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Texas Go Math Grade 5 Lesson 2.8 Answer Key Division

Refer to our Texas Go Math Grade 5 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 5 Lesson 2.8 Answer Key Division.

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Sean and his crew operate a fishing charter company. They caught a blue marlin and amberjack. The weight of the blue marlin was 12 times as great as the weight of the amberjack. The combined weight of both fish was 1,014 pounds. How much did each fish weigh?

What do I need to find? I need to find the weight of each fish.

What information am I given?

I know that they caught a total of 1,014 pounds of fish and the weight of the blue marlin was 12 times as great as the weight of the amberjack.

I can use the strategy of Addition and Substitution and then divide. I can draw and use a strip diagram to write the division problem that helps me find the weight of each fish.

Try Another Problem

Jason, Murray, and Dana went fishing. Dana caught red snapper. Jason caught a tuna with a weight 3 times as great as the weight of the red snapper. Murray caught a sailfish with a weight 12 times as great as the weight of the red snapper. If the combined weight of the three fish was 208 pounds, how much did the tuna weigh?

What do I need to find? Answer: I need to find the weight of tuna

What information am I given? Answer: I know that Jason, Murray, and Dana went fishing. Dana caught red snapper. Jason caught a tuna with a weight 3 times as great as the weight of the red snapper. Murray caught a sailfish with a weight 12 times as great as the weight of the red snapper and the combined weight of the three fish was 208 pounds

What is my plan or strategy? Answer: I can use the strategy of Addition and Substitution and then divide

Solve It is given that Jason, Murray, and Dana went fishing. Dana caught red snapper. Jason caught a tuna with a weight 3 times as great as the weight of the red snapper. Murray caught a sailfish with a weight 12 times as great as the weight of the red snapper and the combined weight of the three fish was 208 pounds Now, Let the weight of the red snapper be: x Pounds So, The weight of the fish caught by Dana = x Pounds The weight of the tuna caught by Jason = 3x Pounds The weight of the saltfish caught by Murray = 12x Pounds Now, According to the combined information, x + 3x + 12x = 208 Pounds 16x = 208 x = \(\frac{208}{16}\) = 13 Pounds So, The weight of the tuna caught by Jason = 3x = 3 × 13 = 39 Pounds So, The tuna weighed 39 pounds.

How can you check if your answer is correct? Answer: Substitute the weight of the tuna in the total weight of the three fishes and check whether the answer is equal to the combined weight of the fishes caught by Dana and Murray

Math Talk Mathematical Processes

Explain how you could use another strategy to solve this problem. Answer: The other strategy to solve the above problem is: Step 1: Read the given information Step 2: Plan the strategy how to find the required quantity from the given information Step 3: Solve the problem and find the required quantity

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Texas Test Prep

Texas Go Math Grade 5 Lesson 2.8 Homework and Practice Answer Key

Eddie’s Moving Company moved 3 boxes out of Mrs. Diaz’s house. The box labeled “Kitchen” was 4 times heavier than the box labeled “Bedroom.” The box labeled “Library” was 14 times heavier than the box marked “Bedroom.” If the combined weight of the boxes was 817 pounds, how much did the box labeled “Kitchen” weigh?

Question 1. What do I need to find? Answer: I need to find the weight of the box labeled “Kitchen”

Question 2. What information am I given? Answer: I know that Eddie’s Moving Company moved 3 boxes out of Mrs. Diaz’s house. The box labeled “Kitchen” was 4 times heavier than the box labeled “Bedroom.” The box labeled “Library” was 14 times heavier than the box marked “Bedroom” and the combined weight of the boxes was 817 pounds

Question 4. Solve. Let the weight of the box labeled “Bedroom” be: x Pounds So, x + 4x + 14x = 817 Pounds 19x = 817 So, 817 ÷ 19 = 43 So, I can multiply 4 by 43 to find the weight of the “Kitchen” box. So, The box labeled “Kitchen” weighed 172 pounds.

Question 5. An athlete ran 1,200 laps around a track over a two-month period. He ran 4 times the number of laps in the second month than he ran in the first month. How many laps did the athlete run the first month? Answer: It is given that An athlete ran 1,200 laps around a track over a two-month period. He ran 4 times the number of laps in the second month than he ran in the first month Now, Let the number of laps run by an athlete in the first month be: x laps So, The number of laps run by an athlete in the first month be: 4x laps Now, According to the given information, x + 4x = 1,200 5x = 1,200 x = \(\frac{1,200}{5}\) x = 240 laps Hence, from the above, We can conclude that The number of laps did the athlete run in the first month is: 240 laps

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Math Expressions Answer Key for Grade 5, 4, 3, 2, 1, and Kindergarten K | Math Expressions Common Core Grades K-5

Houghton mifflin math expressions common core answer key for grade 5, 4, 3, 2, 1, and kindergarten k.

• Math Expressions Grade 5 Homework and Remembering Answer Key
• Math Expressions Grade 4 Homework and Remembering Answer Key
• Math Expressions Grade 3 Homework and Remembering Answer Key
• Math Expressions Grade 2 Homework and Remembering Answer Key
• Math Expressions Grade 1 Homework and Remembering Answer Key
• Math Expressions Kindergarten Homework and Remembering Answer Key
• Math Expressions Grade 5 Student Activity Book Answer Key
• Math Expressions Grade 4 Student Activity Book Answer Key
• Math Expressions Grade 3 Student Activity Book Answer Key
• Math Expressions Grade 2 Student Activity Book Answer Key
• Math Expressions Grade 1 Student Activity Book Answer Key
• Math Expressions Kindergarten Student Activity Book Answer Key

Math Expressions Common Core Grade 5 Homework and Remembering Answer Key

Math Expressions Grade 5 Homework and Remembering Volume 1 Answer Key | Math Expressions Common Core Grade 5 Volume 1 Answer Key

Unit 1 Addition and Subtraction with Fractions

• Math Expressions Grade 5 Unit 1 Lesson 1 Answer Key Introducing the MathBoard
• Math Expressions Grade 5 Unit 1 Lesson 2 Answer Key Explain Equivalent Fractions
• Math Expressions Grade 5 Unit 1 Lesson 3 Answer Key Equivalent Fractions and Multipliers
• Math Expressions Grade 5 Unit 1 Lesson 4 Answer Key Strategies for Comparing Fractions
• Math Expressions Grade 5 Unit 1 Lesson 5 Answer Key Fractions Greater Than One
• Math Expressions Grade 5 Unit 1 Lesson 6 Answer Key Add and Subtract Like Mixed Numbers
• Math Expressions Grade 5 Unit 1 Lesson 7 Answer Key Add Unlike Fractions
• Math Expressions Grade 5 Unit 1 Lesson 8 Answer Key Subtract Unlike Fractions
• Math Expressions Grade 5 Unit 1 Lesson 9 Answer Key Solve with Unlike Mixed Numbers
• Math Expressions Grade 5 Unit 1 Lesson 10 Answer Key Practice with Unlike Mixed Numbers
• Math Expressions Grade 5 Unit 1 Lesson 11 Answer Key Reasonable Answers
• Math Expressions Grade 5 Unit 1 Lesson 12 Answer Key Real-World Problems
• Math Expressions Grade 5 Unit 1 Lesson 13 Answer Key Focus on Mathematical Practices

Unit 2 Addition and Subtraction with Decimals

• Math Expressions Grade 5 Unit 2 Lesson 1 Answer Key Decimals as Equal Divisions
• Math Expressions Grade 5 Unit 2 Lesson 2 Answer Key Thousands to Thousandths
• Math Expressions Grade 5 Unit 2 Lesson 3 Answer Key Equate and Compare Thousandths
• Math Expressions Grade 5 Unit 2 Lesson 4 Answer Key Adding and Subtracting Decimals
• Math Expressions Grade 5 Unit 2 Lesson 5 Answer Key Add Whole Numbers and Decimals
• Math Expressions Grade 5 Unit 2 Lesson 6 Answer Key Subtract Whole and Decimal Numbers
• Math Expressions Grade 5 Unit 2 Lesson 7 Answer Key Properties and Strategies
• Math Expressions Grade 5 Unit 2 Lesson 8 Answer Key Round and Estimate with Decimals
• Math Expressions Grade 5 Unit 2 Lesson 9 Answer Key Graph with Decimal Numbers
• Math Expressions Grade 5 Unit 2 Lesson 10 Answer Key Focus on Mathematical Practices

Unit 3 Multiplication and Division with Fractions

• Math Expressions Grade 5 Unit 3 Lesson 1 Answer Key Basic Multiplication Concepts
• Math Expressions Grade 5 Unit 3 Lesson 2 Answer Key Multiplication with Non-Unit Fractions
• Math Expressions Grade 5 Unit 3 Lesson 3 Answer Key Multiplication with Fractional Solutions
• Math Expressions Grade 5 Unit 3 Lesson 4 Answer Key Multiply a Fraction by a Fraction
• Math Expressions Grade 5 Unit 3 Lesson 5 Answer Key Multiplication Strategies
• Math Expressions Grade 5 Unit 3 Lesson 6 Answer Key Multiply Mixed Numbers
• Math Expressions Grade 5 Unit 3 Lesson 7 Answer Key Relate Fraction Operations
• Math Expressions Grade 5 Unit 3 Lesson 8 Answer Key Solve Real-World Problems
• Math Expressions Grade 5 Unit 3 Lesson 9 Answer Key Make Generalizations
• Math Expressions Grade 5 Unit 3 Lesson 10 Answer Key When Dividing is Also Multiplying
• Math Expressions Grade 5 Unit 3 Lesson 11 Answer Key Solve Division Problems
• Math Expressions Grade 5 Unit 3 Lesson 12 Answer Key Distinguish Multiplication from Division
• Math Expressions Grade 5 Unit 3 Lesson 13 Answer Key Review Operations with Fractions
• Math Expressions Grade 5 Unit 3 Lesson 14 Answer Key Focus on Mathematical Practices

Unit 4 Multiplication with Whole Numbers and Decimals

• Math Expressions Grade 5 Unit 4 Lesson 1 Answer Key Shift Patterns in Multiplication
• Math Expressions Grade 5 Unit 4 Lesson 2 Answer Key Patterns with Fives and Zeros
• Math Expressions Grade 5 Unit 4 Lesson 3 Answer Key Sharing Methods for Multiplication
• Math Expressions Grade 5 Unit 4 Lesson 4 Answer Key Multiply Two-Digit Numbers
• Math Expressions Grade 5 Unit 4 Lesson 5 Answer Key Practice Multiplication
• Math Expressions Grade 5 Unit 4 Lesson 6 Answer Key Multiply Decimals by Whole Numbers
• Math Expressions Grade 5 Unit 4 Lesson 7 Answer Key Multiply by Decimals
• Math Expressions Grade 5 Unit 4 Lesson 8 Answer Key Multiply with Decimals Greater Than 1
• Math Expressions Grade 5 Unit 4 Lesson 9 Answer Key Compare Shift Patterns
• Math Expressions Grade 5 Unit 4 Lesson 10 Answer Key Estimate Products
• Math Expressions Grade 5 Unit 4 Lesson 11 Answer Key Multiplication Practice
• Math Expressions Grade 5 Unit 4 Lesson 12 Answer Key Focus on Mathematical Practices

Math Expressions Grade 5 Homework and Remembering Volume 2 Answer Key | Math Expressions Common Core Grade 5 Volume 2 Answer Key

Math Expressions Common Core Grade 5 Answer Key Unit 5 Division with Whole Numbers and Decimals

• Math Expressions Grade 5 Unit 5 Lesson 1 Answer Key Divide Whole Numbers by One Digit
• Math Expressions Grade 5 Unit 5 Lesson 2 Answer Key Explore Dividing by Two-Digit Whole Numbers
• Math Expressions Grade 5 Unit 5 Lesson 3 Answer Key Too Large, Too Small, or Just Right?
• Math Expressions Grade 5 Unit 5 Lesson 4 Answer Key Interpret Remainders
• Math Expressions Grade 5 Unit 5 Lesson 5 Answer Key Division Practice
• Math Expressions Grade 5 Unit 5 Lesson 6 Answer Key Divide Decimal Numbers by Whole Numbers
• Math Expressions Grade 5 Unit 5 Lesson 7 Answer Key Divide Whole Numbers by Decimal Numbers
• Math Expressions Grade 5 Unit 5 Lesson 8 Answer Key Divide with Two Decimal Numbers
• Math Expressions Grade 5 Unit 5 Lesson 9 Answer Key Division Practice
• Math Expressions Grade 5 Unit 5 Lesson 10 Answer Key Distinguish Between Multiplication and Division
• Math Expressions Grade 5 Unit 5 Lesson 11 Answer Key Focus on Mathematical Practices

Houghton Mifflin Harcourt Math Expressions Grade 5 Answer Key Unit 6 Operations and Word Problems

• Math Expressions Grade 5 Unit 6 Lesson 1 Answer Key Situation and Solution Equations for Addition and Subtraction
• Math Expressions Grade 5 Unit 6 Lesson 2 Answer Key Situation and Solution Equations for Multiplication and Division
• Math Expressions Grade 5 Unit 6 Lesson 3 Answer Key Write Word Problems
• Math Expressions Grade 5 Unit 6 Lesson 4 Answer Key Determine Reasonable Answers
• Math Expressions Grade 5 Unit 6 Lesson 5 Answer Key Language of Comparison Problems
• Math Expressions Grade 5 Unit 6 Lesson 6 Answer Key Multiplicative Comparison Problems
• Math Expressions Grade 5 Unit 6 Lesson 7 Answer Key Types of Comparison Problems
• Math Expressions Grade 5 Unit 6 Lesson 8 Answer Key Equations and Parentheses
• Math Expressions Grade 5 Unit 6 Lesson 9 Answer Key Multistep Word Problems
• Math Expressions Grade 5 Unit 6 Lesson 10 Answer Key Practice Problem Solving
• Math Expressions Grade 5 Unit 6 Lesson 11 Answer Key Focus on Mathematical Practices

Math Expressions Common Core Grade 5 Volume 2 Answer Key Unit 7 Algebra, Patterns, and Coordinate Graphs

• Math Expressions Grade 5 Unit 7 Lesson 1 Answer Key Read and Write Expressions
• Math Expressions Grade 5 Unit 7 Lesson 2 Answer Key Simplify Expressions
• Math Expressions Grade 5 Unit 7 Lesson 3 Answer Key Evaluate Expressions
• Math Expressions Grade 5 Unit 7 Lesson 4 Answer Key Patterns and Relationships
• Math Expressions Grade 5 Unit 7 Lesson 5 Answer Key The Coordinate Plane
• Math Expressions Grade 5 Unit 7 Lesson 6 Answer Key Graph Ordered Pairs
• Math Expressions Grade 5 Unit 7 Lesson 7 Answer Key Focus on Mathematical Practices

Math Expressions Grade 5 Homework and Remembering Volume 2 Answer Key Unit 8 Measurement and Geometry

• Math Expressions Grade 5 Unit 8 Lesson 1 Answer Key Convert Metric Units of Length
• Math Expressions Grade 5 Unit 8 Lesson 2 Answer Key Metric Units of Liquid Volume
• Math Expressions Grade 5 Unit 8 Lesson 3 Answer Key Metric Units of Mass
• Math Expressions Grade 5 Unit 8 Lesson 4 Answer Key Customary Units of Length
• Math Expressions Grade 5 Unit 8 Lesson 5 Answer Key Customary Measures of Liquid Volume
• Math Expressions Grade 5 Unit 8 Lesson 6 Answer Key Customary Units of Weight
• Math Expressions Grade 5 Unit 8 Lesson 7 Answer Key Read and Make Line Plots
• Math Expressions Grade 5 Unit 8 Lesson 8 Answer Key Perimeter and Area of Rectangles
• Math Expressions Grade 5 Unit 8 Lesson 9 Answer Key Cubic Units and Volume
• Math Expressions Grade 5 Unit 8 Lesson 10 Answer Key Visualize Volume
• Math Expressions Grade 5 Unit 8 Lesson 11 Answer Key Introduce Volume Formulas
• Math Expressions Grade 5 Unit 8 Lesson 12 Answer Key Relate Length, Area, and Volume
• Math Expressions Grade 5 Unit 8 Lesson 13 Answer Key Volume of Composite Solid Figures
• Math Expressions Grade 5 Unit 8 Lesson 14 Answer Key Attributes of Quadrilaterals
• Math Expressions Grade 5 Unit 8 Lesson 15 Answer Key Attributes of Triangles
• Math Expressions Grade 5 Unit 8 Lesson 16 Answer Key Attributes of Two-Dimensional Shapes
• Math Expressions Grade 5 Unit 8 Lesson 17 Answer Key Focus on Mathematical Practices

Math Expressions Common Core Grade 4 Homework and Remembering Answer Key

Math Expressions Grade 4 Homework and Remembering Volume 1 Answer Key | Math Expressions Common Core Grade 4 Volume 1 Answer Key

Unit 1 Place Value and Multidigit Addition and Subtraction

• Math Expressions Grade 4 Unit 1 Lesson 1 Answer Key Place Value to Thousands
• Math Expressions Grade 4 Unit 1 Lesson 2 Answer Key Place Value Patterns
• Math Expressions Grade 4 Unit 1 Lesson 3 Answer Key Round Numbers
• Math Expressions Grade 4 Unit 1 Lesson 4 Answer Key Numbers to One Million
• Math Expressions Grade 4 Unit 1 Lesson 5 Answer Key Compare and Round Greater Numbers
• Math Expressions Grade 4 Unit 1 Lesson 6 Answer Key Make New Groups for Addition
• Math Expressions Grade 4 Unit 1 Lesson 7 Answer Key Add Greater Numbers
• Math Expressions Grade 4 Unit 1 Lesson 8 Answer Key Estimation and Mental Math
• Math Expressions Grade 4 Unit 1 Lesson 9 Answer Key Subtract from Thousands
• Math Expressions Grade 4 Unit 1 Lesson 10 Answer Key Subtraction Undoes Addition
• Math Expressions Grade 4 Unit 1 Lesson 11 Answer Key Subtract Greater Numbers
• Math Expressions Grade 4 Unit 1 Lesson 12 Answer Key Practice Addition and Subtraction
• Math Expressions Grade 4 Unit 1 Lesson 13 Answer Key Problem Solving with Greater Numbers
• Math Expressions Grade 4 Unit 1 Lesson 14 Answer Key Focus on Mathematical Practices

Unit 2 Multiplication with Whole Numbers

• Math Expressions Grade 4 Unit 2 Lesson 1 Answer Key Arrays and Area Models
• Math Expressions Grade 4 Unit 2 Lesson 2 Answer Key Connect Place Value and Multiplication
• Math Expressions Grade 4 Unit 2 Lesson 3 Answer Key Mental Math and Multiplication
• Math Expressions Grade 4 Unit 2 Lesson 4 Answer Key Model One-Digit by Two-Digit Multiplication
• Math Expressions Grade 4 Unit 2 Lesson 5 Answer Key Estimate Products
• Math Expressions Grade 4 Unit 2 Lesson 6 Answer Key Use Place Value to Multiply
• Math Expressions Grade 4 Unit 2 Lesson 7 Answer Key Algebraic Notation Method
• Math Expressions Grade 4 Unit 2 Lesson 8 Answer Key Compare Methods of One-Digit by Two-Digit Multiplication
• Math Expressions Grade 4 Unit 2 Lesson 9 Answer Key Discuss Different Methods
• Math Expressions Grade 4 Unit 2 Lesson 10 Answer Key One-Digit by Three-Digit Multiplication
• Math Expressions Grade 4 Unit 2 Lesson 11 Answer Key Multistep Word Problems
• Math Expressions Grade 4 Unit 2 Lesson 12 Answer Key Two-Digit by Two-Digit Multiplication
• Math Expressions Grade 4 Unit 2 Lesson 13 Answer Key Different Methods for Two-Digit Multiplication
• Math Expressions Grade 4 Unit 2 Lesson 14 Answer Key Check Products of Two-Digit Numbers
• Math Expressions Grade 4 Unit 2 Lesson 15 Answer Key Practice Multiplication
• Math Expressions Grade 4 Unit 2 Lesson 16 Answer Key Multiply One-Digit and Four-Digit Numbers
• Math Expressions Grade 4 Unit 2 Lesson 17 Answer Key Use the Shortcut Method
• Math Expressions Grade 4 Unit 2 Lesson 18 Answer Key Practice Multiplying
• Math Expressions Grade 4 Unit 2 Lesson 19 Answer Key Focus on Mathematical Practices

Unit 3 Division with Whole Numbers

• Math Expressions Grade 4 Unit 3 Lesson 1 Answer Key Divide with Remainders
• Math Expressions Grade 4 Unit 3 Lesson 2 Answer Key Relate 3-Digit Multiplication to Division
• Math Expressions Grade 4 Unit 3 Lesson 3 Answer Key Discuss 2-Digit and 4-Digit Quotients
• Math Expressions Grade 4 Unit 3 Lesson 4 Answer Key Digit-by-Digit Method
• Math Expressions Grade 4 Unit 3 Lesson 5 Answer Key Relate Three Methods
• Math Expressions Grade 4 Unit 3 Lesson 6 Answer Key Divide by Any Method
• Math Expressions Grade 4 Unit 3 Lesson 7 Answer Key Just-Under Quotient Digits
• Math Expressions Grade 4 Unit 3 Lesson 8 Answer Key Estimate to Check Quotients
• Math Expressions Grade 4 Unit 3 Lesson 9 Answer Key Make Sense of Remainders
• Math Expressions Grade 4 Unit 3 Lesson 10 Answer Key Mixed Problem Solving
• Math Expressions Grade 4 Unit 3 Lesson 11 Answer Key Focus on Mathematical Practices

Unit 4 Equations and Word Problems

• Math Expressions Grade 4 Unit 4 Lesson 1 Answer Key Properties and Algebraic Notation
• Math Expressions Grade 4 Unit 4 Lesson 2 Answer Key Situation and Solution Equations for Addition and Subtraction
• Math Expressions Grade 4 Unit 4 Lesson 3 Answer Key Situation and Solution Equations for Multiplication and Division
• Math Expressions Grade 4 Unit 4 Lesson 4 Answer Key Multiplication Comparisons
• Math Expressions Grade 4 Unit 4 Lesson 5 Answer Key Discuss Comparison Problems
• Math Expressions Grade 4 Unit 4 Lesson 6 Answer Key Graphs and Comparison Problems
• Math Expressions Grade 4 Unit 4 Lesson 7 Answer Key Solve Two-Step Problems
• Math Expressions Grade 4 Unit 4 Lesson 8 Answer Key Solve Multistep Problems
• Math Expressions Grade 4 Unit 4 Lesson 9 Answer Key Practice with Multistep Problems
• Math Expressions Grade 4 Unit 4 Lesson 10 Answer Key Factors and Prime Numbers
• Math Expressions Grade 4 Unit 4 Lesson 11 Answer Key Analyze Patterns
• Math Expressions Grade 4 Unit 4 Lesson 12 Answer Key Focus on Mathematical Practices

Math Expressions Grade 4 Homework and Remembering Volume 2 Answer Key | Math Expressions Common Core Grade 4 Volume 2 Answer Key

Grade 4 Answer Key Unit 5 Measurement

• Math Expressions Grade 4 Unit 5 Lesson 1 Answer Key Measure Length
• Math Expressions Grade 4 Unit 5 Lesson 2 Answer Key Metric Measures of Liquid Volume and Mass
• Math Expressions Grade 4 Unit 5 Lesson 3 Answer Key Units of Time
• Math Expressions Grade 4 Unit 5 Lesson 4 Answer Key Customary Measures of Length
• Math Expressions Grade 4 Unit 5 Lesson 5 Answer Key Customary Units of Weight and Liquid Volume
• Math Expressions Grade 4 Unit 5 Lesson 6 Answer Key Perimeter and Area of Rectangles
• Math Expressions Grade 4 Unit 5 Lesson 7 Answer Key Solve Measurement Problems
• Math Expressions Grade 4 Unit 5 Lesson 8 Answer Key Focus on Mathematical Practices

Unit 6 Fraction Concepts and Operations

• Math Expressions Grade 4 Unit 6 Lesson 1 Answer Key Understand Fractions
• Math Expressions Grade 4 Unit 6 Lesson 2 Answer Key Fractions That Add to One
• Math Expressions Grade 4 Unit 6 Lesson 3 Answer Key Add and Subtract Fractions with Like Denominators
• Math Expressions Grade 4 Unit 6 Lesson 4 Answer Key Mixed Numbers and Fractions Greater Than 1
• Math Expressions Grade 4 Unit 6 Lesson 5 Answer Key Add and Subtract Mixed Numbers with Like Denominators
• Math Expressions Grade 4 Unit 6 Lesson 6 Answer Key Practice with Fractions and Mixed Numbers
• Math Expressions Grade 4 Unit 6 Lesson 7 Answer Key Multiply a Fraction by a Whole Number
• Math Expressions Grade 4 Unit 6 Lesson 8 Answer Key Practice Multiplying a Fraction by a Whole Number
• Math Expressions Grade 4 Unit 6 Lesson 9 Answer Key Mixed Practice
• Math Expressions Grade 4 Unit 6 Lesson 10 Answer Key Focus on Mathematical Practices

Unit 7 Fractions and Decimals

• Math Expressions Grade 4 Unit 7 Lesson 1 Answer Key Compare Fractions
• Math Expressions Grade 4 Unit 7 Lesson 2 Answer Key Fractions on the Number Line
• Math Expressions Grade 4 Unit 7 Lesson 3 Answer Key Fractions of Different-Size Wholes
• Math Expressions Grade 4 Unit 7 Lesson 4 Answer Key Equivalent Fractions Using Multiplication
• Math Expressions Grade 4 Unit 7 Lesson 5 Answer Key Equivalent Fractions Using Division
• Math Expressions Grade 4 Unit 7 Lesson 6 Answer Key Compare Fractions with Unlike Denominators
• Math Expressions Grade 4 Unit 7 Lesson 7 Answer Key Fractions and Line Plots
• Math Expressions Grade 4 Unit 7 Lesson 8 Answer Key Relate Fractions and Decimals
• Math Expressions Grade 4 Unit 7 Lesson 9 Answer Key Explore Decimal Numbers
• Math Expressions Grade 4 Unit 7 Lesson 10 Answer Key Compare Decimals to Hundredths
• Math Expressions Grade 4 Unit 7 Lesson 11 Answer Key Decimals Greater Than 1
• Math Expressions Grade 4 Unit 7 Lesson 12 Answer Key Compare Decimals Greater Than 1
• Math Expressions Grade 4 Unit 7 Lesson 13 Answer Key Focus on Mathematical Practices

Unit 8 Geometry

• Math Expressions Grade 4 Unit 8 Lesson 1 Answer Key Points, Rays, and Angles
• Math Expressions Grade 4 Unit 8 Lesson 2 Answer Key Measuring Angles
• Math Expressions Grade 4 Unit 8 Lesson 3 Answer Key Circles and Angles
• Math Expressions Grade 4 Unit 8 Lesson 4 Answer Key Name Triangles
• Math Expressions Grade 4 Unit 8 Lesson 5 Answer Key Compose and Decompose Angles
• Math Expressions Grade 4 Unit 8 Lesson 6 Answer Key Real World Problems
• Math Expressions Grade 4 Unit 8 Lesson 7 Answer Key Parallel and Perpendicular Lines and Line Segments
• Math Expressions Grade 4 Unit 8 Lesson 8 Answer Key Classifying Quadrilaterals
• Math Expressions Grade 4 Unit 8 Lesson 9 Answer Key Decompose Quadrilaterals and Triangles
• Math Expressions Grade 4 Unit 8 Lesson 10 Answer Key Classify Polygons
• Math Expressions Grade 4 Unit 8 Lesson 11 Answer Key Line Symmetry
• Math Expressions Grade 4 Unit 8 Lesson 12 Answer Key Focus on Mathematical Practices

Math Expressions Common Core Grade 3 Homework and Remembering Answer Key

Math Expressions Grade 3 Homework and Remembering Volume 1 Answer Key | Math Expressions Common Core Grade 3 Volume 1 Answer Key

Unit 1 Multiplication and Division with 0-5, 9 and 10

• Math Expressions Grade 3 Unit 1 Lesson 1 Answer Key Multiply with 5
• Math Expressions Grade 3 Unit 1 Lesson 2 Answer Key Multiplication as Equal Groups
• Math Expressions Grade 3 Unit 1 Lesson 3 Answer Key Multiplication and Arrays
• Math Expressions Grade 3 Unit 1 Lesson 4 Answer Key The Meaning of Division
• Math Expressions Grade 3 Unit 1 Lesson 5 Answer Key Multiply and Divide with 2
• Math Expressions Grade 3 Unit 1 Lesson 6 Answer Key Building Fluency with 2s and 5s
• Math Expressions Grade 3 Unit 1 Lesson 7 Answer Key Multiply and Divide with 10
• Math Expressions Grade 3 Unit 1 Lesson 8 Answer Key Multiply and Divide with 9
• Math Expressions Grade 3 Unit 1 Lesson 9 Answer Key Building Fluency with 2s, 5s, 9s, and 10s
• Math Expressions Grade 3 Unit 1 Lesson 10 Answer Key Multiply and Divide with 3
• Math Expressions Grade 3 Unit 1 Lesson 11 Answer Key Multiplication and Area
• Math Expressions Grade 3 Unit 1 Lesson 12 Answer Key Multiply and Divide with 4
• Math Expressions Grade 3 Unit 1 Lesson 13 Answer Key Use the Strategy Cards
• Math Expressions Grade 3 Unit 1 Lesson 14 Answer Key Building Fluency with 2s, 3s, 4s, 5s, 9s, and 10s
• Math Expressions Grade 3 Unit 1 Lesson 15 Answer Key Multiply and Divide with 1 and 0
• Math Expressions Grade 3 Unit 1 Lesson 16 Answer Key Solve and create Word Problems
• Math Expressions Grade 3 Unit 1 Lesson 17 Answer Key Play Multiplication and Division Games
• Math Expressions Grade 3 Unit 1 Lesson 18 Answer Key Building Fluency with 0s, 1s, 2s, 3s, 4s, 5s, 9s, 10s
• Math Expressions Grade 3 Unit 1 Lesson 19 Answer Key Focus on Mathematical Practices

Unit 2 Multiplication and Division with 6, 7, and 8, Multiply with Multiples of 10, and Problem Solving

• Math Expressions Grade 3 Unit 2 Lesson 1 Answer Key Multiply and Divide with 6
• Math Expressions Grade 3 Unit 2 Lesson 2 Answer Key Solve Area Word Problems
• Math Expressions Grade 3 Unit 2 Lesson 3 Answer Key Multiply and Divide with 8
• Math Expressions Grade 3 Unit 2 Lesson 4 Answer Key Write Word Problems and Equations
• Math Expressions Grade 3 Unit 2 Lesson 5 Answer Key Multiply and Divide with 7
• Math Expressions Grade 3 Unit 2 Lesson 6 Answer Key Square Numbers
• Math Expressions Grade 3 Unit 2 Lesson 7 Answer Key Practice with 6s, 7s, and 8s
• Math Expressions Grade 3 Unit 2 Lesson 8 Answer Key Building Fluency with 0s – 10s
• Math Expressions Grade 3 Unit 2 Lesson 9 Answer Key Equations and Word Problems
• Math Expressions Grade 3 Unit 2 Lesson 10 Answer Key Write First Step Questions for Two-Step Problems
• Math Expressions Grade 3 Unit 2 Lesson 11 Answer Key Make Sense of Two-Step Word Problems
• Math Expressions Grade 3 Unit 2 Lesson 12 Answer Key Multiply with Multiples of 10
• Math Expressions Grade 3 Unit 2 Lesson 13 Answer Key Play Multiplication and Division Games
• Math Expressions Grade 3 Unit 2 Lesson 14 Answer Key Building Fluency with 0s – 10s
• Math Expressions Grade 3 Unit 2 Lesson 15 Answer Key Focus on Mathematical Practices

Unit 3 Measurement, Time, and Graphs

• Math Expressions Grade 3 Unit 3 Lesson 1 Answer Key Customary Units of Length
• Math Expressions Grade 3 Unit 3 Lesson 2 Answer Key Customary Units of Liquid Volume
• Math Expressions Grade 3 Unit 3 Lesson 3 Answer Key Metric Units of Liquid Volume
• Math Expressions Grade 3 Unit 3 Lesson 4 Answer Key Customary Units of Weight and Metric Units of Mass
• Math Expressions Grade 3 Unit 3 Lesson 5 Answer Key Solve Word Problems Involving Liquid Volume and Mass
• Math Expressions Grade 3 Unit 3 Lesson 6 Answer Key Tell Time
• Math Expressions Grade 3 Unit 3 Lesson 7 Answer Key Before and After the Hour
• Math Expressions Grade 3 Unit 3 Lesson 8 Answer Key Elapsed Time
• Math Expressions Grade 3 Unit 3 Lesson 9 Answer Key Add and Subtract Time
• Math Expressions Grade 3 Unit 3 Lesson 10 Answer Key Solve Word Problems Involving Time
• Math Expressions Grade 3 Unit 3 Lesson 11 Answer Key Read and Create Pictographs and Bar Graphs
• Math Expressions Grade 3 Unit 3 Lesson 12 Answer Key Read and Create Bar Graphs with Multidigit Numbers
• Math Expressions Grade 3 Unit 3 Lesson 13 Answer Key Represent and Organize Data
• Math Expressions Grade 3 Unit 3 Lesson 14 Answer Key Use Graphs to Solve Time and Measurement Word Problems
• Math Expressions Grade 3 Unit 3 Lesson 15 Answer Key Focus on Mathematical Practices

Math Expressions Grade 3 Homework and Remembering Volume 3 Answer Key | Math Expressions Common Core Grade 3 Volume 2 Answer Key

Unit 4 Multidigit Addition and Subtraction

• Math Expressions Grade 3 Unit 4 Lesson 1 Answer Key Make Place Value Drawings
• Math Expressions Grade 3 Unit 4 Lesson 2 Answer Key Build Numbers
• Math Expressions Grade 3 Unit 4 Lesson 3 Answer Key Place Value in Word Problems
• Math Expressions Grade 3 Unit 4 Lesson 4 Answer Key Practice with Place Value
• Math Expressions Grade 3 Unit 4 Lesson 5 Answer Key Round to the Nearest Hundred
• Math Expressions Grade 3 Unit 4 Lesson 6 Answer Key Round to the Nearest Ten
• Math Expressions Grade 3 Unit 4 Lesson 7 Answer Key Explore Multidigit Addition
• Math Expressions Grade 3 Unit 4 Lesson 8 Answer Key Discuss Addition Methods
• Math Expressions Grade 3 Unit 4 Lesson 9 Answer Key The Grouping Concept in Addition
• Math Expressions Grade 3 Unit 4 Lesson 10 Answer Key Practice Addition
• Math Expressions Grade 3 Unit 4 Lesson 11 Answer Key Ungroup to Subtract
• Math Expressions Grade 3 Unit 4 Lesson 12 Answer Key Subtract Across Zeros
• Math Expressions Grade 3 Unit 4 Lesson 13 Answer Key Discuss Methods of Subtracting
• Math Expressions Grade 3 Unit 4 Lesson 14 Answer Key Relate Addition and Subtraction
• Math Expressions Grade 3 Unit 4 Lesson 15 Answer Key Subtraction Practice
• Math Expressions Grade 3 Unit 4 Lesson 16 Answer Key Addition and Subtraction Practice
• Math Expressions Grade 3 Unit 4 Lesson 17 Answer Key Solve Word Problems
• Math Expressions Grade 3 Unit 4 Lesson 18 Answer Key Focus on Mathematical Practices

Unit 5 Write Equations to Solve Word Problems

• Math Expressions Grade 3 Unit 5 Lesson 1 Answer Key Addition and Subtraction Situations
• Math Expressions Grade 3 Unit 5 Lesson 2 Answer Key Word Problems with Unknown Addends or Unknown factors
• Math Expressions Grade 3 Unit 5 Lesson 3 Answer Key Word Problems with Unknown Starts
• Math Expressions Grade 3 Unit 5 Lesson 4 Answer Key Comparison Problems
• Math Expressions Grade 3 Unit 5 Lesson 5 Answer Key Comparison Problems with Misleading Language
• Math Expressions Grade 3 Unit 5 Lesson 6 Answer Key Word Problems with Extra, Hidden, or Not Enough Information
• Math Expressions Grade 3 Unit 5 Lesson 7 Answer Key Write First Step Questions for Two-Step Problems
• Math Expressions Grade 3 Unit 5 Lesson 8 Answer Key Solve Two-Step Word Problems
• Math Expressions Grade 3 Unit 5 Lesson 9 Answer Key Equations and Two-Step Word Problems
• Math Expressions Grade 3 Unit 5 Lesson 10 Answer Key Practice with Two-Step Word Problems
• Math Expressions Grade 3 Unit 5 Lesson 11 Answer Key Focus on Mathematical Practices

Unit 6 Polygons, Perimeter, and Area

• Math Expressions Grade 3 Unit 6 Lesson 1 Answer Key Triangles
• Math Expressions Grade 3 Unit 6 Lesson 2 Answer Key Parallelograms, Rectangles, Squares, and Rhombuses
• Math Expressions Grade 3 Unit 6 Lesson 3 Answer Key Draw Quadrilaterals
• Math Expressions Grade 3 Unit 6 Lesson 4 Answer Key Classify Quadrilaterals
• Math Expressions Grade 3 Unit 6 Lesson 5 Answer Key Perimeter and Area
• Math Expressions Grade 3 Unit 6 Lesson 6 Answer Key Side Lengths with Area and Perimeter
• Math Expressions Grade 3 Unit 6 Lesson 7 Answer Key Compare Areas and Perimeters
• Math Expressions Grade 3 Unit 6 Lesson 8 Answer Key Area of Rectilinear Figures
• Math Expressions Grade 3 Unit 6 Lesson 9 Answer Key Solve Perimeter and Area Problems
• Math Expressions Grade 3 Unit 6 Lesson 10 Answer Key Tangram Shapes and Area
• Math Expressions Grade 3 Unit 6 Lesson 11 Answer Key Focus on Mathematical Practices

Unit 7 Explore Fractions

• Math Expressions Grade 3 Unit 7 Lesson 1 Answer Key Understand Fractions
• Math Expressions Grade 3 Unit 7 Lesson 2 Answer Key Model Fractions
• Math Expressions Grade 3 Unit 7 Lesson 3 Answer Key Locate Fractions on the Number Line
• Math Expressions Grade 3 Unit 7 Lesson 4 Answer Key Compare Unit Fractions
• Math Expressions Grade 3 Unit 7 Lesson 5 Answer Key Compare Fractions
• Math Expressions Grade 3 Unit 7 Lesson 6 Answer Key Introduce Equivalence
• Math Expressions Grade 3 Unit 7 Lesson 7 Answer Key Equivalent Fractions
• Math Expressions Grade 3 Unit 7 Lesson 8 Answer Key Problem Solving with Fractions
• Math Expressions Grade 3 Unit 7 Lesson 9 Answer Key Focus on Mathematical Practices

Math Expressions Common Core Grade 2 Homework and Remembering Answer Key

Math Expressions Grade 2 Homework and Remembering Volume 1 Answer Key | Math Expressions Common Core Grade 2 Volume 1 Answer Key

Unit 1 Addition and Subtraction Within 20

• Math Expressions Grade 2 Unit 1 Lesson 1 Answer Key Represent Addition and Subtraction
• Math Expressions Grade 2 Unit 1 Lesson 2 Answer Key Relate Addition and Subtraction
• Math Expressions Grade 2 Unit 1 Lesson 3 Answer Key Make-a-Ten Strategies
• Math Expressions Grade 2 Unit 1 Lesson 4 Answer Key Relate Unknown Addends and Subtraction
• Math Expressions Grade 2 Unit 1 Lesson 5 Answer Key More Practice with Unknown Addends and Teen Totals
• Math Expressions Grade 2 Unit 1 Lesson 6 Answer Key Odd and Even Numbers
• Math Expressions Grade 2 Unit 1 Lesson 7 Answer Key Strategies Using Doubles
• Math Expressions Grade 2 Unit 1 Lesson 8 Answer Key Equations, Equation Chains, and Vertical Form
• Math Expressions Grade 2 Unit 1 Lesson 9 Answer Key Add Three or Four Addends
• Math Expressions Grade 2 Unit 1 Lesson 10 Answer Key Add To and Take From Word Problems
• Math Expressions Grade 2 Unit 1 Lesson 11 Answer Key Add To and Take From Problems – Unknown in All Positions
• Math Expressions Grade 2 Unit 1 Lesson 12 Answer Key Put Together/Take Apart Problems
• Math Expressions Grade 2 Unit 1 Lesson 13 Answer Key Special Put Together/Take Apart Problems
• Math Expressions Grade 2 Unit 1 Lesson 14 Answer Key Compare Word Problems
• Math Expressions Grade 2 Unit 1 Lesson 15 Answer Key More Compare Word Problems
• Math Expressions Grade 2 Unit 1 Lesson 16 Answer Key Mixed Word Problems
• Math Expressions Grade 2 Unit 1 Lesson 17 Answer Key Problems with Not Enough, Extra, or Hidden Information
• Math Expressions Grade 2 Unit 1 Lesson 18 Answer Key More Complex Compare Problems
• Math Expressions Grade 2 Unit 1 Lesson 19 Answer Key Two-Step Word Problems
• Math Expressions Grade 2 Unit 1 Lesson 20 Answer Key Mixed Word Problems
• Math Expressions Grade 2 Unit 1 Lesson 21 Answer Key Focus on Mathematical Practices

Unit 2 Addition Within 200

• Math Expressions Grade 2 Unit 2 Lesson 1 Answer Key Ones, Tens, and Hundreds
• Math Expressions Grade 2 Unit 2 Lesson 2 Answer Key Draw Quick Tens and Quick Hundreds
• Math Expressions Grade 2 Unit 2 Lesson 3 Answer Key Represent Numbers in Different Ways
• Math Expressions Grade 2 Unit 2 Lesson 4 Answer Key Combine Ones, Tens, and Hundreds
• Math Expressions Grade 2 Unit 2 Lesson 5 Answer Key Compare Numbers within 200
• Math Expressions Grade 2 Unit 2 Lesson 6 Answer Key Explore 2-Digit Addition
• Math Expressions Grade 2 Unit 2 Lesson 7 Answer Key Addition – Show All Totals Method
• Math Expressions Grade 2 Unit 2 Lesson 8 Answer Key Addition – New Groups Below Method
• Math Expressions Grade 2 Unit 2 Lesson 9 Answer Key Practice Addition with Sums over 100
• Math Expressions Grade 2 Unit 2 Lesson 10 Answer Key Choose an Addition Method
• Math Expressions Grade 2 Unit 2 Lesson 11 Answer Key Buy with Pennies and Dimes
• Math Expressions Grade 2 Unit 2 Lesson 12 Answer Key Pennies, Nickels, and Dimes
• Math Expressions Grade 2 Unit 2 Lesson 13 Answer Key Fluency: Addition Within 100
• Math Expressions Grade 2 Unit 2 Lesson 14 Answer Key Add Three or Four 2-Digit Addends
• Math Expressions Grade 2 Unit 2 Lesson 15 Answer Key Focus on Mathematical Practices

Unit 3 Length and Shapes

• Math Expressions Grade 2 Unit 3 Lesson 1 Answer Key Measure Length
• Math Expressions Grade 2 Unit 3 Lesson 2 Answer Key Recognize and Draw Shapes
• Math Expressions Grade 2 Unit 3 Lesson 3 Answer Key Estimate and Measure
• Math Expressions Grade 2 Unit 3 Lesson 4 Answer Key Draw, Estimate, and Measure
• Math Expressions Grade 2 Unit 3 Lesson 5 Answer Key Draw Using Faces
• Math Expressions Grade 2 Unit 3 Lesson 6 Answer Key Estimate and Measure with Centimeters
• Math Expressions Grade 2 Unit 3 Lesson 7 Answer Key Estimate and Measure with Inches
• Math Expressions Grade 2 Unit 3 Lesson 8 Answer Key Measure for and Make Line Plots
• Math Expressions Grade 2 Unit 3 Lesson 9 Answer Key Focus on Mathematical Practices

Math Expressions Grade 2 Homework and Remembering Volume 3 Answer Key | Math Expressions Common Core Grade 2 Volume 2 Answer Key

Unit 4 Subtract 2-Digit Numbers

• Math Expressions Grade 2 Unit 4 Lesson 1 Answer Key Explore Quarters
• Math Expressions Grade 2 Unit 4 Lesson 2 Answer Key Explore Dollars
• Math Expressions Grade 2 Unit 4 Lesson 3 Answer Key Addends and Subtraction
• Math Expressions Grade 2 Unit 4 Lesson 4 Answer Key Subtraction Word Problems
• Math Expressions Grade 2 Unit 4 Lesson 5 Answer Key Two Methods of Subtraction
• Math Expressions Grade 2 Unit 4 Lesson 6 Answer Key Practice and Explain a Method
• Math Expressions Grade 2 Unit 4 Lesson 7 Answer Key Subtract from 200
• Math Expressions Grade 2 Unit 4 Lesson 8 Answer Key Ungroup from the Left or from the Right
• Math Expressions Grade 2 Unit 4 Lesson 9 Answer Key Zero in the Ones or Tens Place
• Math Expressions Grade 2 Unit 4 Lesson 10 Answer Key Model Subtraction with Money
• Math Expressions Grade 2 Unit 4 Lesson 11 Answer Key Fluency: Subtraction Within 100
• Math Expressions Grade 2 Unit 4 Lesson 12 Answer Key Word Problems with Addition and Subtraction
• Math Expressions Grade 2 Unit 4 Lesson 13 Answer Key Equations with Greater Numbers
• Math Expressions Grade 2 Unit 4 Lesson 14 Answer Key Practice Addition and Subtraction
• Math Expressions Grade 2 Unit 4 Lesson 15 Answer Key Buy and Sell with One Dollar
• Math Expressions Grade 2 Unit 4 Lesson 16 Answer Key Word Problems with Unknown Addends
• Math Expressions Grade 2 Unit 4 Lesson 17 Answer Key More Word Problems with Unknown Addends
• Math Expressions Grade 2 Unit 4 Lesson 18 Answer Key Start Unknown Problems
• Math Expressions Grade 2 Unit 4 Lesson 19 Answer Key Compare Word Problems
• Math Expressions Grade 2 Unit 4 Lesson 20 Answer Key Mixed Word Problems
• Math Expressions Grade 2 Unit 4 Lesson 21 Answer Key Two-Step Problems
• Math Expressions Grade 2 Unit 4 Lesson 22 Answer Key More Two-Step Word Problems
• Math Expressions Grade 2 Unit 4 Lesson 23 Answer Key Focus on Mathematical Practices

Unit 5 Time, Graphs, and Word Problems

• Math Expressions Grade 2 Unit 5 Lesson 1 Answer Key Hours and A.M. or P.M
• Math Expressions Grade 2 Unit 5 Lesson 2 Answer Key Hours and Minutes
• Math Expressions Grade 2 Unit 5 Lesson 3 Answer Key Discuss Picture Graphs
• Math Expressions Grade 2 Unit 5 Lesson 4 Answer Key Read Picture Graphs
• Math Expressions Grade 2 Unit 5 Lesson 5 Answer Key Introduce Bar Graphs
• Math Expressions Grade 2 Unit 5 Lesson 6 Answer Key Read Bar Graphs
• Math Expressions Grade 2 Unit 5 Lesson 7 Answer Key Solve Problems Using a Bar Graph
• Math Expressions Grade 2 Unit 5 Lesson 8 Answer Key Collect and Graph Data
• Math Expressions Grade 2 Unit 5 Lesson 9 Answer Key Make Graphs and Interpret Data
• Math Expressions Grade 2 Unit 5 Lesson 10 Answer Key Focus on Mathematical Practices

3-Digit Addition and Subtraction

• Math Expressions Grade 2 Unit 6 Lesson 1 Answer Key Count Numbers to 1,000
• Math Expressions Grade 2 Unit 6 Lesson 2 Answer Key Place Value
• Math Expressions Grade 2 Unit 6 Lesson 3 Answer Key Compare Numbers Within 999
• Math Expressions Grade 2 Unit 6 Lesson 4 Answer Key Count by Ones and by Tens
• Math Expressions Grade 2 Unit 6 Lesson 5 Answer Key Add Ones, Tens, and Hundreds
• Math Expressions Grade 2 Unit 6 Lesson 6 Answer Key 3-Digit Addition
• Math Expressions Grade 2 Unit 6 Lesson 7 Answer Key Discuss 3-Digit Addition
• Math Expressions Grade 2 Unit 6 Lesson 8 Answer Key Word Problems: Unknown Addends
• Math Expressions Grade 2 Unit 6 Lesson 9 Answer Key Subtract from Hundreds Numbers
• Math Expressions Grade 2 Unit 6 Lesson 10 Answer Key Subtract from Numbers with Zeros
• Math Expressions Grade 2 Unit 6 Lesson 11 Answer Key Subtract from Any 3-Digit Number
• Math Expressions Grade 2 Unit 6 Lesson 12 Answer Key Practice Ungrouping
• Math Expressions Grade 2 Unit 6 Lesson 13 Answer Key Relationships Between Addition and Subtraction Methods
• Math Expressions Grade 2 Unit 6 Lesson 14 Answer Key Mixed Addition and Subtraction Word Problems
• Math Expressions Grade 2 Unit 6 Lesson 15 Answer Key Focus on Mathematical Practices

Unit 7 Arrays, Equal Shares, and Adding or Subtracting

• Math Expressions Grade 2 Unit 7 Lesson 1 Answer Key Arrays, Partitioned Rectangles, and Equal Shares
• Math Expressions Grade 2 Unit 7 Lesson 2 Answer Key Find Equal Shares
• Math Expressions Grade 2 Unit 7 Lesson 3 Answer Key Length Word Problems and Number Line Diagrams
• Math Expressions Grade 2 Unit 7 Lesson 4 Answer Key Add Three and Four Lengths
• Math Expressions Grade 2 Unit 7 Lesson 5 Answer Key More Length Word Problems
• Math Expressions Grade 2 Unit 7 Lesson 6 Answer Key Focus on Mathematical Practices

Math Expressions Common Core Grade 1 Homework and Remembering Answer Key

Math Expressions Grade 1 Homework and Remembering Volume 1 Answer Key | Math Expressions Common Core Grade 1 Volume 1 Answer Key

Unit 1 Partners and Number Patterns Through 10

• Math Expressions Grade 1 Unit 1 Lesson 1 Answer Key Discuss Numbers 1 – 10
• Math Expressions Grade 1 Unit 1 Lesson 2 Answer Key Visualize Numbers as a 5-Group and Ones
• Math Expressions Grade 1 Unit 1 Lesson 3 Answer Key Partners of 2 Through 5
• Math Expressions Grade 1 Unit 1 Lesson 4 Answer Key Partners of 6
• Math Expressions Grade 1 Unit 1 Lesson 5 Answer Key Partners of 7
• Math Expressions Grade 1 Unit 1 Lesson 6 Answer Key Partners of 8
• Math Expressions Grade 1 Unit 1 Lesson 7 Answer Key Partners of 9
• Math Expressions Grade 1 Unit 1 Lesson 8 Answer Key Partners of 10
• Math Expressions Grade 1 Unit 1 Lesson 9 Answer Key Focus on Mathematical Practices

Unit 2 Addition and Subtraction Strategies

• Math Expressions Grade 1 Unit 2 Lesson 1 Answer Key Represent Addition
• Math Expressions Grade 1 Unit 2 Lesson 2 Answer Key Addition with Circle Drawings
• Math Expressions Grade 1 Unit 2 Lesson 3 Answer Key Addition Equations
• Math Expressions Grade 1 Unit 2 Lesson 4 Answer Key Addition Equations and Stories
• Math Expressions Grade 1 Unit 2 Lesson 5 Answer Key Explore Solution Methods
• Math Expressions Grade 1 Unit 2 Lesson 6 Answer Key Addition Strategies: Counting On
• Math Expressions Grade 1 Unit 2 Lesson 7 Answer Key Count On from the Greater Number
• Math Expressions Grade 1 Unit 2 Lesson 8 Answer Key Addition Game: Unknown Totals
• Math Expressions Grade 1 Unit 2 Lesson 9 Answer Key Practice Counting On
• Math Expressions Grade 1 Unit 2 Lesson 10 Answer Key Represent Subtraction
• Math Expressions Grade 1 Unit 2 Lesson 11 Answer Key Subtraction with Drawings and Equations
• Math Expressions Grade 1 Unit 2 Lesson 12 Answer Key Practice with Subtraction
• Math Expressions Grade 1 Unit 2 Lesson 13 Answer Key Generate Subtraction Problems
• Math Expressions Grade 1 Unit 2 Lesson 14 Answer Key Relate Addition and Subtraction
• Math Expressions Grade 1 Unit 2 Lesson 15 Answer Key Mixed Practice with Equations
• Math Expressions Grade 1 Unit 2 Lesson 16 Answer Key Focus on Mathematical Practices

Unit 3 Unknown Numbers in Addition and Subtraction

• Math Expressions Grade 1 Unit 3 Lesson 1 Answer Key Explore Unknowns
• Math Expressions Grade 1 Unit 3 Lesson 2 Answer Key Problems with Unknown Partners
• Math Expressions Grade 1 Unit 3 Lesson 3 Answer Key Solve Equations with Unknown Partners
• Math Expressions Grade 1 Unit 3 Lesson 4 Answer Key Addition Game: Unknown Partners
• Math Expressions Grade 1 Unit 3 Lesson 5 Answer Key Practice with Unknown Partners
• Math Expressions Grade 1 Unit 3 Lesson 6 Answer Key Subtraction Strategies
• Math Expressions Grade 1 Unit 3 Lesson 7 Answer Key Subtraction Stories and Games
• Math Expressions Grade 1 Unit 3 Lesson 8 Answer Key Practice with Subtraction Stories
• Math Expressions Grade 1 Unit 3 Lesson 9 Answer Key Relate Addition and Subtraction Situations
• Math Expressions Grade 1 Unit 3 Lesson 10 Answer Key Solve Mixed Problems
• Math Expressions Grade 1 Unit 3 Lesson 11 Answer Key Practice with Mixed Problems
• Math Expressions Grade 1 Unit 3 Lesson 12 Answer Key Focus on Mathematical Practices

Unit 4 Place Value Concepts

• Math Expressions Grade 1 Unit 4 Lesson 1 Answer Key Introduction to Tens Groupings
• Math Expressions Grade 1 Unit 4 Lesson 2 Answer Key Explore Teen Numbers
• Math Expressions Grade 1 Unit 4 Lesson 3 Answer Key Represent and Compare Teen Numbers
• Math Expressions Grade 1 Unit 4 Lesson 4 Answer Key Visualize Teen Addition
• Math Expressions Grade 1 Unit 4 Lesson 5 Answer Key Teen Addition Strategies
• Math Expressions Grade 1 Unit 4 Lesson 6 Answer Key Investigate Doubles
• Math Expressions Grade 1 Unit 4 Lesson 7 Answer Key Understand Tens and Ones
• Math Expressions Grade 1 Unit 4 Lesson 8 Answer Key Integrate Tens and Ones
• Math Expressions Grade 1 Unit 4 Lesson 9 Answer Key Practice Grouping Ones into Tens
• Math Expressions Grade 1 Unit 4 Lesson 10 Answer Key Add with Groups of Ten
• Math Expressions Grade 1 Unit 4 Lesson 11 Answer Key Practice with Tens and Ones
• Math Expressions Grade 1 Unit 4 Lesson 12 Answer Key Use Place Value to Compare Numbers
• Math Expressions Grade 1 Unit 4 Lesson 13 Answer Key Add Tens or Ones
• Math Expressions Grade 1 Unit 4 Lesson 14 Answer Key Mixed Addition with Tens and Ones
• Math Expressions Grade 1 Unit 4 Lesson 15 Answer Key Counting On Strategy: 2-Digit Numbers
• Math Expressions Grade 1 Unit 4 Lesson 16 Answer Key Practice with 2-Digit Numbers
• Math Expressions Grade 1 Unit 4 Lesson 17 Answer Key 2-Digit Addition Games
• Math Expressions Grade 1 Unit 4 Lesson 18 Answer Key Focus on Mathematical Practices

Math Expressions Grade 1 Homework and Remembering Volume 3 Answer Key | Math Expressions Common Core Grade 1 Volume 2 Answer Key

Unit 5 Place Value Situations

• Math Expressions Grade 1 Unit 5 Lesson 1 Answer Key Unknown Partners with Teen Totals
• Math Expressions Grade 1 Unit 5 Lesson 2 Answer Key Subtraction with Teen Numbers
• Math Expressions Grade 1 Unit 5 Lesson 3 Answer Key Mixed Practice with Teen Problems
• Math Expressions Grade 1 Unit 5 Lesson 4 Answer Key Small Group Practice with Teen Problems
• Math Expressions Grade 1 Unit 5 Lesson 5 Answer Key Teen Problems with Various Unknowns
• Math Expressions Grade 1 Unit 5 Lesson 6 Answer Key Problems with Three Addends
• Math Expressions Grade 1 Unit 5 Lesson 7 Answer Key Count with Groups of 10
• Math Expressions Grade 1 Unit 5 Lesson 8 Answer Key Numbers Through 120
• Math Expressions Grade 1 Unit 5 Lesson 9 Answer Key Add and Subtract Tens
• Math Expressions Grade 1 Unit 5 Lesson 10 Answer Key Add and Subtract Multiples of 10
• Math Expressions Grade 1 Unit 5 Lesson 11 Answer Key Focus on Mathematical Practices

Unit 6 Comparisons and Data

• Math Expressions Grade 1 Unit 6 Lesson 1 Answer Key Explore Representing Data
• Math Expressions Grade 1 Unit 6 Lesson 2 Answer Key Organize Categorical Data
• Math Expressions Grade 1 Unit 6 Lesson 3 Answer Key Use Stair Steps to Represent Data
• Math Expressions Grade 1 Unit 6 Lesson 4 Answer Key Data Sets with Three Categories
• Math Expressions Grade 1 Unit 6 Lesson 5 Answer Key Data Collecting
• Math Expressions Grade 1 Unit 6 Lesson 6 Answer Key Introduce Comparison Bars
• Math Expressions Grade 1 Unit 6 Lesson 7 Answer Key Comparison Bars and Comparing Language
• Math Expressions Grade 1 Unit 6 Lesson 8 Answer Key Solve Compare Problems
• Math Expressions Grade 1 Unit 6 Lesson 9 Answer Key Focus on Mathematical Practices

Unit 7 Geometry, Measurement, and Equal Shares

• Math Expressions Grade 1 Unit 7 Lesson 1 Answer Key Introduction to Time
• Math Expressions Grade 1 Unit 7 Lesson 2 Answer Key Tell and Write Time in Hours
• Math Expressions Grade 1 Unit 7 Lesson 3 Answer Key Time in Our Day
• Math Expressions Grade 1 Unit 7 Lesson 4 Answer Key Tell and Write Time in Half-Hours
• Math Expressions Grade 1 Unit 7 Lesson 5 Answer Key Practice Telling and Writing Time
• Math Expressions Grade 1 Unit 7 Lesson 6 Answer Key Squares and Other Rectangles
• Math Expressions Grade 1 Unit 7 Lesson 7 Answer Key Triangles and Circles
• Math Expressions Grade 1 Unit 7 Lesson 8 Answer Key Equal Shares
• Math Expressions Grade 1 Unit 7 Lesson 9 Answer Key Compose 2-Dimensional Shapes
• Math Expressions Grade 1 Unit 7 Lesson 10 Answer Key 3-Dimensional Shapes
• Math Expressions Grade 1 Unit 7 Lesson 11 Answer Key Compose 3-Dimensional Shapes
• Math Expressions Grade 1 Unit 7 Lesson 12 Answer Key Order by Length
• Math Expressions Grade 1 Unit 7 Lesson 13 Answer Key Measure with Length Units
• Math Expressions Grade 1 Unit 7 Lesson 14 Answer Key Focus on Mathematical Practices

Unit 8 Two-Digit Addition

• Math Expressions Grade 1 Unit 8 Lesson 1 Answer Key Explore 2-Digit Addition
• Math Expressions Grade 1 Unit 8 Lesson 2 Answer Key Methods of 2-Digit Addition
• Math Expressions Grade 1 Unit 8 Lesson 3 Answer Key Addition of Tens and Ones
• Math Expressions Grade 1 Unit 8 Lesson 4 Answer Key Discuss Solution Methods
• Math Expressions Grade 1 Unit 8 Lesson 5 Answer Key Practice 2-Digit Addition
• Math Expressions Grade 1 Unit 8 Lesson 6 Answer Key Focus on Mathematical Practices

Math Expressions Common Core Kindergarten Homework and Remembering Answer Key

Math Expressions Kindergarten Homework and Remembering Volume 1 Answer Key | Math Expressions Common Core Grade K Volume 1 Answer Key

• Math Expressions Grade K Unit 1 Answer Key Understand Numbers 1 – 10
• Math Expressions Grade K Unit 2 Answer Key 5-Groups in Numbers 6 – 10
• Math Expressions Grade K Unit 3 Answer Key Teen Numbers as Tens and Ones

Math Expressions Kindergarten Homework and Remembering Volume 3 Answer Key | Math Expressions Common Core Grade K Volume 2 Answer Key

• Math Expressions Grade K Unit 4 Answer Key Partners, Problem Drawings, and Tens
• Math Expressions Grade K Unit 5 Answer Key Consolidation of Concepts

• Oct 1, 2019

How to Use a Math Medic Answer Key

Updated: Aug 7

Answer key might be the wrong term here. Sure, the Math Medic answer keys do provide the correct answers to the questions for a lesson, but they have been carefully designed to do much more than this. They are meant to be the official guide to teaching the lesson, providing specific instructions for what to do and say to make a successful learning experience for your students.

Before we look at the details of the answer key, let's make sure we understand the instructional model first.

Experience First, Formalize Later (EFFL)

A typical Math Medic lesson always has the same four parts: Activity, Debrief Activity, QuickNotes, and Check Your Understanding. Here are the cliff notes:

Activity: Students are in groups of 2 - 4 working collaboratively through the questions in the Activity. The teacher is checking in with groups and using questions, prompts, and cues to get students to refine their communication and understanding. As groups finish the activity, the teacher asks students to go to the whiteboard to write up their answers to the questions.

Debrief Activity: In the whole group setting, the teacher leads a discussion about the student responses to the questions in the activity, often asking students to explain their thinking and reasoning about their answers. The teacher then formalizes the learning by highlighting key concepts and introducing new vocabulary, notation, and formulas in the margins.

QuickNotes: The teacher provides a few key summary statements from the activity in the QuickNotes box - making connections to the learning targets for the lesson.

Check Your Understanding: Students are then asked to apply their learning from the lesson to a new context in the Check Your Understanding (CYU) problem. This can be done individually or in small groups. The CYU is very flexible in its use, as it can be used as an exit ticket, a homework problem, or a quick review the next day.

How Do I See EFFL in the Answer Key?

You will see EFFL in the answer key like this:

Activity (blue), Debrief Activity (red), QuickNotes (red), Check Your Understanding (blue)

Anything written in blue is something we expect our students to produce. This might not be quite what we expect by the end of the lesson, but provides us with a starting point when we move to formalization.

Anything written in red is an idea added by the teacher - the formalization of the learning that happened during the Activity. Students are expected to add these "notes" to their Activity using a red pen or marker.

What Do Students Write Down For Notes?

By the end of the lesson, students will have written down everything you see on the Math Medic Answer Keys. The most important transition is when students finish the Activity and we move to Debrief Activity.

"Students, now is the time for you to put down your pencils and get out your your red Paper Mate flair pens"

We give each student a Paper Mate flair pen at the beginning of the school year and tell them they must cherish and protect it with their life. They all think we should be sponsored by Paper Mate (anyone have any leads on this?)

The lessons you see on Math Medic are all of the notes we use with our students. We do not have some secret collection of guided notes.

Do Students Have Access to Answer Keys?

Yes! Any student can create a free Math Medic account to get access to the answer keys. We often send students to the website when they are absent from a lesson or when we don't quite finish the lesson in class. We are comfortable with students having access to these answer keys because we do not think Math Medic lessons should be used as a summative assessment or be used for a grade (unless it's for completion). Our lessons are meant to be the first steps in the formative process of learning new concepts.

• AP Precalculus
• AP Calculus
• AP Statistics

Recent Posts

AP Stats Lessons on a Block Schedule

AP Daily Notes for AP Precalculus

We've Got Your Syllabus for AP Precalc!

Be Prepared

18 x + 30 18 x + 30

3 − 2 n 3 − 2 n

2 x − 6 2 x − 6

0.045 0.045

w − 3 w − 3

0.35 x + 0.4 0.35 x + 0.4

2 c + 3 2 c + 3

0.042 0.042

15 15 is greater than x x .

15 < x 15 < x

2 5 x + 4 2 5 x + 4

− x + 4 − x + 4

a. >; b. >; c. >; d. >

m = 2 m = 2

a = 0 a = 0

u = 2 u = 2

x = 4 x = 4

p = −2 p = −2

q = −8 q = −8

y = − 17 5 y = − 17 5

z = 0 z = 0

identity; all real numbers

conditional equation; q = − 9 11 q = − 9 11

conditional equation; k = 201 14 k = 201 14

contradiction; no solution

x = 1 2 x = 1 2

x = −2 x = −2

x = 12 x = 12

u = −12 u = −12

n = 2 n = 2

m = −1 m = −1

r = 1 r = 1

s = −8 s = −8

n = 9 n = 9

d = 16 d = 16

He bought two notebooks.

He did seven crosswords puzzles.

−15 , −8 −15 , −8

−29 , 11 −29 , 11

−33 , −32 , −31 −33 , −32 , −31

−13 , −12 , −11 −13 , −12 , −11

−10 , −8 , −6 −10 , −8 , −6

The average cost was $5,000.

The median price was $19,300.

ⓐ 36 ⓑ $26 ⓒ 125 % 125 %

ⓐ 33 ⓑ $36 ⓐ 175 % 175 %

8.8 % 8.8 %

ⓐ $600 ⓑ $1,800

ⓐ $2,975 ⓑ $11,475

He will earn $2,500.

She earned $7,020.

The rate of simple interest was 6%.

The rate of simple interest was 5.5%.

He paid $17,590.

She deposited $9,600.

b = 2 A h b = 2 A h

h = 2 A b h = 2 A b

C = 5 9 ( F − 32 ) C = 5 9 ( F − 32 )

b = 2 A − B h h b = 2 A − B h h

t = A − P P r t = A − P P r

r = A − P P t r = A − P P t

y = 9 − 4 x 7 y = 9 − 4 x 7

y = 1 − 5 x 8 y = 1 − 5 x 8

The window’s height is 12 meters.

The length of the base is 6 feet.

The measures of the angles are 20°, 70°, and 90°.

The measures of the angles are 30°, 60°, and 90°.

The length of the leg is 8.

The length of the leg is 12.

The length is 39 inches and the width is 16 inches.

The length is 17 yards and the width is 26 yards.

The lengths of the sides of the triangle are 5, 11 and 12 inches.

The lengths of the sides of the triangle are 4, 7 and 9 feet.

The length of the swimming pool is 70 feet and the width is 30 feet.

The length of the garden is 90 yards and the width is 60 yards.

The ladder reaches 12 feet.

He should attach the lights 8 feet from the base of the mast.

Jess has 41 nickels and 18 quarters.

Elane has 22 nickels and 59 dimes.

Eric bought thirty-two 49-cent stamps and twelve 35-cent stamps.

Kailee bought twenty-six 49-cent stamps and ten 20-cent stamps.

84 adult tickets, 31 student tickets

615 children’s tickets and 195 adult tickets

Orlando mixed five pounds of cereal squares and 25 pounds of nuts.

Becca mixed 21 gallons of fruit punch and seven gallons of soda.

The speed of the local train is 48 mph and the speed of the express train is 60 mph.

Jeromy drove at a speed of 80 mph and his mother drove 60 mph.

Christopher’s speed was 50 mph and his parents’ speed was 40 mph.

Ashley’s parents drove 55 mph and Ashley drove 62 mph.

Pierre and Monique will be 429 miles apart in 3 hours.

Thanh and Nhat will be 330 miles apart in 2.2 hours.

Suzy’s speed uphill is 1.8 1.8 mph and downhill is three mph.

The boat’s speed upstream is eight mph and downstream is12 mph.

Hamilton drove 40 mph in the city and 70 mph in the desert.

Phuong rode uphill at a speed of 12 mph and on the flat street at 20 mph.

Angie can buy 7 packs of juice.

Daniel can have 11 people at the party.

Sergio and Lizeth can travel no more than 500 miles.

Rameen can use no more than 76 therms.

Caleb must work at least 96 hours.

Elliot must work at least 85 jobs.

Brenda must babysit at least 27 hours.

Josue must shovel at least 20 driveways.

The homeowner can use 5–20 hcf and still fall within the “conservation usage” billing range.

The homeowner can use 16–40 hcf and still fall within the “normal usage” billing range.

ⓐ ± 2 ± 2 ⓑ no solution ⓒ 0

ⓐ ± 11 ± 11 ⓑ no solution ⓒ 0

x = 4 , x = − 2 3 x = 4 , x = − 2 3

x = −1 , x = 5 2 x = −1 , x = 5 2

x = 8 , x = 0 x = 8 , x = 0

x = 8 , x = 2 x = 8 , x = 2

No solution

x = − 2 5 , x = − 2 5 , x = 5 2 x = 5 2

x = 3 , x = 3 , x = 1 9 x = 1 9

The diameter of the rod can be between 79.991 and 80.009 mm.

The diameter of the rod can be between 74.95 and 75.05 mm.

Section 2.1 Exercises

y = 5 y = 5

w = −18 w = −18

q = 3 q = 3

x = 14 x = 14

c = 4 c = 4

c = 5 2 c = 5 2

y = −5 y = −5

s = 10 s = 10

p = −4 p = −4

c = −4 c = −4

h = 3 4 h = 3 4

m = 6 m = 6

conditional equation; j = 2 5 j = 2 5

conditional equation; m = 16 5 m = 16 5

x = −1 x = −1

y = −1 y = −1

a = 3 4 a = 3 4

w = 9 4 w = 9 4

b = 12 b = 12

p = −41 p = −41

x = − 5 2 x = − 5 2

n = −3 n = −3

u = 3 u = 3

x = 18 x = 18

x = 20 x = 20

d = 8 d = 8

L = 19.75 L = 19.75 feet

Answers will vary.

Section 2.2 Exercises

58 hardback books

−11 , −12 , −13 −11 , −12 , −13

−69 , −71 , −73 −69 , −71 , −73

ⓐ 54 ⓑ 108 ⓐ 30%

ⓐ 162.5 162.5 ⓑ $35 ⓐ 150%

$ 11.88 $ 11.88

−2.5 % −2.5 %

−11 % −11 %

ⓐ $ 26.97 $ 26.97 ⓑ $ 17.98 $ 17.98

ⓐ $576 ⓑ 30%

ⓐ $ 7.20 $ 7.20 ⓑ $ 23.20 $ 23.20

ⓐ $ 0.20 $ 0.20 ⓑ $ 0.80 $ 0.80

3.75 % 3.75 %

21.2 % 21.2 %

Section 2.3 Exercises

d = C π d = C π

L = V W H L = V W H

d 1 = 2 A d 2 d 1 = 2 A d 2

b 1 = 2 A h − b 2 b 1 = 2 A h − b 2

a = 2 h − 108 t t 2 a = 2 h − 108 t t 2

a = 180 − b − c a = 180 − b − c

p = 2 A − 2 B l p = 2 A − 2 B l

L = P − 2 W 2 L = P − 2 W 2

y = 15 − 8 x y = 15 − 8 x

y = −6 + 4 x y = −6 + 4 x

y = 4 + x y = 4 + x

y = 7 − 4 x 3 y = 7 − 4 x 3

y = 12 − 2 x 3 y = 12 − 2 x 3

y = 18 − 3 x −2 y = 18 − 3 x −2

45 ° , 45 ° , 90 ° 45 ° , 45 ° , 90 °

30 ° , 60 ° , 90 ° 30 ° , 60 ° , 90 °

18 meters, 11 meters

13.5 13.5 m, 12.8 12.8 m

25 ft, 50 ft

12 ft, 13 ft, 14 ft

3 ft, 6 ft, 8 ft

120 yd, 160 yd

40 ft, 85 ft

104 ° F 104 ° F

ⓐ Answers will vary. ⓑ The areas are the same. The 2 × 8 2 × 8 rectangle has a larger perimeter than the 4 × 4 4 × 4 square. ⓒ Answers will vary.

Section 2.4 Exercises

nine nickels, 16 dimes

ten $10 bills, five $5 bills

63 dimes, 20 quarters

16 nickels, 12 dimes, seven quarters

330 day passes, 367 tournament passes

40 postcards, 100 stamps

15 $10 shares, five $12 shares

34 general, 61 youth

114 general, 246 student

Four pounds of macadamia nuts, eight pounds almonds

3.6 3.6 lbs Bermuda seed, 5.4 5.4 lbs Fescue seed

$33,000 in Fund A, $22,000 in Fund B

5.9 % 5.9 %

Kathy 5 mph, Cheryl 3 mph

commercial 550 mph, private plane 340 mph

Violet 65 mph, Charlie 55 mph

Ethan 22 mph, Leo 16 mph

DaMarcus 16 mph, Fabian 22 mph

uphill 1.6 1.6 mph, downhill 4.8 4.8 mph

light traffic 54 mph, heavy traffic 30 mph

freeway 67 mph, mountain road 22.3 mph

running eight mph, walking three mph

ⓐ 15 minutes ⓑ 20 minutes ⓒ one hour (d) 1:25

Section 2.5 Exercises

A maximum of 14 people can safely ride in the elevator.

five drinks

260 messages

62 necklaces

seven lawns

Section 2.6 Exercises

5 ≤ n ≤ 24 5 ≤ n ≤ 24

6 ≤ w ≤ 12 6 ≤ w ≤ 12

ⓐ answers vary ⓑ answers vary

Section 2.7 Exercises

ⓐ x = 4 , x = −4 x = 4 , x = −4 ⓑ no solution ⓒ z = 0 z = 0

ⓐ x = 3 , x = −3 x = 3 , x = −3 ⓑ no solution ⓒ z = 0 z = 0

x = 1 , x = − 1 2 x = 1 , x = − 1 2

x = −1 , x = − 5 2 x = −1 , x = − 5 2

x = 7 , x = 1 x = 7 , x = 1

x = 1 , x = −5 x = 1 , x = −5

no solution

x = −1 , x = − 2 3 x = −1 , x = − 2 3

x = −3 , x = 3 x = −3 , x = 3

x = 2 , x = 1 4 x = 2 , x = 1 4

x = 3 , x = 2 x = 3 , x = 2

x = 3 , x = − 11 3 x = 3 , x = − 11 3

x = 3 2 , x = − 1 2 x = 3 2 , x = − 1 2

The minimum to maximum expected production is 207,500 to 2,225,000 bottles

The acceptable weight is 22.5 to 25.5 ounces.

Review Exercises

s = −22 s = −22

m = −14 m = −14

q = 18 q = 18

k = 3 4 k = 3 4

k = 23 k = 23

x = 5 x = 5

There are 116 people.

−3 , −10 −3 , −10

$ 3.89 $ 3.89

ⓐ $105 ⓑ 52.5 % 52.5 %

d 2 = 2 A d 1 d 2 = 2 A d 1

y = 4 x 3 − 4 y = 4 x 3 − 4

22.5 ° , 67.5 ° , 90 ° 22.5 ° , 67.5 ° , 90 °

24.5 24.5 cm, 12.5 12.5 cm

9 ft, 14 ft, 12 ft

nine pennies, six dimes, 12 quarters

57 students, 68 general admission

2.2 2.2 lbs of raisins, 7.8 7.8 lbs of nuts

9.7 % 9.7 %

Louellen 65 mph, Tracy 66 mph

upstream 3 mph, downstream 5 mph

heavy traffic 32 mph, light traffic 68 mph

$33 per day

at least $300,000

at least 112 jobs

x = 2 , x = 2 3 x = 2 , x = 2 3

x = 9 , x = −3 x = 9 , x = −3

The minimum to maximum expected usage is 210,000 to 220,000 bottles

Practice Test

x = −5 x = −5

a = 41 a = 41

x = 6 x = 6

x = −2 , x = − 1 3 x = −2 , x = − 1 3

−57 , −55 −57 , −55

12 dimes, seven quarters

2.5 2.5 hours

At most $55.56 per costume.

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• Publication date: May 6, 2020
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Spectrum Math Grade 7 Answer Key Online Pdf | Spectrum Math 7th Grade Answers

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Spectrum Math Grade 7 Chapters 1-4 Mid-Test

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