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Division Situations

Grade 5: Unit 2: Lesson 4

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Lesson Purpose

The purpose of this lesson is for students to solve division problems when the quotient is a fraction or mixed number.

Lesson Narrative

In previous lessons students solved equal sharing problems involving division of whole numbers with answers in the form of mixed numbers and fractions using diagrams. They noticed patterns and made generalizations about the relationship between the expression and the fraction for specific values of and . Students have observed that the numerator of the fraction is the number of objects being shared, while the denominator is the number of equal shares. This lesson brings all of these ideas together through contexts, equations, and diagrams. Students continue to notice patterns across these contexts and build flexibility with interpreting fractions in terms of division by creating their own situations. Fluently moving between representations gives students the ability to choose an appropriate representation to solve a problem (MP1).

Consider what division situations students or their families might be familiar with. Measurement contexts often present situations when division results in a fraction or mixed number. For example, making something with fabric, dividing large amounts of food in to smaller containers, or measuring and cutting wood for a project.

Learning Goals

•Solve problems involving division of whole numbers leading to answers in the form of fractions.

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Let’s solve and represent division problems.

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Number Talk: Division

Warm-Up

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Pounds of Blueberries

Activity 1

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Launch

•Display image:

•“Where do you see division situations in this picture?” (The berries are split into 6 groups. )

•Groups of 3

•Assign groups. Make sure each student knows who is Partner A, Partner B, and Partner C.

Student Work Time

•6–8 minutes: independent work time (problems 1, 2, 3)

•4–5 minutes: group discussion

•Monitor for students who write division situations, for , where represents the amount to be shared and represents the number of equal shares.

Student Responses

a. Sample response for partner A: There are 4 bags of popcorn being shared equally with 6 people. How much popcorn does each person get?

B. Sample response for partner B: There are 6 students sharing 4 sandwiches equally. How much

sandwich does each student get?

C. Sample response for partner C:

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Activity Synthesis

• Select 2–3 students to share their problems and solutions. Show a variety of accurate student

representations.

• Display equation: .

• “How did you use the equation to help determine the number of objects and equal shares in

your story?”

The numerator is the number of objects. The denominator is the number of shares. This story

needs 4 objects and 6 equal shares.

• Display image:

• “How did you use the diagram to help determine the number of objects and equal shares in

your story?”

The number of objects is the number of wholes or large rectangles and the number of shares is

the number of equal pieces each rectangle is divided into. There are 4 objects and 6 equal

shares.

• “How were your stories the same? How were they different?”

There were 4 objects in each and there are divided into 6 equal shares, but our contexts were

different.

If students do not think of a situation that is represented by the equation, show them the image

from the launch and ask, “How can the equation represent some people sharing some pounds of

blueberries?”

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Launch

•Display image:

•“Where do you see division situations in this picture?” (The berries are split into 6 groups. )

•Groups of 3

•Assign groups. Make sure each student knows who is Partner A, Partner B, and Partner C.

Student Work Time

•6–8 minutes: independent work time (problems 1, 2, 3)

•4–5 minutes: group discussion

•Monitor for students who write division situations, for , where represents the amount to be shared and represents the number of equal shares.

Student Responses

a. Sample response for partner A: There are 4 bags of popcorn being shared equally with 6 people. How much popcorn does each person get?

B. Sample response for partner B: There are 6 students sharing 4 sandwiches equally. How much

sandwich does each student get?

C. Sample response for partner C:

4/6

Activity Synthesis

• Select 2–3 students to share their problems and solutions. Show a variety of accurate student

representations.

• Display equation: .

• “How did you use the equation to help determine the number of objects and equal shares in

your story?”

The numerator is the number of objects. The denominator is the number of shares. This story

needs 4 objects and 6 equal shares.

• Display image:

• “How did you use the diagram to help determine the number of objects and equal shares in

your story?”

The number of objects is the number of wholes or large rectangles and the number of shares is

the number of equal pieces each rectangle is divided into. There are 4 objects and 6 equal

shares.

• “How were your stories the same? How were they different?”

There were 4 objects in each and there are divided into 6 equal shares, but our contexts were

different.

If students do not think of a situation that is represented by the equation, show them the image

from the launch and ask, “How can the equation represent some people sharing some pounds of

blueberries?”

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Launch

•Display image:

•“Where do you see division situations in this picture?” (The berries are split into 6 groups. )

•Groups of 3

•Assign groups. Make sure each student knows who is Partner A, Partner B, and Partner C.

Student Work Time

•6–8 minutes: independent work time (problems 1, 2, 3)

•4–5 minutes: group discussion

•Monitor for students who write division situations, for , where represents the amount to be shared and represents the number of equal shares.

Student Responses

a. Sample response for partner A: There are 4 bags of popcorn being shared equally with 6 people. How much popcorn does each person get?

B. Sample response for partner B: There are 6 students sharing 4 sandwiches equally. How much

sandwich does each student get?

C. Sample response for partner C:

4/6

Activity Synthesis

• Select 2–3 students to share their problems and solutions. Show a variety of accurate student

representations.

• Display equation: .

• “How did you use the equation to help determine the number of objects and equal shares in

your story?”

The numerator is the number of objects. The denominator is the number of shares. This story

needs 4 objects and 6 equal shares.

• Display image:

• “How did you use the diagram to help determine the number of objects and equal shares in

your story?”

The number of objects is the number of wholes or large rectangles and the number of shares is

the number of equal pieces each rectangle is divided into. There are 4 objects and 6 equal

shares.

• “How were your stories the same? How were they different?”

There were 4 objects in each and there are divided into 6 equal shares, but our contexts were

different.

If students do not think of a situation that is represented by the equation, show them the image

from the launch and ask, “How can the equation represent some people sharing some pounds of

blueberries?”

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Launch

•Display image:

•“Where do you see division situations in this picture?” (The berries are split into 6 groups. )

•Groups of 3

•Assign groups. Make sure each student knows who is Partner A, Partner B, and Partner C.

Student Work Time

•6–8 minutes: independent work time (problems 1, 2, 3)

•4–5 minutes: group discussion

•Monitor for students who write division situations, for , where represents the amount to be shared and represents the number of equal shares.

Student Responses

a. Sample response for partner A: There are 4 bags of popcorn being shared equally with 6 people. How much popcorn does each person get?

B. Sample response for partner B: There are 6 students sharing 4 sandwiches equally. How much

sandwich does each student get?

C. Sample response for partner C:

4/6

Activity Synthesis

• Select 2–3 students to share their problems and solutions. Show a variety of accurate student

representations.

• Display equation: .

• “How did you use the equation to help determine the number of objects and equal shares in

your story?”

The numerator is the number of objects. The denominator is the number of shares. This story

needs 4 objects and 6 equal shares.

• Display image:

• “How did you use the diagram to help determine the number of objects and equal shares in

your story?”

The number of objects is the number of wholes or large rectangles and the number of shares is

the number of equal pieces each rectangle is divided into. There are 4 objects and 6 equal

shares.

• “How were your stories the same? How were they different?”

There were 4 objects in each and there are divided into 6 equal shares, but our contexts were

different.

If students do not think of a situation that is represented by the equation, show them the image

from the launch and ask, “How can the equation represent some people sharing some pounds of

blueberries?”

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Problem 2:

Discuss both your solutions with your group. What is the same? What is different?

Launch

•Display image:

•“Where do you see division situations in this picture?” (The berries are split into 6 groups. )

•Groups of 3

•Assign groups. Make sure each student knows who is Partner A, Partner B, and Partner C.

Student Work Time

•6–8 minutes: independent work time (problems 1, 2, 3)

•4–5 minutes: group discussion

•Monitor for students who write division situations, for , where represents the amount to be shared and represents the number of equal shares.

Student Responses

a. Sample response for partner A: There are 4 bags of popcorn being shared equally with 6 people. How much popcorn does each person get?

B. Sample response for partner B: There are 6 students sharing 4 sandwiches equally. How much

sandwich does each student get?

C. Sample response for partner C:

4/6

Activity Synthesis

• Select 2–3 students to share their problems and solutions. Show a variety of accurate student

representations.

• Display equation: .

• “How did you use the equation to help determine the number of objects and equal shares in

your story?”

The numerator is the number of objects. The denominator is the number of shares. This story

needs 4 objects and 6 equal shares.

• Display image:

• “How did you use the diagram to help determine the number of objects and equal shares in

your story?”

The number of objects is the number of wholes or large rectangles and the number of shares is

the number of equal pieces each rectangle is divided into. There are 4 objects and 6 equal

shares.

• “How were your stories the same? How were they different?”

There were 4 objects in each and there are divided into 6 equal shares, but our contexts were

different.

If students do not think of a situation that is represented by the equation, show them the image

from the launch and ask, “How can the equation represent some people sharing some pounds of

blueberries?”

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Grams of Gold

Activity 2

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Launch

•Display first image.

•“Tell a story about what is happening in this image.”

•1 minute: quiet think time

•1 minute: partner discussion

•Display second image.

•“This is gold dust.”

•“We are going to solve some problems about panning for gold.”

Student Work Time

•5-8 minutes: partner work time

•Monitor for students who:

◦draw a diagram to explain or show the relationship between the number of friends and the denominator.

◦use words to explain or show the relationship between the number of friends and the denominator.

Student Responses

4/3 grams each. 4 grams of gold total.
6 friends

Activity Synthesis

•Invite previously selected students to share their responses.

•Display the first situation that describes 3 friends sharing gold and each friend gets grams of gold.

•“What do we know about the situation?”

There are 3 friends and each friend gets grams of gold.

•Display:4/3

•“How does 4/3 represent the situation of friends sharing gold?”

It is the amount of gold each friend got.

•“What does the 3 represent in ?”

Thirds. The amount they collected was split into 3 equal parts because there are 3 friends.

•“What does the 4 represent in 4/3?”

It represents how many thirds there are and also how many friends there are.

If students don’t have a way to start the problem, ask: “What do you know about the problem? What are you still trying to figure out?”

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Lesson Synthesis

How does this equation represent the situation about friends sharing gold?

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Lesson Synthesis

What number makes this equation true? How do you know?

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How Much Milk?

Cool-Down

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Cool Down: Complete the table below.

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Image Citations

https://pixabay.com/photos/blueberries-bunch-berries-fruits-1326154/

https://pixabay.com/photos/blueberries-berries-fresh-fruits-2278921/

https://pixabay.com/photos/blueberries-fruits-food-fresh-4011294/

https://pixabay.com/photos/physalis-food-photograpie-gold-berry-2914964/

https://pixabay.com/photos/blueberries-milk-breakfast-fruit-1576409/

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