypesoffaces,andthenumberofedgesandvertices.

Compose and decompose three-dimensionalshapes.

Buildsolidsusingunitcubes.

Congruence and Symmetry

Develop initial understanding ofcongruenceandsymmetry.


Identifysymmetricalfiguresandonelineofsymmetry.

Identifylineandrotationalsymmetry.

Solveproblemsinvolvingcongruency.

Relaterotationalsymmetrytoturnsandcongruency.

Transformations Transformations Identifypairsofshapesthatshowaflip,slide,andturn.

Usetransformationstoformtessellations.

Demonstratethatfiguresandtheirflip,slide,andturnimagesarecongruent.

Coordinate Geometry

Coordinate Geometry

Develop coordinate readiness withtablesandlinegraphs.

Plotpointsonacoordinategrid.

Measurement Measurement

Length and Dis-tance

Compare lengths and heights usingnon-standardunits.

Comparetwolengthsbycomparingeachwithathirdlength(transitivity).

Demonstrate linear measure as aniterationofunits.


Select appropriate units and tools to estimate and measure length.

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.

Measurelengthtothenearesthalfinchandinch.

Explaintheneedforequal-lengthunitstomeasure.

Usereferentstoestimatedistance.

21




Sortandclassifythree-dimensionalshapes.



Identifycylinders,spheres,andcones.


Describecylinders,spheres,andconesbythenumberofandtypesoffaces,andthenumberofedgesandvertices.

Compose and decompose three-dimensionalshapes.

Buildsolidsusingunitcubes.


Develop initial understanding ofcongruenceandsymmetry.


Identifysymmetricalfiguresandonelineofsymmetry.

Identifylineandrotationalsymmetry.

Solveproblemsinvolvingcongruency.

Relaterotationalsymmetrytoturnsandcongruency.

Transformations Transformations Identifypairsofshapesthatshowaflip,slide,andturn.

Usetransformationstoformtessellations.


Coordinate Geometry

Coordinate Geometry

Develop coordinate readiness withtablesandlinegraphs.

Plotpointsonacoordinategrid.

Measurement Measurement


Compare lengths and heights usingnon-standardunits.

Comparetwolengthsbycomparingeachwithathirdlength(transitivity).

Demonstrate linear measure as aniterationofunits.


Select appropriate units and tools to estimate and measure length.

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.

Measurelengthtothenearesthalfinchandinch.


Usereferentstoestimatedistance.

22


Measurement (continued) Measurement (continued)

Length and Dis-tance (continued)



Countlengthunitsingroupsof10sand1s.

Compare and measure lengths usingcustomary andmetricunits.

Estimateandmeasurelength,distance,andheightinmeters,centimeters,andkilometers.

Compare measurements made usingdifferentunits.

Demonstrate partitioning and transitivityinrelation tolength.

Convertamongmetricunitsoflength.

Understand the inverse relationshipbetweenthesizeofaunitandthenumberofunits.

Solveproblemsinvolvingestimating,measuring,andcomputinglength.

Solveone-andtwo-stepreal-worldproblemsinmeasurement.

Weight/Mass Orderobjectsbyweight. Compareandmeasureweightsusingnon-standardunits.

Compareandmeasuremasses. Weight/Mass Select appropriate units and tools to estimate and measure weight.

Compareweightsusingnon-standardunits.

Comparetwomassesbycomparingeachwithathirdmass(transitivity).

Usereferentstoestimateweight.

Estimateandfindmasses ofobjects.

Solveweightproblems. Solvemassproblems. Convertamongunitsofmass.

Capacity/ Volume

Compare capacities using non-standardunits.

Measurevolume(capacity) inliters.

Capacity/ Volume

Select appropriate tools and units to estimate and measure volumeandcapacity.

Solvevolumeproblems. Determine the volume and capacityofacontainer.

Relatetheunitsofcustomarycapacitytooneanother.

Usereferentstoestimatecapacity.

23






Countlengthunitsingroupsof10sand1s.

Compare and measure lengths usingcustomary andmetricunits.

Estimateandmeasurelength,distance,andheightinmeters,centimeters,andkilometers.

Compare measurements made usingdifferentunits.

Demonstrate partitioning and transitivityinrelation tolength.

Convertamongmetricunitsoflength.

Understand the inverse relationshipbetweenthesizeofaunitandthenumberofunits.

Solveproblemsinvolvingestimating,measuring,andcomputinglength.

Solveone-andtwo-stepreal-worldproblemsinmeasurement.

Weight/Mass Orderobjectsbyweight. Compareandmeasureweightsusingnon-standardunits.

Compareandmeasuremasses. Weight/Mass Select appropriate units and tools to estimate and measure weight.

Compareweightsusingnon-standardunits.

Comparetwomassesbycomparingeachwithathirdmass(transitivity).

Usereferentstoestimateweight.

Estimateandfindmasses ofobjects.

Solveweightproblems. Solvemassproblems. Convertamongunitsofmass.

Capacity/ Volume

Compare capacities using non-standardunits.

Measurevolume(capacity) inliters.

Capacity/ Volume

Select appropriate tools and units to estimate and measure volumeandcapacity.

Solvevolumeproblems. Determine the volume and capacityofacontainer.

Relatetheunitsofcustomarycapacitytooneanother.

Usereferentstoestimatecapacity.

24



Capacity/ Volume (continued)


Estimateandmeasurecapacityinlitersandmilliliters.

Convertamongmetricunitsofcapacity.

Time Nameandorderthedaysoftheweekandthemonthsoftheyear.

Readacalendartoidentifythedaysoftheweek,months,andseasonsof theyear.

Time

Recognizethecorrectwaytowritethedate.

UseA.M.andP.M.towritetime. Readtimeonadigitalclock.

Telltimetothehourandhalfhour.

Telltimetofiveminutes. Convertbetweenhoursandminutes.

Comparedurationsofevents. Findelapsedtime. Determineelapsedtime.

Addandsubtractunitsoftime.

Temperature Temperature Read a Fahrenheit thermometer.

Choose the appropriate tool and unit to measure temperature.

Usereferentstoestimatetemperature.

Angles Angles Compare angles to right angles.

Estimate and measure angles withaprotractor.

Applytheideathatthesumofangles on a straight line is180°.

Classifyanglesbyanglemeasure.

Applytheideathatverticalanglesareequalinmeasure.

Relate1/4-,1/2-,3/4-,andfullturnstothenumberofrightangles.

Applytheideathatthesumofanglesatapointis360°.

Perimeter Perimeter Measureperimeterofplanefigures.

Findtheperimeterofcompositefigures.

25





Estimateandmeasurecapacityinlitersandmilliliters.

Convertamongmetricunitsofcapacity.

Time Nameandorderthedaysoftheweekandthemonthsoftheyear.

Readacalendartoidentifythedaysoftheweek,months,andseasonsof theyear.

Time

Recognizethecorrectwaytowritethedate.

UseA.M.andP.M.towritetime. Readtimeonadigitalclock.

Telltimetothehourandhalfhour.

Telltimetofiveminutes. Convertbetweenhoursandminutes.

Comparedurationsofevents. Findelapsedtime. Determineelapsedtime.

Addandsubtractunitsoftime.

Temperature Temperature Read a Fahrenheit thermometer.

Choose the appropriate tool and unit to measure temperature.

Usereferentstoestimatetemperature.

Angles Angles Compare angles to right angles.

Estimate and measure angles withaprotractor.

Applytheideathatthesumofangles on a straight line is180°.

Classifyanglesbyanglemeasure.

Applytheideathatverticalanglesareequalinmeasure.

Relate1/4-,1/2-,3/4-,andfullturnstothenumberofrightangles.


Perimeter Perimeter Measureperimeterofplanefigures.

Findtheperimeterofcompositefigures.

26



Perimeter (continued)


Choosetheappropriatetool,unit,andstrategytomeasureperimeter.

Solveproblemsinvolvingtheperimeterofsquares,rectangles,andcompositefigures.

Estimatetheperimeterofsurfacesandobjects.

Area Compare areas using non-standardunits.

Composeanddecomposetwo-dimensional shapes (foundationforunderstandingarea).


Area Find and compare the area ofplanefiguresindifferentsquareunits.

Explainareaasanattributeoftwo-dimensionalfigures.

Makedifferentplanefigureswiththesamearea.

Connect area measure to the areamodelformultiplication;useittojustifytheformulafortheareaofarectangle.

Findtheareaoftriangles.

Estimateareaofsmallandlargesurfaces.

Estimate and measure area in squareunits.

Compare the area and perimeteroftwoplanefigures.

Selectappropriateunits,strategies,andtoolstosolveareaproblems.

Findtheareaofrectanglesandcompositefigures.

Explaintherelationshipsamongareaformulasofdifferentpolygons.

Surface Area and Volume


Decomposesolidfigurestofindthesurfacearea.

Estimate and measure volume incubicunits.

Data Analysis Data Analysis

Classifying and Sorting

Understanding similarities anddifferencesinobjectsandshapes.

Sortandclassifygeometricshapes.

Sortandclassifytwo-andthree-dimensional shapes byproperties.



Sortingandclassifyingobjectsusingoneortwoattributes.

Sortingandclassifyingdatainordertomakegraphs.

Collectandorganizedatainpicturegraphs.

Collectandorganizedatainbargraphsandlineplots.

Constructlineplots,stem-and-leafplots,tables,andlinegraphs.

Representdatainadoublebargraph.

27





Choosetheappropriatetool,unit,andstrategytomeasureperimeter.

Solveproblemsinvolvingtheperimeterofsquares,rectangles,andcompositefigures.

Estimatetheperimeterofsurfacesandobjects.

Area Compare areas using non-standardunits.

Composeanddecomposetwo-dimensional shapes (foundationforunderstandingarea).


Area Find and compare the area ofplanefiguresindifferentsquareunits.

Explainareaasanattributeoftwo-dimensionalfigures.

Makedifferentplanefigureswiththesamearea.

Connect area measure to the areamodelformultiplication;useittojustifytheformulafortheareaofarectangle.

Findtheareaoftriangles.

Estimateareaofsmallandlargesurfaces.

Estimate and measure area in squareunits.

Compare the area and perimeteroftwoplanefigures.

Selectappropriateunits,strategies,andtoolstosolveareaproblems.

Findtheareaofrectanglesandcompositefigures.




Decomposesolidfigurestofindthesurfacearea.

Estimate and measure volume incubicunits.

Data Analysis Data Analysis


Understanding similarities anddifferencesinobjectsandshapes.

Sortandclassifygeometricshapes.

Sortandclassifytwo-andthree-dimensional shapes byproperties.



Sortingandclassifyingobjectsusingoneortwoattributes.

Sortingandclassifyingdatainordertomakegraphs.

Collectandorganizedatainpicturegraphs.

Collectandorganizedatainbargraphsandlineplots.

Constructlineplots,stem-and-leafplots,tables,andlinegraphs.


28


Data Analysis (continued) Data Analysis (continued)

Collect and Organize Data

Organizedataforapicturegraph.

Collectandorganizedataindifferentways.



Represent Data Representdatainpictographs. Represent measurements and datainpicturegraphs,tallycharts,andbargraphs.

Represent data in picture graphs.

Represent Data

Interpret/ Analyze Data

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,andrangeofadataset.

Probability Probability

Outcomes Outcomes Decidewhetheranoutcomeiscertain,morelikely,equallylikely,lesslikely,orimpossible.

Determineexperimentalprobabilityofanoutcome.

Expressing Probability


Expresstheprobabilityofaneventasafraction.

Comparetheresultsofanexperimentwiththeoreticalprobability.

Findallpossiblecombinationsbylisting,makingatreediagram,andmultiplying.

Problem Solving Problem Solving

Build Skills Through Problem Solving

Build skills in addition and subtractionthroughproblemsolving.

Buildskillsinaddition,subtraction,andmeasurementthroughproblemsolving.

Buildskillsinaddition,subtraction,multiplication,division,andmeasurementthroughproblemsolving.



Buildskillsinmultiplication,division,fractionconcepts,dataanalysis,andmeasurementthroughproblemsolving.

Buildskillsinmultiplication;division;fractionconcepts,decimals,ratios,andpercents;dataanalysis;andmeasurementthroughproblemsolving.

29


Data Analysis (continued) Data Analysis (continued)


Organizedataforapicturegraph.




Represent Data Representdatainpictographs. Represent measurements and datainpicturegraphs,tallycharts,andbargraphs.


Represent Data



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,andrangeofadataset.

Probability Probability

Outcomes Outcomes Decidewhetheranoutcomeiscertain,morelikely,equallylikely,lesslikely,orimpossible.

Determineexperimentalprobabilityofanoutcome.



Expresstheprobabilityofaneventasafraction.

Comparetheresultsofanexperimentwiththeoreticalprobability.

Findallpossiblecombinationsbylisting,makingatreediagram,andmultiplying.

Problem Solving Problem Solving


Build skills in addition and subtractionthroughproblemsolving.

Buildskillsinaddition,subtraction,andmeasurementthroughproblemsolving.




Buildskillsinmultiplication,division,fractionconcepts,dataanalysis,andmeasurementthroughproblemsolving.

Buildskillsinmultiplication;division;fractionconcepts,decimals,ratios,andpercents;dataanalysis;andmeasurementthroughproblemsolving.

30


Problem Solving (continued) Problem Solving (continued)

Solve Real-World Problems

Solvereal-worldproblemsinvolving addition and subtraction.


Solvereal-worldproblemsinvolvingaddition,subtraction,multiplication,division,andmeasurement.



Solvereal-worldproblemsinvolvingmultiplication,division,fractionconcepts,dataanalysis,andmeasurement.

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

Use Appropriate Strategies and Thinking Skills to Solve Problems

ApplyproblemsolvingstrategiesinPutonYourThinkingCap!andProblemSolvingactivities.




Use appropriate strategies to solvereal-worldproblems.


Apply and Explain Problem Solving

Solvereal-worldproblems. ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.

ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.





Explore Concepts

Usemodelstoexplainreasoning.

ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.


Explore Concepts




ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.





Investigate Mathematical Ideas

Investigateideaswithtwo-dimensionalshapes.

Further investigate mathematicalideasbycompleting critical thinking skillsactivities.





Further investigate mathematicalideasbycompleting critical thinking skills activities.

Identify, Demonstrate, and Explain Mathematical Proof

Demonstratethatonlyafewbigthingsfitintosmallspacesandmanysmallthingsfitintobigspaces.

Exploretransitivitybycomparinglengthsandweightsofthreedifferentobjects.

Demonstrate the inverse relationshipbetweenthe sizeofaunitandthenumberofunits.



Showthatsomefigurescanbeturned and not change shape orsize(rotationalsymmetry).

Applytheideathatthesumofanglesonastraightlineis180°.


Describe,sort,andclassifytwo-andthree-dimensionalshapes.

Identifyanddescribeattributesandpropertiesoftwo-andthree-dimensionalshapes.

Identify,describe,sort,andclassifytwo-andthree-dimensionalshapes.

Identifypairsofshapesthatshowaflip,slide,andturn.

Usepropertiesofsquaresandrectanglestosolveproblems.


31










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









Solvereal-worldproblems. ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.






Explore Concepts

Usemodelstoexplainreasoning.



Explore Concepts










Investigateideaswithtwo-dimensionalshapes.






Further investigate mathematicalideasbycompleting critical thinking skills activities.


Demonstratethatonlyafewbigthingsfitintosmallspacesandmanysmallthingsfitintobigspaces.

Exploretransitivitybycomparinglengthsandweightsofthreedifferentobjects.

Demonstrate the inverse relationshipbetweenthe sizeofaunitandthenumberofunits.



Showthatsomefigurescanbeturned and not change shape orsize(rotationalsymmetry).

Applytheideathatthesumofanglesonastraightlineis180°.


Describe,sort,andclassifytwo-andthree-dimensionalshapes.

Identifyanddescribeattributesandpropertiesoftwo-andthree-dimensionalshapes.

Identify,describe,sort,andclassifytwo-andthree-dimensionalshapes.

Identifypairsofshapesthatshowaflip,slide,andturn.

Usepropertiesofsquaresandrectanglestosolveproblems.


32



Identify, Demonstrate, and Explain Mathematical Proof (continued)


Interpretpicturegraphs,tallycharts,andbargraphs.

Interpret picture graphs withscales.


Interpretbargraphswithscales.

Analyzeadatasetbyfindingitsmean,median,mode,andrange.

Comparetheresultsofanexperimenttovalidatetheuseoftheoreticalprobability.

Identifyandextendrepeatingshapepatterns.

Identifyandextendgrowingnumberpatternsandrepeatingshapepatterns.


Createandanalyzemultiplication and division patterns.



Use a Variety of Reasoning Skills

Sortandclassifyusingattributes.





Usepropertiesofsquaresandrectanglestosolveproblemsaboutareaandperimeter.

Exploretherelationshipamonglists,treediagrams,and multiplication to calculate combinations.


Use the Commutative and Associativeproperties,and10sand1stosolvetwo-digitadditionandsubtractionproblems.

Exploretheinverserelationshipbetweenadditionandsubtraction.

Exploretheinverserelationshipbetweenmultiplicationanddivision.

Usepropertiesofmultiplication(including theDistributiveProperty)inestimationandmentalmath.

Use estimation to check reasonableness.

Use estimation to check reasonableness(whole-numberaddition,subtraction,multiplicationanddivision).

Communication Communication

Consolidate Mathematical Thinking

Consolidate thinking in independentactivities.

PresentmathematicalthinkingthroughMathJournalactivities.






Communicate with Peers, Teachers, and Others

Discuss mathematical ideas in paired and small-group activities.

Discuss mathematical ideas in Let’sExploreactivities.





Discuss mathematical ideas inLet’sExploreactivities.

Work together in pairs or groupsinLet’sExplore,Games,andotheractivities.

Work together in pairs or groups inLet’sExplore,Games,andotheractivities.




Share Mathematical Thinking

Share mathematical ideas in paired and small-group activities.

SharemathematicalideaswithothersduringLet’sExploreandHands-Onactivities.






33





Interpretpicturegraphs,tallycharts,andbargraphs.

Interpret picture graphs withscales.


Interpretbargraphswithscales.

Analyzeadatasetbyfindingitsmean,median,mode,andrange.

Comparetheresultsofanexperimenttovalidatetheuseoftheoreticalprobability.

Identifyandextendrepeatingshapepatterns.

Identifyandextendgrowingnumberpatternsandrepeatingshapepatterns.






Sortandclassifyusingattributes.





Usepropertiesofsquaresandrectanglestosolveproblemsaboutareaandperimeter.

Exploretherelationshipamonglists,treediagrams,and multiplication to calculate combinations.


Use the Commutative and Associativeproperties,and10sand1stosolvetwo-digitadditionandsubtractionproblems.

Exploretheinverserelationshipbetweenadditionandsubtraction.

Exploretheinverserelationshipbetweenmultiplicationanddivision.

Usepropertiesofmultiplication(including theDistributiveProperty)inestimationandmentalmath.

Use estimation to check reasonableness.

Use estimation to check reasonableness(whole-numberaddition,subtraction,multiplicationanddivision).

Communication Communication


Consolidate thinking in independentactivities.








Discuss mathematical ideas in paired and small-group activities.






Discuss mathematical ideas inLet’sExploreactivities.







Share mathematical ideas in paired and small-group activities.







34


Communication (continued) Communication (continued)

Express Mathematical Ideas

Expressideasinpairedandsmallgroupactivities.

ExpressideasinMathJournalactivities,usinglessonvocabulary.






Use chapter and lesson vocabularycorrectly.





Connections Connections

Recognize Con-nections in Mathematical Ideas

Understand the connection betweenquantitiesandwrittennumerals.

Understand the relationship betweencountingandadditionandsubtraction.

Examineandapplytheinverserelationshipbetweenadditionandsubtraction.


Applytheinverserelationshipbetweenmultiplicationanddivision.

Demonstrate that decimal notationisanextensionofthebase-tensystem.

Relatefractionsanddivision.

Understand the relationships amongthenumbersinfactfamilies.

Connect geometric concepts withunitfractions.


Examinetherelationshipbetweenfractionsanddecimals.

Understand the connection amongfractions,decimals,ratios,andpercentsaswaystorepresentpartsofawhole.

Connect addition and multiplication (repeated addition).

Connectsubtractionanddivision(repeatedsubtraction).

Connecttheunitsofcustomarycapacitytooneanother.

Makeconnectionsamongmultiplication,division,factors,andmultiples.

Examinetherelationshipsbetweenthree-dimensionalfiguresandthetwo-dimensionalfiguresthatformthem.

Recognizeandapplydifferentstrategiesforaddingandsubtracting one-andtwo-digitnumbers.

Recognizeandapplydifferentstrategiesformultiplicationanddivisionfacts.

Understand the relationships betweenthenumbersinmultiplication-divisionfactfamilies.

Convertamongmixednumbersandimproperfractions.


Understand How Concepts Build on One Another

Explorerelationshipsamongcounting,ordering,andordinalnumbers.

Learnhowplacevalueconceptsapplytoregroupinginadditionandsubtraction.

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 notationisanextensionofthebase-tensystem.


Understand the relationships amongthenumbersinfactfamilies.

Connect geometric concepts withunitfractions.


Examinetherelationshipbetweenfractionsanddecimals.

Understand the connection amongfractions,decimals,ratios,andpercentsaswaystorepresentpartsofawhole.

Connect addition and multiplication (repeated addition).

Connectsubtractionanddivision(repeatedsubtraction).

Connecttheunitsofcustomarycapacitytooneanother.

Makeconnectionsamongmultiplication,division,factors,andmultiples.

Examinetherelationshipsbetweenthree-dimensionalfiguresandthetwo-dimensionalfiguresthatformthem.

Recognizeandapplydifferentstrategiesforaddingandsubtracting one-andtwo-digitnumbers.

Recognizeandapplydifferentstrategiesformultiplicationanddivisionfacts.

Understand the relationships betweenthenumbersinmultiplication-divisionfactfamilies.

Convertamongmixednumbersandimproperfractions.



Explorerelationshipsamongcounting,ordering,andordinalnumbers.

Learnhowplacevalueconceptsapplytoregroupinginadditionandsubtraction.

Understandhowpatternscanbedescribedusingnumbers,operations,anddatadisplays.






Connectequivalentfractions,decimals,andpercents.

Recognizetherelationshipbetweenbarmodels,numbersentences,andnumberpatterns.

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

Makeconnectionsamongthegreatestcommonfactor,leastcommonmultiple,andoperationswithfractions.

36


Connections (continued) Connections (continued)

Solve Real-World Problems in Contexts Outside of Mathematics

Solvereal-worldproblemsinvolvingmoreandless.

Solvereal-worldproblems involvingaddition,subtraction,andmeasurement.

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




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

Solvereal-worldproblemsrelatedtomoney.

Compareexperimentalresultsandtheoreticalprobability.

Representation Representation

Use Representations to Model, Organize, and Record

Use concrete models to create asetwithagivennumberofobjects(upto20).


Use concrete and pictorial modelstocreateasetwith agivennumberofobjects(upto1,000).


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


Explorenegativenumbersincontext.

Usenumbersandnumeralstorepresentquantitiesupto20.



Representnumbersindifferentequivalentforms.



Use picture cards to communicate understanding ofcomparisons(biggerandsmaller).

Usenumberbondstorepresentnumbers.



Usesymbolicnotation(<and>)tocomparenumbers.


Modeldecimalstotenthsandhundredths.



Usethe+,−,and=symbolstorepresentreal-worldadditionandsubtractionsituations.

Usebarmodelstorepresentadditionandsubtractionsituations.

Solveadditionandsubtractionproblemswithgreaternumbersbyusingabarmodel

Writeadditionandsubtractionnumbersentencesforreal-worldproblemswithfractionsanddecimals.

Exploretheuseoflettersasvariablesinexpressionsandinequalities.


Represent numerical data usingpicturegraphs,tallycharts,andbargraphs.

Represent numerical data using picturegraphswithscales,tallycharts,andbargraphs.

Represent multiplication and divisionindifferentways.

Usemodelstoshowrelationshipsbetweenimproperfractionsandmixednumbers.

Convertfractionsanddecimalstopercents.



Useavarietyofrepresentationsformultiplicationanddivision,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-worldproblemsinvolvingmultiplication;division;fraction,decimal,ratio,andpercentconcepts;dataanalysis;andmeasurement.


Compareexperimentalresultsandtheoreticalprobability.

Representation Representation


Use concrete models to create asetwithagivennumberofobjects(upto20).


Use concrete and pictorial modelstocreateasetwith agivennumberofobjects(upto1,000).


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


Explorenegativenumbersincontext.

Usenumbersandnumeralstorepresentquantitiesupto20.



Representnumbersindifferentequivalentforms.



Use picture cards to communicate understanding ofcomparisons(biggerandsmaller).

Usenumberbondstorepresentnumbers.



Usesymbolicnotation(<and>)tocomparenumbers.


Modeldecimalstotenthsandhundredths.



Usethe+,−,and=symbolstorepresentreal-worldadditionandsubtractionsituations.

Usebarmodelstorepresentadditionandsubtractionsituations.

Solveadditionandsubtractionproblemswithgreaternumbersbyusingabarmodel


Exploretheuseoflettersasvariablesinexpressionsandinequalities.


Represent numerical data usingpicturegraphs,tallycharts,andbargraphs.

Represent numerical data using picturegraphswithscales,tallycharts,andbargraphs.

Represent multiplication and divisionindifferentways.

Usemodelstoshowrelationshipsbetweenimproperfractionsandmixednumbers.

Convertfractionsanddecimalstopercents.



Useavarietyofrepresentationsformultiplicationanddivision,suchasarrays,areamodels,numberlines,grouping,andsharing.


Representcombinationswithlists,treediagrams,andmultiplication.

38


Representation (continued) Representation (continued)

Use Representations to Model, Organize, and Record (continued)

Representmultiplicationwithskipcounting,dotpaperarrays,andbarmodels.





Represent division as repeated subtractionsentences.

Describeandextendshapepatterns.








Identifyarulefornumberandcountingpatterns.



Select and Apply Representations to Model Problems

Representquantitieswithobjects,numbercubes,andnumerals.




Useavarietyofmodelstorepresentfractionsandequivalentfractions.

Translatebetweenequivalentimproperfractionsandmixednumbers.

Translatebetweenfractionsandpercents.




Useavarietyofmodelsformulti-digit multiplication and divisionofwholenumbers.

Selectthemostusefulformofthequotient.

Representmultiplicationwithskipcountingandarrays.

Usecustomaryunits(includingfractions)tomeasurelength,weight,andcapacity.

Useavarietyofmodelsforadditionandsubtractionoffractionsanddecimals.

Useanettofindthesurfaceareaofaprism.

Interpret Phenomena through Representations

Showunderstandingofbig,middle-sized,small,andsamesize.

Measureandcomparelengthsandweightsusingnon-standardunits.

Usemetricandcustomaryunitstomeasurelength,volume(capacity),weight,andmass.


Usereferentstoestimatelength,capacity,andweight.

Measureperimeterandareaincustomaryandmetricunits.

Measurevolumeofarectangularprism.



39




Representmultiplicationwithskipcounting,dotpaperarrays,andbarmodels.





Represent division as repeated subtractionsentences.

Describeandextendshapepatterns.








Identifyarulefornumberandcountingpatterns.




Representquantitieswithobjects,numbercubes,andnumerals.




Useavarietyofmodelstorepresentfractionsandequivalentfractions.

Translatebetweenequivalentimproperfractionsandmixednumbers.

Translatebetweenfractionsandpercents.




Useavarietyofmodelsformulti-digit multiplication and divisionofwholenumbers.

Selectthemostusefulformofthequotient.

Representmultiplicationwithskipcountingandarrays.

Usecustomaryunits(includingfractions)tomeasurelength,weight,andcapacity.

Useavarietyofmodelsforadditionandsubtractionoffractionsanddecimals.

Useanettofindthesurfaceareaofaprism.


Showunderstandingofbig,middle-sized,small,andsamesize.

Measureandcomparelengthsandweightsusingnon-standardunits.

Usemetricandcustomaryunitstomeasurelength,volume(capacity),weight,andmass.


Usereferentstoestimatelength,capacity,andweight.

Measureperimeterandareaincustomaryandmetricunits.

Measurevolumeofarectangularprism.



40



Interpret Phenomena through Representations (continued)


Identifyreal-worldtwo-andthree-dimensionalshapes.


Usefrequencytables,bargraphs,picturegraphs,andlineplotstosolveproblems.

Collectdataandorganizeitinatable.


Represent measurements and datainpicturegraphsandbargraphs.


Representdatainbargraphsandpicturegraphs.

Createalinegraphfromdatainatable.

Represent an equation as a graphedline.

Orderanumberofobjectsaccordingtolength,height,orweight.

Solveproblemsaboutsharingequallyandmakingequalgroups.

Solvereal-worldproblemsaboutsocialphenomena.

Solvereal-worldproblemsinvolvingsocialsituations.

Usemeasuresofcentraltendencytodescribetypicalvaluesofdatasets(social).

Use one-to-one correspondence.

Useavarietyofmodelsforaddingandsubtracting.

Usebarmodelstorepresentaddition,subtraction,multiplication,anddivisionsituations.




Usetechnology(virtualmanipulativesandcomputers)tomodelanddraw.





Useacalculatortomodel,compute,andsolveproblems.

41





Identifyreal-worldtwo-andthree-dimensionalshapes.


Usefrequencytables,bargraphs,picturegraphs,andlineplotstosolveproblems.

Collectdataandorganizeitinatable.


Represent measurements and datainpicturegraphsandbargraphs.


Representdatainbargraphsandpicturegraphs.

Createalinegraphfromdatainatable.

Represent an equation as a graphedline.

Orderanumberofobjectsaccordingtolength,height,orweight.

Solveproblemsaboutsharingequallyandmakingequalgroups.

Solvereal-worldproblemsaboutsocialphenomena.


Usemeasuresofcentraltendencytodescribetypicalvaluesofdatasets(social).

Use one-to-one correspondence.

Useavarietyofmodelsforaddingandsubtracting.

Usebarmodelstorepresentaddition,subtraction,multiplication,anddivisionsituations.









Useacalculatortomodel,compute,andsolveproblems.

42

Aligned with National and International Research Recommendations

NationalMathAdvisoryPanel

“Useshouldbemadeofwhatisclearlyknownfrom

rigorousresearchabouthowchildrenlearn,especiallyby

recognizingthemutually-reinforcingbenefitsofconceptual

understanding,proceduralfluency,andautomatic(i.e.,

quickandeffortless)recalloffacts.”

—Foundations for Success,2008

Math in Focusaddresses fewer topics in greater depth

at each level.

• Knowledgeisbuiltcarefullyandthoroughlywithboth

multi-page lessons and multi-daylessons.

• Timeisbuiltintotheprogramtodevelopunderstanding

withhands-on activitieswithmanipulatives,aswellas

extensive skills practice.

Math in Focusdevelops concepts and skills in tandem.

• Manipulativesandvisualrepresentationsprovidea

conceptualbackbone.

• Skills are connected to concepts through visual

representations.

• Extensiveproblemsolvingmerges conceptual

understanding with computational skills.

NationalCouncilofTeachersofMathematics

“Acurriculumismorethanacollectionofactivities:itmust

becoherent,focusedonimportantmathematics,andwell

articulatedacrossthegrades.”

—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

SingaporeMinistryofEducation

“Mathematicalproblemsolvingiscentraltomathematics

learning.Itinvolvestheacquisitionandapplication

ofmathematicsconceptsandskillsinawiderangeof

situations,includingnon-routine,

open-ended,andreal-worldproblems.”

—Mathematics Syllabus: Primary,2006

Bar Model: a visual

representationofa

wordproblem

(Grade2)

Math in Focususes a scaffolded approach to solving word

problems, focusing on model drawing to

build success and confidence.

• Thevisualrepresentationofwordproblemsleadsto

symbolicsolutionsofrich and complex problems.

• Studentsdrawonpriorknowledge,aswellasrecently

acquiredconceptsandskills,astheycombineproblem

solving strategies with critical thinking skills.

Emphasis on Problem Solving

NationalResearchCouncil

“Opportunitiesshouldinvolveconnectingsymbolic

representationsandoperationswithphysicalorpictorial

representations,aswellastranslatingbetweenvarious

symbolicrepresentations.”

—Adding It Up: Helping Children Learn Mathematics,2001

Math in Focususes clear and engaging visuals that present

concepts and model solutions.

• Minimal textandsimple,directvisualsallowallstudents,

regardlessoflanguageskills,tofocusonthemathlesson.

• Theuseofmodel drawingsofferavisualrepresentationof

wordproblems,leadingtosymbolicsolutionsofrichand

complexproblems.

• Consistentuseoftheconcrete–pictorial–abstract pedagogy

repeatedly“models”themodel-drawingproblemsolving

strategy.

Number Bonds: a visual

forcomposingand

decomposingnumbers

(Grade1)

Clear Visuals and Use of Models

104

6

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hmheducation.com/singaporemath•800.289.4490

Grade K

Grade 3

Grade 1

Grade 4

Grade 2

Grade 5

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

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