Grades K–5 Scope and Sequence Your 1 Choice for …4 Kindergarten Grade 1 Grade 2 Grade 3 Grade 4...
Transcript of Grades K–5 Scope and Sequence Your 1 Choice for …4 Kindergarten Grade 1 Grade 2 Grade 3 Grade 4...
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
3
Concept and skill development through hands-on instruction and practice
Key Differences and Distinguishing Characteristics
• basicfacts
• placevalue
• mentalmath
• geometryconcepts
• fractions• decimals
• ratios• modeldrawing
• expressions,equations,andinequalities
Scope and Sequence Grades K–5
Articulated SequenceMath in 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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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.
Number Representation
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.
Compareandorderwholenumbersto100,000.
Compareandorderwholenumbersto10,000,000.
Compare and order using the terms fewer,more,andless.
Compare and order using the terms same,more,fewer,greater than,less than,equal to,greatest,andleast.
Use<,>,and=tocomparewholenumbers.
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 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.
Number Representation
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.
Compareandorderwholenumbersto100,000.
Compareandorderwholenumbersto10,000,000.
Compare and order using the terms fewer,more,andless.
Compare and order using the terms same,more,fewer,greater than,less than,equal to,greatest,andleast.
Use<,>,and=tocomparewholenumbers.
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 (continued) Number and Operations (continued)
Place Value (continued)
Expressnumbersto100instandardandwordforms.
Expressnumbersto1,000 intermsofplacevalue.
Place Value (continued)
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.
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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Number and Operations (continued) Number and Operations (continued)
Place Value (continued)
Expressnumbersto100instandardandwordforms.
Expressnumbersto1,000 intermsofplacevalue.
Place Value (continued)
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.
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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Number and Operations (continued) Number and Operations (continued)
Decimal Concepts (continued)
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
Ratio, Proportion, and Percent
Useratiostosolveproblems.
Findequivalentratios.
Solveproblemswithpercent.
Convertfractionstopercents.
Findapercentofanumber.
Whole Number Computation: Addition and Subtraction
Modeljoiningandseparatingsets.
Modeladditionandsubtractionsituations.
Modeladditionandsubtractionwithplacevalue.
Whole Number Computation: Addition and Subtraction
Modelregroupinginadditionandsubtractionwithplacevalue.
Use+,-,and=towritenumbersentencesforadditionandsubtractionstories.
Usemodels,numbers,andsymbolsforadditionandsubtractionfactsto20.
Recalladditionandsubtractionfacts.
Usetheorder,grouping,andzeropropertiestodevelopadditionandsubtractionfactstrategies.
Use different methods to developfluencyinaddingandsubtractingmulti-digitnumbers.
Addandsubtractupto2-digitnumberswithandwithoutregrouping
Addandsubtractwholenumbersto1,000.
Addandsubtractwholenumbersto10,000.
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Number and Operations (continued) Number and Operations (continued)
Decimal Concepts (continued)
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
Ratio, Proportion, and Percent
Useratiostosolveproblems.
Findequivalentratios.
Solveproblemswithpercent.
Convertfractionstopercents.
Findapercentofanumber.
Whole Number Computation: Addition and Subtraction
Modeljoiningandseparatingsets.
Modeladditionandsubtractionsituations.
Modeladditionandsubtractionwithplacevalue.
Whole Number Computation: Addition and Subtraction
Modelregroupinginadditionandsubtractionwithplacevalue.
Use+,-,and=towritenumbersentencesforadditionandsubtractionstories.
Usemodels,numbers,andsymbolsforadditionandsubtractionfactsto20.
Recalladditionandsubtractionfacts.
Usetheorder,grouping,andzeropropertiestodevelopadditionandsubtractionfactstrategies.
Use different methods to developfluencyinaddingandsubtractingmulti-digitnumbers.
Addandsubtractupto2-digitnumberswithandwithoutregrouping
Addandsubtractwholenumbersto1,000.
Addandsubtractwholenumbersto10,000.
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Number and Operations (continued) Number and Operations (continued)
Whole Number Computation: Addition and Subtraction Real-World Problems
Represent addition and subtractionstories.
Formulate addition and subtractionstories.
Whole Number Computation: Addition and Subtraction Real-World Problems
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.
Whole Number Computation: Multiplication and Division Concepts
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
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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Number and Operations (continued) Number and Operations (continued)
Whole Number Computation: Addition and Subtraction Real-World Problems
Represent addition and subtractionstories.
Formulate addition and subtractionstories.
Whole Number Computation: Addition and Subtraction Real-World Problems
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.
Whole Number Computation: Multiplication and Division Concepts
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
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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Number and Operations (continued) Number and Operations (continued)
Whole Number Computation: Multiplication and Division Real-World Problems
Usebarmodelstorepresentmultiplication and division situations.
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).
Fraction Computation
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 to addandsubtract.
Estimation and Mental Math
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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Number and Operations (continued) Number and Operations (continued)
Whole Number Computation: Multiplication and Division Real-World Problems
Usebarmodelstorepresentmultiplication and division situations.
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).
Fraction Computation
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 to addandsubtract.
Estimation and Mental Math
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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Number and Operations (continued) Number and Operations (continued)
Estimation and Mental Math (continued)
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
Identifyoddandevennumbers.
Find the greatest common factorandleastcommonmultiple.
Identifyprimeandcompositenumbers.
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Number and Operations (continued) Number and Operations (continued)
Estimation and Mental Math (continued)
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
Identifyoddandevennumbers.
Find the greatest common factorandleastcommonmultiple.
Identifyprimeandcompositenumbers.
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Algebra (continued) Alegbra (continued)
Functional Relationships
Understand the relationships betweenthenumbersinfactfamilies.
Recognizehowbarmodelsshowrelationshipsbetweennumbersandunknownsinnumbersentences.
Functional Relationships
Understand the relationships betweenthenumbersinmultiplicationanddivisionfactfamilies.
Understand the relationships betweenthenumbersandsymbolsinformulasforareaandperimeter.
Understand the relationships betweenthenumbersandsymbolsinformulasforsurfaceareaandvolume.
Describenumberrelationshipsincontext.
Describenumberrelationshipsincontext.
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.
Number Sentences and Equations
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.
Determine the missing parts (quantitiesorsymbols)innumbersentences.
Graphlinearequations.
Equality and In-equality
Understandthemeaningofthe=signinnumbersentences.
Understand the difference betweenequalityandinequality.
Use and create models that demonstrateequalityorinequality.
Equality and In-equality
Understandequalityandinequality.
Understandequalityandinequality.
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)
Functional Relationships
Understand the relationships betweenthenumbersinfactfamilies.
Recognizehowbarmodelsshowrelationshipsbetweennumbersandunknownsinnumbersentences.
Functional Relationships
Understand the relationships betweenthenumbersinmultiplicationanddivisionfactfamilies.
Understand the relationships betweenthenumbersandsymbolsinformulasforareaandperimeter.
Understand the relationships betweenthenumbersandsymbolsinformulasforsurfaceareaandvolume.
Describenumberrelationshipsincontext.
Describenumberrelationshipsincontext.
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.
Number Sentences and Equations
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.
Determine the missing parts (quantitiesorsymbols)innumbersentences.
Graphlinearequations.
Equality and In-equality
Understandthemeaningofthe=signinnumbersentences.
Understand the difference betweenequalityandinequality.
Use and create models that demonstrateequalityorinequality.
Equality and In-equality
Understandequalityandinequality.
Understandequalityandinequality.
Understandequalityandinequality.
Use<,>,and=towritenumbersentences.
Writeandsolveinequalities.
Geometry Geometry
Size and Position
Understandbig,middle-sized,andsmall.
Describepositionwithleftandright.
Size and Position
18
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Geometry (continued) Geometry (continued)
Size and Position (continued)
Describeandcompareobjectsbyposition.
Usepositionalwordstodescribelocation.
Size and Position (continued)
Lines and Angles
Identifypartsoflinesandcurves.
Lines and Angles
Identifyperpendicularandparallellines.
Drawperpendicularandparallellines.
Workwithanglesonastraightline.
Identifyrightanglesandcompare angles to right angles.
Constructandmeasureangles. Workwithanglesatapoint.
Two- Dimensional Shapes
Identifysimilaritiesanddifferences.
Two- Dimensional Shapes
Nameflatshapesthatmakeupreal-worldobjects.
Identifyreal-worldtwo-dimensionalshapes.
Identify,describe,sort,andclassifytwo-dimensionalshapes.
Identifyanddescribeattributesandpropertiesoftwo-dimensionalshapes.
Identify,describe,sort,andclassifytwo-dimensionalshapes.
Describe,analyze,compare,andclassifytwo-dimensionalshapesbytheirsidesandangles.
Applythepropertiesofsquaresandrectangles.
Applythepropertiesofright,isosceles,andequilateraltriangles.
Sortandclassifytwo-dimensionalshapes.
Identifypartsoflinesandcurves.
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.
Understand the relationships betweenthenumbersandsymbolsinformulasforareaandperimeter.
Findtheareaofatriangle.
Three- Dimensional Shapes
Nameandsortsolidshapes. Identifyreal-worldthree-dimensionalshapes.
Three- Dimensional Shapes
Identifyandclassifyprismsandpyramids.
Understand that three-dimensional shapes are made upoftwo-dimensionalshapes.
Identifytwo-dimensionalshapes in three-dimensional shapes.
Identify,describe,sort,andclassifythree-dimensionalshapes.
Identifythesolidthatcanbemadefromanet.
19
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Geometry (continued) Geometry (continued)
Size and Position (continued)
Describeandcompareobjectsbyposition.
Usepositionalwordstodescribelocation.
Size and Position (continued)
Lines and Angles
Identifypartsoflinesandcurves.
Lines and Angles
Identifyperpendicularandparallellines.
Drawperpendicularandparallellines.
Workwithanglesonastraightline.
Identifyrightanglesandcompare angles to right angles.
Constructandmeasureangles. Workwithanglesatapoint.
Two- Dimensional Shapes
Identifysimilaritiesanddifferences.
Two- Dimensional Shapes
Nameflatshapesthatmakeupreal-worldobjects.
Identifyreal-worldtwo-dimensionalshapes.
Identify,describe,sort,andclassifytwo-dimensionalshapes.
Identifyanddescribeattributesandpropertiesoftwo-dimensionalshapes.
Identify,describe,sort,andclassifytwo-dimensionalshapes.
Describe,analyze,compare,andclassifytwo-dimensionalshapesbytheirsidesandangles.
Applythepropertiesofsquaresandrectangles.
Applythepropertiesofright,isosceles,andequilateraltriangles.
Sortandclassifytwo-dimensionalshapes.
Identifypartsoflinesandcurves.
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.
Understand the relationships betweenthenumbersandsymbolsinformulasforareaandperimeter.
Findtheareaofatriangle.
Three- Dimensional Shapes
Nameandsortsolidshapes. Identifyreal-worldthree-dimensionalshapes.
Three- Dimensional Shapes
Identifyandclassifyprismsandpyramids.
Understand that three-dimensional shapes are made upoftwo-dimensionalshapes.
Identifytwo-dimensionalshapes in three-dimensional shapes.
Identify,describe,sort,andclassifythree-dimensionalshapes.
Identifythesolidthatcanbemadefromanet.
20
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Geometry (continued) Geometry (continued)
Three- Dimensional Shapes (continued)
Sortandclassifythree-dimensionalshapes.
Identifysurfacesthatslide,stack,androll.
Three- Dimensional Shapes (continued)
Identifycylinders,spheres,andcones.
Recognizeshapesfromdifferentperspectives.
Describecylinders,spheres,andconesbythenumberofandtypesoffaces,andthenumberofedgesandvertices.
Compose and decompose three-dimensionalshapes.
Buildsolidsusingunitcubes.
Congruence and Symmetry
Develop initial understanding ofcongruenceandsymmetry.
Congruence and Symmetry
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.
Length and Dis-tance
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
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Geometry (continued) Geometry (continued)
Three- Dimensional Shapes (continued)
Sortandclassifythree-dimensionalshapes.
Identifysurfacesthatslide,stack,androll.
Three- Dimensional Shapes (continued)
Identifycylinders,spheres,andcones.
Recognizeshapesfromdifferentperspectives.
Describecylinders,spheres,andconesbythenumberofandtypesoffaces,andthenumberofedgesandvertices.
Compose and decompose three-dimensionalshapes.
Buildsolidsusingunitcubes.
Congruence and Symmetry
Develop initial understanding ofcongruenceandsymmetry.
Congruence and Symmetry
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.
Length and Dis-tance
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.
22
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Measurement (continued) Measurement (continued)
Length and Dis-tance (continued)
Explaintheneedforequal-lengthunitstomeasure.
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
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Measurement (continued) Measurement (continued)
Length and Dis-tance (continued)
Explaintheneedforequal-lengthunitstomeasure.
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.
24
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Measurement (continued) Measurement (continued)
Capacity/ Volume (continued)
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
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Measurement (continued) Measurement (continued)
Capacity/ Volume (continued)
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.
26
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Measurement (continued) Measurement (continued)
Perimeter (continued)
Perimeter (continued)
Choosetheappropriatetool,unit,andstrategytomeasureperimeter.
Solveproblemsinvolvingtheperimeterofsquares,rectangles,andcompositefigures.
Estimatetheperimeterofsurfacesandobjects.
Area Compare areas using non-standardunits.
Composeanddecomposetwo-dimensional shapes (foundationforunderstandingarea).
Developfoundationsforunderstandingarea.
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
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.
Classifying and Sorting
Classifyandsortpolygonsandquadrilateralsbyattributesandproperties.
Sortingandclassifyingobjectsusingoneortwoattributes.
Sortingandclassifyingdatainordertomakegraphs.
Collectandorganizedatainpicturegraphs.
Collectandorganizedatainbargraphsandlineplots.
Constructlineplots,stem-and-leafplots,tables,andlinegraphs.
Representdatainadoublebargraph.
27
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Measurement (continued) Measurement (continued)
Perimeter (continued)
Perimeter (continued)
Choosetheappropriatetool,unit,andstrategytomeasureperimeter.
Solveproblemsinvolvingtheperimeterofsquares,rectangles,andcompositefigures.
Estimatetheperimeterofsurfacesandobjects.
Area Compare areas using non-standardunits.
Composeanddecomposetwo-dimensional shapes (foundationforunderstandingarea).
Developfoundationsforunderstandingarea.
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
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.
Classifying and Sorting
Classifyandsortpolygonsandquadrilateralsbyattributesandproperties.
Sortingandclassifyingobjectsusingoneortwoattributes.
Sortingandclassifyingdatainordertomakegraphs.
Collectandorganizedatainpicturegraphs.
Collectandorganizedatainbargraphsandlineplots.
Constructlineplots,stem-and-leafplots,tables,andlinegraphs.
Representdatainadoublebargraph.
28
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Data Analysis (continued) Data Analysis (continued)
Collect and Organize Data
Organizedataforapicturegraph.
Collectandorganizedataindifferentways.
Collectandorganizedataindifferentways.
Collect and Organize Data
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.
Interpret/ Analyze Data
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
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.
Build Skills Through Problem Solving
Buildskillsinaddition,subtraction,multiplication,division,andmeasurementthroughproblemsolving.
Buildskillsinmultiplication,division,fractionconcepts,dataanalysis,andmeasurementthroughproblemsolving.
Buildskillsinmultiplication;division;fractionconcepts,decimals,ratios,andpercents;dataanalysis;andmeasurementthroughproblemsolving.
29
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Data Analysis (continued) Data Analysis (continued)
Collect and Organize Data
Organizedataforapicturegraph.
Collectandorganizedataindifferentways.
Collectandorganizedataindifferentways.
Collect and Organize Data
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.
Interpret/ Analyze Data
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
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.
Build Skills Through Problem Solving
Buildskillsinaddition,subtraction,multiplication,division,andmeasurementthroughproblemsolving.
Buildskillsinmultiplication,division,fractionconcepts,dataanalysis,andmeasurementthroughproblemsolving.
Buildskillsinmultiplication;division;fractionconcepts,decimals,ratios,andpercents;dataanalysis;andmeasurementthroughproblemsolving.
30
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Problem Solving (continued) Problem Solving (continued)
Solve Real-World Problems
Solvereal-worldproblemsinvolving addition and subtraction.
Solvereal-worldproblemsinvolving addition and subtraction.
Solvereal-worldproblemsinvolvingaddition,subtraction,multiplication,division,andmeasurement.
Solve Real-World Problems
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.
ApplyproblemsolvingstrategiesinPutonYourThinkingCap!andProblemSolvingactivities.
Use Appropriate Strategies and Thinking Skills to Solve Problems
ApplyproblemsolvingstrategiesinPutonYourThinkingCap!andProblemSolvingactivities.
Use appropriate strategies to solvereal-worldproblems.
Use appropriate strategies to solvereal-worldproblems.
Apply and Explain Problem Solving
Solvereal-worldproblems. ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
Apply and Explain Problem Solving
ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
Explore Concepts
Usemodelstoexplainreasoning.
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
Explore Concepts
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
Investigate Mathematical Ideas
Investigateideaswithtwo-dimensionalshapes.
Further investigate mathematicalideasbycompleting critical thinking skillsactivities.
Further investigate mathematicalideasbycompleting critical thinking skillsactivities.
Investigate Mathematical Ideas
Further investigate mathematicalideasbycompleting critical thinking skillsactivities.
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.
Identify, Demonstrate, and Explain Mathematical Proof
Demonstratethatfiguresandtheirflip,slide,andturnimagesarecongruent.
Showthatsomefigurescanbeturned and not change shape orsize(rotationalsymmetry).
Applytheideathatthesumofanglesonastraightlineis180°.
Applytheideathatthesumofanglesatapointis360°.
Describe,sort,andclassifytwo-andthree-dimensionalshapes.
Identifyanddescribeattributesandpropertiesoftwo-andthree-dimensionalshapes.
Identify,describe,sort,andclassifytwo-andthree-dimensionalshapes.
Identifypairsofshapesthatshowaflip,slide,andturn.
Usepropertiesofsquaresandrectanglestosolveproblems.
Explaintherelationshipsamongareaformulasofdifferentpolygons.
31
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Problem Solving (continued) Problem Solving (continued)
Solve Real-World Problems
Solvereal-worldproblemsinvolving addition and subtraction.
Solvereal-worldproblemsinvolving addition and subtraction.
Solvereal-worldproblemsinvolvingaddition,subtraction,multiplication,division,andmeasurement.
Solve Real-World Problems
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.
ApplyproblemsolvingstrategiesinPutonYourThinkingCap!andProblemSolvingactivities.
Use Appropriate Strategies and Thinking Skills to Solve Problems
ApplyproblemsolvingstrategiesinPutonYourThinkingCap!andProblemSolvingactivities.
Use appropriate strategies to solvereal-worldproblems.
Use appropriate strategies to solvereal-worldproblems.
Apply and Explain Problem Solving
Solvereal-worldproblems. ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
Apply and Explain Problem Solving
ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
ApplyandexplainproblemsolvingprocessesinPutonYourThinkingCap!andotheractivities.
Explore Concepts
Usemodelstoexplainreasoning.
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
Explore Concepts
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
ExploreconceptsmoredeeplyandjustifyreasoninginLet’sExploreandHands-Onactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
ApplyThinkingSkills,PutonYourThinkingCap!,ChallengingPractice,andProblemSolvingactivities.
Investigate Mathematical Ideas
Investigateideaswithtwo-dimensionalshapes.
Further investigate mathematicalideasbycompleting critical thinking skillsactivities.
Further investigate mathematicalideasbycompleting critical thinking skillsactivities.
Investigate Mathematical Ideas
Further investigate mathematicalideasbycompleting critical thinking skillsactivities.
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.
Identify, Demonstrate, and Explain Mathematical Proof
Demonstratethatfiguresandtheirflip,slide,andturnimagesarecongruent.
Showthatsomefigurescanbeturned and not change shape orsize(rotationalsymmetry).
Applytheideathatthesumofanglesonastraightlineis180°.
Applytheideathatthesumofanglesatapointis360°.
Describe,sort,andclassifytwo-andthree-dimensionalshapes.
Identifyanddescribeattributesandpropertiesoftwo-andthree-dimensionalshapes.
Identify,describe,sort,andclassifytwo-andthree-dimensionalshapes.
Identifypairsofshapesthatshowaflip,slide,andturn.
Usepropertiesofsquaresandrectanglestosolveproblems.
Explaintherelationshipsamongareaformulasofdifferentpolygons.
32
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Problem Solving (continued) Problem Solving (continued)
Identify, Demonstrate, and Explain Mathematical Proof (continued)
Interpretdataintallychartsandpictographs.
Interpretpicturegraphs,tallycharts,andbargraphs.
Interpret picture graphs withscales.
Identify, Demonstrate, and Explain Mathematical Proof (continued)
Interpretbargraphswithscales.
Analyzeadatasetbyfindingitsmean,median,mode,andrange.
Comparetheresultsofanexperimenttovalidatetheuseoftheoreticalprobability.
Identifyandextendrepeatingshapepatterns.
Identifyandextendgrowingnumberpatternsandrepeatingshapepatterns.
Identifyrulesfornumberpatterns.
Createandanalyzemultiplication and division patterns.
Identify,describe,andextendnumeric and non-numeric patterns.
Identify,describe,andextendnumeric patterns involving alloperations.
Use a Variety of Reasoning Skills
Sortandclassifyusingattributes.
Recognizeshapesfromdifferentperspectives.
Identifysurfacesthatslide,stack,androll.
Use a Variety of Reasoning Skills
Model,define,andexplainpropertiesofmultiplication.
Usepropertiesofsquaresandrectanglestosolveproblemsaboutareaandperimeter.
Exploretherelationshipamonglists,treediagrams,and multiplication to calculate combinations.
Identifysimilaritiesanddifferences.
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.
PresentmathematicalthinkingthroughMathJournalactivities.
Consolidate Mathematical Thinking
PresentmathematicalthinkingthroughMathJournalactivities.
PresentmathematicalthinkingthroughMathJournalactivities.
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 in Let’sExploreactivities.
Communicate with Peers, Teachers, and Others
Discuss mathematical ideas in Let’sExploreactivities.
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.
Work together in pairs or groupsinLet’sExplore,Games,andotheractivities.
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.
SharemathematicalideaswithothersduringLet’sExploreandHands-Onactivities.
Share Mathematical Thinking
SharemathematicalideaswithothersduringLet’sExploreandHands-Onactivities.
SharemathematicalideaswithothersduringLet’sExploreandHands-Onactivities.
SharemathematicalideaswithothersduringLet’sExploreandHands-Onactivities.
33
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Problem Solving (continued) Problem Solving (continued)
Identify, Demonstrate, and Explain Mathematical Proof (continued)
Interpretdataintallychartsandpictographs.
Interpretpicturegraphs,tallycharts,andbargraphs.
Interpret picture graphs withscales.
Identify, Demonstrate, and Explain Mathematical Proof (continued)
Interpretbargraphswithscales.
Analyzeadatasetbyfindingitsmean,median,mode,andrange.
Comparetheresultsofanexperimenttovalidatetheuseoftheoreticalprobability.
Identifyandextendrepeatingshapepatterns.
Identifyandextendgrowingnumberpatternsandrepeatingshapepatterns.
Identifyrulesfornumberpatterns.
Createandanalyzemultiplication and division patterns.
Identify,describe,andextendnumeric and non-numeric patterns.
Identify,describe,andextendnumeric patterns involving alloperations.
Use a Variety of Reasoning Skills
Sortandclassifyusingattributes.
Recognizeshapesfromdifferentperspectives.
Identifysurfacesthatslide,stack,androll.
Use a Variety of Reasoning Skills
Model,define,andexplainpropertiesofmultiplication.
Usepropertiesofsquaresandrectanglestosolveproblemsaboutareaandperimeter.
Exploretherelationshipamonglists,treediagrams,and multiplication to calculate combinations.
Identifysimilaritiesanddifferences.
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.
PresentmathematicalthinkingthroughMathJournalactivities.
Consolidate Mathematical Thinking
PresentmathematicalthinkingthroughMathJournalactivities.
PresentmathematicalthinkingthroughMathJournalactivities.
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 in Let’sExploreactivities.
Communicate with Peers, Teachers, and Others
Discuss mathematical ideas in Let’sExploreactivities.
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.
Work together in pairs or groupsinLet’sExplore,Games,andotheractivities.
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.
SharemathematicalideaswithothersduringLet’sExploreandHands-Onactivities.
Share Mathematical Thinking
SharemathematicalideaswithothersduringLet’sExploreandHands-Onactivities.
SharemathematicalideaswithothersduringLet’sExploreandHands-Onactivities.
SharemathematicalideaswithothersduringLet’sExploreandHands-Onactivities.
34
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Communication (continued) Communication (continued)
Express Mathematical Ideas
Expressideasinpairedandsmallgroupactivities.
ExpressideasinMathJournalactivities,usinglessonvocabulary.
ExpressideasinMathJournalactivities,usinglessonvocabulary.
Express Mathematical Ideas
ExpressideasinMathJournalactivities,usinglessonvocabulary.
ExpressideasinMathJournalactivities,usinglessonvocabulary.
ExpressideasinMathJournalactivities,usinglessonvocabulary.
Use chapter and lesson vocabularycorrectly.
Use chapter and lesson vocabularycorrectly.
Use chapter and lesson vocabularycorrectly.
Use chapter and lesson vocabularycorrectly.
Use chapter and lesson vocabularycorrectly.
Connections Connections
Recognize Con-nections in Mathematical Ideas
Understand the connection betweenquantitiesandwrittennumerals.
Understand the relationship betweencountingandadditionandsubtraction.
Examineandapplytheinverserelationshipbetweenadditionandsubtraction.
Recognize Con-nections in Mathematical Ideas
Applytheinverserelationshipbetweenmultiplicationanddivision.
Demonstrate that decimal notationisanextensionofthebase-tensystem.
Relatefractionsanddivision.
Understand the relationships amongthenumbersinfactfamilies.
Connect geometric concepts withunitfractions.
Understandthatthesizeofafractionalpartisrelativetothesizeofthewhole.
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.
Relatefractionsanddivision.
Understand How Concepts Build on One Another
Explorerelationshipsamongcounting,ordering,andordinalnumbers.
Learnhowplacevalueconceptsapplytoregroupinginadditionandsubtraction.
Understandhowpatternscanbedescribedusingnumbers,operations,anddatadisplays.
Understand How Concepts Build on One Another
Understand the meanings andusesoffractionsincludingfractionofaset.
Describenumberrelationshipsincontext.
Explaintherelationshipsamongareaformulasofdifferentpolygons.
Connectequivalentfractionsanddecimals.
Connectequivalentfractions,decimals,andpercents.
Recognizetherelationshipbetweenbarmodels,numbersentences,andnumberpatterns.
Useaddition,subtraction,multiplication,anddivisiontoconstructandanalyzegraphs,frequencytables,andlineplots.
Makeconnectionsamongthegreatestcommonfactor,leastcommonmultiple,andoperationswithfractions.
35
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Communication (continued) Communication (continued)
Express Mathematical Ideas
Expressideasinpairedandsmallgroupactivities.
ExpressideasinMathJournalactivities,usinglessonvocabulary.
ExpressideasinMathJournalactivities,usinglessonvocabulary.
Express Mathematical Ideas
ExpressideasinMathJournalactivities,usinglessonvocabulary.
ExpressideasinMathJournalactivities,usinglessonvocabulary.
ExpressideasinMathJournalactivities,usinglessonvocabulary.
Use chapter and lesson vocabularycorrectly.
Use chapter and lesson vocabularycorrectly.
Use chapter and lesson vocabularycorrectly.
Use chapter and lesson vocabularycorrectly.
Use chapter and lesson vocabularycorrectly.
Connections Connections
Recognize Con-nections in Mathematical Ideas
Understand the connection betweenquantitiesandwrittennumerals.
Understand the relationship betweencountingandadditionandsubtraction.
Examineandapplytheinverserelationshipbetweenadditionandsubtraction.
Recognize Con-nections in Mathematical Ideas
Applytheinverserelationshipbetweenmultiplicationanddivision.
Demonstrate that decimal notationisanextensionofthebase-tensystem.
Relatefractionsanddivision.
Understand the relationships amongthenumbersinfactfamilies.
Connect geometric concepts withunitfractions.
Understandthatthesizeofafractionalpartisrelativetothesizeofthewhole.
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.
Relatefractionsanddivision.
Understand How Concepts Build on One Another
Explorerelationshipsamongcounting,ordering,andordinalnumbers.
Learnhowplacevalueconceptsapplytoregroupinginadditionandsubtraction.
Understandhowpatternscanbedescribedusingnumbers,operations,anddatadisplays.
Understand How Concepts Build on One Another
Understand the meanings andusesoffractionsincludingfractionofaset.
Describenumberrelationshipsincontext.
Explaintherelationshipsamongareaformulasofdifferentpolygons.
Connectequivalentfractionsanddecimals.
Connectequivalentfractions,decimals,andpercents.
Recognizetherelationshipbetweenbarmodels,numbersentences,andnumberpatterns.
Useaddition,subtraction,multiplication,anddivisiontoconstructandanalyzegraphs,frequencytables,andlineplots.
Makeconnectionsamongthegreatestcommonfactor,leastcommonmultiple,andoperationswithfractions.
36
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
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.
Solve Real-World Problems in Contexts Outside of Mathematics
Solvereal-worldproblemsinvolvingaddition,subtraction,multiplication,division,andmeasurement.
Solvereal-worldproblemsinvolvingmultiplication,division,fractionconcepts,dataanalysis,andmeasurement.
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 modelstocreateasetwithagivennumberofobjects(upto100).
Use concrete and pictorial modelstocreateasetwith agivennumberofobjects(upto1,000).
Use Representations to Model, Organize, and Record
Use place value models to read,write,andrepresentnumbersto10,000.
Representnumbersto100,000invariouscontexts.
Explorenegativenumbersincontext.
Usenumbersandnumeralstorepresentquantitiesupto20.
Representnumbersto100onanumberline.
Representnumbersto1,000onanumberline.
Representnumbersindifferentequivalentforms.
Expressnumbersto100,000instandard,expanded,andwordforms.
Expressnumbersto10,000,000invariousforms.
Use picture cards to communicate understanding ofcomparisons(biggerandsmaller).
Usenumberbondstorepresentnumbers.
Understandthemeaningofthe=signinnumbersentences.
Understandequalityandinequality.
Usesymbolicnotation(<and>)tocomparenumbers.
Use the dollar sign and decimal pointinmoneyamounts.
Modeldecimalstotenthsandhundredths.
Findequivalentratios.
Modeladditionandsubtractionstorieswithadditionandsubtractionnumbersentences.
Usethe+,−,and=symbolstorepresentreal-worldadditionandsubtractionsituations.
Usebarmodelstorepresentadditionandsubtractionsituations.
Solveadditionandsubtractionproblemswithgreaternumbersbyusingabarmodel
Writeadditionandsubtractionnumbersentencesforreal-worldproblemswithfractionsanddecimals.
Exploretheuseoflettersasvariablesinexpressionsandinequalities.
Represent addition and subtractionstories.
Represent numerical data usingpicturegraphs,tallycharts,andbargraphs.
Represent numerical data using picturegraphswithscales,tallycharts,andbargraphs.
Represent multiplication and divisionindifferentways.
Usemodelstoshowrelationshipsbetweenimproperfractionsandmixednumbers.
Convertfractionsanddecimalstopercents.
Representsharingequallyandmakingequalgroups.
Usethe×,÷,and=symbolstorepresent multiplication and divisionsituations.
Useavarietyofrepresentationsformultiplicationanddivision,suchasarrays,areamodels,numberlines,grouping,andsharing.
Applyunderstandingofmodelsformultiplicationanddivision.
Representcombinationswithlists,treediagrams,andmultiplication.
37
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
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.
Solve Real-World Problems in Contexts Outside of Mathematics
Solvereal-worldproblemsinvolvingaddition,subtraction,multiplication,division,andmeasurement.
Solvereal-worldproblemsinvolvingmultiplication,division,fractionconcepts,dataanalysis,andmeasurement.
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 modelstocreateasetwithagivennumberofobjects(upto100).
Use concrete and pictorial modelstocreateasetwith agivennumberofobjects(upto1,000).
Use Representations to Model, Organize, and Record
Use place value models to read,write,andrepresentnumbersto10,000.
Representnumbersto100,000invariouscontexts.
Explorenegativenumbersincontext.
Usenumbersandnumeralstorepresentquantitiesupto20.
Representnumbersto100onanumberline.
Representnumbersto1,000onanumberline.
Representnumbersindifferentequivalentforms.
Expressnumbersto100,000instandard,expanded,andwordforms.
Expressnumbersto10,000,000invariousforms.
Use picture cards to communicate understanding ofcomparisons(biggerandsmaller).
Usenumberbondstorepresentnumbers.
Understandthemeaningofthe=signinnumbersentences.
Understandequalityandinequality.
Usesymbolicnotation(<and>)tocomparenumbers.
Use the dollar sign and decimal pointinmoneyamounts.
Modeldecimalstotenthsandhundredths.
Findequivalentratios.
Modeladditionandsubtractionstorieswithadditionandsubtractionnumbersentences.
Usethe+,−,and=symbolstorepresentreal-worldadditionandsubtractionsituations.
Usebarmodelstorepresentadditionandsubtractionsituations.
Solveadditionandsubtractionproblemswithgreaternumbersbyusingabarmodel
Writeadditionandsubtractionnumbersentencesforreal-worldproblemswithfractionsanddecimals.
Exploretheuseoflettersasvariablesinexpressionsandinequalities.
Represent addition and subtractionstories.
Represent numerical data usingpicturegraphs,tallycharts,andbargraphs.
Represent numerical data using picturegraphswithscales,tallycharts,andbargraphs.
Represent multiplication and divisionindifferentways.
Usemodelstoshowrelationshipsbetweenimproperfractionsandmixednumbers.
Convertfractionsanddecimalstopercents.
Representsharingequallyandmakingequalgroups.
Usethe×,÷,and=symbolstorepresent multiplication and divisionsituations.
Useavarietyofrepresentationsformultiplicationanddivision,suchasarrays,areamodels,numberlines,grouping,andsharing.
Applyunderstandingofmodelsformultiplicationanddivision.
Representcombinationswithlists,treediagrams,andmultiplication.
38
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Representation (continued) Representation (continued)
Use Representations to Model, Organize, and Record (continued)
Representmultiplicationwithskipcounting,dotpaperarrays,andbarmodels.
Use Representations to Model, Organize, and Record (continued)
Determine the missing parts (quantitiesorsymbols)innumbersentences.
Writeadditionandsubtractionnumbersentencesforreal-worldproblemswithfractionsanddecimals.
Writeandsolveequations.
Represent division as repeated subtractionsentences.
Describeandextendshapepatterns.
Identify,describe,andextendtwo-andthree-dimensionalshapepatterns.
Describe,extend,andcreatetwo-dimensionalshapepatterns.
Createandanalyzemultiplication and division patterns.
Describearuleforsortingobjects.
Identifyaruleforsortingobjects.
Identifyandextendgrowingandrepeatingpatterns.
Identifyrulesfornumberpatterns.
Identifyarulefornumberandcountingpatterns.
Usearuletodescribeasequenceofnumbersorobjects.
Findrulestocompletenumberpatterns.
Select and Apply Representations to Model Problems
Representquantitieswithobjects,numbercubes,andnumerals.
Usenumberbondstorepresentnumbercombinations.
Use place value models to create equivalentrepresentationsofnumbers.
Select and Apply Representations to Model Problems
Useavarietyofmodelstorepresentfractionsandequivalentfractions.
Translatebetweenequivalentimproperfractionsandmixednumbers.
Translatebetweenfractionsandpercents.
Useavarietyofconcrete,pictorial,andsymbolicmodelsforadditionandsubtraction.
Useavarietyofconcrete,pictorial,andsymbolicmodelsforaddition,subtraction,multiplication,anddivision.
Useavarietyofconcrete,pictorial,andsymbolicmodelsformulti-digitaddition,subtraction,multiplication,anddivision.
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.
Interpret Phenomena through Representations
Usereferentstoestimatelength,capacity,andweight.
Measureperimeterandareaincustomaryandmetricunits.
Measurevolumeofarectangularprism.
Describeandcompareobjectsbyposition.
Usepositionalwordstodescribelocation.
39
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Representation (continued) Representation (continued)
Use Representations to Model, Organize, and Record (continued)
Representmultiplicationwithskipcounting,dotpaperarrays,andbarmodels.
Use Representations to Model, Organize, and Record (continued)
Determine the missing parts (quantitiesorsymbols)innumbersentences.
Writeadditionandsubtractionnumbersentencesforreal-worldproblemswithfractionsanddecimals.
Writeandsolveequations.
Represent division as repeated subtractionsentences.
Describeandextendshapepatterns.
Identify,describe,andextendtwo-andthree-dimensionalshapepatterns.
Describe,extend,andcreatetwo-dimensionalshapepatterns.
Createandanalyzemultiplication and division patterns.
Describearuleforsortingobjects.
Identifyaruleforsortingobjects.
Identifyandextendgrowingandrepeatingpatterns.
Identifyrulesfornumberpatterns.
Identifyarulefornumberandcountingpatterns.
Usearuletodescribeasequenceofnumbersorobjects.
Findrulestocompletenumberpatterns.
Select and Apply Representations to Model Problems
Representquantitieswithobjects,numbercubes,andnumerals.
Usenumberbondstorepresentnumbercombinations.
Use place value models to create equivalentrepresentationsofnumbers.
Select and Apply Representations to Model Problems
Useavarietyofmodelstorepresentfractionsandequivalentfractions.
Translatebetweenequivalentimproperfractionsandmixednumbers.
Translatebetweenfractionsandpercents.
Useavarietyofconcrete,pictorial,andsymbolicmodelsforadditionandsubtraction.
Useavarietyofconcrete,pictorial,andsymbolicmodelsforaddition,subtraction,multiplication,anddivision.
Useavarietyofconcrete,pictorial,andsymbolicmodelsformulti-digitaddition,subtraction,multiplication,anddivision.
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.
Interpret Phenomena through Representations
Usereferentstoestimatelength,capacity,andweight.
Measureperimeterandareaincustomaryandmetricunits.
Measurevolumeofarectangularprism.
Describeandcompareobjectsbyposition.
Usepositionalwordstodescribelocation.
40
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Representation (continued) Representation (continued)
Interpret Phenomena through Representations (continued)
Nameflatshapesthatmakeupreal-worldobjects.
Identifyreal-worldtwo-andthree-dimensionalshapes.
Interpret Phenomena through Representations (continued)
Usefrequencytables,bargraphs,picturegraphs,andlineplotstosolveproblems.
Collectdataandorganizeitinatable.
Representdatainadoublebargraph.
Represent measurements and datainpicturegraphsandbargraphs.
Represent data in picture graphs.
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.
Solvereal-worldproblemsrelatedtomoney.
Solvereal-worldproblemsinvolvingmultiplication,division,fractionconcepts,dataanalysis,andmeasurement.
Solvereal-worldproblemsinvolvingsocialsituations.
Usetechnology(virtualmanipulativesandcomputers)tomodelanddraw.
Usetechnology(virtualmanipulativesandcomputers)tomodelanddraw.
Usetechnology(virtualmanipulativesandcomputers)tomodelanddraw.
Usetechnology(virtualmanipulativesandcomputers)tomodelanddraw.
Usetechnology(virtualmanipulativesandcomputers)tomodelanddraw.
Useacalculatortomodel,compute,andsolveproblems.
41
Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Representation (continued) Representation (continued)
Interpret Phenomena through Representations (continued)
Nameflatshapesthatmakeupreal-worldobjects.
Identifyreal-worldtwo-andthree-dimensionalshapes.
Interpret Phenomena through Representations (continued)
Usefrequencytables,bargraphs,picturegraphs,andlineplotstosolveproblems.
Collectdataandorganizeitinatable.
Representdatainadoublebargraph.
Represent measurements and datainpicturegraphsandbargraphs.
Represent data in picture graphs.
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.
Solvereal-worldproblemsrelatedtomoney.
Solvereal-worldproblemsinvolvingmultiplication,division,fractionconcepts,dataanalysis,andmeasurement.
Solvereal-worldproblemsinvolvingsocialsituations.
Usetechnology(virtualmanipulativesandcomputers)tomodelanddraw.
Usetechnology(virtualmanipulativesandcomputers)tomodelanddraw.
Usetechnology(virtualmanipulativesandcomputers)tomodelanddraw.
Usetechnology(virtualmanipulativesandcomputers)tomodelanddraw.
Usetechnology(virtualmanipulativesandcomputers)tomodelanddraw.
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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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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