IXL skill plan | 3rd grade plan for Investigations 3

Skill plan for Investigations 3 - 3rd grade

IXL provides skill alignments with recommended IXL skills for each unit. Find the IXL skills that are right for you below!

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1	Unit 1 Understanding Equal Groups
Investigation 1 - Things That Come in Groups
Session 1.1: Many Things Come in Groups		1. Skip-count 2. Count equal groups
Session 1.1: Many Things Come in Groups
1. Skip-count 2. Count equal groups

Session 1.2: How Many in Several Groups?		1. Write multiplication sentences for equal groups 2. Relate addition and multiplication for equal groups Also consider: • Identify multiplication expressions for equal groups
Session 1.2: How Many in Several Groups?
1. Write multiplication sentences for equal groups 2. Relate addition and multiplication for equal groups Also consider: • Identify multiplication expressions for equal groups

Session 1.3: Solving Multiplication Problems		1. Skip-counting sequences 2. Use equal groups to solve multiplication word problems
Session 1.3: Solving Multiplication Problems
1. Skip-counting sequences 2. Use equal groups to solve multiplication word problems

Session 1.4: Solving Problems About Our Pictures		1. Multiplication word problems with factors up to 5
Session 1.4: Solving Problems About Our Pictures
1. Multiplication word problems with factors up to 5
Investigation 2 - Skip Counting and 100 Charts
Session 2.1: Highlighting Multiples on 100 Charts		1. Skip-counting sequences: count by twos 2. Multiply 2 by numbers up to 10 3. Multiply 5 by numbers up to 10 4. Multiply 10 by numbers up to 10
Session 2.1: Highlighting Multiples on 100 Charts
1. Skip-counting sequences: count by twos 2. Multiply 2 by numbers up to 10 3. Multiply 5 by numbers up to 10 4. Multiply 10 by numbers up to 10

Session 2.2: More Multiples		1. Multiply by 5 and 10 2. Skip-counting sequences: count by threes 3. Skip-counting sequences: count by sixes
Session 2.2: More Multiples
1. Multiply by 5 and 10 2. Skip-counting sequences: count by threes 3. Skip-counting sequences: count by sixes

Session 2.3: Solving Related Story Problems		1. Multiply 3 by numbers up to 10 2. Multiply 6 by numbers up to 10
Session 2.3: Solving Related Story Problems
1. Multiply 3 by numbers up to 10 2. Multiply 6 by numbers up to 10

Session 2.4: Patterns and Relationships		1. Find the area of figures made of unit squares: customary and metric units 2. Multiply by 3 and 6 Also consider: • Multiply using the distributive property
Session 2.4: Patterns and Relationships
1. Find the area of figures made of unit squares: customary and metric units 2. Multiply by 3 and 6 Also consider: • Multiply using the distributive property

Session 2.5: Finding Products of Related Problems		1. Skip-counting sequences: count by fours 2. Multiply 4 by numbers up to 10
Session 2.5: Finding Products of Related Problems
1. Skip-counting sequences: count by fours 2. Multiply 4 by numbers up to 10

Session 2.6: Using Multiplication		1. Multiply by 5 and 6 2. Multiplication facts for 2, 3, 4, 5, and 10
Session 2.6: Using Multiplication
1. Multiply by 5 and 6 2. Multiplication facts for 2, 3, 4, 5, and 10
Investigation 3 - Arrays
Session 3.1: Arranging Chairs		1. Make arrays to model multiplication: given products Also consider: • Identify multiplication expressions for arrays
Session 3.1: Arranging Chairs
1. Make arrays to model multiplication: given products Also consider: • Identify multiplication expressions for arrays

Session 3.2: Investigating Arrays		1. Write multiplication sentences for arrays 2. Write two multiplication sentences for an array 3. Multiply one-digit numbers with grids: using facts up to 5
Session 3.2: Investigating Arrays
1. Write multiplication sentences for arrays 2. Write two multiplication sentences for an array 3. Multiply one-digit numbers with grids: using facts up to 5

Session 3.3: What's the Area?		1. Tile a rectangle and find the area 2. Make arrays to model multiplication
Session 3.3: What's the Area?
1. Tile a rectangle and find the area 2. Make arrays to model multiplication

Session 3.4: Array Games—Part 1		1. Multiply to find the area of a rectangle made of unit squares Also consider: • Multiplication facts for 2, 3, 4, 5, and 10: true or false?
Session 3.4: Array Games—Part 1
1. Multiply to find the area of a rectangle made of unit squares Also consider: • Multiplication facts for 2, 3, 4, 5, and 10: true or false?

Session 3.5: Using What You Know		1. Multiply one-digit numbers using grids 2. Multiplication facts up to 10
Session 3.5: Using What You Know
1. Multiply one-digit numbers using grids 2. Multiplication facts up to 10

Session 3.6: Learning Multiplication Facts		1. Multiply by 0 or 1 2. Multiply by 0 or 1: complete the sentence Also consider: • Multiplication facts up to 10: true or false?
Session 3.6: Learning Multiplication Facts
1. Multiply by 0 or 1 2. Multiply by 0 or 1: complete the sentence Also consider: • Multiplication facts up to 10: true or false?

Session 3.7: Array Games—Part 2		1. Multiplication facts for 2, 3, 4, 5, and 10: sorting
Session 3.7: Array Games—Part 2
1. Multiplication facts for 2, 3, 4, 5, and 10: sorting
Investigation 4 - Understanding Division
Session 4.1: Solving Division Problems		1. Use equal groups to solve division word problems Also consider: • Divide by counting equal groups • Multiplication facts for 2, 3, 4, 5, and 10: find the missing factor
Session 4.1: Solving Division Problems
1. Use equal groups to solve division word problems Also consider: • Divide by counting equal groups • Multiplication facts for 2, 3, 4, 5, and 10: find the missing factor

Session 4.2: Multiply or Divide?		1. Multiplication and division word problems: factors up to 5 2. Write division sentences for groups 3. Relate multiplication and division for groups
Session 4.2: Multiply or Divide?
1. Multiplication and division word problems: factors up to 5 2. Write division sentences for groups 3. Relate multiplication and division for groups

Session 4.3: Writing Story Problems		1. Write division sentences for arrays 2. Make arrays to model division 3. Relate multiplication and division for arrays
Session 4.3: Writing Story Problems
1. Write division sentences for arrays 2. Make arrays to model division 3. Relate multiplication and division for arrays

Session 4.4: Missing Factors		1. Multiplication facts up to 10: find the missing factor 2. Multiply by 2, 5, and 10 Also consider: • Multiply 1 by numbers up to 10
Session 4.4: Missing Factors
1. Multiplication facts up to 10: find the missing factor 2. Multiply by 2, 5, and 10 Also consider: • Multiply 1 by numbers up to 10

Session 4.5: Solving Multiplication and Division Problems		1. Multiplication word problems with factors up to 10: find the missing number
Session 4.5: Solving Multiplication and Division Problems
1. Multiplication word problems with factors up to 10: find the missing number

Session 4.6: Solving Multiplication and Division Problems, continued		1. Multiplication and division word problems: identify the product Also consider: • Multiplication facts up to 10: sorting • Division facts for 2, 3, 4, 5, and 10
Session 4.6: Solving Multiplication and Division Problems, continued
1. Multiplication and division word problems: identify the product Also consider: • Multiplication facts up to 10: sorting • Division facts for 2, 3, 4, 5, and 10

2	Unit 2 Graphs and Line Plots
Investigation 1 - Modeling with Data
Session 1.1: Places Where We Like to Eat		1. Which tally chart is correct?
Session 1.1: Places Where We Like to Eat
1. Which tally chart is correct?

Session 1.2: Representing the Class Data		1. Interpret tally charts Also consider: • Interpret bar graphs: numbers up to 10
Session 1.2: Representing the Class Data
1. Interpret tally charts Also consider: • Interpret bar graphs: numbers up to 10

Session 1.3: What Do Our Data Show About Our Class?		1. Interpret data in tables Also consider: • Interpret picture graphs: numbers up to 10 • Create picture graphs: numbers up to 10
Session 1.3: What Do Our Data Show About Our Class?
1. Interpret data in tables Also consider: • Interpret picture graphs: numbers up to 10 • Create picture graphs: numbers up to 10

Session 1.4: Solving Problems with Bar Graphs		1. Interpret scaled bar graphs 2. Create scaled bar graphs
Session 1.4: Solving Problems with Bar Graphs
1. Interpret scaled bar graphs 2. Create scaled bar graphs

Session 1.5: Bar Graphs and Pictographs		1. Interpret scaled picture graphs 2. Create scaled picture graphs
Session 1.5: Bar Graphs and Pictographs
1. Interpret scaled picture graphs 2. Create scaled picture graphs

Session 1.6: Interpreting Bar Graphs and Pictographs and Developing a Survey Question		1. Use bar graphs to solve problems 2. Create bar graphs: multi-digit numbers
Session 1.6: Interpreting Bar Graphs and Pictographs and Developing a Survey Question
1. Use bar graphs to solve problems 2. Create bar graphs: multi-digit numbers

Session 1.7: Describing Data		1. Interpret bar graphs: multi-digit numbers 2. Interpret double bar graphs
Session 1.7: Describing Data
1. Interpret bar graphs: multi-digit numbers 2. Interpret double bar graphs

Session 1.8: Choosing Categories		1. Complete double bar graphs 2. Interpret picture graphs: multiples of 10
Session 1.8: Choosing Categories
1. Complete double bar graphs 2. Interpret picture graphs: multiples of 10

Session 1.9: Comparing Groups		1. Interpret bar graphs: two-step problems Also consider: • Interpret a table
Session 1.9: Comparing Groups
1. Interpret bar graphs: two-step problems Also consider: • Interpret a table
Investigation 2 - Collecting, Representing, and Analyzing Measurement Data
Session 2.1: Using a Line Plot to Represent Data		1. Create line plots
Session 2.1: Using a Line Plot to Represent Data
1. Create line plots

Session 2.2: Is Your Foot a Foot Long?		1. Measure using an inch ruler: nearest 1/2 inch 2. Interpret line plots Also consider: • Measure using an inch ruler: nearest inch
Session 2.2: Is Your Foot a Foot Long?
1. Measure using an inch ruler: nearest 1/2 inch 2. Interpret line plots Also consider: • Measure using an inch ruler: nearest inch

Session 2.3: Why Are Our Measurements Different?		1. Which customary unit of length is appropriate?
Session 2.3: Why Are Our Measurements Different?
1. Which customary unit of length is appropriate?

Session 2.4: Feet and Inches		1. Create line plots with halves Also consider: • Compare and convert customary units of length
Session 2.4: Feet and Inches
1. Create line plots with halves Also consider: • Compare and convert customary units of length

Session 2.5: Describing the Pattern Block Data		1. Create and interpret line plots with halves
Session 2.5: Describing the Pattern Block Data
1. Create and interpret line plots with halves

Session 2.6: Reading and Interpreting Data		1. Create data displays: bar graphs, picture graphs, and line plots
Session 2.6: Reading and Interpreting Data
1. Create data displays: bar graphs, picture graphs, and line plots

3	Unit 3 Travel Stories and Collections
Investigation 1 - Working With 100
Session 1.1: Capture 5		1. Add a multiple of ten and a two-digit number 2. Subtract multiples of 10 Also consider: • One or ten more/less • Add two multiples of 10
Session 1.1: Capture 5
1. Add a multiple of ten and a two-digit number 2. Subtract multiples of 10 Also consider: • One or ten more/less • Add two multiples of 10

Session 1.2: Sticker Station Problems		1. Input/output tables: add and subtract by 10 2. Use models to add two-digit numbers Also consider: • Place value: ones and tens
Session 1.2: Sticker Station Problems
1. Input/output tables: add and subtract by 10 2. Use models to add two-digit numbers Also consider: • Place value: ones and tens

Session 1.3: How Many More Stickers to Get 100?		1. Complete the addition sentence: make 100 2. Use number lines to add two-digit numbers Also consider: • Complete the addition sentence: make ten
Session 1.3: How Many More Stickers to Get 100?
1. Complete the addition sentence: make 100 2. Use number lines to add two-digit numbers Also consider: • Complete the addition sentence: make ten

Session 1.4: Close to 100		1. Add two-digit numbers: sums up to 100 Also consider: • Complete the addition sentence: up to two digits
Session 1.4: Close to 100
1. Add two-digit numbers: sums up to 100 Also consider: • Complete the addition sentence: up to two digits

Session 1.5: Solving Addition and Subtraction Problems		1. Regroup tens and ones - ways to make a number 2. Convert between place values: ones, tens, and hundreds 3. Add two-digit numbers: sums up to 200 Also consider: • Write numbers using place value
Session 1.5: Solving Addition and Subtraction Problems
1. Regroup tens and ones - ways to make a number 2. Convert between place values: ones, tens, and hundreds 3. Add two-digit numbers: sums up to 200 Also consider: • Write numbers using place value
Investigation 2 - Building 1,000
Session 2.1: Making a 1,000 Chart		1. Place value models up to hundreds Also consider: • Compare numbers up to 1,000 • Number lines up to 1,000 • Number lines up to 1,200: multiples of 10 and 100
Session 2.1: Making a 1,000 Chart
1. Place value models up to hundreds Also consider: • Compare numbers up to 1,000 • Number lines up to 1,000 • Number lines up to 1,200: multiples of 10 and 100

Session 2.2: Collections and Quantities on the 1,000 Chart		1. Value of a digit: up to hundreds 2. Order numbers up to 1,000 Also consider: • Writing numbers up to 1,000 in words - convert words to digits • Writing numbers up to 1,000 in words - convert digits to words
Session 2.2: Collections and Quantities on the 1,000 Chart
1. Value of a digit: up to hundreds 2. Order numbers up to 1,000 Also consider: • Writing numbers up to 1,000 in words - convert words to digits • Writing numbers up to 1,000 in words - convert digits to words

Session 2.3: Go Collecting		1. Use models to add three-digit numbers: with regrouping Also consider: • Use models to add three-digit numbers: without regrouping
Session 2.3: Go Collecting
1. Use models to add three-digit numbers: with regrouping Also consider: • Use models to add three-digit numbers: without regrouping

Session 2.4: Rounding Numbers		1. Round to the nearest ten or hundred using a number line
Session 2.4: Rounding Numbers
1. Round to the nearest ten or hundred using a number line
Investigation 3 - Addition
Session 3.1: How Many Stickers?		1. Addition word problems: up to 100 2. Break apart a two-digit number to add: sums up to 100 3. Use expanded form to add three-digit numbers 4. Use number lines to add three-digit numbers
Session 3.1: How Many Stickers?
1. Addition word problems: up to 100 2. Break apart a two-digit number to add: sums up to 100 3. Use expanded form to add three-digit numbers 4. Use number lines to add three-digit numbers

Session 3.2: Combining Collections		1. Estimate sums by rounding: up to 1,000 2. Estimate sums by rounding: word problems 3. Add two numbers up to three digits using place value Also consider: • Estimate sums using compatible numbers
Session 3.2: Combining Collections
1. Estimate sums by rounding: up to 1,000 2. Estimate sums by rounding: word problems 3. Add two numbers up to three digits using place value Also consider: • Estimate sums using compatible numbers

Session 3.3: Place Value of 3-Digit Numbers		1. Add or subtract multiples of 10 or 100 2. Round to the nearest ten or hundred 3. Addition word problems: up to 200 Also consider: • Add multiples of 10 or 100 • Add or subtract two multiples of 100
Session 3.3: Place Value of 3-Digit Numbers
1. Add or subtract multiples of 10 or 100 2. Round to the nearest ten or hundred 3. Addition word problems: up to 200 Also consider: • Add multiples of 10 or 100 • Add or subtract two multiples of 100

Session 3.4: Addition Starter Problems		1. Add two numbers up to three digits: without regrouping Also consider: • Round to the nearest ten or hundred in a table
Session 3.4: Addition Starter Problems
1. Add two numbers up to three digits: without regrouping Also consider: • Round to the nearest ten or hundred in a table

Session 3.5: Addition Strategies		1. Add two numbers up to three digits: with regrouping
Session 3.5: Addition Strategies
1. Add two numbers up to three digits: with regrouping
Investigation 4 - Finding the Difference
Session 4.1: Over and Under 100		1. Read clocks and write times: to the nearest 5 minutes
Session 4.1: Over and Under 100
1. Read clocks and write times: to the nearest 5 minutes

Session 4.2: Travel Problems—Crossing Over 100		1. Complete the addition sentence: sums to 100
Session 4.2: Travel Problems—Crossing Over 100
1. Complete the addition sentence: sums to 100

Session 4.3: Finding the Difference Between Two Numbers		1. Use number lines to subtract two-digit numbers 2. Subtract using a related addition fact: up to two digits
Session 4.3: Finding the Difference Between Two Numbers
1. Use number lines to subtract two-digit numbers 2. Subtract using a related addition fact: up to two digits

Session 4.4: How Far Did They Travel?		1. Complete the addition sentence: sums to 200
Session 4.4: How Far Did They Travel?
1. Complete the addition sentence: sums to 200

Session 4.5: The Trip Home		1. Subtraction word problems: up to 100
Session 4.5: The Trip Home
1. Subtraction word problems: up to 100
Investigation 5 - Subtraction Stories
Session 5.1: Comparing Lengths and Heights		1. Compare lengths: word problems
Session 5.1: Comparing Lengths and Heights
1. Compare lengths: word problems

Session 5.2: Comparing Quantities		1. Subtract two-digit numbers: with regrouping
Session 5.2: Comparing Quantities
1. Subtract two-digit numbers: with regrouping

Session 5.3: Related Problems		1. Use compensation to subtract: up to two digits Also consider: • Use compensation to subtract on a number line: up to two digits • Use models to subtract two-digit numbers: with regrouping
Session 5.3: Related Problems
1. Use compensation to subtract: up to two digits Also consider: • Use compensation to subtract on a number line: up to two digits • Use models to subtract two-digit numbers: with regrouping

Session 5.4: How Many Are Left?		1. Subtract multiples of 10 or 100
Session 5.4: How Many Are Left?
1. Subtract multiples of 10 or 100

Session 5.5: Solving Subtraction Problems		1. Subtract from three-digit numbers: word problems
Session 5.5: Solving Subtraction Problems
1. Subtract from three-digit numbers: word problems

Session 5.6: Addition and Subtraction Problems		1. Add and subtract numbers up to 100 2. Addition and subtraction word problems: up to 100
Session 5.6: Addition and Subtraction Problems
1. Add and subtract numbers up to 100 2. Addition and subtraction word problems: up to 100

4	Unit 4 Perimeter, Area, and Polygons
Investigation 1 - Linear Measurement
Session 1.1: Using U.S. and Metric Units to Measure Length		1. Which metric unit of length is appropriate? Also consider: • Measure using a centimeter ruler
Session 1.1: Using U.S. and Metric Units to Measure Length
1. Which metric unit of length is appropriate? Also consider: • Measure using a centimeter ruler

Session 1.2: Introducing Perimeter		1. Perimeter of rectangles Also consider: • Perimeter of figures on grids
Session 1.2: Introducing Perimeter
1. Perimeter of rectangles Also consider: • Perimeter of figures on grids

Session 1.3: Measuring Perimeter		1. Perimeter of polygons 2. Perimeter: find the missing side length Also consider: • Find the perimeter: word problems
Session 1.3: Measuring Perimeter
1. Perimeter of polygons 2. Perimeter: find the missing side length Also consider: • Find the perimeter: word problems

Session 1.4: Perimeter Problems		1. Perimeter of quadrilaterals Also consider: • Perimeter word problems: find the missing side length of a rectangle
Session 1.4: Perimeter Problems
1. Perimeter of quadrilaterals Also consider: • Perimeter word problems: find the missing side length of a rectangle

Session 1.5: Ordering Shapes by Perimeter		1. Perimeter: word problems Also consider: • Perimeter of rectilinear shapes • Perimeter of regular polygons
Session 1.5: Ordering Shapes by Perimeter
1. Perimeter: word problems Also consider: • Perimeter of rectilinear shapes • Perimeter of regular polygons
Investigation 2 - Understanding and Finding Area
Session 2.1: Tetrominoes		1. Select two figures with the same area Also consider: • Create figures with a given area
Session 2.1: Tetrominoes
1. Select two figures with the same area Also consider: • Create figures with a given area

Session 2.2: Which Tetrominoes Fit?		1. Find the area of figures made of unit squares Also consider: • Select figures with a given area
Session 2.2: Which Tetrominoes Fit?
1. Find the area of figures made of unit squares Also consider: • Select figures with a given area

Session 2.3: Using Square Inches to Measure		1. Area of figures on grids
Session 2.3: Using Square Inches to Measure
1. Area of figures on grids

Session 2.4: Same Area, Different Perimeter; Same Perimeter, Different Area		1. Tile a rectangle and find the area: customary and metric units 2. Create rectangles with a given area 3. Rectangles with the same perimeter or area Also consider: • Relationship between area and perimeter: find the perimeter • Relationship between area and perimeter: find the area
Session 2.4: Same Area, Different Perimeter; Same Perimeter, Different Area
1. Tile a rectangle and find the area: customary and metric units 2. Create rectangles with a given area 3. Rectangles with the same perimeter or area Also consider: • Relationship between area and perimeter: find the perimeter • Relationship between area and perimeter: find the area

Session 2.5: Area Activities		1. Find the area of complex figures by dividing them into rectangles Also consider: • Find the area of rectangles and squares
Session 2.5: Area Activities
1. Find the area of complex figures by dividing them into rectangles Also consider: • Find the area of rectangles and squares

Session 2.6: Area Activities, continued		1. Find the area or perimeter of figures on grids 2. Find the area of complex figures
Session 2.6: Area Activities, continued
1. Find the area or perimeter of figures on grids 2. Find the area of complex figures

Session 2.7: Finding Area		1. Find the area or perimeter of rectangles and squares Also consider: • Find the area of rectangles: word problems • Find the missing side length of a rectangle
Session 2.7: Finding Area
1. Find the area or perimeter of rectangles and squares Also consider: • Find the area of rectangles: word problems • Find the missing side length of a rectangle
Investigation 3 - Triangles and Quadrilaterals
Session 3.1: Triangles		1. Angles greater than, less than, or equal to a right angle Also consider: • Identify congruent shapes • Scalene, isosceles, and equilateral triangles • Acute, obtuse, and right triangles
Session 3.1: Triangles
1. Angles greater than, less than, or equal to a right angle Also consider: • Identify congruent shapes • Scalene, isosceles, and equilateral triangles • Acute, obtuse, and right triangles

Session 3.2: Is It a Triangle?		1. Count and compare sides and vertices Also consider: • Open and closed shapes • Is it a polygon?
Session 3.2: Is It a Triangle?
1. Count and compare sides and vertices Also consider: • Open and closed shapes • Is it a polygon?

Session 3.3: Squares, Rectangles, and Other Quadrilaterals		1. Identify rectangles
Session 3.3: Squares, Rectangles, and Other Quadrilaterals
1. Identify rectangles

Session 3.4: Rectangles and Rhombuses		1. Identify rhombuses 2. Classify rectangles and rhombuses
Session 3.4: Rectangles and Rhombuses
1. Identify rhombuses 2. Classify rectangles and rhombuses

Session 3.5: Area and Quadrilaterals		1. Draw squares, rectangles, and rhombuses
Session 3.5: Area and Quadrilaterals
1. Draw squares, rectangles, and rhombuses

5	Unit 5 Cube Patterns, Arrays, and Multiples of 10
Investigation 1 - Relationship between Multiplication and Division
Session 1.1: Groups of 3		1. Multiplication facts up to 10: select the missing factors
Session 1.1: Groups of 3
1. Multiplication facts up to 10: select the missing factors

Session 1.2: Groups of 3, 4, and 6		1. Identify multiples of 2, 3, 4, 5, or 6
Session 1.2: Groups of 3, 4, and 6
1. Identify multiples of 2, 3, 4, 5, or 6

Session 1.3: Equations for Multiples and Non-Multiples of 3, 4, or 6		1. Understanding parentheses with addition, subtraction, and multiplication
Session 1.3: Equations for Multiples and Non-Multiples of 3, 4, or 6
1. Understanding parentheses with addition, subtraction, and multiplication

Session 1.4: Multiplication and Division Equations		1. Relate multiplication and division Also consider: • Multiplication input/output tables
Session 1.4: Multiplication and Division Equations
1. Relate multiplication and division Also consider: • Multiplication input/output tables

Session 1.5: Relating Multiplication and Division		1. Relate multiplication and division 2. Write multiplication and division sentences for arrays Also consider: • Write multiplication and division sentences for equal groups • Multiplication and division facts up to 5: true or false?
Session 1.5: Relating Multiplication and Division
1. Relate multiplication and division 2. Write multiplication and division sentences for arrays Also consider: • Write multiplication and division sentences for equal groups • Multiplication and division facts up to 5: true or false?
Investigation 2 - Solving Multiplication and Division Problems
Session 2.1: Arrays and Multiplication Facts		1. Multiplication facts for 6, 7, 8, and 9: true or false?
Session 2.1: Arrays and Multiplication Facts
1. Multiplication facts for 6, 7, 8, and 9: true or false?

Session 2.2: Array Cover-Up		1. Multiply 8 by numbers up to 10 2. Multiplication facts for 6, 7, 8, and 9: sorting
Session 2.2: Array Cover-Up
1. Multiply 8 by numbers up to 10 2. Multiplication facts for 6, 7, 8, and 9: sorting

Session 2.3: Related Story Problems		1. Multiplication word problems: identify the product 2. Multiply by 2, 4, and 8 Also consider: • Multiply 9 by numbers up to 10
Session 2.3: Related Story Problems
1. Multiplication word problems: identify the product 2. Multiply by 2, 4, and 8 Also consider: • Multiply 9 by numbers up to 10

Session 2.4: Missing Factors		1. Multiplication facts for 6, 7, 8, and 9: find the missing factor Also consider: • Divide by 2: quotients up to 10 • Divide by 3: quotients up to 10 • Divide by 4: quotients up to 10
Session 2.4: Missing Factors
1. Multiplication facts for 6, 7, 8, and 9: find the missing factor Also consider: • Divide by 2: quotients up to 10 • Divide by 3: quotients up to 10 • Divide by 4: quotients up to 10

Session 2.5: Division Strategies		1. Word problems with multiplication Also consider: • Divide by 5: quotients up to 10 • Divide by 6: quotients up to 10 • Divide by 7: quotients up to 10 • Multiplication input/output tables: find the rule
Session 2.5: Division Strategies
1. Word problems with multiplication Also consider: • Divide by 5: quotients up to 10 • Divide by 6: quotients up to 10 • Divide by 7: quotients up to 10 • Multiplication input/output tables: find the rule

Session 2.6: Multiplication and Division Problems		1. Multiply 7 by numbers up to 10 2. Division word problems: divisors and quotients up to 5 Also consider: • Divide by 8: quotients up to 10 • Divide by 9: quotients up to 10 • Divide by 10: quotients up to 10 • Multiplication and division facts up to 10: true or false?
Session 2.6: Multiplication and Division Problems
1. Multiply 7 by numbers up to 10 2. Division word problems: divisors and quotients up to 5 Also consider: • Divide by 8: quotients up to 10 • Divide by 9: quotients up to 10 • Divide by 10: quotients up to 10 • Multiplication and division facts up to 10: true or false?
Investigation 3 - Multiplying by Multiples of 10
Session 3.1: The Toy Factory: Multiples of Ten		1. Multiply by a multiple of ten
Session 3.1: The Toy Factory: Multiples of Ten
1. Multiply by a multiple of ten

Session 3.2: Multiplying by Tens		1. Multiply by a multiple of ten using place value
Session 3.2: Multiplying by Tens
1. Multiply by a multiple of ten using place value

Session 3.3: Solving Multi-Step Problems		1. Multiply multiples of ten by one-digit numbers Also consider: • Multiplication word problems with factors up to 10
Session 3.3: Solving Multi-Step Problems
1. Multiply multiples of ten by one-digit numbers Also consider: • Multiplication word problems with factors up to 10

Session 3.4: Solving Division Problems		1. Division word problems: identify the quotient 2. Multiplication facts for 6, 7, 8, and 9
Session 3.4: Solving Division Problems
1. Division word problems: identify the quotient 2. Multiplication facts for 6, 7, 8, and 9

Session 3.5: Problems with Multiple Solutions		1. Multiplication sentences up to 10: true or false? Also consider: • Squares up to 10 x 10
Session 3.5: Problems with Multiple Solutions
1. Multiplication sentences up to 10: true or false? Also consider: • Squares up to 10 x 10

Session 3.6: Solving Word Problems		1. Multiplication and division word problems
Session 3.6: Solving Word Problems
1. Multiplication and division word problems

6	Unit 6 Fair Shares and Fractions on Number Lines
Investigation 1 - Sharing Brownies
Session 1.1: Making Fair Shares		1. Make halves, thirds, fourths, sixths, and eighths 2. Make halves, thirds, and fourths in different ways Also consider: • Identify equal parts • Unit fractions: modeling word problems
Session 1.1: Making Fair Shares
1. Make halves, thirds, fourths, sixths, and eighths 2. Make halves, thirds, and fourths in different ways Also consider: • Identify equal parts • Unit fractions: modeling word problems

Session 1.2: Making Fraction Sets		1. Match unit fractions to models 2. Compare unit fractions Also consider: • Unit fractions: word problems
Session 1.2: Making Fraction Sets
1. Match unit fractions to models 2. Compare unit fractions Also consider: • Unit fractions: word problems

Session 1.3: More Than One Piece		1. Decompose fractions into unit fractions 2. Fractions equivalent to one Also consider: • Understand fractions: area models • Show fractions: area models • Match fractions to models
Session 1.3: More Than One Piece
1. Decompose fractions into unit fractions 2. Fractions equivalent to one Also consider: • Understand fractions: area models • Show fractions: area models • Match fractions to models

Session 1.4: Cutting Up Cookies in Equal Parts		1. Find equivalent fractions using area models: two models Also consider: • Find equivalent fractions using fraction strips • Understand fractions: fraction bars • Show fractions: fraction bars
Session 1.4: Cutting Up Cookies in Equal Parts
1. Find equivalent fractions using area models: two models Also consider: • Find equivalent fractions using fraction strips • Understand fractions: fraction bars • Show fractions: fraction bars

Session 1.5: Fractions on a Number Line		1. Identify fractions on number lines 2. Graph fractions less than 1 on number lines 3. Identify equivalent fractions on number lines Also consider: • Fractions of number lines: unit fractions
Session 1.5: Fractions on a Number Line
1. Identify fractions on number lines 2. Graph fractions less than 1 on number lines 3. Identify equivalent fractions on number lines Also consider: • Fractions of number lines: unit fractions

Session 1.6: Measuring to the Nearest Fourth Inch		1. Measure using an inch ruler: nearest ¼ inch 2. Create and interpret line plots with fractions Also consider: • Create line plots with fractions
Session 1.6: Measuring to the Nearest Fourth Inch
1. Measure using an inch ruler: nearest ¼ inch 2. Create and interpret line plots with fractions Also consider: • Create line plots with fractions

Session 1.7: Sharing Brownies		1. Graph fractions equivalent to 1 on number lines 2. Identify equivalent fractions Also consider: • Find equivalent fractions using number lines • Find equivalent fractions using area models: one model • Fractions of a whole: modeling word problems • Select fractions equivalent to whole numbers using models
Session 1.7: Sharing Brownies
1. Graph fractions equivalent to 1 on number lines 2. Identify equivalent fractions Also consider: • Find equivalent fractions using number lines • Find equivalent fractions using area models: one model • Fractions of a whole: modeling word problems • Select fractions equivalent to whole numbers using models

Session 1.8: Naming Fractional Parts		1. Graph fractions greater than 1 on number lines 2. Graph equivalent fractions on number lines 3. Fractions of a whole: word problems Also consider: • Match mixed numbers to models • Decompose fractions multiple ways • Write an improper fraction as a sum of unit fractions • Write fractions using numbers and words
Session 1.8: Naming Fractional Parts
1. Graph fractions greater than 1 on number lines 2. Graph equivalent fractions on number lines 3. Fractions of a whole: word problems Also consider: • Match mixed numbers to models • Decompose fractions multiple ways • Write an improper fraction as a sum of unit fractions • Write fractions using numbers and words
Investigation 2 - Many Ways to Make a Share
Session 2.1: The Fraction Cookie Game		1. Find equivalent fractions
Session 2.1: The Fraction Cookie Game
1. Find equivalent fractions

Session 2.2: Locating and Comparing Fractions on Number Lines		1. Compare fractions using number lines Also consider: • Graph fractions on number lines
Session 2.2: Locating and Comparing Fractions on Number Lines
1. Compare fractions using number lines Also consider: • Graph fractions on number lines

Session 2.3: Making Half-Yellow Designs		1. Graph and compare fractions on number lines: up to 2 2. Compare fractions using models 3. Compare fractions Also consider: • Compare fractions in recipes • Graph and order fractions on number lines • Order fractions
Session 2.3: Making Half-Yellow Designs
1. Graph and compare fractions on number lines: up to 2 2. Compare fractions using models 3. Compare fractions Also consider: • Compare fractions in recipes • Graph and order fractions on number lines • Order fractions

Session 2.4: Which Fraction Is Greater?		1. Compare fractions with like denominators using models 2. Graph and compare fractions with like denominators on number lines 3. Compare fractions with like denominators Also consider: • Order fractions with like denominators
Session 2.4: Which Fraction Is Greater?
1. Compare fractions with like denominators using models 2. Graph and compare fractions with like denominators on number lines 3. Compare fractions with like denominators Also consider: • Order fractions with like denominators

Session 2.5: Representing and Comparing Fractions		1. Graph and compare fractions on number lines 2. Compare fractions with like numerators using models 3. Compare fractions with like numerators Also consider: • Graph and compare fractions with like numerators on number lines • Order fractions with like numerators
Session 2.5: Representing and Comparing Fractions
1. Graph and compare fractions on number lines 2. Compare fractions with like numerators using models 3. Compare fractions with like numerators Also consider: • Graph and compare fractions with like numerators on number lines • Order fractions with like numerators

7	Unit 7 How Many Miles?
Investigation 1 - Numbers in the Hundreds
Session 1.1: Measuring Liquid Volume		1. Measure liquid volumes - metric units 2. Which metric unit of volume is appropriate?
Session 1.1: Measuring Liquid Volume
1. Measure liquid volumes - metric units 2. Which metric unit of volume is appropriate?

Session 1.2: Measuring Mass		1. Which metric unit of mass is appropriate? 2. Measurement word problems Also consider: • Read a scale - metric units
Session 1.2: Measuring Mass
1. Which metric unit of mass is appropriate? 2. Measurement word problems Also consider: • Read a scale - metric units

Session 1.3: Paper Clip Problems		1. Subtract from multiples of 100 Also consider: • Multiply by a multiple of 100 • Multiplication patterns: multiples of 10 and 100
Session 1.3: Paper Clip Problems
1. Subtract from multiples of 100 Also consider: • Multiply by a multiple of 100 • Multiplication patterns: multiples of 10 and 100

Session 1.4: Capture from 300 to 600		1. Use models to subtract numbers up to three-digits: without regrouping Also consider: • Subtract with two-digit or three-digit numbers
Session 1.4: Capture from 300 to 600
1. Use models to subtract numbers up to three-digits: without regrouping Also consider: • Subtract with two-digit or three-digit numbers

Session 1.5: Related Subtraction Problems		1. Estimate differences: round to hundreds Also consider: • Estimate differences using compatible numbers • Round to the nearest hundred using a number line
Session 1.5: Related Subtraction Problems
1. Estimate differences: round to hundreds Also consider: • Estimate differences using compatible numbers • Round to the nearest hundred using a number line

Session 1.6: Solving Subtraction Problems		1. Estimate differences by rounding: word problems Also consider: • Estimate differences by rounding: up to 1,000 • Round to the nearest ten using a number line
Session 1.6: Solving Subtraction Problems
1. Estimate differences by rounding: word problems Also consider: • Estimate differences by rounding: up to 1,000 • Round to the nearest ten using a number line

Session 1.7: Practicing Subtraction and Addition		1. Estimate sums and differences by rounding: up to 1,000 2. Estimate sums and differences: word problems Also consider: • Round to the nearest ten • Round to the nearest hundred
Session 1.7: Practicing Subtraction and Addition
1. Estimate sums and differences by rounding: up to 1,000 2. Estimate sums and differences: word problems Also consider: • Round to the nearest ten • Round to the nearest hundred
Investigation 2 - Addition Strategies
Session 2.1: Making an Easier Problem		1. Use compensation to add: up to three digits Also consider: • Balance addition equations: up to three digits
Session 2.1: Making an Easier Problem
1. Use compensation to add: up to three digits Also consider: • Balance addition equations: up to three digits

Session 2.2: Addition Starter Problems		1. Add two numbers up to three digits
Session 2.2: Addition Starter Problems
1. Add two numbers up to three digits

Session 2.3: Categorizing Addition Strategies		1. Add three-digit numbers 2. Add two numbers up to three digits: word problems
Session 2.3: Categorizing Addition Strategies
1. Add three-digit numbers 2. Add two numbers up to three digits: word problems

Session 2.4: Adding More Than Two Numbers		1. Add three numbers up to three digits each Also consider: • Add data from tables: up to three digits
Session 2.4: Adding More Than Two Numbers
1. Add three numbers up to three digits each Also consider: • Add data from tables: up to three digits

Session 2.5: Addition Problems		1. Add three numbers up to three digits each: word problems
Session 2.5: Addition Problems
1. Add three numbers up to three digits each: word problems
Investigation 3 - Subtraction
Session 3.1: Subtraction		1. Use number lines to subtract three-digit numbers 2. Subtract three-digit numbers: without regrouping 3. Complete the addition sentence: up to three digits Also consider: • Use models to subtract numbers up to three-digits: with regrouping
Session 3.1: Subtraction
1. Use number lines to subtract three-digit numbers 2. Subtract three-digit numbers: without regrouping 3. Complete the addition sentence: up to three digits Also consider: • Use models to subtract numbers up to three-digits: with regrouping

Session 3.2: Subtraction Strategies		1. Subtract three-digit numbers: with regrouping Also consider: • Use expanded form to subtract three-digit numbers • Use compensation to subtract: up to three digits
Session 3.2: Subtraction Strategies
1. Subtract three-digit numbers: with regrouping Also consider: • Use expanded form to subtract three-digit numbers • Use compensation to subtract: up to three digits

Session 3.3: Subtracting Whole Dollars		1. Subtract across zeros 2. Add and subtract money amounts Also consider: • Making change
Session 3.3: Subtracting Whole Dollars
1. Subtract across zeros 2. Add and subtract money amounts Also consider: • Making change

Session 3.4: Strategies for Subtraction		1. Subtract numbers up to three digits: word problems 2. Subtract numbers up to three digits Also consider: • Subtract numbers up to three digits: without regrouping
Session 3.4: Strategies for Subtraction
1. Subtract numbers up to three digits: word problems 2. Subtract numbers up to three digits Also consider: • Subtract numbers up to three digits: without regrouping

Session 3.5: What Combinations Can I Make?		1. Subtract numbers up to three digits: with regrouping Also consider: • Add money amounts - word problems • Add and subtract data from tables: up to three digits
Session 3.5: What Combinations Can I Make?
1. Subtract numbers up to three digits: with regrouping Also consider: • Add money amounts - word problems • Add and subtract data from tables: up to three digits

Session 3.6: Solving Addition and Subtraction Problems		1. Add and subtract three-digit numbers 2. Addition and subtraction word problems: up to three digits Also consider: • Two-step addition and subtraction word problems • Price lists
Session 3.6: Solving Addition and Subtraction Problems
1. Add and subtract three-digit numbers 2. Addition and subtraction word problems: up to three digits Also consider: • Two-step addition and subtraction word problems • Price lists

8	Unit 8 Larger Numbers and Multi-Step Problems
Investigation 1 - Solving Division Problems
Session 1.1: Solving Division Problems		1. Division word problems Also consider: • Multiplication and division facts up to 10
Session 1.1: Solving Division Problems
1. Division word problems Also consider: • Multiplication and division facts up to 10

Session 1.2: Learning Division Facts		1. Divide by 1, 2, 5, and 10 2. Division sentences with 1 and 0 Also consider: • Multiply and divide with 1 and 0 • Multiply and divide by 2 and 5
Session 1.2: Learning Division Facts
1. Divide by 1, 2, 5, and 10 2. Division sentences with 1 and 0 Also consider: • Multiply and divide with 1 and 0 • Multiply and divide by 2 and 5

Session 1.3: Related Division Problems		1. Multiply and divide by 6 and 7 Also consider: • Use the distributive property to multiply by 3, 4, or 5 • Division facts for 1, 2, and 5: true or false? • Multiplication facts for 2, 5, and 10: find the missing factor • Multiply and divide by 5 and 10
Session 1.3: Related Division Problems
1. Multiply and divide by 6 and 7 Also consider: • Use the distributive property to multiply by 3, 4, or 5 • Division facts for 1, 2, and 5: true or false? • Multiplication facts for 2, 5, and 10: find the missing factor • Multiply and divide by 5 and 10

Session 1.4: Division with Remainders		1. Divide two-digit numbers by one-digit numbers using arrays Also consider: • Divide two-digit numbers by one-digit numbers: divisors up to 5 • Multiply and divide by 2 and 4
Session 1.4: Division with Remainders
1. Divide two-digit numbers by one-digit numbers using arrays Also consider: • Divide two-digit numbers by one-digit numbers: divisors up to 5 • Multiply and divide by 2 and 4

Session 1.5: Division Facts and Multiplication and Division Practice, Part 1		1. Divide two-digit numbers by one-digit numbers: divisors up to 10 2. Division facts for 2, 3, 4, 5, and 10: sorting Also consider: • Division facts for 2, 3, 4, 5, and 10: true or false? • Multiply and divide by 2, 4, and 8
Session 1.5: Division Facts and Multiplication and Division Practice, Part 1
1. Divide two-digit numbers by one-digit numbers: divisors up to 10 2. Division facts for 2, 3, 4, 5, and 10: sorting Also consider: • Division facts for 2, 3, 4, 5, and 10: true or false? • Multiply and divide by 2, 4, and 8

Session 1.6: Division Facts and Multiplication and Division Practice, Part 2		1. Division facts up to 10 Also consider: • Division facts for 6, 7, 8, and 9: true or false? • Division facts for 6, 7, 8, and 9: sorting
Session 1.6: Division Facts and Multiplication and Division Practice, Part 2
1. Division facts up to 10 Also consider: • Division facts for 6, 7, 8, and 9: true or false? • Division facts for 6, 7, 8, and 9: sorting
Investigation 2 - Solving Multiplication and Division Problems
Session 2.1: Multiplying a 2-Digit Number		1. Multiply one-digit numbers by two-digit numbers: word problems 2. Break apart two-digit numbers to multiply Also consider: • Division facts up to 10: sorting • Multiply 11 by numbers up to 12 • Multiply 12 by numbers up to 12
Session 2.1: Multiplying a 2-Digit Number
1. Multiply one-digit numbers by two-digit numbers: word problems 2. Break apart two-digit numbers to multiply Also consider: • Division facts up to 10: sorting • Multiply 11 by numbers up to 12 • Multiply 12 by numbers up to 12

Session 2.2: Using Arrays for Multiplication		1. Multiply one-digit numbers by teen numbers using grids 2. Multiply one-digit numbers by teen numbers Also consider: • Division facts up to 10: true or false? • Multiply one-digit numbers by two-digit numbers using area models I
Session 2.2: Using Arrays for Multiplication
1. Multiply one-digit numbers by teen numbers using grids 2. Multiply one-digit numbers by teen numbers Also consider: • Division facts up to 10: true or false? • Multiply one-digit numbers by two-digit numbers using area models I

Session 2.3: Dividing 2-Digit Numbers by 1-Digit Numbers		1. Divide two-digit numbers by one-digit numbers: word problems 2. Multiply one-digit numbers by two-digit numbers with regrouping: word problems 3. Division facts for 6, 7, 8, and 9 Also consider: • Divide two-digit numbers by one-digit numbers: without remainders
Session 2.3: Dividing 2-Digit Numbers by 1-Digit Numbers
1. Divide two-digit numbers by one-digit numbers: word problems 2. Multiply one-digit numbers by two-digit numbers with regrouping: word problems 3. Division facts for 6, 7, 8, and 9 Also consider: • Divide two-digit numbers by one-digit numbers: without remainders

Session 2.4: Solving Multiplication and Division Problems, Part 1		1. Division word problems involving remainders 2. Two-step multiplication and division word problems Also consider: • Divide two-digit numbers by one-digit numbers: with remainders • Division facts up to 10: select the missing numbers • Multiply one-digit numbers by two-digit numbers using area models II
Session 2.4: Solving Multiplication and Division Problems, Part 1
1. Division word problems involving remainders 2. Two-step multiplication and division word problems Also consider: • Divide two-digit numbers by one-digit numbers: with remainders • Division facts up to 10: select the missing numbers • Multiply one-digit numbers by two-digit numbers using area models II

Session 2.5: Solving Multiplication and Division Problems, Part 2		1. Two-step mixed operation word problems Also consider: • Division sentences up to 10: true or false? • Multiplication and division facts up to 12 • Multiplication facts up to 12: select the missing factors • Division facts up to 12: select the missing numbers
Session 2.5: Solving Multiplication and Division Problems, Part 2
1. Two-step mixed operation word problems Also consider: • Division sentences up to 10: true or false? • Multiplication and division facts up to 12 • Multiplication facts up to 12: select the missing factors • Division facts up to 12: select the missing numbers
Investigation 3 - Solving Multi-Step Problems
Session 3.1: Representing Multi-Step Problems: The Marbles of Rhomaar		1. Skip-counting sequences Also consider: • Find the next shape in a pattern
Session 3.1: Representing Multi-Step Problems: The Marbles of Rhomaar
1. Skip-counting sequences Also consider: • Find the next shape in a pattern

Session 3.2: Identifying and Explaining Arithmetic Patterns		1. Shape patterns Also consider: • Find the next row in a growing pattern
Session 3.2: Identifying and Explaining Arithmetic Patterns
1. Shape patterns Also consider: • Find the next row in a growing pattern

Session 3.3: Applying a General Rule		1. Use a rule to complete an addition pattern 2. Multiplication and division: real-world patterns
Session 3.3: Applying a General Rule
1. Use a rule to complete an addition pattern 2. Multiplication and division: real-world patterns

Session 3.4: Using Equations to Model Multi-Step Problems		1. Division facts up to 10: find the missing number 2. Multiply one-digit numbers by two-digit numbers
Session 3.4: Using Equations to Model Multi-Step Problems
1. Division facts up to 10: find the missing number 2. Multiply one-digit numbers by two-digit numbers

Session 3.5: Solving Multi-Step Problems		1. What is true about the addition pattern?
Session 3.5: Solving Multi-Step Problems
1. What is true about the addition pattern?

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