1	Unit 1 Addition and Subtraction with Fractions
Big Idea 1 - Equivalent Fractions
1-1:  Introduce the MathBoard		1. Fractions review Also consider: • Decompose fractions multiple ways: sums up to 1
1-1:  Introduce the MathBoard
1. Fractions review Also consider: • Decompose fractions multiple ways: sums up to 1
1-2:  Explain Equivalent Fractions		1. Identify equivalent fractions using number lines 2. Equivalent fractions: word problems
1-2:  Explain Equivalent Fractions
1. Identify equivalent fractions using number lines 2. Equivalent fractions: word problems
1-3:  Equivalent Fractions and Multipliers		1. Patterns of equivalent fractions Also consider: • Find equivalent fractions using area models • Identify equivalent fractions • Equivalent fractions • Write fractions in lowest terms
1-3:  Equivalent Fractions and Multipliers
1. Patterns of equivalent fractions Also consider: • Find equivalent fractions using area models • Identify equivalent fractions • Equivalent fractions • Write fractions in lowest terms
1-4:  Strategies for Comparing Fractions		1. Compare fractions with like numerators or denominators 2. Inequalities with fractions 3. Compare fractions: word problems Also consider: • Least common denominator • Graph and compare fractions on number lines • Compare fractions using benchmarks
1-4:  Strategies for Comparing Fractions
1. Compare fractions with like numerators or denominators 2. Inequalities with fractions 3. Compare fractions: word problems Also consider: • Least common denominator • Graph and compare fractions on number lines • Compare fractions using benchmarks
1-5:  Fractions Greater Than One		1. Convert between improper fractions and mixed numbers
1-5:  Fractions Greater Than One
1. Convert between improper fractions and mixed numbers
Big Idea 2 - Addition and Subtraction of Fractions
1-6:  Add and Subtract Like Mixed Numbers		1. Add and subtract mixed numbers with like denominators 2. Add and subtract mixed numbers with like denominators: word problems Also consider: • Add and subtract fractions with like denominators • Add and subtract fractions with like denominators: word problems
1-6:  Add and Subtract Like Mixed Numbers
1. Add and subtract mixed numbers with like denominators 2. Add and subtract mixed numbers with like denominators: word problems Also consider: • Add and subtract fractions with like denominators • Add and subtract fractions with like denominators: word problems
1-7:  Add Unlike Fractions		1. Add fractions with unlike denominators using models 2. Add fractions with unlike denominators Also consider: • Represent addition of fractions with unlike denominators using objects • Add fractions with unlike denominators using objects
1-7:  Add Unlike Fractions
1. Add fractions with unlike denominators using models 2. Add fractions with unlike denominators Also consider: • Represent addition of fractions with unlike denominators using objects • Add fractions with unlike denominators using objects
1-8:  Subtract Unlike Fractions		1. Subtract fractions with unlike denominators 2. Add and subtract fractions with unlike denominators: word problems Also consider: • Subtract fractions with unlike denominators using models • Represent subtraction of fractions with unlike denominators using objects • Subtract fractions with unlike denominators using objects • Complete addition and subtraction sentences with fractions
1-8:  Subtract Unlike Fractions
1. Subtract fractions with unlike denominators 2. Add and subtract fractions with unlike denominators: word problems Also consider: • Subtract fractions with unlike denominators using models • Represent subtraction of fractions with unlike denominators using objects • Subtract fractions with unlike denominators using objects • Complete addition and subtraction sentences with fractions
1-9:  Add and Subtract Unlike Mixed Numbers		1. Add and subtract mixed numbers with unlike denominators 2. Add and subtract mixed numbers with unlike denominators: word problems
1-9:  Add and Subtract Unlike Mixed Numbers
1. Add and subtract mixed numbers with unlike denominators 2. Add and subtract mixed numbers with unlike denominators: word problems
1-10:  Practice with Unlike Mixed Numbers		1. Add and subtract fractions and mixed numbers Also consider: • Add or subtract three fractions with unlike denominators • Complete addition and subtraction sentences with mixed numbers
1-10:  Practice with Unlike Mixed Numbers
1. Add and subtract fractions and mixed numbers Also consider: • Add or subtract three fractions with unlike denominators • Complete addition and subtraction sentences with mixed numbers
1-11:  Reasonable Answers		1. Estimate sums and differences of fractions using benchmarks 2. Estimate sums and differences of mixed numbers
1-11:  Reasonable Answers
1. Estimate sums and differences of fractions using benchmarks 2. Estimate sums and differences of mixed numbers
1-12:  Real World Problems		1. Add and subtract fractions and mixed numbers: word problems Also consider: • Add 3 or more fractions with unlike denominators
1-12:  Real World Problems
1. Add and subtract fractions and mixed numbers: word problems Also consider: • Add 3 or more fractions with unlike denominators
1-13:  Focus on Problem Solving		1. Add and subtract fractions and mixed numbers in recipes
1-13:  Focus on Problem Solving
1. Add and subtract fractions and mixed numbers in recipes

2	Unit 2 Addition and Subtraction with Decimals
Big Idea 1 - Read and Write Whole Numbers and Decimals
2-1:  Decimals as Equal Divisions		1. Convert fractions and mixed numbers to decimals: denominators of 10, 100, or 1,000 Also consider: • What decimal number is illustrated?
2-1:  Decimals as Equal Divisions
1. Convert fractions and mixed numbers to decimals: denominators of 10, 100, or 1,000 Also consider: • What decimal number is illustrated?
2-2:  Thousands to Thousandths		1. Understanding decimals expressed in words 2. Expanded form for decimals 3. Convert decimals between standard and expanded form using fractions Also consider: • Place values in decimal numbers • Relationship between decimal place values
2-2:  Thousands to Thousandths
1. Understanding decimals expressed in words 2. Expanded form for decimals 3. Convert decimals between standard and expanded form using fractions Also consider: • Place values in decimal numbers • Relationship between decimal place values
2-3:  Equate and Compare Thousandths		1. Equivalent decimals 2. Compare decimals Also consider: • Graph decimals on number lines • Compare decimals on number lines • Put decimal numbers in order
2-3:  Equate and Compare Thousandths
1. Equivalent decimals 2. Compare decimals Also consider: • Graph decimals on number lines • Compare decimals on number lines • Put decimal numbers in order
Big Idea 2 - Addition and Subtraction
2-4:  Adding and Subtracting Decimals		1. Explore metric measures of length 2. Add and subtract decimals: word problems
2-4:  Adding and Subtracting Decimals
1. Explore metric measures of length 2. Add and subtract decimals: word problems
2-5:  Add Whole Numbers and Decimals		1. Add decimal numbers 2. Add money amounts
2-5:  Add Whole Numbers and Decimals
1. Add decimal numbers 2. Add money amounts
2-6:  Subtract Whole and Decimal Numbers		1. Subtract decimal numbers 2. Subtract money amounts 3. Add and subtract money: word problems Also consider: • Add and subtract decimal numbers • Choose decimals with a particular sum or difference • Complete the decimal addition or subtraction sentence • Compare sums and differences of decimals
2-6:  Subtract Whole and Decimal Numbers
1. Subtract decimal numbers 2. Subtract money amounts 3. Add and subtract money: word problems Also consider: • Add and subtract decimal numbers • Choose decimals with a particular sum or difference • Complete the decimal addition or subtraction sentence • Compare sums and differences of decimals
2-7:  Properties and Strategies		1. Properties of addition 2. Add using properties 3. Distributive property: find the missing number Also consider: • Add 3 fractions or mixed numbers using properties of addition
2-7:  Properties and Strategies
1. Properties of addition 2. Add using properties 3. Distributive property: find the missing number Also consider: • Add 3 fractions or mixed numbers using properties of addition
Big Idea 3 - Round and Estimate with Decimals
2-8:  Round and Estimate with Decimals		1. Round decimals 2. Estimate sums and differences of decimals using rounding Also consider: • Estimate sums and differences of decimals using benchmarks
2-8:  Round and Estimate with Decimals
1. Round decimals 2. Estimate sums and differences of decimals using rounding Also consider: • Estimate sums and differences of decimals using benchmarks
2-9:  Graphs with Decimal Numbers		1. Compare, order, and round decimals: word problems 2. Interpret bar graphs: one-step problems Also consider: • Complete bar graphs
2-9:  Graphs with Decimal Numbers
1. Compare, order, and round decimals: word problems 2. Interpret bar graphs: one-step problems Also consider: • Complete bar graphs
2-10:  Focus on Problem Solving		1. Add and subtract money amounts: two-step word problems
2-10:  Focus on Problem Solving
1. Add and subtract money amounts: two-step word problems
Big Idea 4 - Percents
2-11:  Meaning of Percent		1. What percentage is illustrated? 2. Convert between percents and fractions
2-11:  Meaning of Percent
1. What percentage is illustrated? 2. Convert between percents and fractions
2-12:  Fractions, Decimals, and Percent		1. Convert between percents, fractions, and decimals: denominators of 10 or 100
2-12:  Fractions, Decimals, and Percent
1. Convert between percents, fractions, and decimals: denominators of 10 or 100
Big Idea 5 - Millions to Millionths
2-13:  Place Value Patterns		1. Convert between standard and expanded form 2. Write numbers in words 3. Order numbers up to one billion Also consider: • Compare numbers up to millions
2-13:  Place Value Patterns
1. Convert between standard and expanded form 2. Write numbers in words 3. Order numbers up to one billion Also consider: • Compare numbers up to millions
2-14:  Use Place Value		1. Relationship between place values
2-14:  Use Place Value
1. Relationship between place values

3	Unit 3 Multiplication and Division with Fractions
Big Idea 1 - Multiplication with Fractions
3-1:  Basic Multiplication Concepts		1. Multiply unit fractions by whole numbers Also consider: • Multiply unit fractions by whole numbers using number lines • Multiples of unit fractions: find the missing numbers • Multiply unit fractions and whole numbers: sorting
3-1:  Basic Multiplication Concepts
1. Multiply unit fractions by whole numbers Also consider: • Multiply unit fractions by whole numbers using number lines • Multiples of unit fractions: find the missing numbers • Multiply unit fractions and whole numbers: sorting
3-2:  Multiplication with Non-Unit Fractions		1. Multiply fractions by whole numbers I 2. Fractions of a number I 3. Fractions of a number: word problems Also consider: • Multiply fractions by whole numbers using arrays
3-2:  Multiplication with Non-Unit Fractions
1. Multiply fractions by whole numbers I 2. Fractions of a number I 3. Fractions of a number: word problems Also consider: • Multiply fractions by whole numbers using arrays
3-3:  Multiplication with Fractional Solutions		1. Multiply fractions by whole numbers using models: complete the equation 2. Multiply fractions by whole numbers using number lines 3. Multiply fractions by whole numbers II Also consider: • Multiply fractions by whole numbers: word problems • Multiples of fractions: find the missing numbers • Multiply fractions and whole numbers: sorting
3-3:  Multiplication with Fractional Solutions
1. Multiply fractions by whole numbers using models: complete the equation 2. Multiply fractions by whole numbers using number lines 3. Multiply fractions by whole numbers II Also consider: • Multiply fractions by whole numbers: word problems • Multiples of fractions: find the missing numbers • Multiply fractions and whole numbers: sorting
3-4:  Multiply a Fraction by a Fraction		1. Multiply two fractions using models 2. Multiply two fractions 3. Multiply two fractions: word problems
3-4:  Multiply a Fraction by a Fraction
1. Multiply two fractions using models 2. Multiply two fractions 3. Multiply two fractions: word problems
3-5:  Multiplication Strategies		1. Multiply fractions with common factors Also consider: • Multiply three fractions and whole numbers • Complete the fraction multiplication sentence I • Complete the fraction multiplication sentence II
3-5:  Multiplication Strategies
1. Multiply fractions with common factors Also consider: • Multiply three fractions and whole numbers • Complete the fraction multiplication sentence I • Complete the fraction multiplication sentence II
3-6:  Multiply Mixed Numbers		1. Multiply mixed numbers, fractions, and whole numbers 2. Multiplication with mixed numbers: word problems Also consider: • Multiply fractions and mixed numbers in recipes • Multiply three mixed numbers, fractions, and whole numbers
3-6:  Multiply Mixed Numbers
1. Multiply mixed numbers, fractions, and whole numbers 2. Multiplication with mixed numbers: word problems Also consider: • Multiply fractions and mixed numbers in recipes • Multiply three mixed numbers, fractions, and whole numbers
Big Idea 2 - Multiplication Links
3-7:  Relate Fraction Operations		1. Add, subtract, and multiply fractions and mixed numbers Also consider: • Properties of multiplication • Multiply using properties
3-7:  Relate Fraction Operations
1. Add, subtract, and multiply fractions and mixed numbers Also consider: • Properties of multiplication • Multiply using properties
3-8:  Solve Real World Problems		1. Add, subtract, and multiply fractions and mixed numbers: word problems
3-8:  Solve Real World Problems
1. Add, subtract, and multiply fractions and mixed numbers: word problems
3-9:  Make Generalizations		1. Scaling by fractions and mixed numbers Also consider: • Scaling whole numbers by fractions: justify your answer
3-9:  Make Generalizations
1. Scaling by fractions and mixed numbers Also consider: • Scaling whole numbers by fractions: justify your answer
Big Idea 3 - Division with Fractions
3-10:  When Dividing Is Also Multiplying		1. Relate division and fractions 2. Divide unit fractions and whole numbers using area models 3. Divide unit fractions and whole numbers Also consider: • Divide unit fractions by whole numbers using models • Divide whole numbers by unit fractions using models
3-10:  When Dividing Is Also Multiplying
1. Relate division and fractions 2. Divide unit fractions and whole numbers using area models 3. Divide unit fractions and whole numbers Also consider: • Divide unit fractions by whole numbers using models • Divide whole numbers by unit fractions using models
3-11:  Solve Division Problems		1. Understand fractions as division: word problems 2. Divide unit fractions and whole numbers: word problems
3-11:  Solve Division Problems
1. Understand fractions as division: word problems 2. Divide unit fractions and whole numbers: word problems
3-12:  Distinguish Multiplication from Division		1. Multiply and divide unit fractions and whole numbers: word problems
3-12:  Distinguish Multiplication from Division
1. Multiply and divide unit fractions and whole numbers: word problems
3-13:  Review Operations with Fractions		1. Add, subtract, multiply, and divide fractions and mixed numbers 2. Add, subtract, multiply, and divide fractions and mixed numbers: word problems
3-13:  Review Operations with Fractions
1. Add, subtract, multiply, and divide fractions and mixed numbers 2. Add, subtract, multiply, and divide fractions and mixed numbers: word problems
3-14:  Focus on Problem Solving		1. Circle graphs
3-14:  Focus on Problem Solving
1. Circle graphs

4	Unit 4 Multiplication with Whole Numbers and Decimals
Big Idea 1 - Multiplication with Whole Numbers
4-1:  Shift Patterns in Multiplication		1. Multiply by multiples of 10, 100, or 1000 2. Powers of ten 3. Multiply a whole number by a power of ten
4-1:  Shift Patterns in Multiplication
1. Multiply by multiples of 10, 100, or 1000 2. Powers of ten 3. Multiply a whole number by a power of ten
4-2:  Patterns with Fives and Zeros		1. Multiply numbers ending in zeros 2. Multiply numbers ending in zeros: word problems Also consider: • Multiplication patterns over increasing place values
4-2:  Patterns with Fives and Zeros
1. Multiply numbers ending in zeros 2. Multiply numbers ending in zeros: word problems Also consider: • Multiplication patterns over increasing place values
4-3:  Sharing Methods for Multiplication		1. Multiply 2-digit numbers by 2-digit numbers using area models 2. Multiply 2-digit numbers using partial products
4-3:  Sharing Methods for Multiplication
1. Multiply 2-digit numbers by 2-digit numbers using area models 2. Multiply 2-digit numbers using partial products
4-4:  Multiply Two-Digit Numbers		1. Multiply 2-digit numbers by 2-digit numbers 2. Multiply 2-digit by 2-digit numbers: word problems Also consider: • Multiply by 2-digit numbers: complete the missing steps
4-4:  Multiply Two-Digit Numbers
1. Multiply 2-digit numbers by 2-digit numbers 2. Multiply 2-digit by 2-digit numbers: word problems Also consider: • Multiply by 2-digit numbers: complete the missing steps
4-5:  Practice Multiplication		1. Multiply by 1-digit and 2-digit numbers
4-5:  Practice Multiplication
1. Multiply by 1-digit and 2-digit numbers
Big Idea 2 - Multiplication with Decimal Numbers
4-6:  Multiply Decimals by Whole Numbers		1. Multiply whole numbers by decimals 2. Multiply decimals and whole numbers: word problems Also consider: • Multiply a decimal by a one-digit whole number using blocks • Multiply a decimal by a one-digit whole number using the distributive property • Multiply a decimal by a two-digit whole number using area models
4-6:  Multiply Decimals by Whole Numbers
1. Multiply whole numbers by decimals 2. Multiply decimals and whole numbers: word problems Also consider: • Multiply a decimal by a one-digit whole number using blocks • Multiply a decimal by a one-digit whole number using the distributive property • Multiply a decimal by a two-digit whole number using area models
4-7:  Multiply by Decimals		1. Multiply by a power of ten with decimals: find the missing number 2. Multiply two decimals: where does the decimal point go?
4-7:  Multiply by Decimals
1. Multiply by a power of ten with decimals: find the missing number 2. Multiply two decimals: where does the decimal point go?
4-8:  Multiply with Decimals Greater Than 1		1. Multiply two decimals: products up to thousandths 2. Solve using properties of multiplication: with decimals Also consider: • Multiply decimals less than one using grids • Multiply decimals using grids • Decimal multiplication: compare products up to thousandths
4-8:  Multiply with Decimals Greater Than 1
1. Multiply two decimals: products up to thousandths 2. Solve using properties of multiplication: with decimals Also consider: • Multiply decimals less than one using grids • Multiply decimals using grids • Decimal multiplication: compare products up to thousandths
4-9:  Compare Shift Patterns		1. Multiply a decimal by a power of ten 2. Multiply by 0.1 or 0.01 3. Multiply a decimal by a power of ten: with exponents Also consider: • Relationship between decimal place values
4-9:  Compare Shift Patterns
1. Multiply a decimal by a power of ten 2. Multiply by 0.1 or 0.01 3. Multiply a decimal by a power of ten: with exponents Also consider: • Relationship between decimal place values
4-10:  Estimate Products		1. Estimate products: multiply by 2-digit numbers 2. Estimate products of decimals
4-10:  Estimate Products
1. Estimate products: multiply by 2-digit numbers 2. Estimate products of decimals
4-11:  Multiplication Practice		1. Multiply with decimals
4-11:  Multiplication Practice
1. Multiply with decimals
4-12:  Focus on Problem Solving		1. Price lists
4-12:  Focus on Problem Solving
1. Price lists

5	Unit 5 Division with Whole Numbers and Decimals
Big Idea 1 - Division with Whole Numbers
5-1:  Divide Whole Numbers by One Digit		1. Divide multi-digit numbers by 1-digit numbers 2. Divide 4-digit numbers by 1-digit numbers: word problems 3. Estimate quotients: word problems
5-1:  Divide Whole Numbers by One Digit
1. Divide multi-digit numbers by 1-digit numbers 2. Divide 4-digit numbers by 1-digit numbers: word problems 3. Estimate quotients: word problems
5-2:  Explore Dividing by Two-Digit Whole Numbers		1. Divide 4-digit numbers by 2-digit numbers 2. Divide 4-digit numbers by 2-digit numbers: word problems Also consider: • Divide by 2-digit numbers using models • Divide by 2-digit numbers using partial quotients • Estimate quotients: 2-digit divisors
5-2:  Explore Dividing by Two-Digit Whole Numbers
1. Divide 4-digit numbers by 2-digit numbers 2. Divide 4-digit numbers by 2-digit numbers: word problems Also consider: • Divide by 2-digit numbers using models • Divide by 2-digit numbers using partial quotients • Estimate quotients: 2-digit divisors
5-3:  Too Large, Too Small, or Just Right?		1. Adjust quotients
5-3:  Too Large, Too Small, or Just Right?
1. Adjust quotients
5-4:  Interpret Remainders		1. Divide 3-digit by 2-digit numbers: interpret remainders
5-4:  Interpret Remainders
1. Divide 3-digit by 2-digit numbers: interpret remainders
5-5:  Division Practice		1. Divide larger numbers by 1-digit and 2-digit numbers 2. Multiplication and division up to thousands: word problems
5-5:  Division Practice
1. Divide larger numbers by 1-digit and 2-digit numbers 2. Multiplication and division up to thousands: word problems
Big Idea 2 - Division with Decimal Numbers
5-6:  Divide Decimal Numbers by Whole Numbers		1. Decimal division patterns over increasing place values 2. Division with decimal quotients Also consider: • Divide by powers of ten • Divide by a power of ten: with exponents • Divide by a power of ten with decimals: find the missing number • Estimate decimal quotients
5-6:  Divide Decimal Numbers by Whole Numbers
1. Decimal division patterns over increasing place values 2. Division with decimal quotients Also consider: • Divide by powers of ten • Divide by a power of ten: with exponents • Divide by a power of ten with decimals: find the missing number • Estimate decimal quotients
5-7:  Divide Whole Numbers by Decimal Numbers		1. Divide whole numbers by decimals
5-7:  Divide Whole Numbers by Decimal Numbers
1. Divide whole numbers by decimals
5-8:  Divide a Decimal Number by a Decimal Number		1. Divide by 0.1, 0.01, or 0.001 2. Divide by decimals without adding zeros 3. Divide decimals by decimals
5-8:  Divide a Decimal Number by a Decimal Number
1. Divide by 0.1, 0.01, or 0.001 2. Divide by decimals without adding zeros 3. Divide decimals by decimals
5-9:  Division Practice		1. Division with decimals
5-9:  Division Practice
1. Division with decimals
5-10:  Distinguish Between Multiplication and Division		1. Multiply and divide with decimals 2. Multiply and divide decimals: word problems Also consider: • Inequalities with decimal division • Decimal multiplication: compare products up to thousandths
5-10:  Distinguish Between Multiplication and Division
1. Multiply and divide with decimals 2. Multiply and divide decimals: word problems Also consider: • Inequalities with decimal division • Decimal multiplication: compare products up to thousandths
5-11:  Focus on Problem Solving		1. Unit prices
5-11:  Focus on Problem Solving
1. Unit prices

6	Unit 6 Operations and Word Problems
Big Idea 1 - Equations and Problem Solving
6-1:  Situation and Solution Equations for Addition and Subtraction		1. Write and solve addition and subtraction equations using diagrams: word problems
6-1:  Situation and Solution Equations for Addition and Subtraction
1. Write and solve addition and subtraction equations using diagrams: word problems
6-2:  Situation and Solution Equations for Multiplication and Division		1. Write and solve multiplication and division equations using diagrams: word problems Also consider: • Write variable equations: word problems
6-2:  Situation and Solution Equations for Multiplication and Division
1. Write and solve multiplication and division equations using diagrams: word problems Also consider: • Write variable equations: word problems
6-3:  Write Word Problems		1. Which word problem matches the one-step equation?
6-3:  Write Word Problems
1. Which word problem matches the one-step equation?
6-4:  Determine Reasonable Answers		1. Estimate sums and differences: word problems 2. Estimate products and quotients: word problems 3. Estimate products word problems: identify reasonable answers Also consider: • Add, subtract, multiply, and divide whole numbers: word problems • Solve one-step equations: word problems
6-4:  Determine Reasonable Answers
1. Estimate sums and differences: word problems 2. Estimate products and quotients: word problems 3. Estimate products word problems: identify reasonable answers Also consider: • Add, subtract, multiply, and divide whole numbers: word problems • Solve one-step equations: word problems
Big Idea 2 - Comparison Word Problems
6-5:  Language of Comparison Problems		1. Comparison word problems
6-5:  Language of Comparison Problems
1. Comparison word problems
6-6:  Multiplicative Comparison Situations		1. Compare numbers using multiplication: word problems
6-6:  Multiplicative Comparison Situations
1. Compare numbers using multiplication: word problems
6-7:  Types of Comparison Problems		1. Comparison word problems: addition or multiplication?
6-7:  Types of Comparison Problems
1. Comparison word problems: addition or multiplication?
Big Idea 3 - Problems with More Than One Step
6-8:  Equations and Parentheses		1. Two-step word problems with money 2. Word problems with extra or missing information
6-8:  Equations and Parentheses
1. Two-step word problems with money 2. Word problems with extra or missing information
6-9:  Multistep Word Problems		1. Multi-step word problems 2. Multi-step word problems involving remainders Also consider: • Multi-step word problems: identify reasonable answers
6-9:  Multistep Word Problems
1. Multi-step word problems 2. Multi-step word problems involving remainders Also consider: • Multi-step word problems: identify reasonable answers
6-10:  Practice Problem Solving		1. Multiply money amounts: multi-step word problems 2. Represent multi-step problems using equations Also consider: • Multi-step word problems: multiplicative comparison
6-10:  Practice Problem Solving
1. Multiply money amounts: multi-step word problems 2. Represent multi-step problems using equations Also consider: • Multi-step word problems: multiplicative comparison
6-11:  Focus on Problem Solving		1. Interpret bar graphs: multi-step problems
6-11:  Focus on Problem Solving
1. Interpret bar graphs: multi-step problems

7	Unit 7 Algebra, Patterns, Data, and Graphs
Big Idea 1 - Algebraic Reasoning and Expressions
7-1:  Read and Write Expressions		1. Write numerical expressions: one operation 2. Write numerical expressions: two operations 3. Write variable expressions
7-1:  Read and Write Expressions
1. Write numerical expressions: one operation 2. Write numerical expressions: two operations 3. Write variable expressions
7-2:  Simplify Expressions		1. Evaluate numerical expressions with and without parentheses 2. Evaluate numerical expressions with parentheses and brackets Also consider: • Identify mistakes involving the order of operations • Evaluate numerical expressions with parentheses in different places
7-2:  Simplify Expressions
1. Evaluate numerical expressions with and without parentheses 2. Evaluate numerical expressions with parentheses and brackets Also consider: • Identify mistakes involving the order of operations • Evaluate numerical expressions with parentheses in different places
7-3:  Expressions, Equations, and Inequalities		1. Evaluate variable expressions 2. Write variable expressions: word problems Also consider: • Write numerical expressions for word problems • Solutions to inequalities
7-3:  Expressions, Equations, and Inequalities
1. Evaluate variable expressions 2. Write variable expressions: word problems Also consider: • Write numerical expressions for word problems • Solutions to inequalities
Big Idea 2 - Patterns and Graphs
7-4:  Patterns and Relationships		1. Use a rule to complete an addition pattern Also consider: • Compare patterns
7-4:  Patterns and Relationships
1. Use a rule to complete an addition pattern Also consider: • Compare patterns
7-5:  The Coordinate Plane		1. Describe the coordinate plane 2. Points on a coordinate plane 3. Graph points on a coordinate plane Also consider: • Graph triangles and quadrilaterals • Distance between two points
7-5:  The Coordinate Plane
1. Describe the coordinate plane 2. Points on a coordinate plane 3. Graph points on a coordinate plane Also consider: • Graph triangles and quadrilaterals • Distance between two points
7-6:  Graph Ordered Pairs		1. Use a rule to complete a table and a graph 2. Complete a table from a graph 3. Complete a table and make a graph: word problems Also consider: • Analyze graphed relationships
7-6:  Graph Ordered Pairs
1. Use a rule to complete a table and a graph 2. Complete a table from a graph 3. Complete a table and make a graph: word problems Also consider: • Analyze graphed relationships
7-7:  Focus on Problem Solving		1. Coordinate planes as maps 2. Follow directions on a coordinate plane
7-7:  Focus on Problem Solving
1. Coordinate planes as maps 2. Follow directions on a coordinate plane
Big Idea 3 - Integers and Interpreting Data
7-8:  Negative Numbers		1. Understanding integers 2. Graph integers on horizontal and vertical number lines
7-8:  Negative Numbers
1. Understanding integers 2. Graph integers on horizontal and vertical number lines
7-9:  Double Bar Graphs and Line Graphs		1. Interpret double bar graphs 2. Interpret line graphs Also consider: • Complete double bar graphs • Create line graphs
7-9:  Double Bar Graphs and Line Graphs
1. Interpret double bar graphs 2. Interpret line graphs Also consider: • Complete double bar graphs • Create line graphs
7-10:  Testing a Hypothesis
7-10:  Testing a Hypothesis
7-11:  Mean, Median, and Range		1. Find the mean 2. Find the median 3. Find the range Also consider: • Interpret charts and graphs to find the mean • Interpret charts and graphs to find the median • Interpret charts and graphs to find the range
7-11:  Mean, Median, and Range
1. Find the mean 2. Find the median 3. Find the range Also consider: • Interpret charts and graphs to find the mean • Interpret charts and graphs to find the median • Interpret charts and graphs to find the range

8	Unit 8 Measurement and Geometry
Big Idea 1 - Length, Area, and Volume
8-1:  Metric Units of Length		1. Convert metric units of length
8-1:  Metric Units of Length
1. Convert metric units of length
8-2:  Customary Units of Length		1. Convert customary units of length
8-2:  Customary Units of Length
1. Convert customary units of length
8-3:  Perimeter and Area of Rectangles		1. Area of squares and rectangles 2. Understand fraction multiplication and area 3. Find the perimeter or area: mixed number side lengths Also consider: • Area and perimeter: word problems
8-3:  Perimeter and Area of Rectangles
1. Area of squares and rectangles 2. Understand fraction multiplication and area 3. Find the perimeter or area: mixed number side lengths Also consider: • Area and perimeter: word problems
8-4:  Cubic Units and Volume		1. Volume of rectangular prisms made of unit cubes Also consider: • Compare and apply cubic units • Volume of irregular figures made of unit cubes
8-4:  Cubic Units and Volume
1. Volume of rectangular prisms made of unit cubes Also consider: • Compare and apply cubic units • Volume of irregular figures made of unit cubes
8-5:  Visualize Volume		1. Volume of cubes and rectangular prisms
8-5:  Visualize Volume
1. Volume of cubes and rectangular prisms
8-6:  Introduce Volume Formulas		1. Apply volume formulas for rectangular prisms 2. Volume of cubes and rectangular prisms: word problems Also consider: • Volume of cubes and rectangular prisms with decimal side lengths
8-6:  Introduce Volume Formulas
1. Apply volume formulas for rectangular prisms 2. Volume of cubes and rectangular prisms: word problems Also consider: • Volume of cubes and rectangular prisms with decimal side lengths
8-7:  Relate Length, Area, and Volume		1. Volume of rectangular prisms made of unit cubes: word problems
8-7:  Relate Length, Area, and Volume
1. Volume of rectangular prisms made of unit cubes: word problems
8-8:  Volume of Composite Solid Figures		1. Volume of compound figures
8-8:  Volume of Composite Solid Figures
1. Volume of compound figures
Big Idea 2 - Liquid Volume, Mass, and Weight
8-9:  Metric Units of Liquid Volume		1. Convert metric units of volume
8-9:  Metric Units of Liquid Volume
1. Convert metric units of volume
8-10:  Metric Units of Mass		1. Convert metric units of mass Also consider: • Multi-step problems with metric unit conversions • Choose the appropriate metric unit of measure • Compare and convert metric units • Convert metric units involving decimals • Conversion tables - metric units
8-10:  Metric Units of Mass
1. Convert metric units of mass Also consider: • Multi-step problems with metric unit conversions • Choose the appropriate metric unit of measure • Compare and convert metric units • Convert metric units involving decimals • Conversion tables - metric units
8-11:  Customary Units of Liquid Volume		1. Convert customary units of volume
8-11:  Customary Units of Liquid Volume
1. Convert customary units of volume
8-12:  Customary Units of Weight		1. Convert customary units of weight Also consider: • Multi-step problems with customary unit conversions • Choose the appropriate customary unit of measure • Compare and convert customary units • Conversion tables - customary units • Compare customary units by multiplying • Convert customary units involving fractions
8-12:  Customary Units of Weight
1. Convert customary units of weight Also consider: • Multi-step problems with customary unit conversions • Choose the appropriate customary unit of measure • Compare and convert customary units • Conversion tables - customary units • Compare customary units by multiplying • Convert customary units involving fractions
8-13:  Read and Make Line Plots		1. Interpret line plots with whole numbers 2. Create line plots with fractions 3. Create and interpret line plots with fractions
8-13:  Read and Make Line Plots
1. Interpret line plots with whole numbers 2. Create line plots with fractions 3. Create and interpret line plots with fractions
Big Idea 3 - Attributes of Two-Dimensional Figures
8-14:  Attributes of Quadrilaterals		1. Pick all the names for a quadrilateral 2. Draw quadrilaterals 3. Identify the relationships between quadrilaterals Also consider: • Classify quadrilaterals • Describe relationships among quadrilaterals
8-14:  Attributes of Quadrilaterals
1. Pick all the names for a quadrilateral 2. Draw quadrilaterals 3. Identify the relationships between quadrilaterals Also consider: • Classify quadrilaterals • Describe relationships among quadrilaterals
8-15:  Attributes of Triangles		1. Classify triangles
8-15:  Attributes of Triangles
1. Classify triangles
8-16:  Attributes of Two-Dimensional Shapes		1. Is it a polygon? 2. Regular and irregular polygons Also consider: • Number of sides in polygons • Sort polygons into Venn diagrams • Properties of polygons
8-16:  Attributes of Two-Dimensional Shapes
1. Is it a polygon? 2. Regular and irregular polygons Also consider: • Number of sides in polygons • Sort polygons into Venn diagrams • Properties of polygons
8-17:  Focus on Problem Solving		1. Compare volumes and dimensions of rectangular prisms: word problems
8-17:  Focus on Problem Solving
1. Compare volumes and dimensions of rectangular prisms: word problems
Big Idea 4 - Perimeter and Area of Other Polygons
8-18:  Area of a Right Triangle		1. Understanding area of a right triangle 2. Area of right triangles
8-18:  Area of a Right Triangle
1. Understanding area of a right triangle 2. Area of right triangles
8-19:  Area of a Parallelogram		1. Understanding area of a parallelogram 2. Area of parallelograms
8-19:  Area of a Parallelogram
1. Understanding area of a parallelogram 2. Area of parallelograms
8-20:  Area of Any Triangle		1. Understanding area of a triangle 2. Area of acute and right triangles 3. Area of obtuse triangles
8-20:  Area of Any Triangle
1. Understanding area of a triangle 2. Area of acute and right triangles 3. Area of obtuse triangles
8-21:  Area of Other Figures		1. Perimeter with whole number side lengths 2. Area of compound figures Also consider: • Find the perimeter or area: whole number side lengths
8-21:  Area of Other Figures
1. Perimeter with whole number side lengths 2. Area of compound figures Also consider: • Find the perimeter or area: whole number side lengths
Big Idea 5 - Attributes of Three-Dimensional Figures
8-22:  Three-Dimensional Figures		1. Identify three-dimensional figures
8-22:  Three-Dimensional Figures
1. Identify three-dimensional figures
8-23:  Prisms and Pyramids		1. Nets of three-dimensional figures 2. Surface area 3. Surface area of triangular prisms Also consider: • Bases of prisms
8-23:  Prisms and Pyramids
1. Nets of three-dimensional figures 2. Surface area 3. Surface area of triangular prisms Also consider: • Bases of prisms
8-24:  Compare Three-Dimensional Figures		1. Count vertices, edges, and faces - cubes and rectangular prisms
8-24:  Compare Three-Dimensional Figures
1. Count vertices, edges, and faces - cubes and rectangular prisms

This document includes the IXL® skill alignments to Houghton Mifflin Harcourt's Math Expressions curriculum. IXL provides skill alignments as a service to teachers, students, and parents. The skill alignments are provided by IXL and are not affiliated with, sponsored by, reviewed, approved or endorsed by Houghton Mifflin Harcourt or any other third party. IXL® and IXL Learning® are registered trademarks of IXL Learning, Inc. All other intellectual property rights (e.g., unregistered and registered trademarks and copyrights) are the property of their respective owners.