IXL skill plan | Level 3 plan for Eureka Math2

Skill plan for Eureka Math² - Level 3

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1	Module 1 Multiplication and Division with Units of 2, 3, 4, 5, and 10
Topic A - Conceptual Understanding of Multiplication
Lesson 1: Organize, count, and represent a collection of objects.		1. Skip-count
Lesson 1: Organize, count, and represent a collection of objects.
1. Skip-count

Lesson 2: Interpret equal groups as multiplication.		1. Relate addition and multiplication for equal groups: factors up to 5 2. Write multiplication sentences for equal groups: factors up to 5 Also consider: • Identify multiplication expressions for equal groups
Lesson 2: Interpret equal groups as multiplication.
1. Relate addition and multiplication for equal groups: factors up to 5 2. Write multiplication sentences for equal groups: factors up to 5 Also consider: • Identify multiplication expressions for equal groups

Lesson 3: Relate multiplication to the array model.		1. Identify multiplication expressions for arrays 2. Write multiplication sentences for arrays Also consider: • Multiply 5 by numbers up to 10 • Multiply 10 by numbers up to 10
Lesson 3: Relate multiplication to the array model.
1. Identify multiplication expressions for arrays 2. Write multiplication sentences for arrays Also consider: • Multiply 5 by numbers up to 10 • Multiply 10 by numbers up to 10

Lesson 4: Interpret the meaning of factors as number of groups or number in each group.		1. Count equal groups: factors up to 5 Also consider: • Multiply by 5 and 10
Lesson 4: Interpret the meaning of factors as number of groups or number in each group.
1. Count equal groups: factors up to 5 Also consider: • Multiply by 5 and 10

Lesson 5: Represent and solve multiplication word problems by using drawings and equations.		1. Multiplication word problems with 5 and 10
Lesson 5: Represent and solve multiplication word problems by using drawings and equations.
1. Multiplication word problems with 5 and 10
Topic B - Conceptual Understanding of Division
Lesson 6: Explore measurement and partitive division by modeling concretely and drawing.		1. Divide by counting equal groups Also consider: • Count equal groups
Lesson 6: Explore measurement and partitive division by modeling concretely and drawing.
1. Divide by counting equal groups Also consider: • Count equal groups

Lesson 7: Model measurement and partitive division by drawing equal groups.		1. Write division sentences for groups 2. Relate multiplication and division for groups Also consider: • Divide by 5: quotients up to 10 • Divide by 10: quotients up to 10
Lesson 7: Model measurement and partitive division by drawing equal groups.
1. Write division sentences for groups 2. Relate multiplication and division for groups Also consider: • Divide by 5: quotients up to 10 • Divide by 10: quotients up to 10

Lesson 8: Model measurement and partitive division by drawing arrays.		1. Write division sentences for arrays 2. Make arrays to model division 3. Relate multiplication and division for arrays Also consider: • Multiply and divide by 5 and 10
Lesson 8: Model measurement and partitive division by drawing arrays.
1. Write division sentences for arrays 2. Make arrays to model division 3. Relate multiplication and division for arrays Also consider: • Multiply and divide by 5 and 10

Lesson 9: Represent and solve division word problems using drawings and equations.		1. Division word problems: divisors and quotients up to 5
Lesson 9: Represent and solve division word problems using drawings and equations.
1. Division word problems: divisors and quotients up to 5
Topic C - Properties of Multiplication
Lesson 10: Demonstrate the commutative property of multiplication using a unit of 2 and the array model.		1. Write multiplication sentences for arrays: multiply by 2 2. Multiply 2 by numbers up to 10 Also consider: • Skip-counting sequences: count by twos • Multiply by 2 using a number line
Lesson 10: Demonstrate the commutative property of multiplication using a unit of 2 and the array model.
1. Write multiplication sentences for arrays: multiply by 2 2. Multiply 2 by numbers up to 10 Also consider: • Skip-counting sequences: count by twos • Multiply by 2 using a number line

Lesson 11: Demonstrate the commutative property of multiplication using a unit of 4 and the array model.		1. Write multiplication sentences for arrays: multiply by 4 Also consider: • Multiply by 4 using a number line • Multiply by 2 and 4 in recipes
Lesson 11: Demonstrate the commutative property of multiplication using a unit of 4 and the array model.
1. Write multiplication sentences for arrays: multiply by 4 Also consider: • Multiply by 4 using a number line • Multiply by 2 and 4 in recipes

Lesson 12: Demonstrate the distributive property using a unit of 4.		1. Multiply 4 by numbers up to 10
Lesson 12: Demonstrate the distributive property using a unit of 4.
1. Multiply 4 by numbers up to 10

Lesson 13: Demonstrate the commutative property of multiplication using a unit of 3 and the array model.		1. Write multiplication sentences for arrays: multiply by 3 2. Multiply 3 by numbers up to 10 Also consider: • Make arrays to model multiplication with 2 and 3 • Multiplication facts for 2 and 3: sorting
Lesson 13: Demonstrate the commutative property of multiplication using a unit of 3 and the array model.
1. Write multiplication sentences for arrays: multiply by 3 2. Multiply 3 by numbers up to 10 Also consider: • Make arrays to model multiplication with 2 and 3 • Multiplication facts for 2 and 3: sorting

Lesson 14: Demonstrate the distributive property using units of 2, 3, 4, 5, and 10.		1. Multiply one-digit numbers with grids: using facts up to 5 2. Use the distributive property to multiply by 3, 4, or 5 Also consider: • Multiplication facts for 2, 3, 4, 5, and 10 • Multiplication facts for 2, 3, 4, 5, and 10: sorting
Lesson 14: Demonstrate the distributive property using units of 2, 3, 4, 5, and 10.
1. Multiply one-digit numbers with grids: using facts up to 5 2. Use the distributive property to multiply by 3, 4, or 5 Also consider: • Multiplication facts for 2, 3, 4, 5, and 10 • Multiplication facts for 2, 3, 4, 5, and 10: sorting
Topic D - Two Interpretations of Division
Lesson 15: Model division as an unknown factor problem.		1. Multiplication word problems with factors up to 5: find the missing number 2. Multiplication facts for 2, 3, 4, 5, and 10: find the missing factor Also consider: • Relate multiplication and division: divisors of 2, 3, 4, 5, and 10 • Write multiplication and division sentences for equal groups • Write multiplication and division sentences for arrays • Divide by 2: quotients up to 10 • Divide by 3: quotients up to 10 • Divide by 4: quotients up to 10
Lesson 15: Model division as an unknown factor problem.
1. Multiplication word problems with factors up to 5: find the missing number 2. Multiplication facts for 2, 3, 4, 5, and 10: find the missing factor Also consider: • Relate multiplication and division: divisors of 2, 3, 4, 5, and 10 • Write multiplication and division sentences for equal groups • Write multiplication and division sentences for arrays • Divide by 2: quotients up to 10 • Divide by 3: quotients up to 10 • Divide by 4: quotients up to 10

Lesson 16: Model the quotient as the number of groups using units of 2, 3, 4, 5, and 10.		1. Division word problems: how many equal groups?
Lesson 16: Model the quotient as the number of groups using units of 2, 3, 4, 5, and 10.
1. Division word problems: how many equal groups?

Lesson 17: Model the quotient as the size of each group using units of 2, 3, 4, 5, and 10.		1. Division word problems: how many in each group?
Lesson 17: Model the quotient as the size of each group using units of 2, 3, 4, 5, and 10.
1. Division word problems: how many in each group?

Lesson 18: Represent and solve measurement and partitive division word problems.		1. Use equal groups and arrays to solve division word problems Also consider: • Division facts for 2, 3, 4, 5, and 10: sorting
Lesson 18: Represent and solve measurement and partitive division word problems.
1. Use equal groups and arrays to solve division word problems Also consider: • Division facts for 2, 3, 4, 5, and 10: sorting
Topic E - Application of Multiplication and Division Concepts
Lesson 19: Use the distributive property to break apart multiplication problems into known facts.		1. Multiply using the distributive property
Lesson 19: Use the distributive property to break apart multiplication problems into known facts.
1. Multiply using the distributive property

Lesson 20: Use the distributive property to break apart division problems into known facts.		1. Division facts for 2, 3, 4, 5, and 10
Lesson 20: Use the distributive property to break apart division problems into known facts.
1. Division facts for 2, 3, 4, 5, and 10

Lesson 21: Compose and decompose arrays to create expressions with three factors.		1. Multiply three numbers
Lesson 21: Compose and decompose arrays to create expressions with three factors.
1. Multiply three numbers

Lesson 22: Represent and solve two-step word problems using the properties of multiplication. Lesson 23: Represent and solve two-step word problems using drawings and equations.		1. Two-step multiplication and division word problems Also consider: • Multiplication and division word problems: factors up to 5
Lesson 22: Represent and solve two-step word problems using the properties of multiplication. Lesson 23: Represent and solve two-step word problems using drawings and equations.
1. Two-step multiplication and division word problems Also consider: • Multiplication and division word problems: factors up to 5

2	Module 2 Place Value Concepts Through Metric Measurement
Topic A - Understanding Place Value Concepts Through Metric Measurement
Lesson 1: Connect the composition of 1 kilogram to the composition of 1 thousand.		1. Convert between place values - up to thousands Also consider: • Place value models up to hundreds
Lesson 1: Connect the composition of 1 kilogram to the composition of 1 thousand.
1. Convert between place values - up to thousands Also consider: • Place value models up to hundreds

Lesson 2: Estimate the weight of familiar objects and read scales when weighing objects.		1. Which metric unit of mass is appropriate? 2. Read a scale - metric units Also consider: • Compare and convert metric units of mass
Lesson 2: Estimate the weight of familiar objects and read scales when weighing objects.
1. Which metric unit of mass is appropriate? 2. Read a scale - metric units Also consider: • Compare and convert metric units of mass

Lesson 3: Use all four operations to solve one-step word problems involving weight.		1. Addition, subtraction, multiplication, and division word problems
Lesson 3: Use all four operations to solve one-step word problems involving weight.
1. Addition, subtraction, multiplication, and division word problems

Lesson 4: Connect decomposition of 1 liter to the decomposition of 1 thousand. Lesson 5: Estimate and measure liquid volume using a vertical number line and connect composition of 1 liter to composition of 1 thousand.		1. Measure liquid volumes - metric units Also consider: • Compare and convert metric units of volume • Which metric unit of volume is appropriate?
Lesson 4: Connect decomposition of 1 liter to the decomposition of 1 thousand. Lesson 5: Estimate and measure liquid volume using a vertical number line and connect composition of 1 liter to composition of 1 thousand.
1. Measure liquid volumes - metric units Also consider: • Compare and convert metric units of volume • Which metric unit of volume is appropriate?

Lesson 6: Use all four operations to solve one-step word problems involving liquid volume. Lesson 7: Solve one-step word problems using metric units.		1. Measurement word problems Also consider: • Choose the appropriate measuring tool
Lesson 6: Use all four operations to solve one-step word problems involving liquid volume. Lesson 7: Solve one-step word problems using metric units.
1. Measurement word problems Also consider: • Choose the appropriate measuring tool
Topic B - Rounding to the Nearest Ten and Hundred
Lesson 8: Read temperatures on a thermometer using number line concepts.		1. Read a thermometer Also consider: • Number lines up to 100: multiples of ten • Number lines up to 100
Lesson 8: Read temperatures on a thermometer using number line concepts.
1. Read a thermometer Also consider: • Number lines up to 100: multiples of ten • Number lines up to 100

Lesson 9: Round two-digit numbers to the nearest ten on the vertical number line.		1. Round to the nearest ten using a number line 2. Round to the nearest ten Also consider: • Measure using a centimeter ruler
Lesson 9: Round two-digit numbers to the nearest ten on the vertical number line.
1. Round to the nearest ten using a number line 2. Round to the nearest ten Also consider: • Measure using a centimeter ruler

Lesson 10: Round two- and three-digit numbers to the nearest ten on the vertical number line. Lesson 11: Round to the nearest hundred on the vertical number line.		1. Round to the nearest ten or hundred in a table Also consider: • Round to the nearest ten or hundred using a number line • Round to the nearest ten or hundred
Lesson 10: Round two- and three-digit numbers to the nearest ten on the vertical number line. Lesson 11: Round to the nearest hundred on the vertical number line.
1. Round to the nearest ten or hundred in a table Also consider: • Round to the nearest ten or hundred using a number line • Round to the nearest ten or hundred

Lesson 12: Estimate sums and differences by rounding.		1. Estimate sums by rounding: up to 1,000 2. Estimate differences by rounding: up to 1,000 3. Estimate sums and differences: word problems Also consider: • Estimate sums and differences using compatible numbers
Lesson 12: Estimate sums and differences by rounding.
1. Estimate sums by rounding: up to 1,000 2. Estimate differences by rounding: up to 1,000 3. Estimate sums and differences: word problems Also consider: • Estimate sums and differences using compatible numbers
Topic C - Simplifying Strategies to Find Sums and Differences
Lesson 13: Collect and represent data in a scaled bar graph and solve related problems.		1. Interpret scaled bar graphs 2. Use bar graphs to solve problems 3. Create scaled bar graphs
Lesson 13: Collect and represent data in a scaled bar graph and solve related problems.
1. Interpret scaled bar graphs 2. Use bar graphs to solve problems 3. Create scaled bar graphs

Lesson 14: Use place value understanding to add and subtract like units.		1. Use expanded form to add three-digit numbers: without regrouping 2. Use models to subtract numbers up to three-digits: without regrouping Also consider: • Use models to add three-digit numbers: without regrouping
Lesson 14: Use place value understanding to add and subtract like units.
1. Use expanded form to add three-digit numbers: without regrouping 2. Use models to subtract numbers up to three-digits: without regrouping Also consider: • Use models to add three-digit numbers: without regrouping

Lesson 15: Use the associative property to make the next ten to add.		1. Add two numbers up to three digits using place value Also consider: • Use number lines to add three-digit numbers • Complete the addition sentence: make ten • Complete the addition sentence: make 100
Lesson 15: Use the associative property to make the next ten to add.
1. Add two numbers up to three digits using place value Also consider: • Use number lines to add three-digit numbers • Complete the addition sentence: make ten • Complete the addition sentence: make 100

Lesson 16: Use compensation to add.		1. Use compensation to add: up to three digits Also consider: • Use compensation to add: sums up to 200
Lesson 16: Use compensation to add.
1. Use compensation to add: up to three digits Also consider: • Use compensation to add: sums up to 200

Lesson 17: Use place value understanding to subtract efficiently using take from a ten.		1. Subtract with two-digit or three-digit numbers
Lesson 17: Use place value understanding to subtract efficiently using take from a ten.
1. Subtract with two-digit or three-digit numbers

Lesson 18: Use place value understanding to subtract efficiently using take from a hundred.		1. Subtract three-digit numbers: with regrouping Also consider: • Use expanded form to subtract three-digit numbers • Use number lines to subtract three-digit numbers • Subtract three-digit numbers: without regrouping
Lesson 18: Use place value understanding to subtract efficiently using take from a hundred.
1. Subtract three-digit numbers: with regrouping Also consider: • Use expanded form to subtract three-digit numbers • Use number lines to subtract three-digit numbers • Subtract three-digit numbers: without regrouping

Lesson 19: Use compensation to subtract.		1. Use compensation to subtract: up to three digits Also consider: • Use compensation to subtract: up to two digits
Lesson 19: Use compensation to subtract.
1. Use compensation to subtract: up to three digits Also consider: • Use compensation to subtract: up to two digits
Topic D - Two- and Three-Digit Measurement Addition and Subtraction
Lesson 20: Add measurements using the standard algorithm to compose larger units once.		1. Use models to add three-digit numbers: regroup tens or ones Also consider: • Add two numbers up to three digits: without regrouping
Lesson 20: Add measurements using the standard algorithm to compose larger units once.
1. Use models to add three-digit numbers: regroup tens or ones Also consider: • Add two numbers up to three digits: without regrouping

Lesson 21: Add measurements using the standard algorithm to compose larger units twice.		1. Use models to add three-digit numbers: with regrouping 2. Add two numbers up to three digits: with regrouping 3. Add two numbers up to three digits: word problems Also consider: • Add mixed units
Lesson 21: Add measurements using the standard algorithm to compose larger units twice.
1. Use models to add three-digit numbers: with regrouping 2. Add two numbers up to three digits: with regrouping 3. Add two numbers up to three digits: word problems Also consider: • Add mixed units

Lesson 22: Subtract measurements using the standard algorithm to decompose larger units once.		1. Use models to subtract numbers up to three-digits: with regrouping 2. Subtract three-digit numbers: regroup tens or hundreds Also consider: • Subtract two-digit numbers: with regrouping • Subtract numbers up to three digits: without regrouping
Lesson 22: Subtract measurements using the standard algorithm to decompose larger units once.
1. Use models to subtract numbers up to three-digits: with regrouping 2. Subtract three-digit numbers: regroup tens or hundreds Also consider: • Subtract two-digit numbers: with regrouping • Subtract numbers up to three digits: without regrouping

Lesson 23: Subtract measurements using the standard algorithm to decompose larger units twice.		1. Subtract three-digit numbers: regroup tens and hundreds 2. Subtract numbers up to three digits: word problems Also consider: • Subtract mixed units
Lesson 23: Subtract measurements using the standard algorithm to decompose larger units twice.
1. Subtract three-digit numbers: regroup tens and hundreds 2. Subtract numbers up to three digits: word problems Also consider: • Subtract mixed units

Lesson 24: Subtract measurements using the standard algorithm to decompose larger units across two place values.		1. Subtract across zeros
Lesson 24: Subtract measurements using the standard algorithm to decompose larger units across two place values.
1. Subtract across zeros

Lesson 25: Solve two-step word problems.		1. Two-step addition and subtraction word problems Also consider: • Addition and subtraction word problems: up to three digits
Lesson 25: Solve two-step word problems.
1. Two-step addition and subtraction word problems Also consider: • Addition and subtraction word problems: up to three digits

3	Module 3 Multiplication and Division with Units of 0, 1, 6, 7, 8, and 9
Topic A - Multiplication and Division Concepts with an Emphasis on Units of 6 and 8
Lesson 1: Organize, count, and represent a collection of objects.		1. Skip-count with tables
Lesson 1: Organize, count, and represent a collection of objects.
1. Skip-count with tables

Lesson 2: Count by units of 6 to multiply and divide by using arrays.		1. Skip-counting sequences: count by threes 2. Skip-counting sequences: count by sixes
Lesson 2: Count by units of 6 to multiply and divide by using arrays.
1. Skip-counting sequences: count by threes 2. Skip-counting sequences: count by sixes

Lesson 3: Count by units of 8 to multiply and divide by using arrays.		1. Skip-counting sequences: count by fours 2. Skip-counting sequences: count by eights
Lesson 3: Count by units of 8 to multiply and divide by using arrays.
1. Skip-counting sequences: count by fours 2. Skip-counting sequences: count by eights

Lesson 4: Decompose pictorial arrays to create expressions with three factors.
Lesson 4: Decompose pictorial arrays to create expressions with three factors.


Lesson 5: Use the break apart and distribute strategy to multiply with units of 6 and 8.		1. Multiply 6 by numbers up to 10 2. Multiply 8 by numbers up to 10
Lesson 5: Use the break apart and distribute strategy to multiply with units of 6 and 8.
1. Multiply 6 by numbers up to 10 2. Multiply 8 by numbers up to 10

Lesson 6: Use the break apart and distribute strategy to divide with units of 6 and 8.		1. Divide by 6: quotients up to 10 2. Divide by 8: quotients up to 10
Lesson 6: Use the break apart and distribute strategy to divide with units of 6 and 8.
1. Divide by 6: quotients up to 10 2. Divide by 8: quotients up to 10
Topic B - Multiplication and Division Concepts with an Emphasis on the Unit of 7
Lesson 7: Count by units of 7 to multiply and divide by using arrays and tape diagrams.		1. Skip-counting sequences: count by sevens
Lesson 7: Count by units of 7 to multiply and divide by using arrays and tape diagrams.
1. Skip-counting sequences: count by sevens

Lesson 8: Use the break apart and distribute strategy to multiply with units of 7.		1. Multiply 7 by numbers up to 10
Lesson 8: Use the break apart and distribute strategy to multiply with units of 7.
1. Multiply 7 by numbers up to 10

Lesson 9: Model the associative property as a strategy to multiply.		1. Properties of multiplication
Lesson 9: Model the associative property as a strategy to multiply.
1. Properties of multiplication

Lesson 10: Use parentheses in expressions with different operations.		1. Understanding parentheses
Lesson 10: Use parentheses in expressions with different operations.
1. Understanding parentheses

Lesson 11: Use the break apart and distribute strategy to divide with units of 7.		1. Divide by 7: quotients up to 10
Lesson 11: Use the break apart and distribute strategy to divide with units of 7.
1. Divide by 7: quotients up to 10

Lesson 12: Solve one-step word problems involving multiplication and division.		1. Multiplication and division word problems
Lesson 12: Solve one-step word problems involving multiplication and division.
1. Multiplication and division word problems
Topic C - Analysis of Patterns Using Units of 9, 0, and 1
Lesson 13: Count by units of 9 to multiply.		1. Skip-counting sequences: count by nines Also consider: • Multiplication facts for 6, 7, 8, and 9 • Write two multiplication sentences for an array
Lesson 13: Count by units of 9 to multiply.
1. Skip-counting sequences: count by nines Also consider: • Multiplication facts for 6, 7, 8, and 9 • Write two multiplication sentences for an array

Lesson 14: Apply strategies and identify patterns to multiply with units of 9.		1. Multiply 9 by numbers up to 10 Also consider: • Multiplication facts for 6, 7, 8, and 9: sorting • Multiplication facts for 6, 7, 8, and 9: find the missing factor • Divide by 9: quotients up to 10
Lesson 14: Apply strategies and identify patterns to multiply with units of 9.
1. Multiply 9 by numbers up to 10 Also consider: • Multiplication facts for 6, 7, 8, and 9: sorting • Multiplication facts for 6, 7, 8, and 9: find the missing factor • Divide by 9: quotients up to 10

Lesson 15: Reason about and explain patterns of multiplication and division with units of 1 and 0.		1. Multiply by 0 or 1 2. Division sentences with 1 and 0 3. Multiply by 0 or 1: complete the sentence Also consider: • Multiply and divide with 1 and 0
Lesson 15: Reason about and explain patterns of multiplication and division with units of 1 and 0.
1. Multiply by 0 or 1 2. Division sentences with 1 and 0 3. Multiply by 0 or 1: complete the sentence Also consider: • Multiply and divide with 1 and 0

Lesson 16: Identify patterns by using the multiplication table.		1. Even or odd: multiplication patterns 2. Identify multiplication patterns in tables
Lesson 16: Identify patterns by using the multiplication table.
1. Even or odd: multiplication patterns 2. Identify multiplication patterns in tables

Lesson 17: Identify and complete patterns with input–output tables.		1. Multiplication and division: real-world patterns 2. Multiplication input/output tables 3. Division input/output tables Also consider: • Multiplication input/output tables: find the rule • Division input/output tables: find the rule
Lesson 17: Identify and complete patterns with input–output tables.
1. Multiplication and division: real-world patterns 2. Multiplication input/output tables 3. Division input/output tables Also consider: • Multiplication input/output tables: find the rule • Division input/output tables: find the rule

Lesson 18: Create multiplication and division word problems.		1. Write equations with unknown numbers to represent word problems: multiplication and division only 2. Division facts up to 10 3. Multiplication facts up to 10 Also consider: • Multiplication facts up to 10: sorting • Multiplication facts up to 10: select the missing factors • Division facts up to 10: find the missing number
Lesson 18: Create multiplication and division word problems.
1. Write equations with unknown numbers to represent word problems: multiplication and division only 2. Division facts up to 10 3. Multiplication facts up to 10 Also consider: • Multiplication facts up to 10: sorting • Multiplication facts up to 10: select the missing factors • Division facts up to 10: find the missing number

Lesson 19: Solve two-step word problems by using the four operations and assess the reasonableness of solutions.		1. Two-step word problems: identify reasonable answers 2. Two-step mixed operation word problems
Lesson 19: Solve two-step word problems by using the four operations and assess the reasonableness of solutions.
1. Two-step word problems: identify reasonable answers 2. Two-step mixed operation word problems
Topic D - Multiplication with Multiples of 10 and Further Application of Concepts
Lesson 20: Multiply by multiples of 10 by using the place value chart.		1. Multiply by a multiple of ten using place value
Lesson 20: Multiply by multiples of 10 by using the place value chart.
1. Multiply by a multiple of ten using place value

Lesson 21: Multiply by multiples of 10 by using place value strategies and the associative property.		1. Multiply by a multiple of ten
Lesson 21: Multiply by multiples of 10 by using place value strategies and the associative property.
1. Multiply by a multiple of ten

Lesson 22: Solve two-step word problems involving multiplication of single-digit factors and multiples of 10.		1. Multiply multiples of ten by one-digit numbers
Lesson 22: Solve two-step word problems involving multiplication of single-digit factors and multiples of 10.
1. Multiply multiples of ten by one-digit numbers

Lesson 23: Identify patterns and apply strategies to multiply with units of 11 and 12. (Optional)		1. Multiply 11 by numbers up to 12 2. Multiply 12 by numbers up to 12 Also consider: • Multiplication facts to 12 • Multiplication facts up to 12: find the missing factor
Lesson 23: Identify patterns and apply strategies to multiply with units of 11 and 12. (Optional)
1. Multiply 11 by numbers up to 12 2. Multiply 12 by numbers up to 12 Also consider: • Multiplication facts to 12 • Multiplication facts up to 12: find the missing factor

Lesson 24: Organize, count, and represent a collection of objects.		1. Estimate the number of objects to the nearest ten
Lesson 24: Organize, count, and represent a collection of objects.
1. Estimate the number of objects to the nearest ten

Lesson 25: Apply multiplication and division concepts to complete a multi-part task. (Optional)		1. Write equations with unknown numbers to represent word problems
Lesson 25: Apply multiplication and division concepts to complete a multi-part task. (Optional)
1. Write equations with unknown numbers to represent word problems

4	Module 4 Multiplication and Area
Topic A - Foundations for Understanding Area
Lesson 1: Explore attributes of squares, rectangles, and trapezoids.		1. Sides and angles of quadrilaterals 2. Identify trapezoids Also consider: • Identify rectangles • Open and closed shapes
Lesson 1: Explore attributes of squares, rectangles, and trapezoids.
1. Sides and angles of quadrilaterals 2. Identify trapezoids Also consider: • Identify rectangles • Open and closed shapes

Lesson 2: Recognize area as an attribute of polygons.		1. Find the area of figures made of unit squares 2. Area of figures on grids
Lesson 2: Recognize area as an attribute of polygons.
1. Find the area of figures made of unit squares 2. Area of figures on grids

Lesson 3: Tile polygons to find their areas.		1. Select two figures with the same area 2. Create figures with a given area
Lesson 3: Tile polygons to find their areas.
1. Select two figures with the same area 2. Create figures with a given area

Lesson 4: Compose rectangles to compare areas.		1. Tile a rectangle and find the area Also consider: • Select figures with a given area
Lesson 4: Compose rectangles to compare areas.
1. Tile a rectangle and find the area Also consider: • Select figures with a given area

Lesson 5: Relate side lengths to the number of tiles on a side.		1. Measure using an inch ruler: nearest inch 2. Measure using a centimeter ruler 3. Create rectangles with a given area
Lesson 5: Relate side lengths to the number of tiles on a side.
1. Measure using an inch ruler: nearest inch 2. Measure using a centimeter ruler 3. Create rectangles with a given area
Topic B - Concepts of Area Measurement
Lesson 6: Tile rectangles with squares to make arrays and relate the side lengths to area.		1. Multiply to find the area of a rectangle made of unit squares
Lesson 6: Tile rectangles with squares to make arrays and relate the side lengths to area.
1. Multiply to find the area of a rectangle made of unit squares

Lesson 7: Draw rows and columns to complete a rectangular array and determine its area.		1. Make arrays to model multiplication
Lesson 7: Draw rows and columns to complete a rectangular array and determine its area.
1. Make arrays to model multiplication

Lesson 8: Determine the area of a rectangle by using side lengths.		1. Find the area of rectangles: side lengths up to 5 units
Lesson 8: Determine the area of a rectangle by using side lengths.
1. Find the area of rectangles: side lengths up to 5 units

Lesson 9: Multiply side lengths to find the area of a rectangle.		1. Find the area of rectangles and squares 2. Find the missing side length of a rectangle 3. Find the area of rectangles: word problems
Lesson 9: Multiply side lengths to find the area of a rectangle.
1. Find the area of rectangles and squares 2. Find the missing side length of a rectangle 3. Find the area of rectangles: word problems
Topic C - Applying Properties of Operations to Area
Lesson 10: Compose large rectangles and reason about their areas. Lesson 11: Decompose to find the total area of a rectangle.		1. Multiply one-digit numbers by teen numbers using grids Also consider: • Break apart two-digit numbers to multiply
Lesson 10: Compose large rectangles and reason about their areas. Lesson 11: Decompose to find the total area of a rectangle.
1. Multiply one-digit numbers by teen numbers using grids Also consider: • Break apart two-digit numbers to multiply

Lesson 12: Find all possible side lengths of rectangles with a given area.		1. Make arrays to model multiplication: given products Also consider: • Multiplication sentences up to 10: true or false?
Lesson 12: Find all possible side lengths of rectangles with a given area.
1. Make arrays to model multiplication: given products Also consider: • Multiplication sentences up to 10: true or false?
Topic D - Applications of Area
Lesson 13: Apply area understanding to real-world situations.		1. Word problems with area
Lesson 13: Apply area understanding to real-world situations.
1. Word problems with area

Lesson 14: Reason to find the area of composite shapes by using grids.		1. Find the area of complex figures by dividing them into rectangles Also consider: • Find the area of rectangles with missing unit squares
Lesson 14: Reason to find the area of composite shapes by using grids.
1. Find the area of complex figures by dividing them into rectangles Also consider: • Find the area of rectangles with missing unit squares

Lesson 15: Reason to find the area of composite shapes by using rectangles.		1. Find the area of complex figures 2. Find the area between two rectangles
Lesson 15: Reason to find the area of composite shapes by using rectangles.
1. Find the area of complex figures 2. Find the area between two rectangles

Lesson 16: Solve historical math problems involving area.
Lesson 16: Solve historical math problems involving area.


Lesson 17: Apply area concepts to a real-world context.		1. Find the area of complex figures with missing side lengths
Lesson 17: Apply area concepts to a real-world context.
1. Find the area of complex figures with missing side lengths

Lesson 18: Find the area of shapes and represent area data on a line plot.		1. Create line plots 2. Interpret line plots
Lesson 18: Find the area of shapes and represent area data on a line plot.
1. Create line plots 2. Interpret line plots

Lesson 19: Apply area concepts to complete a multi-part task.		1. Find the area of complex figures: word problems
Lesson 19: Apply area concepts to complete a multi-part task.
1. Find the area of complex figures: word problems

5	Module 5 Fractions as Numbers
Topic A - Partition a Whole into Equal Parts
Lesson 1: Partition a whole into equal parts and name the fractional unit.		1. Identify equal parts 2. Identify halves, thirds, and fourths 3. Make halves, thirds, and fourths Also consider: • Make halves, thirds, and fourths in different ways
Lesson 1: Partition a whole into equal parts and name the fractional unit.
1. Identify equal parts 2. Identify halves, thirds, and fourths 3. Make halves, thirds, and fourths Also consider: • Make halves, thirds, and fourths in different ways

Lesson 2: Partition different wholes into fractional units concretely.		1. Make halves, thirds, fourths, sixths, and eighths Also consider: • Make sixths and eighths
Lesson 2: Partition different wholes into fractional units concretely.
1. Make halves, thirds, fourths, sixths, and eighths Also consider: • Make sixths and eighths

Lesson 3: Partition a whole into fractional units by folding fraction strips. Lesson 4: Partition a whole into fractional units pictorially and identify the unit fraction.		1. Match fraction words to models: denominators up to 10
Lesson 3: Partition a whole into fractional units by folding fraction strips. Lesson 4: Partition a whole into fractional units pictorially and identify the unit fraction.
1. Match fraction words to models: denominators up to 10

Lesson 5: Partition a whole into fractional units and write fractions in fraction form.		1. Match unit fractions to models 2. Unit fractions: modeling word problems Also consider: • Unit fractions: word problems
Lesson 5: Partition a whole into fractional units and write fractions in fraction form.
1. Match unit fractions to models 2. Unit fractions: modeling word problems Also consider: • Unit fractions: word problems
Topic B - Unit Fractions and Their Relationship to the Whole
Lesson 6: Build non-unit fractions less than 1 from unit fractions concretely.		1. Understand fractions: fraction bars 2. Show fractions: fraction bars 3. Fractions of a whole: modeling word problems Also consider: • Match fractions to models • Understand fractions: area models • Show fractions: area models
Lesson 6: Build non-unit fractions less than 1 from unit fractions concretely.
1. Understand fractions: fraction bars 2. Show fractions: fraction bars 3. Fractions of a whole: modeling word problems Also consider: • Match fractions to models • Understand fractions: area models • Show fractions: area models

Lesson 7: Identify and represent a whole as two parts: a unit fraction and a non-unit fraction. Lesson 8: Identify and represent a whole as two non-unit fractions.		1. Fractions of a whole: word problems Also consider: • Decompose fractions into unit fractions using models • Decompose fractions into unit fractions • Decompose fractions multiple ways
Lesson 7: Identify and represent a whole as two parts: a unit fraction and a non-unit fraction. Lesson 8: Identify and represent a whole as two non-unit fractions.
1. Fractions of a whole: word problems Also consider: • Decompose fractions into unit fractions using models • Decompose fractions into unit fractions • Decompose fractions multiple ways

Lesson 9: Compare unit fractions by reasoning about their size concretely.		1. Compare unit fractions
Lesson 9: Compare unit fractions by reasoning about their size concretely.
1. Compare unit fractions

Lesson 10: Compare non-unit fractions less than 1 with the same numerator by using tape diagrams.		1. Use words to compare fractions with like numerators
Lesson 10: Compare non-unit fractions less than 1 with the same numerator by using tape diagrams.
1. Use words to compare fractions with like numerators
Topic C - Fractions on the Number Line
Lesson 11: Locate fractions from 0 to 1 on a number line by using fraction tiles.		1. Fractions of number lines: unit fractions 2. Fractions of number lines
Lesson 11: Locate fractions from 0 to 1 on a number line by using fraction tiles.
1. Fractions of number lines: unit fractions 2. Fractions of number lines

Lesson 12: Represent fractions from 0 to 1 on a number line.		1. Identify fractions on number lines 2. Graph fractions less than 1 on number lines Also consider: • Fractions equivalent to one
Lesson 12: Represent fractions from 0 to 1 on a number line.
1. Identify fractions on number lines 2. Graph fractions less than 1 on number lines Also consider: • Fractions equivalent to one

Lesson 13: Identify equivalent fractions from 0 to 1 with tape diagrams and on number lines.		1. Find equivalent fractions using fraction strips 2. Find equivalent fractions using number lines Also consider: • Identify equivalent fractions on number lines
Lesson 13: Identify equivalent fractions from 0 to 1 with tape diagrams and on number lines.
1. Find equivalent fractions using fraction strips 2. Find equivalent fractions using number lines Also consider: • Identify equivalent fractions on number lines

Lesson 14: Recognize that equivalent fractions share the same location on a number line.		1. Graph equivalent fractions on number lines
Lesson 14: Recognize that equivalent fractions share the same location on a number line.
1. Graph equivalent fractions on number lines

Lesson 15: Identify fractions on a ruler as numbers on a number line.		1. Measure using an inch ruler: nearest ¼ inch
Lesson 15: Identify fractions on a ruler as numbers on a number line.
1. Measure using an inch ruler: nearest ¼ inch

Lesson 16: Measure lengths and record data on a line plot.		1. Create and interpret line plots with fractions
Lesson 16: Measure lengths and record data on a line plot.
1. Create and interpret line plots with fractions
Topic D - Comparing Fractions
Lesson 17: Represent fractions greater than 1 on a number line and identify fractions equivalent to whole numbers.		1. Graph fractions equivalent to 1 on number lines 2. Graph fractions greater than 1 on number lines 3. Select fractions equivalent to whole numbers
Lesson 17: Represent fractions greater than 1 on a number line and identify fractions equivalent to whole numbers.
1. Graph fractions equivalent to 1 on number lines 2. Graph fractions greater than 1 on number lines 3. Select fractions equivalent to whole numbers

Lesson 18: Compare fractions with like units by using a number line.		1. Graph and compare fractions with like denominators: up to 2 Also consider: • Graph smaller or larger fractions on a number line
Lesson 18: Compare fractions with like units by using a number line.
1. Graph and compare fractions with like denominators: up to 2 Also consider: • Graph smaller or larger fractions on a number line

Lesson 19: Compare fractions with unlike units but the same numerator by using number lines.		1. Graph and compare fractions with like numerators on number lines Also consider: • Graph and compare fractions on number lines
Lesson 19: Compare fractions with unlike units but the same numerator by using number lines.
1. Graph and compare fractions with like numerators on number lines Also consider: • Graph and compare fractions on number lines

Lesson 20: Compare fractions with related units by using a number line.		1. Graph and compare fractions on number lines: up to 2
Lesson 20: Compare fractions with related units by using a number line.
1. Graph and compare fractions on number lines: up to 2

Lesson 21: Compare various fractions by representing them on number lines.		1. Compare fractions with different numerators and denominators Also consider: • Compare fractions and justify your answer
Lesson 21: Compare various fractions by representing them on number lines.
1. Compare fractions with different numerators and denominators Also consider: • Compare fractions and justify your answer
Topic E - Equivalent Fractions
Lesson 22: Identify fractions equivalent to whole numbers by using number lines.		1. Find fractions equivalent to whole numbers Also consider: • Select fractions equivalent to whole numbers using models
Lesson 22: Identify fractions equivalent to whole numbers by using number lines.
1. Find fractions equivalent to whole numbers Also consider: • Select fractions equivalent to whole numbers using models

Lesson 23: Reason to find fractions equivalent to whole numbers by using patterns and number lines.		1. Identify equivalent fractions
Lesson 23: Reason to find fractions equivalent to whole numbers by using patterns and number lines.
1. Identify equivalent fractions

Lesson 24: Generate equivalent fractions greater than 1 by using a number line.		1. Find equivalent fractions
Lesson 24: Generate equivalent fractions greater than 1 by using a number line.
1. Find equivalent fractions

Lesson 25: Express whole numbers as fractions with a denominator of 1.
Lesson 25: Express whole numbers as fractions with a denominator of 1.


Lesson 26: Create a ruler with 1-inch, half-inch, and quarter-inch intervals.
Lesson 26: Create a ruler with 1-inch, half-inch, and quarter-inch intervals.


Lesson 27: Apply fraction concepts to complete a multi-part task. (Optional)		1. Compare fractions in recipes Also consider: • Compare fractions • Order fractions
Lesson 27: Apply fraction concepts to complete a multi-part task. (Optional)
1. Compare fractions in recipes Also consider: • Compare fractions • Order fractions

6	Module 6 Geometry, Measurement, and Data
Topic A - Tell Time and Solve Time Interval Problems
Lesson 1: Relate skip-counting by fives on the clock to telling time on the number line.		1. Read clocks and write times: to the nearest 5 minutes
Lesson 1: Relate skip-counting by fives on the clock to telling time on the number line.
1. Read clocks and write times: to the nearest 5 minutes

Lesson 2: Count by fives and ones on the number line as a strategy for telling time to the nearest minute on the clock.		1. Match analog and digital clocks 2. Read clocks and write times Also consider: • Match clocks and times
Lesson 2: Count by fives and ones on the number line as a strategy for telling time to the nearest minute on the clock.
1. Match analog and digital clocks 2. Read clocks and write times Also consider: • Match clocks and times

Lesson 3: Solve time word problems where the end time is unknown.		1. Elapsed time: find the end time - up to 1 minute intervals Also consider: • Find the end time: word problems
Lesson 3: Solve time word problems where the end time is unknown.
1. Elapsed time: find the end time - up to 1 minute intervals Also consider: • Find the end time: word problems

Lesson 4: Solve time word problems where the start time is unknown.		1. Find the start time: word problems
Lesson 4: Solve time word problems where the start time is unknown.
1. Find the start time: word problems

Lesson 5: Solve time word problems where the change in time is unknown.		1. Find the elapsed time: up to 1 hour 2. Find the elapsed time: word problems
Lesson 5: Solve time word problems where the change in time is unknown.
1. Find the elapsed time: up to 1 hour 2. Find the elapsed time: word problems

Lesson 6: Solve time word problems and use time data to create a line plot.		1. Word problems about start time, end time, and elapsed time: up to 1 hour Also consider: • Find start and end times: two-step word problems
Lesson 6: Solve time word problems and use time data to create a line plot.
1. Word problems about start time, end time, and elapsed time: up to 1 hour Also consider: • Find start and end times: two-step word problems

Lesson 7: Count coins and create money word problems. (Optional)		1. Count money - pennies, nickels, dimes, and quarters 2. Purchases up to $2 - do you have enough money 3. Multiply money amounts: word problems Also consider: • Correct amount of change
Lesson 7: Count coins and create money word problems. (Optional)
1. Count money - pennies, nickels, dimes, and quarters 2. Purchases up to $2 - do you have enough money 3. Multiply money amounts: word problems Also consider: • Correct amount of change
Topic B - Attributes of Two-Dimensional Figures
Lesson 8: Compare and classify quadrilaterals.		1. Classify squares, rectangles, rhombuses, parallelograms, and trapezoids 2. Name quadrilaterals more than one way 3. Parallel sides in quadrilaterals Also consider: • Identify parallelograms • Identify rhombuses
Lesson 8: Compare and classify quadrilaterals.
1. Classify squares, rectangles, rhombuses, parallelograms, and trapezoids 2. Name quadrilaterals more than one way 3. Parallel sides in quadrilaterals Also consider: • Identify parallelograms • Identify rhombuses

Lesson 9: Compare and classify other polygons.		1. Is it a polygon? Also consider: • Count and compare sides and vertices
Lesson 9: Compare and classify other polygons.
1. Is it a polygon? Also consider: • Count and compare sides and vertices

Lesson 10: Draw polygons with specified attributes.		1. Draw squares, rectangles, rhombuses, parallelograms, and trapezoids Also consider: • Angles greater than, less than, or equal to a right angle
Lesson 10: Draw polygons with specified attributes.
1. Draw squares, rectangles, rhombuses, parallelograms, and trapezoids Also consider: • Angles greater than, less than, or equal to a right angle

Lesson 11: Reason about composing polygons by using tetrominoes.		1. Create rectangles and squares with a given area
Lesson 11: Reason about composing polygons by using tetrominoes.
1. Create rectangles and squares with a given area

Lesson 12: Reason about composing polygons by using tangrams.		1. Compose two-dimensional shapes
Lesson 12: Reason about composing polygons by using tangrams.
1. Compose two-dimensional shapes
Topic C - Problem Solving with Perimeter
Lesson 13: Decompose quadrilaterals to understand perimeter as the boundary of a shape.		1. Perimeter of figures on grids
Lesson 13: Decompose quadrilaterals to understand perimeter as the boundary of a shape.
1. Perimeter of figures on grids

Lesson 14: Measure side lengths in whole-number units to determine the perimeters of polygons.		1. Perimeter of rectangles 2. Perimeter of polygons Also consider: • Perimeter of quadrilaterals
Lesson 14: Measure side lengths in whole-number units to determine the perimeters of polygons.
1. Perimeter of rectangles 2. Perimeter of polygons Also consider: • Perimeter of quadrilaterals

Lesson 15: Recognize perimeter as an attribute of shapes and solve problems with unknown measurements.		1. Find the perimeter of rectangles and squares: use properties 2. Perimeter of regular polygons Also consider: • Perimeter of polygons: find the missing side lengths
Lesson 15: Recognize perimeter as an attribute of shapes and solve problems with unknown measurements.
1. Find the perimeter of rectangles and squares: use properties 2. Perimeter of regular polygons Also consider: • Perimeter of polygons: find the missing side lengths

Lesson 16: Solve problems to determine the perimeters of rectangles with the same area.		1. Rectangles with the same area and different perimeters Also consider: • Find the area or perimeter of rectangles and squares • Relationship between area and perimeter: find the perimeter
Lesson 16: Solve problems to determine the perimeters of rectangles with the same area.
1. Rectangles with the same area and different perimeters Also consider: • Find the area or perimeter of rectangles and squares • Relationship between area and perimeter: find the perimeter

Lesson 17: Solve problems to determine the areas of rectangles with the same perimeter.		1. Rectangles with the same perimeter and different areas Also consider: • Find the area, perimeter, or side length: word problems • Relationship between area and perimeter: find the area
Lesson 17: Solve problems to determine the areas of rectangles with the same perimeter.
1. Rectangles with the same perimeter and different areas Also consider: • Find the area, perimeter, or side length: word problems • Relationship between area and perimeter: find the area

Lesson 18: Solve real-world problems involving perimeter and unknown measurements by using all four operations.		1. Perimeter of rectilinear shapes 2. Find the area and perimeter of complex figures: word problems Also consider: • Perimeter: word problems
Lesson 18: Solve real-world problems involving perimeter and unknown measurements by using all four operations.
1. Perimeter of rectilinear shapes 2. Find the area and perimeter of complex figures: word problems Also consider: • Perimeter: word problems
Topic D - Collecting and Displaying Data
Lesson 19: Measure the perimeter of various circles to the nearest quarter inch by using string.		1. Measure using an inch ruler: nearest 1/4 inch
Lesson 19: Measure the perimeter of various circles to the nearest quarter inch by using string.
1. Measure using an inch ruler: nearest 1/4 inch

Lesson 20: Record measurement data in a line plot. Lesson 21: Create and analyze a line plot for measurement data to the nearest half unit and quarter unit.		1. Create line plots with fractions
Lesson 20: Record measurement data in a line plot. Lesson 21: Create and analyze a line plot for measurement data to the nearest half unit and quarter unit.
1. Create line plots with fractions

Lesson 22: Generate categorical data and represent it by using a scaled picture graph.		1. Interpret scaled picture graphs 2. Create scaled picture graphs Also consider: • Interpret tally charts
Lesson 22: Generate categorical data and represent it by using a scaled picture graph.
1. Interpret scaled picture graphs 2. Create scaled picture graphs Also consider: • Interpret tally charts

Lesson 23: Solve problems by creating scaled picture graphs and scaled bar graphs.		1. Create bar graphs: multi-digit numbers 2. Interpret bar graphs: multi-digit numbers 3. Interpret bar graphs: two-step problems
Lesson 23: Solve problems by creating scaled picture graphs and scaled bar graphs.
1. Create bar graphs: multi-digit numbers 2. Interpret bar graphs: multi-digit numbers 3. Interpret bar graphs: two-step problems

Lesson 24: Organize, count, and represent a collection of objects.		1. Place value names up to millions
Lesson 24: Organize, count, and represent a collection of objects.
1. Place value names up to millions

Lesson 25: Name and count numbers greater than 1,000. (Optional)		1. Word names for numbers up to one million Also consider: • Convert between place values
Lesson 25: Name and count numbers greater than 1,000. (Optional)
1. Word names for numbers up to one million Also consider: • Convert between place values

Lesson 26: Fluently multiply and divide within 100 and add and subtract within 1,000.		1. Division facts up to 10: sorting 2. Multiplication facts up to 10: find the missing factor 3. Add and subtract three-digit numbers Also consider: • Multiplication and division facts up to 10
Lesson 26: Fluently multiply and divide within 100 and add and subtract within 1,000.
1. Division facts up to 10: sorting 2. Multiplication facts up to 10: find the missing factor 3. Add and subtract three-digit numbers Also consider: • Multiplication and division facts up to 10

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