Pacing Guide A Program Paced for Successassets.pearsonschool.com/asset_mgr/versions/2014... · 8...

Pacing Guide A Program Paced for Success

Common CoreStandards for Mathematical Practice

✔ Makesenseofproblemsandpersevereinsolvingthem.

✔ Reasonabstractlyandquantitatively.

✔ Constructviableargumentsandcritiquethereasoningofothers.

✔ Modelwithmathematics.

✔ Useappropriatetoolsstrategically.

✔ Attendtoprecision.

✔ Lookforandmakeuseofstructure.

✔ Lookforandexpressregularityinrepeatedreasoning.

Grade 4 enVisionMATH Contents

Grade 4 Domain ColorsDomain: Operations and Algebraic ThinkingTopics:1and2

Domain: Number and Operations in Base TenTopics:3,4,5,6,7,8,9,and10

Domain: Number and Operations—FractionsTopics:11,12,and13

Domain: Measurement and DataTopics:14and15

Domain: GeometryTopic:16

13 days Topic 1 MultiplicationandDivision:MeaningsandFacts

8 days Topic 2 GenerateandAnalyzePatterns

9 days Topic 3 PlaceValue

9 days Topic 4 AdditionandSubtractionofWholeNumbers

9 days Topic 5 NumberSense:Multiplyingby1-DigitNumbers

9 days Topic 6 DevelopingFluency:Multiplyingby1-DigitNumbers

10 days Topic 7 NumberSense:Multiplyingby2-DigitNumbers

8 days Topic 8 DevelopingFluency:Multiplyingby2-DigitNumbers

9 days Topic 9 NumberSense:Dividingby1-DigitDivisors

11 days Topic 10 DevelopingFluency:Dividingby1-DigitDivisors

10 days Topic 11 FractionEquivalenceandOrdering

14 days Topic 12 AddingandSubtractingFractionsandMixedNumberswithLikeDenominators

13 days Topic 13 ExtendingFractionConcepts

14 days Topic 14 MeasurementUnitsandConversions

7 days Topic 15 SolvingMeasurementandDataProblems

14 days Topic 16 Lines,Angles,andShapes

10 days Step-Up Step-UptoGrade5Lessons

177 days

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Topic 1 Multiplication and Division: Meanings and Facts Planning

Mathematical Practices Handbook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2A Math Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2G Differentiated Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2I The Language of Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2J Getting to Know Your Math Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Topic Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Math Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Topic 1 Interactive Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Lessons

1-1 Meanings of Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6A1-2 Patterns for Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10A1-3 Multiplication Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12A1-4 3, 4, 6, 7, and 8 as Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14A1-5 Multiplication as Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18A1-6 Meanings of Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20A1-7 Multiplication and Division Comparison Problems . . . . . . . . . . . . . . . . . . 24A1-8 Special Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26A1-9 Using Multiplication Facts to Find Division Facts. . . . . . . . . . . . . . . . . . . . 28A1-10 Problem Solving Draw a Picture and Write an Equation . . . . . . . . . . . . 30A

Review and Assessment

Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Topic 1 Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Performance Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Placement Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36A Basic Facts Timed Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36B

Topic 2 Generate and Analyze Patterns Planning

Math Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37A Differentiated Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37C The Language of Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37D Math Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37E Topic Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Topic 2 Interactive Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Lessons

2-1 Repeating Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40A2-2 Number Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42A2-3 Extending Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44A2-4 Writing Rules for Situations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46A2-5 Geometric Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50A2-6 Problem Solving Act It Out and Use Reasoning . . . . . . . . . . . . . . . . . . 54A


Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Topic 2 Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Performance Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Standards for Mathematical Content

Critical Area Developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends.

Domain Operations and Algebraic Thinking

Cluster Use the four operations with whole numbers to solve problems.

Cluster Generate and analyze patterns.

Standards 4.OA.A.1, 4.OA.A.2, 4.OA.C.5


Connections to Critical Areas

Domain Operations and Algebraic Thinking

Cluster Use the four operations with whole numbers to solve problems.

Cluster Generate and analyze patterns.

Standards 4.OA.A.3, 4.OA.C.5

Content Guide 23

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Topic 3 Place ValuePlanning

MathBackground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63A DifferentiatedInstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63C TheLanguageofMath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63D MathProject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63E TopicOpener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Topic3InteractiveLearning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Lessons

3-1 RepresentingNumbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66A3-2 PlaceValueRelationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68A3-3 ComparingNumbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70A3-4 ComparingGreaterNumbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74A3-5 RoundingWholeNumbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78A3-6 Problem Solving MakeanOrganizedList . . . . . . . . . . . . . . . . . . . . . . 80A

ReviewandAssessment

Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Topic3Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 PerformanceAssessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Topic 4 Addition and Subtraction of Whole NumbersPlanning

MathBackground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87A DifferentiatedInstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87C TheLanguageofMath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87D MathProject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87E TopicOpener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Topic4InteractiveLearning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

Lessons

4-1 UsingMentalMathtoAddandSubtract . . . . . . . . . . . . . . . . . . . . . . . . . 90A4-2 EstimatingSumsandDifferencesofWholeNumbers . . . . . . . . . . . . . . . . 94A4-3 AddingWholeNumbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96A4-4 SubtractingWholeNumbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100A4-5 SubtractingAcrossZeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102A4-6 Problem Solving DrawaPictureandWriteanEquation . . . . . . . . . . . 104A

ReviewandAssessment

Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Topic4Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 PerformanceAssessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 BenchmarkTestTopics1–4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112A

StandardsforMathematicalContent

ConnectionstoCriticalAreas

Domain NumberandOperationsinBaseTen

Cluster Useplacevalueunderstandingandpropertiesofoperationstoperformmulti-digitarithmetic .

Standards 4.NBT.B.4, 4.OA.A.3




Cluster Generalizeplacevalueunderstandingformulti-digitwholenumbers .

Standards 4.NBT.A.1, 4.NBT.A.2, 4.NBT.A.3




Topic 5 Number Sense: Multiplying by 1-Digit Numbers Planning

Math Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113A Differentiated Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113C The Language of Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113D Math Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113E Topic Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Topic 5 Interactive Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Lessons

5-1 Arrays and Multiplying by 10 and 100 . . . . . . . . . . . . . . . . . . . . . . . . 116A5-2 Multiplying by Multiples of 10 and 100 . . . . . . . . . . . . . . . . . . . . . . . . 118A5-3 Breaking Apart to Multiply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120A5-4 Using Mental Math to Multiply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122A5-5 Using Rounding to Estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124A5-6 Problem Solving Reasonableness . . . . . . . . . . . . . . . . . . . . . . . . . . . 126A


Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Topic 5 Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Performance Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

Topic 6 Developing Fluency: Multiplying by 1-Digit Numbers Planning


Lessons

6-1 Arrays and Using an Expanded Algorithm . . . . . . . . . . . . . . . . . . . . . . 138A6-2 Connecting the Expanded and Standard Algorithms. . . . . . . . . . . . . . . . 142A6-3 Multiplying 2-Digit by 1-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . 144A6-4 Multiplying 3- and 4-Digit by 1-Digit Numbers . . . . . . . . . . . . . . . . . . . . 148A6-5 Multiplying by 1-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152A6-6 Problem Solving Missing or Extra Information . . . . . . . . . . . . . . . . . . 154A





Domain Number and Operations inBase Ten

Cluster Generalize place valueunderstanding for multi-digit whole numbers.

Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic.

Standards 4.NBT.A.3, 4.NBT.B.5, 4.OA.A.3




Cluster Generalize place valueunderstanding for multi-digit whole numbers.


Standards 4.NBT.A.3, 4.NBT.B.5, 4.OA.A.2, 4.OA.A.3

Content Guide 25


Topic 7 Number Sense: Multiplying by 2-Digit NumbersPlanning

MathBackground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163A DifferentiatedInstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163C TheLanguageofMath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163D MathProject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163E TopicOpener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Topic7InteractiveLearning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

Lessons

7-1 ArraysandMultiplying2-DigitNumbersbyMultiplesof10 . . . . . . . . . . 166A7-2 UsingMentalMathtoMultiply2-DigitNumbers . . . . . . . . . . . . . . . . . . 170A7-3 UsingRoundingtoEstimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172A7-4 UsingCompatibleNumberstoEstimate . . . . . . . . . . . . . . . . . . . . . . . . 174A7-5 Problem Solving Multiple-StepProblems . . . . . . . . . . . . . . . . . . . . . . 176A

ReviewandAssessment

Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 Topic7Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 PerformanceAssessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

Topic 8 Developing Fluency: Multiplying by 2-Digit NumbersPlanning

MathBackground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183A DifferentiatedInstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183C TheLanguageofMath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183D MathProject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183E TopicOpener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 Topic8InteractiveLearning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

Lessons

8-1 ArraysandMultiplying2-DigitNumbers . . . . . . . . . . . . . . . . . . . . . . . . 186A8-2 ArraysandanExpandedAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 190A8-3 Multiplying2-DigitNumbersbyMultiplesof10 . . . . . . . . . . . . . . . . . . . 192A8-4 Multiplying2-Digitby2-DigitNumbers . . . . . . . . . . . . . . . . . . . . . . . . . 194A8-5 Problem Solving Two-QuestionProblems . . . . . . . . . . . . . . . . . . . . . . 196A

ReviewandAssessment

Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 Topic8Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 PerformanceAssessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 BenchmarkTestTopics5–8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202A


CriticalArea Developingunderstandingandfluencywithmulti-digitmultiplication,anddevelopingunderstandingofdividingtofindquotientsinvolvingmulti-digitdividends .



Standards 4.NBT.B.5, 4.OA.A.3




Cluster Generalizeplacevalueunderstandingformulti-digitwholenumbers .


Standards 4.NBT.A.3, 4.NBT.B.5, 4.OA.A.3




Topic 9 Number Sense: Dividing by 1-Digit Divisors Planning


Lessons

9-1 Using Mental Math to Divide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206A9-2 Estimating Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208A9-3 Estimating Quotients for Greater Dividends . . . . . . . . . . . . . . . . . . . . . . 210A9-4 Dividing with Remainders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212A9-5 Multiplication and Division Stories . . . . . . . . . . . . . . . . . . . . . . . . . . . 214A9-6 Problem Solving Draw a Picture and Write an Equation . . . . . . . . . . . 218A







Standards 4.NBT.B.5, 4.NBT.B.6, 4.OA.A.3

Content Guide 27


Topic 10 Developing Fluency: Dividing by 1-Digit DivisorsPlanning

MathBackground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225A DifferentiatedInstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225C TheLanguageofMath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225D MathProject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225E TopicOpener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 Topic10InteractiveLearning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

Lessons

10-1 DivisionasRepeatedSubtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228A10-2 UsingObjectstoDivide:DivisionasSharing . . . . . . . . . . . . . . . . . . . . . 230A10-3 Dividing2-Digitby1-DigitNumbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 234A10-4 Dividing3-Digitby1-DigitNumbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 238A10-5 DecidingWheretoStartDividing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240A10-6 Dividing4-Digitby1-DigitNumbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 242A10-7 Problem Solving Multiple-StepProblems . . . . . . . . . . . . . . . . . . . . . . 244A

ReviewandAssessment

Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 Topic10Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 PerformanceAssessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

Topic 11 Fraction Equivalence and OrderingPlanning


Lessons

11-1 Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256A11-2 PrimeandCompositeNumbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258A11-3 Multiples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260A11-4 EquivalentFractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262A11-5 NumberLinesandEquivalentFractions . . . . . . . . . . . . . . . . . . . . . . . . . 266A11-6 ComparingFractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268A11-7 OrderingFractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272A11-8 Problem Solving WritingtoExplain . . . . . . . . . . . . . . . . . . . . . . . . . 274A

ReviewandAssessment



CriticalArea Developinganunderstandingoffractionequivalence,addition andsubtractionoffractionswithlike denominators,andmultiplicationoffractionsbywholenumbers .

Domain NumberandOperations—Fractions

Cluster Extendunderstandingoffractionequivalenceandordering .

Standards 4.NF.A.1, 4.NF.A.2, 4.OA.B.4





Standards 4.NBT.B.5, 4.NBT.B.6, 4.OA.A.3




Topic 12 Adding and Subtracting Fractions and Mixed Numbers with Like Denominators Planning

Math Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285A Differentiated Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285C The Language of Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285D Math Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285E Topic Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 Topic 12 Interactive Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

Lessons

12-1 Modeling Addition of Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288A12-2 Adding Fractions with Like Denominators . . . . . . . . . . . . . . . . . . . . . . . 290A12-3 Modeling Subtraction of Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292A12-4 Subtracting Fractions with Like Denominators . . . . . . . . . . . . . . . . . . . . 294A12-5 Adding and Subtracting on the Number Line . . . . . . . . . . . . . . . . . . . . . 296A12-6 Improper Fractions and Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . 300A12-7 Modeling Addition and Subtraction of Mixed Numbers . . . . . . . . . . . . . 304A12-8 Adding Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308A12-9 Subtracting Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310A12-10 Decomposing and Composing Fractions . . . . . . . . . . . . . . . . . . . . . . . . 312A12-11 Problem Solving Draw a Picture and Write an Equation . . . . . . . . . . . 314A


Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 Topic 12 Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 Performance Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 Benchmark Test Topics 9–12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324A


Critical Area Developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers.

Domain Number and Operations—Fractions

Cluster Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Standards 4.NF.B.3a, 4.NF.B.3b, 4.NF.B.3c, 4.NF.B.3d

Content Guide 29


Topic 13 Extending Fraction ConceptsPlanning


Lessons

13-1 FractionsasMultiplesofUnitFractions:UsingModels . . . . . . . . . . . . . . 328A13-2 MultiplyingaFractionbyaWholeNumber:UsingModels . . . . . . . . . . . 330A13-3 MultiplyingaFractionbyaWholeNumber:UsingSymbols . . . . . . . . . . 332A13-4 FractionsandDecimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334A13-5 FractionsandDecimalsontheNumberLine . . . . . . . . . . . . . . . . . . . . . 336A13-6 EquivalentFractionsandDecimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340A13-7 DecimalPlaceValue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344A13-8 ComparingDecimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346A13-9 UsingMoneytoUnderstandDecimals . . . . . . . . . . . . . . . . . . . . . . . . . 350A13-10 Problem Solving DrawaPicture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352A

ReviewandAssessment


Topic 14 Measurement Units and ConversionsPlanning

MathBackground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361A DifferentiatedInstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361C TheLanguageofMath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361D MathProject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361E TopicOpener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 Topic14InteractiveLearning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362

Lessons

14-1 UsingCustomaryUnitsofLength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364A14-2 CustomaryUnitsofCapacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366A14-3 UnitsofWeight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368A14-4 ChangingCustomaryUnits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370A14-5 Problem Solving WritingtoExplain . . . . . . . . . . . . . . . . . . . . . . . . . 374A14-6 UsingMetricUnitsofLength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376A14-7 MetricUnitsofCapacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378A14-8 UnitsofMass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380A14-9 ChangingMetricUnits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382A14-10UnitsofTime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386A14-11 Problem Solving WorkBackward . . . . . . . . . . . . . . . . . . . . . . . . . . . 388A

ReviewandAssessment




Domain MeasurementandData

Cluster Solveproblemsinvolvingmeasurementandconversionofmeasurementsfromalargerunittoasmallerunit .

Standards 4.MD.A.1, 4.MD.A.2


CriticalArea Developinganunderstandingoffractionequivalence,additionandsubtractionoffractionswithlikedenominators,andmultiplicationoffractionsbywholenumbers .

Domain NumberandOperations—Fractions

Cluster Buildfractionsfromunitfractionsbyapplyingandextendingpreviousunderstandingsofoperationsonwholenumbers .

Cluster Understanddecimalnotationforfractions,andcomparedecimalfractions .

Standards 4.NF.B.4a, 4.NF.B.4b, 4.NF.B.4c, 4.NF.C.5, 4.NF.C.6, 4.NF.C.7, 4.MD.A.2




Topic 15 Solving Measurement and Data Problems Planning

Math Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397A Differentiated Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397C The Language of Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397D Math Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397E Topic Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 Topic 15 Interactive Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398

Lessons

15-1 Making Line Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400A15-2 Solving Problems Involving Line Plots . . . . . . . . . . . . . . . . . . . . . . . . . . 402A15-3 Solving Perimeter and Area Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 404A15-4 Solving Measurement Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406A15-5 Solving Problems Involving Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408A15-6 Problem Solving Solve a Simpler Problem and Make a Table . . . . . . . . 410A


Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 Topic 15 Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416 Performance Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418

Topic 16 Lines, Angles, and Shapes Planning

Math Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419A Differentiated Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419C The Language of Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419D Math Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419E Topic Opener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 Topic 16 Interactive Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420

Lessons

16-1 Points, Lines, and Planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422A16-2 Line Segments, Rays, and Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424A16-3 Understanding Angles and Unit Angles . . . . . . . . . . . . . . . . . . . . . . . . 426A16-4 Measuring with Unit Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428A16-5 Measuring Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430A16-6 Adding and Subtracting Angle Measures . . . . . . . . . . . . . . . . . . . . . . . 432A16-7 Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434A16-8 Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436A16-9 Quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438A16-10 Line Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440A16-11 Problem Solving Make and Test Generalizations . . . . . . . . . . . . . . . . 442A


Reteaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 Topic 16 Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448 Performance Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450 Benchmark Test Topics 13–16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450A End-of-Year-Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450B Step-Up Lessons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451


Connections to Critical Areas

Domain Measurement and Data

Cluster Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Cluster Represent and interpret data.

Standards 4.MD.A.2, 4.MD.A.3, 4.MD.B.4


Critical Area Understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

Domain Geometry

Cluster Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Standards 4.G.A.1, 4.G.A.2, 4.G.A.3, 4.OA.C.5, 4.MD.C.5a, 4.MD.C.5b, 4.MD.C.6, 4.MD.C.7

Content Guide 31


*�Teacher’s�Resource�Masters for every lesson (Practice, Reteaching, Enrichment, Centers, Quick Check) are considered part of this correlation.

Grade 4 Standards for Mathematical Content Correlation

DOMAIN�4.OA� Operations�and�Algebraic�Thinking�

Cluster�A Use the four operations with whole numbers to solve problems.

Common�Core�State�Standard Student’s�Edition�Pages Teacher’s�Edition�Pages*

4.OA.A.1� Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

18–19, Lesson 1-524–25, Lesson 1-732–33, Reteaching Sets D, E

18A–19B, Lesson 1-524A–25B, Lesson 1-732–33, Reteaching Sets D, E

4.OA.A.2�Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

20–23, Lesson 1-624–25, Lesson 1-730–31, Lesson 1-1032–33, Reteaching Sets E, G154–157, Lesson 6-6159, Reteaching Set E

20A–23B, Lesson 1-624A–25B, Lesson 1-730A–31B, Lesson 1-1032–33, Reteaching Sets E, G154A–157B, Lesson 6-6159, Reteaching Set E

4.OA.A.3�Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

54–57, Lesson 2-659, Reteaching Set E126–129, Lesson 5-6131, Reteaching Set F176–177, Lesson 7-5179, Reteaching Set E196–197, Lesson 8-5199, Reteaching Set E 206–207, Lesson 9-1220, Reteaching Set A244–245, Lesson 10-7249, Reteaching Set G

54A–57B, Lesson 2-659, Reteaching Set E126A–129B, Lesson 5-6131, Reteaching Set F176A–177B, Lesson 7-5179, Reteaching Set E196A–197B, Lesson 8-5199, Reteaching Set E206A–207B, Lesson 9-1220, Reteaching Set A244A–245B, Lesson 10-7249, Reteaching Set G

Teacher’s Edition Program Overview32


* Teacher’s Resource Masters for every lesson (Practice, Reteaching, Enrichment, Centers, Quick Check) are considered part of this correlation.

DOMAIN 4.OA Operations and Algebraic Thinking cont.

Cluster B Gain familiarity with factors and multiples.

Common Core State Standard Student’s Edition Pages Teacher’s Edition Pages*

4.OA.B.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

256–257, Lesson 11-1258–259, Lesson 11-2260–261, Lesson 11-3278–279, Reteaching Sets A–C

256A-257B, Lesson 11-1258A–259B, Lesson 11-2260A–261B, Lesson 11-3278–279, Reteaching Sets A–C

Cluster C Generate and analyze patterns.

4.OA.C.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

10–11, Lesson 1-232, Reteaching Set B40–41, Lesson 2-142–43, Lesson 2-250–53, Lesson 2-558–59, Reteaching Sets A, B, D

10A–11B, Lesson 1-232, Reteaching Set B40A–41B, Lesson 2-142A–43B, Lesson 2-250A–53B, Lesson 2-558–59, Reteaching Sets A, B, D

Content Guide 33




DOMAIN�4.NBT� Number�and�Operations�in�Base�Ten1

Cluster�A Generalize place value understanding for multi-digit whole numbers.


4.NBT.A.1�Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

66–67, Lesson 3-168–69, Lesson 3-280–81, Lesson 3-682–83, Reteaching Sets A, B, F

66A–67B, Lesson 3-168A–69B, Lesson 3-280A–81B, Lesson 3-682–83, Reteaching Sets A, B, F

4.NBT.A.2�Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

66–67, Lesson 3-170–73, Lesson 3-374–77, Lesson 3-482–83, Reteaching Sets A, C, D

66A–67B, Lesson 3-170A–73B, Lesson 3-374A–77B, Lesson 3-482–83, Reteaching Sets A, C, D

4.NBT.A.3�Use place value understanding to round multi-digit whole numbers to any place.

78–79, Lesson 3-583, Reteaching Set E94–95, Lesson 4-2108, Reteaching Set B124–125, Lesson 5-5131, Reteaching Set E172–173, Lesson 7-3178, Reteaching Set C

78A–79B, Lesson 3-583, Reteaching Set E94A–95B, Lesson 4-2108, Reteaching Set B124A–125B, Lesson 5-5131, Reteaching Set E172A–173B, Lesson 7-3178, Reteaching Set C




DOMAIN 4.NBT Number and Operations in Base Ten1 cont.

Cluster B Use place value understanding and properties of operations to perform multi-digit arithmetic.


4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.

96–99, Lesson 4-3100–101, Lesson 4-4102–103, Lesson 4-5104–107, Lesson 4-6108–109, Reteaching Sets C–F

96A–99B, Lesson 4-3100A–101B, Lesson 4-4102A–103B, Lesson 4-5104A–107B, Lesson 4-6108–109, Reteaching Sets C–F

4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

116–117, Lesson 5-1118–119, Lesson 5-2120–121, Lesson 5-3122–123, Lesson 5-4126–129, Lesson 5-6130–131, Reteaching Sets A–D, F144–147, Lesson 6-3148–151, Lesson 6-4152–153, Lesson 6-5154–157, Lesson 6-6158–159, Reteaching Sets C–E166–169, Lesson 7-1170–171, Lesson 7-2178, Reteaching Sets A, B186–189, Lesson 8-1190–191, Lesson 8-2192–193, Lesson 8-3194–195, Lesson 8-4196–197, Lesson 8-5198–199, Reteaching Sets A–E

116A–117B, Lesson 5-1118A–119B, Lesson 5-2120A–121B, Lesson 5-3122A–123B, Lesson 5-4126A–129B, Lesson 5-6130–131, Reteaching Sets A–D, F144A–147B, Lesson 6-3148A–151B, Lesson 6-4152A–153B, Lesson 6-5154A–157B, Lesson 6-6158–159, Reteaching Sets C–E166A–169B, Lesson 7-1170A–171B, Lesson 7-2178, Reteaching Sets A, B186A–189B, Lesson 8-1190A–191B, Lesson 8-2192A–193B, Lesson 8-3194A–195B, Lesson 8-4196A–197B, Lesson 8-5198–199, Reteaching Sets A–E

4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

206–207, Lesson 9-1212–213, Lesson 9-4214–217, Lesson 9-5218–219, Lesson 9-6220–221, Reteaching Sets A, C–E230–233, Lesson 10-2234–237, Lesson 10-3238–239, Lesson 10-4240–241, Lesson 10-5242–243, Lesson 10-6246–248, Reteaching Sets B–F

206A–207B, Lesson 9-1212A–213B, Lesson 9-4214A–217B, Lesson 9-5218A–219B, Lesson 9-6220–221, Reteaching Sets A, C–E230A–233B, Lesson 10-2234A–237B, Lesson 10-3238A–239B, Lesson 10-4240A–241B, Lesson 10-5242A–243B, Lesson 10-6246–248, Reteaching Sets B–F

Content Guide 35




DOMAIN�4.NF� Number�and�Operations—Fractions2�

Cluster�A Extend understanding of fraction equivalence and ordering.


4.NF.A.1�Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

262–265, Lesson 11-4266–267, Lesson 11-5274–277, Lesson 11-8279–281, Reteaching Sets D, E, H

262A–265B, Lesson 11-4266A–267B, Lesson 11-5274A–277B, Lesson 11-8279–281, Reteaching Sets D, E, H

4.NF.A.2�Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

266–267, Lesson 11-5268–271, Lesson 11-6272–273, Lesson 11-7274–277, Lesson 11-8280–281, Reteaching Sets E–H

266A–267B, Lesson 11-5268A–271B, Lesson 11-6272A–273B, Lesson 11-7274A–277B, Lesson 11-8280–281, Reteaching Sets E–H

Cluster�B Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

4.NF.B.3a�Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

288–289, Lesson 12-1290–291, Lesson 12-2292–293, Lesson 12-3294–295, Lesson 12-4296�–299, Lesson 12-5314–317, Lesson 12-11318–321, Reteaching Sets A–E, K

288A–289B, Lesson 12-1290A–291B, Lesson 12-2292A–293B, Lesson 12-3294A–295B, Lesson 12-4296A–299B, Lesson 12-5314A–317B, Lesson 12-11318–321, Reteaching Sets A–E, K

4.NF.B.3b�Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

300–303, Lesson 12-6304–307, Lesson 12-7312–313, Lesson 12-10319–321, Reteaching Sets F, G, J

300A–303B, Lesson 12-6304A–307B, Lesson 12-7312A–313B, Lesson 12-10319–321, Reteaching Sets F, G, J




DOMAIN 4.NF Number and Operations—Fractions2 cont.


4.NF.B.3c Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

304–307, Lesson 12-7308–309, Lesson 12-8310–311, Lesson 12-9320, Reteaching Sets G–I

304A–307B, Lesson 12-7308A–309B, Lesson 12-8310A–311B, Lesson 12-9320, Reteaching Sets G–I

4.NF.B.3d Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

290–291, Lesson 12-2292–293, Lesson 12-3294–295, Lesson 12-4296 –299, Lesson 12-5314–317, Lesson 12-11318–321, Reteaching Sets B–E, K

290A–291B, Lesson 12-2292A–293B, Lesson 12-3294A–295B, Lesson 12-4296A–299B, Lesson 12-5314A–317B, Lesson 12-11318–321, Reteaching Sets B–E, K

4.NF.B.4a Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).

328–329, Lesson 13-1354, Reteaching Set A

328A–329B, Lesson 13-1354, Reteaching Set A

4.NF.B.4b Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

330–331, Lesson 13-2332–333, Lesson 13-3354, Reteaching Set B

330A–331B, Lesson 13-2332A–333B, Lesson 13-3354, Reteaching Set B

Content Guide 37




DOMAIN�4.NF� Number�and�Operations—Fractions2� cont.


4.NF.B.4c�Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

330–331, Lesson 13-2332–333, Lesson 13-3354, Reteaching Set B

330A–331B, Lesson 13-2332A–333B, Lesson 13-3354, Reteaching Set B

Cluster�C Understand decimal notation for fractions, and compare decimal fractions.

4.NF.C.5�Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.3 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

336–339, Lesson 13-5355, Reteaching Set D

336A–339B, Lesson 13-5355, Reteaching Set D

4.NF.C.6�Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

334–335, Lesson 13-4336–339, Lesson 13-5340–343, Lesson 13-6355–356, Reteaching Sets C–E

334A–335B, Lesson 13-4336A–339B, Lesson 13-5340A–343B, Lesson 13-6355–356, Reteaching Sets C–E

4.NF.C.7�Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

346–349, Lesson 13-8356, Reteaching Set G

346A–349B, Lesson 13-8356, Reteaching Set G




DOMAIN 4.MD Measurement and Data

Cluster A Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.


4.MD.A.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

364–365, Lesson 14-1366–367, Lesson 14-2368–369, Lesson 14-3370–373, Lesson 14-4374–375, Lesson 14-5376–377, Lesson 14-6378–379, Lesson 14-7380–381, Lesson 14-8382–385, Lesson 14-9386–387, Lesson 14-10388–389, Lesson 14-11390–393, Reteaching Sets A–K

364A–365B, Lesson 14-1366A–367B, Lesson 14-2368A–369B, Lesson 14-3370A–373B, Lesson 14-4374A–375B, Lesson 14-5376A–377B, Lesson 14-6378A–379B, Lesson 14-7380A–381B, Lesson 14-8382A–385B, Lesson 14-9386A–387B, Lesson 14-10388A–389B, Lesson 14-11390–393, Reteaching Sets A–K

4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

350–351, Lesson 13-9352–353, Lesson 13-10357, Reteaching Sets H, I 374–375, Lesson 14-5380–381, Lesson 14-8388–389, Lesson 14-11391–393, Reteaching Sets E, H, K406–407, Lesson 15-4408–409, Lesson 15-5410–413, Lesson 15-6415, Reteaching Sets C–E

350A–351B, Lesson 13-9352A–353B, Lesson 13-10357, Reteaching Sets H, I 374A–375B, Lesson 14-5380A–381B, Lesson 14-8388A–389B, Lesson 14-11391–393, Reteaching Sets E, H, K406A–407B, Lesson 15-4408A–409B, Lesson 15-5410A–413B, Lesson 15-6415, Reteaching Sets C–E

4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

404–405, Lesson 15-3414, Reteaching Set B

404A–405B, Lesson 15-3414, Reteaching Set B

Content Guide 39




DOMAIN�4.MD� Measurement�and�Data� cont.

Cluster�B Represent and interpret data.


4.MD.B.4�Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

400–401, Lesson 15-1402–403, Lesson 15-2414, Reteaching Set A

400A–401B, Lesson 15-1402A–403B, Lesson 15-2414, Reteaching Set A

Cluster�C Geometric measurement: understand concepts of angle and measure angles.

4.MD.C.5a�Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

426–427, Lesson 16-3445, Reteaching Set C

426A–427B, Lesson 16-3445, Reteaching Set C

4.MD.C.5b�Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

428–429, Lesson 16-4445, Reteaching Set D

428A–429B, Lesson 16-4445, Reteaching Set D

4.MD.C.6�Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

430–431, Lesson 16-5445, Reteaching Set E

430A–431B, Lesson 16-5445, Reteaching Set E

4.MD.C.7�Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

432–433, Lesson 16-6446, Reteaching Set F

432A–433B, Lesson 16-6446, Reteaching Set F



Notes

1. Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

2. Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

3. Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.


DOMAIN 4.G Geometry

Cluster A Draw and identify lines and angles, and classify shapes by properties of their lines and angles.


4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

422–423, Lesson 16-1424–425, Lesson 16-2436–437, Lesson 16-8438–439, Lesson 16-9444–447, Reteaching Sets A, B, H

422A–423B, Lesson 16-1424A–425B, Lesson 16-2436A–437B, Lesson 16-8438A–439B, Lesson 16-9444–447, Reteaching Sets A, B, H

4.G.A.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

436–437, Lesson 16-8438–439, Lesson 16-9442–443, Lesson 16-11446–447, Reteaching Sets H, J

436A–437B, Lesson 16-8438A–439B, Lesson 16-9442A–443B, Lesson 16-11446–447, Reteaching Sets H, J

4.G.A.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

440–441, Lesson 16-10447, Reteaching Set I

440A–441B, Lesson 16-10447, Reteaching Set I

Content Guide 41


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