lesson 8 homework 5.3 5th grade

5.3 Multiplying and Dividing Fractions

• Students extend multiplication and division of whole numbers to multiply fractions by fractions and divide a whole number and a unit fraction.

Section A Goals

• Recognize that $\frac{a}{b} \times \frac{c}{d}=\frac{a \ \times \ c}{b \ \times \ d}$ and use this generalization to multiply fractions numerically.
• Represent and describe multiplication of a fraction by a fraction using area concepts.

Section B Goals

• Divide a unit fraction by a whole number using whole-number division concepts.
• Divide a whole number by a unit fraction using whole-number division concepts.

Section C Goals

• Solve problems involving fraction multiplication and division.

Section A: Fraction Multiplication

Practicing Standards:   3.OA.A.2

There are 63 students in the cafeteria. There are 9 students at each table.

• At how many tables are the students seated?
• Write a division equation to represent your answer.

For access, consult one of our IM Certified Partners .

Practicing Standards:   3.MD.C.7

What is the area of this figure? Explain your reasoning.

Description: 6-sided shape. Straight sides. All side lengths meet at right angles. Side lengths. Bottom, 10 centimeters. Right side rises question mark, then goes left 4 centimeters, and goes up 6 centimeters. Top side length, question mark. Left side length, 10 centimeters.

Practicing Standards:   4.NF.B.4

Select all expressions that are equivalent to \(\frac{12}{5}\) .

Practicing Standards:   4.NF.B.4.c

Jada has 8 pennies. Each one weighs \(\frac{5}{2}\) grams. How much do Jada’s pennies weigh altogether? Explain your reasoning.

Shade \(\frac{1}{2}\) of \(\frac{1}{5}\) of the square.

• Explain where you see \(\frac{1}{2}\) of \(\frac{1}{5}\) in your drawing.
• Find the value of your expression.
• Explain how the diagram shows each part of your equation.
• Explain how your expression matches the shaded region.
• Explain how the diagram shows your expression.
• What is the area of the shaded region in square units?
• \(\frac{7}{10} \times \frac{3}{5} = \underline{\hspace{0.7cm}}\)
• \(\frac{2}{5} \times \underline{\hspace{0.7cm}} = \frac{8}{45}\)
• \(\underline{\hspace{0.7cm}} \times \frac{4}{9} = \frac{28}{45}\)

This flag of Sweden is \(3\frac{1}{5}\) inches wide and 2 inches tall. The rectangle in the upper right is \(\frac{9}{5}\) inches wide and \(\frac{4}{5}\) inch tall.

What is the area of the whole flag?

Attribution: By Paul Moore. Pixabay. Pixabay. Source .

• What is the area of the rectangle in the upper right?

Exploration

On this American flag the width of the blue rectangle is \(\frac{2}{5}\) the width of the flag. What fraction of the area of the flag is the blue rectangle? Explain or show your reasoning.

Attribution: By Berkan. Pixabay. Pixabay. Source .

Jada folded a square piece of paper in half many times, sometimes horizontally and sometimes vertically. She shaded the folded piece of paper and then unfolded it. Here is a picture.

What fraction of the paper did Jada shade? Explain how you know.

Section B: Fraction Division

For each pair of expressions, decide which is greater. Explain your choice without calculating the value of the expressions.

•   \(210 \div 3\)   \(75 \div 3\)

A pan of macaroni and cheese is \(\frac{1}{3}\) full. Four friends split the remaining macaroni and cheese equally.

• Make a drawing that represents the situation.
• Write a division expression representing how much of a pan each friend gets.
• Explain how the drawing shows the division expression.
• Explain how the diagram shows  \(\frac{1}{5} \div 2\) .
• What is the value of \(\frac{1}{5} \div2\) ?

Mai has a strip of paper that is 3 feet long. She cuts it into \(\frac{1}{4}\) foot strips.

• How many \(\frac{1}{4}\) foot strips does Mai make? Explain or show your reasoning.

Find the value of each expression.

• \(5 \div \frac{1}{4}\)
• \(6 \div \frac{1}{4}\)
• \(3 \div \frac{1}{6}\)
• \(3 \div \frac{1}{7}\)

Solve each problem. Write an equation showing your answer.

• There are 4 liters of water. How many \(\frac{1}{2}\) liter bottles of water is that?
• 4 friends split \(\frac{1}{2}\) pound of dried fruit equally. How many pounds of fruit does each friend get?

Find the value of each expression. Explain or show your reasoning.

• \(3 \div \frac{1}{4}\)
• \(\frac{1}{5} \div 8\)

For each diagram, write a story problem that the tape diagram represents. Then use the diagram to solve the problem.

It takes Earth 1 year to go around the Sun.

• During the time it takes Earth to go around around the Sun, Mercury goes around the Sun about 4 times. How many years does it take Mercury to make 1 full orbit of the Sun? Write an equation showing your answer.
• During the time it takes Earth to go around the Sun, Saturn goes \(\frac{1}{29}\) of the way around the Sun. How many years does it take Saturn to go around the Sun? Write an equation showing your answer.

Section C: Problem Solving with Fractions

• The container holds \(\frac{1}{2}\) gallon of water. It is \(\frac{3}{4}\) full. How many gallons of water are in the container?
• The container has \(\frac{1}{2}\) gallon of water. 6 friends split the water equally. How many gallons of water does each friend get?
• The container has 1 gallon of water. Each bottle holds \(\frac{1}{8}\) of a gallon. How many bottles of water does the container hold?
• Each millimeter is \(\frac{1}{1,000}\) of a meter. There are 1,000 micrometers in a millimeter. How many meters is a micrometer? Explain or show your reasoning.
• There are 1,000 nanometers in a micrometer. How many meters is a nanometer? (A single human hair can be about 50 micrometers thick. Nanometers can be used to describe the size of atoms.)

Jada wants to make a playpen for her dog with at least 70 square feet of space. She has 35 feet of fencing for the frame. Can Jada make a big enough playpen? Explain your reasoning.

Common Core Grade 5 Math (Worksheets, Homework, Lesson Plans)

Looking for video lessons that will help you in your Common Core Grade 5 Math classwork or homework? Looking for Common Core Math Worksheets and Lesson Plans that will help you prepare lessons for Grade 5 students?

The following lesson plans and worksheets are from the New York State Education Department Common Core-aligned educational resources. The Lesson Plans and Worksheets are divided into six modules.

Related Pages Common Core Math Resources, Lesson Plans And Worksheets Common Core Math Video Lessons, Math Worksheets and Games for Grade 5 Common Core Math Video Lessons, Math Worksheets and Games for all grades

Grade 5 Homework, Lesson Plans And Worksheets

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Math Homework Pages and Answers

Topic 1: understand place value.

1-1: Patterns with Exponents and Powers of 10

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1-2: Understand Whole-Number Place Value

1-3: Decimals to Thousandths

1-4: Understand Decimal Place Value

1-5: Compare Decimals

1-6: Round Decimals

Topic 2: Use Models and Strategies to Add and Subtract Decimals

2-2: Estimate Sums and Differences of Decimals

2-3: Use Models to Add and Subtract Decimals

2-4: Use Strategies to Add Decimals

2-5: Use Strategies to Subtract Decimals

2-6: Model with Math

Topic 3: Fluently Multiply Multi-Digit Whole Numbers

3-1: Multiply Greater Numbers by Powers of 10

3-2: Estimate Products

3-3: Multiply by 1-Digit Numbers

3-4: Multiply 2-Digit by 2-Digit Numbers

3-5: Multiply 3-Digit by 2-Digit Numbers

3-6: Multiply Whole Numbers with Zeros

3-7: Practice Multiplying Multi-Digit Numbers

3-8: Solve Word Problems

3-9: Critique Reasoning

Topic 4: Use Models and Strategies to Multiply Decimals

4-1:Multiply Decimals by Powers of 10

4-2: Estimate the Product of a Decimal and a Whole Number 

4-3: Use Models to Multiply a Decimal and a Whole Number

4-4: Multiply a Decimal and a Whole Number

4-5: Use Models to Multiply a Decimal and a Decimal

4-6: Multiply Decimals Using Partial Products

4-7: Use Properties to Multiply Decimals

4-8: Use Number Sense to Multiply Decimals

4-9: Model with Math

Topic 5: Use Models and Strategies to Divide Whole Numbers

Topic 5-1: Use Patterns and Mental Math to Divide

Topic 5-2: Estimate Quotients with 2-Digit Divisors

Topic 5-3: Use Models and Properties to Divide with 2-Digit Divisors

Topic 5-4: Use Partial Quotients to Divide

Topic 5-5: Use Sharing to Divide: Two Digit Divisors

Topic 5-6: Use Sharing to Divide: Greater Dividends

Topic 5-7: Choose a Strategy to Divide 

Lesson 5-8: Make Sense and Persevere

Topic 6: Use Models and Strategies to Divide Decimals

6-1: Patterns for Dividing with Decimals

6-2: Estimate Decimals Quotients

6-3: Use Models to Divide by a 1-Digit Number

6-4: Divide by a 2-digit Whole Number

6-5: Divide by a Decimal

6-6: Reasoning 

Topic 7: Use Equivalent Fractions to Add and Subtract Fractions

7-2: Find Common Denominators

•   Answers

7-3: Add Fractions with Unlike Denominators

7-4: Subtract Fractions with Unlike Denominators

7-5: Add and Subtract Fractions

7-6: Estimate Sums and Differences of Mixed Numbers

7-7: Use Models to Add Mixed Numbers

7-8: Add Mixed Numbers

7-9: Use Models to Subtract Mixed Numbers

7-10: Subtract Mixed Numbers

7-11: Add and Subtract Mixed Numbers

Topic 8: Apply Understanding of Multiplication to Multiply Fractions

8-1: Multiply a Fraction by a Whole Number

8-2: Multiply a Whole Number by a Fraction

8-3: Multiply Fractions and Whole Numbers

8-4: Use Models to Multiply Two Fractions

8-5: Multiply Two Fractions

8-6: Area of a Rectangle

8-7: Multiply Mixed Numbers

Topic 9: Apply Understanding of Division to Divide Fractions

Lesson 9-1: Fractions and Division

Lesson 9-2: Fractions and Mixed Numbers as Quotients

Lesson 9-3: Use Multiplication to Divide

Lesson 9-4: Divide Whole Numbers by Unit Fractions

Lesson 9-5: Divide Unit Fractions by Non-Zero Whole Numbers

Lesson 9-6: Divide Whole Numbers and Unit Fractions

Lesson 9-7: Solve Problems Using Division

Lesson 9-8: Repeated Reasoning

Topic 10: Represent and Interpret Data

Lesson 10-1: Analyze Line Plots

Lesson 10-2: Make Line Plots

Lesson 10-3: Solve Word Problems Using Measurement Data

Lesson 10-4: Critique Reasoning 

Topic 11: Understand Volume Concepts

Lesson 11-1: Model Volume

Lesson 11-2: Develop a Formula

Lesson 11-3: Combine Volume of Prisms

Lesson 11-4: Solve Word Problems Using Volume

Lesson 11-5: Use Appropriate Tools

5th Grade Homework Policy

We value your family time. therefore, we will be intentional with any homework we send home. students’ daily homework will be required reading of at least 30 minutes., students will have nightly math homework which supports our learning in class. there are a lot of new math concepts in 5th grade and it is important for students' growth and understanding. additionally, study guides and other assignments may be sent home periodically throughout the year., please note: if a student exhibits off-task behaviors, fails to complete an assignment, or is struggling to understand a concept, an assignment will be sent home for completion..

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Polygons - Lesson 11.1

Triangles - Lesson 11.2

Quadrilaterals - Lesson 11.3

Three Dimensional Figures - Lesson 11.5

Unit Cubes and Solid Figures - Lesson 11.6

Understanding Volume - Lesson 11.7

Estimate Volume - Lesson 11.8

Volume of a Rectangular Prism - Lesson 11.9

Apply Volume Formulas - Lesson 11.10

Finding Volume of Composite Formulas - Lesson 11.12

Find a Part of a Group - Lesson 7.1

Multiply Fractions and Whole Numbers - Lesson 7.2

Fraction and Whole Number Multiplication - Lesson 7.3

Multiply Fractions - Lesson 7.4

Compare Fraction Factor and Product - Lesson 7.5

Fraction Multiplication - Lesson 7.6

Area and Mixed Numbers - Lesson 7.7

Compare Mixed Number Factors and Products - Lesson 7.8

Multiply Mixed Numbers - Lesson 7.9

Problem Solving - Find Unknown Lengths - Lesson 7.10  

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Line Plots - Lesson 9.1

Ordered Pairs - Lesson 9.2

Graph Data - Lesson 9.3

Line Graphs - Lesson 9.4

Numerical Patterns - Lesson 9.5

Problem Solving - Find a Rule - Lesson 9.6

Graph and Analyze Relationships - Lesson 9.7

Customary Length - Lesson 10.1

Customary Capacity - Lesson 10.2

Weight - Lesson 10.3

Multistep Measurement Problems - Lesson 10.4

Metric Measures - Lesson 10.5

Problem Solving Conversions - Lesson 10.6

Elapsed Time - Lesson 10.7

Division Patterns with Decimals - Lesson 5.1

Divide Decimals by Whole Numbers - Lesson 5.2

Estimate Quotients - lesson 5.3

Division of Decimals by Whole Numbers - Lesson 5.4

Decimal Division - Lesson 5.5

Divide Decimals - Lesson 5.6

Write Zeros in the Dividend - Lesson 5.7

Problem Solving - Decimal Operations - Lesson 5.8

Divide Fractions and Whole Numbers - Lesson 8.1

Problem Solving - Use Multiplication - Lesson 8.2

Connect Fractions to Division - Lesson 8.3

Fraction and Whole Number Division - Lesson 8.4

Interpret Division with Fractions - Lesson 8.5

Addition with Unlike Denominators - Lesson 6.1

Subtraction with Unlike Denominators - Lesson 6.2

Estimate Fraction Sums and Differences - Lesson 6.3

Common Denominators and Equivalent Fractions - Lesson 6.4

Add or Subtract Fractions - Lesson 6.5

Add or Subtract Mixed Numbers - Lesson 6.6

Subtraction with Renaming - Lesson 6.7

Patterns with Fractions - Lesson 6.8

Problem Solving with Addition and Subtraction - Lesson 6.9

Use Properties of Addition - Lesson 6.10

Multiplication Patterns with Decimals - Lesson 4.1

Multiply Decimals and Whole Numbers - Lesson 4.2

Multiply Decimals and Whole Numbers - Lesson 4.3

Multiply Using Expanded Form - Lesson 4.4

Problem Solving - Multiply Money - Lesson 4.5

Decimal Multiplication - Lesson 4.6

Multiply Decimals - Lesson 4.7

Thousandths - Lesson 3.1

Place Value of Decimals - Lesson 3.2

Compare and Order Decimals - Lesson 3.3

Round Decimals - Lesson 3.4

Decimal Addition - Lesson 3.5

Decimal Subtraction - Lesson 3.6

Estimate Decimal Sums and Differences - Lesson 3.7

Add Decimals - Lesson 3.8

Subtract Decimals - Lesson 3.9

Patterns with Decimals - Lesson 3.10

Problem Solving Add and Subtract Money - Lesson 3.11

Choose a Method - Lesson 3.12

Performance Task on Chapter 3

Place the First Digit - Lesson 2.1

Divide by 1-Digit Divisors - Lesson 2.2

Division with 2-Digit Divisors - Lesson 2.3

Partial Quotients - Lesson 2.4

Estimate with 2-Digit Divisors - Lesson 2.5

Divide by 2-Digit Divisors - Lesson 2.6

Interpret the Remainder - Lesson 2.7

Adjust Quotients - Lesson 2.8

Problem Solving - Division - Lesson 2.9

Performance Task on Chapter 2

Fifth Grade 

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Go Math! 5 Student Edition, Grade: 5 Publisher: Houghton Mifflin Harcourt

Go math 5 student edition, title : go math 5 student edition, publisher : houghton mifflin harcourt, isbn : 547352042, isbn-13 : 9780547352046, use the table below to find videos, mobile apps, worksheets and lessons that supplement go math 5 student edition., textbook resources.

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Into Math Grade 8 Module 5 Lesson 3 Answer Key Interpret and Graph Proportional Relationships

We included H MH Into Math Grade 8 Answer Key PDF Module 5 Lesson 3 Interpret and Graph Proportional Relationships to make students experts in learning maths.

HMH Into Math Grade 8 Module 5 Lesson 3 Answer Key Interpret and Graph Proportional Relationships

I Can graph proportional relationships from a table or equation, calculate the unit rate, and determine whether the graph should be continuous or discrete.

Spark Your Learning

Turn and Talk Predict how the graph of the second airplane’s travel will compare to the graph of the first. What will be the same and what will be different?

Build Understanding

B. The airplane travels at a constant rate, so the relationship between distance and time is proportional. You already know that the unit rate of a proportional relationship can be calculated from any point on a graph of the relationship. Use the point (3, 1200) to calculate the number of miles that the airplane travels per hour. Show your work. __________________ Answer: 1200 miles in 3 hours 1200/3 = 400 miles per hour C. A second airplane starts from the same airport and is traveling at a different constant speed. After 4 hours the second airplane has flown 2100 miles from the airport. Calculate the number of miles that the second airplane traveled per hour. Show your work. __________________ Answer: 4 hr = 2100 miles 1 hour = x 4x = 2100 x = 2100/4 x = 525 miles Thus the second airplane traveled 525 miles

E. What can you conclude about the distance that the two airplanes will have traveled after 8 hours? ____________________________ ____________________________ ____________________________ Answer: The unit rate is 1:400 400 miles per hour 8 hours = 8 × 400 = 3200 miles

B. The airplane travels at a constant rate, so the relationship between distance and time is proportional. You already know that the unit rate of a proportional relationship can be calculated from any point on a graph of the relationship. Use the point (3, 1200) to calculate the number of miles that the airplane travels per hour. Show your work. ______________________ Answer: 1200 miles in 3 hours 1200/3 = 400 miles per hour

C. A second airplane starts from the same airport and is traveling at a different constant speed. After 4 hours the second airplane has flown 2100 miles from the airport. Calculate the number of miles that the second airplane traveled per hour. Show your work. ______________________ Answer: 4 hr = 2100 miles 1 hour = x 4x = 2100 x = 2100/4 x = 525 miles Thus the second airplane traveled 525 miles

E. What can you conclude about the distance that the airplanes will have traveled after 8 hours? ____________________________ ____________________________ Answer: 525 mile per hour 8 hours = 8 × 525 = 4200 miles in hours

Step It Out

Connect to Vocabulary A continuous graph is a graph made up of connected points or curves.

You have used a continuous graph to represent situations, such as an airplane’s distance traveled. A discrete graph is a graph made of unconnected points. It represents data that only make sense at certain points.

Check Understanding

Question 1. A. Graph the points ¡n the table. Connect the points with a line if appropriate. __________________________

B. Should the graph be discrete or continuous? Why? __________________________ __________________________

Question 2. What is the unit rate per minute at which the grain silo fills? __________________________ Answer: (50 – 0)/(10 – 0) = 50/10 = 5 The grain silo is filling at a constant rate. The unit rate per minute is 5 tons per minute.

B. Did you represent the situation with a discrete graph or a continuous graph? Why? Answer: Discrete graph

C. What does the point (3, 6) represent on the graph?

D. Why are the complete pages printed the independent variable?

Construct Arguments For each relationship, decide whether you would represent it with a discrete graph or a continuous graph. Explain your reasoning.

Question 4. a graph of the cost of shipping different numbers of identical packages ____________________ Answer: Continuous graph

Question 5. a graph of the amount of fuel remaining in a car’s gas tank while driving ____________________ Answer: continuous graph

Question 6. a graph of how many students can be transported by different numbers of buses ____________________ Answer: Discrete graph

C. Did you draw a discrete graph or a continuous graph? _________________ Answer: Discrete graph

D. Look at the point on the graph at (1, 4). Describe what this point represents. _________________ Answer: 1 represents time in second and 4 represents height in feet.

I’m in a Learning Mindset!

How can I modify the task of interpreting and graphing proportional relationships to maintain an appropriate level of challenge?

Lesson 5.3 More Practice/Homework

B. Is your graph discrete or continuous? Explain.

C. How long does it take for 12 drops to fall? Answer: 1 drop = 30 sec 12 drops = 12 × 30 = 360 sec Thus it takes 360 seconds to fall.

Question 2. Open Ended Explain how the unit rate of a proportional relationship relates to the slope of its graph. Give a quantitative example. Answer: If the relationship between two quantities is a proportional relationship, this relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate. The slope is the rate of change and it will remain the same. For example, 1/4 and 4/16 have a proportional relationship, which means they are the same.

Question 5. A graph showing the distance a person has walked over time is an example of a (continuous / discrete) graph. Answer: The graph shown above is a discrete graph that the distance a person has walked over time.

Spiral Review

Question 6. In the diagram, which two pairs of angles are alternate interior angles? ____________________

Answer: ∠3 and ∠6 are the alternate interior angles ∠4 and ∠5 are the alternate interior angles

Question 8. Juana and Andy completed 20 math problems total. Juana completed 6 more problems than Andy. Write an equation to determine the number of math problems that Andy completed, then solve the equation. How many of the math problems did Andy complete? Answer: Given, Juana and Andy completed 20 math problems total. Juana completed 6 more problems than Andy. 6 + 2 × x = 20 6 + 2x = 20 2x = 20- 6 2x = 14 x = 7

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