scope & sequence - houghton mifflin harcourt

1

TOPIC 1: Equal Groups in Multiplication Topic Objectives CCSS

AlignmentsContent Objectives Selected Examples

Meaning focus:Understand the meaning of multiplication

Procedural focus:Multiply 1-digit factors

3.OA.A.1Generate situations that can be represented by multiplication

3.OA.A.3 4.OA.A.2

Represent multiplication with models and expressions

2.OA.C.3 3.OA.B.5 Calculate products of 1-digit factors

2.OA.C.3 3.OA.B.5

Apply the Commutative Property to calculate products

4.OA.A.1Identify and extend multiplication patterns with whole numbers

Scope & SequenceBlock 1: Multiplicative Thinking

Assessed primarily through TLI Instructional Video

7 x 5

2

Block 1: Multiplicative Thinking (continued)


TOPIC 2: Facts and FactorsTopic Objectives CCSS


Meaning focus:Understand the relationship between factors and products

Procedural focus:Recognize and use the factors of a number

4.NBT.B.5Decompose factors to calculate products of 1-digit factors

4.OA.B.4 Identify factors of whole numbers

3.OA.B.6 Calculate products of 1-digit factors

3.OA.A.3Represent and solve multiplicative equal groups problems using models and equations

3.OA.A.3Interpret the meaning of factors or products in equal groups problems

3

Block 1: Multiplicative Thinking (continued)


TOPIC 3: 10 as a FactorTopic Objectives CCSS


Meaning focus:Recognize and use patterns of multiplication by 10

Procedural focus:Multiply by 10 and by multiples of 10

5.NBT.A.2 Multiply factors by 10

4.NBT.B.5 5.NBT.A.2

Identify patterns in multiples of 10 and compare to place value

4.NBT.B.5Apply properties to multiply by multiples of 10

4.NBT.B.5Apply properties to multiply multiples of 10 by multiples of 10

3.OA.A.3Represent and solve multiplicative comparison problems using models and equations

3.OA.A.3Interpret the meaning of factors or products in multiplicative comparison problems

4

TOPIC 1: Place Value in MultiplicationTopic Objectives CCSS


Meaning focus:Understand place value whenmultiplying 1-digit by 2-digit factors

Procedural focus:Apply the Distributive Property to multiply 1-digit by 2-digit factors

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

Decompose factors to identify partialproducts when multiplying 1-digit by 2-digit factors to 19

3.NBT.A.3 4.NBT.B.5

Apply the Distributive Property to multiply 1-digit by 2-digit factors to 19

3.NBT.A.3 3.OA.B.5

Apply the Distributive Property to multiply 1-digit by 2-digit factors

3.OA.A.3 3.OA.B.5 3.OA.C.7

Analyze multiplicative problems and solve with appropriate models and equations

3.OA.A.3 3.OA.B.5 3.OA.C.7 3.OA.D.8

Describe solution strategies

Block 2: The Distributive Property


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TOPIC 2: Strategies for MultiplicationTopic Objectives CCSS


Meaning focus:Use place valueunderstanding to multiply 1-digit by3-digit factors

Procedural focus:Apply the Distributive Property to multiply 1-digit by 3-digit factors

3.NBT.A.3 4.NBT.B.5

Decompose factors to identify partialproducts when multiplying 1-digitby 3-digit factors

3.OA.B.5 4.NBT.B.5

Apply the Distributive Property when multiplying 1-digit by 3-digit factors

3.OA.B.5 4.NBT.B.5

Apply place = value understanding toestimate and compare products

3.OA.D.9 4.OA.C.5 6.EE.A.3

Identify multiplication patterns with whole numbers and describe with a rule

3.OA.B.5 4.NBT.B.5 4.OA.A.1 4.OA.A.2

Analyze multi-step additive andmultiplicative problems and solve with appropriate models and equations

3.OA.B.5 4.NBT.B.5 4.OA.A.1

Describe and explain reasoning in solution strategies

Block 2: The Distributive Property (continued)


6

Block 2: The Distributive Property (continued)


TOPIC 3: Digit MultiplicationTopic Objectives CCSS


Meaning focus:Use place valueunderstanding to multiply any factors

Procedural focus:Apply the Distributive Property to multiply any factors

3.OA.B.5 4.NBT.B.5

Decompose factors to identify partial products when multiplying 2-digit factors

3.OA.B.5 5.NBT.B.5

Apply the Distributive Property to multiply 2-digit factors

4.OA.A.1 4.OA.A.2

Create problems that can be represented by multiplication equations

4.OA.A.1 4.OA.A.2 4.OA.A.3

Represent and solve multiplicative problems and compare solution strategies

4.OA.A.1 4.OA.A.2 4.OA.A.3

Interpret the meaning of solutions in context

12 x 36

7


TOPIC 1: Equal Groups in DivisionTopic Objectives CCSS


Meaning focus:Understandthe meaning ofdivision

Procedural focus:Divide with1-digit divisorswithin 100

3.OA.A.2 3.OA.A.3 3.OA.A.4

Represent division as taking out equalgroups

3.OA.A.3 3.OA.A.4 3.OA.B.6

Solve division problems with multiplication

3.OA.A.3 4.NBT.B.6 Divide with remainders

3.OA.A.4 3.OA.B.6 4.NBT.B.6

Represent and solve division equal groups problems using models and equations

4.NBT.B.6 4.OA.A.3

Interpret the meaning of divisors, dividends, quotients, or remainders in context

Block 3: Division

8


TOPIC 2: Strategies for DivisionTopic Objectives CCSS


Meaning focus:Recognize and useplace value andrepeated subtractionto divide

Procedural focus:Divide by taking out10 and multiples of10 and 100

4.NBT.B.6 Take out 10 groups to divide

4.NBT.B.6Take out multiples of 10 groups todivide

4.NBT.B.6Take out multiples of 10 and 100 groups to divide

4.NBT.B.6Communicate reasoning aboutproperties of numbers

3.OA.A.4 3.OA.B.6 4.NBT.B.6

Use factors and multiples to classifynumbers and solve problems

Block 3: Division (continued)

9


Block 3: Division (continued)

TOPIC 3: Partial Quotient StrategyTopic Objectives CCSS


Meaning focus:Develop meaning formulti-digit division

Action focus:Divide with2-digit divisors

5.NBT.B.6 Divide by 10 and multiples of 10

4.NBT.B.6Divide 2-digit dividends by 2-digit divisors

5.NBT.B.66.NS.B.2

Divide 3- or 4-digit dividends by 2-digit divisors

4.NBT.B.6 5.NBT.B.6

Estimate quotients relative to multiplesof 10

4.OA.A.2Analyze and solve multi-step problemsituations using all four operations

4.OA.A.2Describe and compare solutionstrategies

10


TOPIC 1: Understanding FractionsTopic Objectives CCSS


Meaning focus:Understandfractions asparts of a whole

Procedural focus:Compose anddecomposefractions

3.NF.A.1 3.NF.A.2b 3.NF.A.3a 3.NF.A.3b 4.NF.B.3a 4.NF.B.3b

Represent equal parts of a whole asfractions

3.NF.A.1 3.NF.A.2b 3.NF.A.3a 3.NF.A.3b

Compose non-unit fractions andwholes from unit fractions

3.NF.A.2b 3.NF.A.3b 4.NF.A.1 4.NF.B.3b

Compare fractions using visualmodels and represent with equationsand inequalities

3.NF.A.2b 4.NF.B.3b

Communicate reasoning about therelative sizes of fractions

3.NF.A.3b 3.NF.A.3d 4.NF.B.3a 4.NF.B.3b

Solve problems by writing andevaluating equations with fractions

Block 4: Fraction Concepts

11


Block 4: Fraction Concepts (continued)

TOPIC 2: Equivalent Fraction ModelsTopic Objectives CCSS


Meaning focus:Developunderstandingof fractionequivalence

Procedural focus:Add with fractionmodels

3.NF.A.1 3.NF.A.3a 3.NF.A.3b 4.NF.B.3b

Extend understanding of unitfractions

5.NF.A.1 Add with fraction models

4.NF.B.3a 4.NF.B.3b

Represent numbers greater than 1 asfractions or mixed numbers

4.NF.B.3b 4.NF.B.3c 4.NF.B.3d

Represent and solve additiveproblems with fractions using models

12


Block 4: Fraction Concepts (continued)

TOPIC 3: Fractions as DivisionTopic Objectives CCSS


Meaning focus:Interpret fractions as division

Procedural focus:Compute quotients of whole numbers and express themas fractions

5.NF.B.3Represent sharing situations withfractions

3.NF.A.3b 5.NF.B.3

Use patterns to connect fractions todivision

3.NF.A.3c 5.NF.B.3

Represent whole numbers asfractions with given denominators

4.NBT.B.6 5.NF.B.3

Represent sharing situations withfractions and mixed numbers

5.NF.A.2 5.NF.B.3

Analyze and solve problem situations withfractions using models and equations

5.NF.A.2 5.NF.B.3

Describe and explain solution strategies for problems with fractions

13


Block 5: Fraction RelationshipsTOPIC 1: Strategies for Comparing FractionsTopic Objectives CCSS


Meaning focus:Use reasoningstrategies tocomparefractions

Procedural focus:Identify commonfeatures anduse benchmarksto comparefractions

4.NF.A.2Use reasoning to compare fractionswith common features

3.NF.A.3b Identify fractions equivalent to

3.NF.A.3bAnalyze and explain patterns innumerators and denominators offractions equivalent to

4.NF.A.2 Use and 1 as benchmarks tocompare fractions

4.NF.A.2Use equivalence and comparison toclassify fractions and solve problems

4.NF.A.2 Justify solutions to fraction problems

1_2

1_2

1_2

14


TOPIC 2: Equivalent Fractions on a Number Line Topic Objectives CCSS


Meaning focus:Recognize and compare equivalentfractions ona number line

Procedural focus:Generate,order, andlocate equivalentfractions ona number line

4.NF.A.1 4.NF.A.2 Generate equivalent fractions

4.NF.A.2Compare fractions by generating equivalents

3.NF.A.2b 4.NF.A.2 Locate fractions on a number line

3.NF.A.2b 4.NF.A.2 Describe relationships among fractions

4.NF.A.1 4.NF.A.2

Analyze and solve problems with one, more than one, or no solutions

Block 5: Fraction Relationships (continued)

15


Block 5: Fraction Relationships (continued)TOPIC 3: Adding and Subtracting FractionsTopic Objectives CCSS


Meaning focus:Apply understanding of addition andsubtraction to fractions

Procedural focus:Add and subtractfractions andmixed numbers

4.NF.B.3a 4.NF.B.3c

Subtract fractions and mixed numberswith the same denominators

5.NF.A.1Add fractions and mixed numbers with different denominators

5.NF.A.1 5.NF.A.2

Subtract fractions and mixed numberswith different denominators

5.NF.A.1 5.NF.A.2

Estimate sums and differences relative to benchmark whole numbers

5.NF.A.2Represent and solve additive problemsituations with fractions using modelsand equations

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TOPIC 1: Unit Fraction MultiplicationTopic Objectives CCSS


Meaning focus:Apply understanding of multiplicationto fractions

Procedural focus:Multiply withunit fractions

5.NF.B.4a Represent parts of sets as fractions

4.NF.B.4aMultiply whole numbers and unitfractions

4.NF.B.4aExplain the relationship between multiplying by unit fractions and dividing by whole numbers

4.NF.B.4a Multiply unit fractions by unit fractions

4.NF.B.4cRepresent and solve multiplicativecomparison problems with fractionsusing models and equations

Block 6: Fraction Multiplication and Division


17

TOPIC 2: Strategies for MultiplicationTopic Objectives CCSS


Meaning focus:Developstrategies tomultiplyfractions

Procedural focus:Multiply non-unitfractions by wholenumbers ornon-unit fractions

4.NF.B.4bMultiply whole numbers by non-unitfractions

5.NF.B.4b Multiply non-unit fractions

5.NF.B.4bApply the Distributive Property tomultiply mixed numbers

5.NBT.B.6 5.NF.B.6

Analyze and solve multi-step problems with fractions using models and equations

5.NBT.B.6 5.NF.B.6

Explain and compare solution strategies for problems with fractions

Block 6: Fraction Multiplication and Division (continued)


18

Block 6: Fraction Multiplication and Division (continued)


TOPIC 3: Strategies for Dividing FractionsTopic Objectives CCSS


Meaning focus:Developreasoningstrategies todivide fractions

Procedural focus:Divide fractions

5.NF.B.3Model division with fractions as takingout equal groups

5.NF.B.7aDivide by unit fractions using acommon denominator method

5.NF.B.7a6.NS.A.1

Divide any fractions using a commondenominator method

5.NF.B.7aIdentify patterns with whole numbersand fractions and describe with more than one rule

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Block 7: Decimals and Place Value


TOPIC 1: Fraction and Decimal RelationshipsTopic Objectives CCSS


Meaning focus:Understand the relationshipof fractionsand decimals

Procedural focus:Express fractions to decimals

4.NF.A.1 4.NF.C.6

Express fractions with denominatorsof 10 and 100 as decimals

4.NF.A.1 4.NF.C.6

Use equivalence to express fractionsless than 1 as decimals

4.NF.A.1 4.NF.C.6

Identify and express decimals inequivalent form

4.NF.A.2 4.NF.C.6

Use equivalence and comparison toclassify fractions and decimals andsolve problems

20

TOPIC 2: Decimal Place ValueTopic Objectives CCSS


Meaning focus:Extend wholenumberunderstandingof place valueto decimals

Procedural focus:Read and write decimals in more than one form

5.NBT.A.3a Identify place value in decimals

5.NBT.A.1Multiply and divide decimals by 10,100, and 1000

5.NF.B.3Express fractions as decimals usingdivision

5.NBT.A.3bCompare decimal place value tosolve problems

5.NBT.A.3bJustify solutions to decimal comparison problems using models and reasoning

Block 7: Decimals and Place Value (continued)


21

Block 7: Decimals and Place Value (continued)


TOPIC 3: Decimals on a Number LineTopic Objectives CCSS


Meaning focus:Extendunderstandingof the numbersystem to decimals

Procedural focus:Compare, order, and locate decimals on anumber line

4.NF.C.6 Locate decimals on a number line

4.NF.C.7 Compare and order decimals

5.NBT.A.3a 5.NBT.A.3b

Apply understanding of place valueand equivalence to name decimalsbetween decimals

5.NBT.BSolve problems by writing andevaluating equations with decimals

3.142

1.3 = k + k + 0.5

= k + k +

k + k =

2k = 0.8

k = 0.4 lb

13—105—10

8—10

22

Block 8: Decimal Operations


TOPIC 1: Adding and Subtracting DecimalsTopic Objectives CCSS


Meaning focus:Apply meaning ofplace value andaddition andsubtractionto decimals

Procedural focus:Add and subtractdecimals

5.NBT.B.7 Apply place value to add decimals

5.NBT.B.7 Add decimals

5.NBT.B.7 Use models to subtract decimals

5.NBT.B.7 Estimate sums and differences ofdecimals relative to benchmarks

5.NBT.B.7Analyze and solve additive problemswith decimals using models andequations

23

Block 8: Decimal Operations (continued)


TOPIC 2: Decimal Multiplication Topic Objectives CCSS


Meaning focus:Understand the relative magnitudeof decimal products

Procedural focus:Multiply decimals

5.NBT.B.7Multiply whole numbers by decimalsless than 1

5.NBT.B.7 Multiply decimals less than 1 bydecimals less than 1

5.NBT.B.7Apply the Distributive Property tomultiply decimals

5.NBT.B.2Identify patterns with decimals and describe with a rule

5.NBT.B.7 Estimate the product of decimals

24

Block 8: Decimal Operations (continued)


TOPIC 3: Patterns in Decimal DivisionTopic Objectives CCSS

AlignmentContent Objectives Selected Examples

Meaning focus:Apply understanding of place value anddivision to decimals

Procedural focus:Divide decimals

5.NBT.B.7 Divide decimals using equal groups

5.NBT.B.7Analyze and explain patterns inequivalent division

5.NBT.B.7 Divide decimals

5.NBT.B.7Estimate decimal quotients relative tobenchmarks

15.NBT.B.7Analyze and solve problems with decimals using models and equations

5.NBT.B.7 Describe and explain solution strategies for problems with decimals

25

Block 9: Both Sides of Zero


TOPIC 1: Rational Numbers on a Number LineTopic Objectives CCSS


Meaning focus:Extendunderstanding of the number system to positive and negative numbers

Procedural focus:Locate positive and negative numbers on a number line

6.NS.C.5 6.NS.C.6c

Generate situations that can berepresented by integers

6.NS.C.6a 6.NS.C.6c

Locate positive and negative numberson a number line

6.NS.C.6a 6.NS.C.7a

Compare and order positive andnegative numbers

6.NS.C.5Use direction on a number line andcomparison to classify numbers and solve problems

26

Block 9: Both Sides of Zero (continued)


TOPIC 2: Adding Rational NumbersTopic Objectives CCSS


Meaning focus:Extend understanding ofaddition topositive andnegative numbers

Procedural focus:Use models toadd and comparepositive andnegative numbers

6.NS.C.5 6.NS.C.7a

Use distance from 0 to add 2 positive or 2 negative numbers

7.NS.A.1a Add positive and negative integers

6.NS.C.5 7.NS.A.1b Add positive and negative numbers

6.NS.C.5 6.NS.C.7a 7.NS.A.1a

Analyze and solve problems withpositive and negative numbers

6.NS.C.5 6.NS.C.7a 7.NS.A.1a

Explain reasoning in problems withpositive and negative numbers

27

Block 9: Both Sides of Zero (continued)


TOPIC 3: Subtracting Rational NumbersTopic Objectives CCSS


Meaning focus:Extend understanding ofsubtraction to positive and negative numbers

Procedural focus:Use models tosubtract positive andnegative numbers

6.NS.C.6cSubtract by finding the distance between 2 positive or negative integers

6.NS.C.5 6.NS.C.6c

Subtract by finding the distance between positive and negative integers

7.NS.A.1a 7.NS.A.1c

Subtract positive and negativenumbers

7.EE.B.4aSolve problems by writing and evaluating equations with positive and negative numbers

Job #6661 6/13

scope & sequence - houghton mifflin harcourt

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