1 of 15

Divide Unit Fractions by Whole Numbers

Grade 5: Unit 3: Lesson 1110

Download for free at openupresources.org.

2022 Open Up Resources |

Lesson Purpose

The purpose of this lesson is for students to divide a unit fraction by a whole number.

Lesson Narrative

The purpose of this lesson is for students to determine the size of the piece when a unit fraction is divided into equally sized parts. Students revisit the context of a pan of macaroni and cheese from earlier lessons when they multiplied unit fractions by unit fractions. The familiar context can help students make connections between multiplication and division. Students should be encouraged to solve the problems in a way that makes sense to them. The relationship between multiplication and division is meant to be exploratory. In later lessons, students will formalize this relationship.

Learning Goals

•Divide a unit fraction by a whole number, in context, in a way that makes sense to them.

2 of 15

Let’s divide a unit fraction by a whole number.

3 of 15

Number Talk:

Double the Divisor

Warm-Up

4 of 15

5 of 15

More Macaroni and Cheese

Activity 1

MLR7: Compare and Connect

6 of 15

What do you notice?

What do you wonder?

Last night, Jada’s aunt baked a pan of macaroni and cheese for dinner. Today, she brought the leftovers to Jada’s home for Jada and her sisters to share.

Launch

•Groups of 2

•Display and read: “Last night, Jada’s aunt baked a pan of macaroni and cheese for dinner. Today, she brought the leftovers to Jada’s home for Jada and her sisters to share.”

•“What do you notice? What do you wonder?” (We solved problems about macaroni and cheese

before. I wonder how much macaroni and cheese Jada’s aunt brought.)

•1–2 minutes: partner discussion

Student Work Time

•1–2 minutes: quiet think time

•6–8 minutes: partner work time

•Monitor for students who:

◦draw diagrams like the ones in the student responses

◦explain the situation as ½ divided into 3 equal pieces.

◦recognize each person will get ⅙ of the whole pan of macaroni and cheese

Student Responses

Check sample responses
Sample response: ½ of the pan of macaroni and cheese is divided into 3 equal pieces.
⅙ of the whole pan

Activity Synthesis

MLR7 Compare and Connect

•“Create a visual display that shows your thinking about the problems. You may want to include details such as notes, diagrams, drawings, etc., to help others understand your thinking.”

•2–5 minutes: independent or group work

•5–7 minutes: gallery walk

•“How does each representation show ½ a pan of macaroni and cheese?”

•“How does each representation show 3 equal pieces?”

•30 seconds: quiet think time

•1 minute: partner discussion

•“How do we know that each person got the same amount of macaroni and cheese?”

I divided the half into 3 equal shares.

•“How much of the whole pan of macaroni and cheese did each person get?”

⅙

•“How do the diagrams show ⅙ ?”

Each ½ of the pan is divided into 3 equal pieces, so each of those pieces is ⅙ of the whole pan.

7 of 15

Launch

•Groups of 2

•Display and read: “Last night, Jada’s aunt baked a pan of macaroni and cheese for dinner. Today, she brought the leftovers to Jada’s home for Jada and her sisters to share.”

•“What do you notice? What do you wonder?” (We solved problems about macaroni and cheese

before. I wonder how much macaroni and cheese Jada’s aunt brought.)

•1–2 minutes: partner discussion

Student Work Time

•1–2 minutes: quiet think time

•6–8 minutes: partner work time

•Monitor for students who:

◦draw diagrams like the ones in the student responses

◦explain the situation as ½ divided into 3 equal pieces.

◦recognize each person will get ⅙ of the whole pan of macaroni and cheese

Student Responses

Check sample responses
Sample response: ½ of the pan of macaroni and cheese is divided into 3 equal pieces.
⅙ of the whole pan

Activity Synthesis

MLR7 Compare and Connect

•“Create a visual display that shows your thinking about the problems. You may want to include details such as notes, diagrams, drawings, etc., to help others understand your thinking.”

•2–5 minutes: independent or group work

•5–7 minutes: gallery walk

•“How does each representation show ½ a pan of macaroni and cheese?”

•“How does each representation show 3 equal pieces?”

•30 seconds: quiet think time

•1 minute: partner discussion

•“How do we know that each person got the same amount of macaroni and cheese?”

I divided the half into 3 equal shares.

•“How much of the whole pan of macaroni and cheese did each person get?”

⅙

•“How do the diagrams show ⅙ ?”

Each ½ of the pan is divided into 3 equal pieces, so each of those pieces is ⅙ of the whole pan.

8 of 15

More People Share

Activity 2

9 of 15

Launch

•Groups of 2

Student Work Time

•1–2 minutes: independent think time

•5–8 minutes: partner work time

•Monitor for students who :

◦draw diagrams like the ones in the student responses

◦describe the amount each person gets as a fraction of the whole pan

◦describe a relationship between the number of people sharing and the size of the serving each person gets

Student Responses

Problem 1

Check student work to see that the diagram shows ½ of the pan divided into 4 equal pieces.
Sample Response: I divided half of the pan into 4 equal pieces.
Sample Response: Each person gets ¼ of ½ of the pan, or each person gets ⅛ of the whole pan.

Problem 2

Diagram shows ½ of the pan divided into 5 equal pieces.
Sample Response: I divided half of the pan into 5 equal pieces.
Each person gets ⅕ of ½, or each person gets 1/10 of the whole pan.

Problem 3

Sample response: Both groups are sharing ½ of a pan of macaroni and cheese, but there are different numbers of people in each group. The amount of macaroni and cheese each person gets is different.

Activity Synthesis

Both situations are about ½ a pan of macaroni and cheese, but this one has more people sharing it, so each person gets less macaroni and cheese. When 4 people share, each person gets ⅛ of the whole pan. When 5 people share, each person gets 1/10 of the whole pan.

10 of 15

Launch

•Groups of 2

Student Work Time

•1–2 minutes: independent think time

•5–8 minutes: partner work time

•Monitor for students who :

◦draw diagrams like the ones in the student responses

◦describe the amount each person gets as a fraction of the whole pan

◦describe a relationship between the number of people sharing and the size of the serving each person gets

Student Responses

Problem 1

Check student work to see that the diagram shows ½ of the pan divided into 4 equal pieces.
Sample Response: I divided half of the pan into 4 equal pieces.
Sample Response: Each person gets ¼ of ½ of the pan, or each person gets ⅛ of the whole pan.

Problem 2

Diagram shows ½ of the pan divided into 5 equal pieces.
Sample Response: I divided half of the pan into 5 equal pieces.
Each person gets ⅕ of ½, or each person gets 1/10 of the whole pan.

Problem 3

Sample response: Both groups are sharing ½ of a pan of macaroni and cheese, but there are different numbers of people in each group. The amount of macaroni and cheese each person gets is different.

Activity Synthesis

Both situations are about ½ a pan of macaroni and cheese, but this one has more people sharing it, so each person gets less macaroni and cheese. When 4 people share, each person gets ⅛ of the whole pan. When 5 people share, each person gets 1/10 of the whole pan.

11 of 15

Lesson Synthesis

What did you learn about division today? How can we show examples of what we learned?

If you taught the previous optional lesson, display the poster from the previous lesson’s synthesis. “What can we add to our poster to show what we learned about division today?” (We can divide unit fractions by whole numbers.) “How can we show examples of what we learned?” (We can show equations and representations.)

If you did not teach the previous optional lesson, ask: “What did you learn about division today? How can we show examples of what we learned?” Record responses on a poster to be used in future lessons.

“What do you still wonder about division?” (Can you divide fractions? When would you ever need to divide a fraction? Does the answer get smaller or bigger when you divide fractions?)

Record student responses for all to see. Keep the display visible. Refer back to it in future lessons.

12 of 15

Lesson Synthesis

What do you still wonder about division?

If you taught the previous optional lesson, display the poster from the previous lesson’s synthesis. “What can we add to our poster to show what we learned about division today?” (We can divide unit fractions by whole numbers.) “How can we show examples of what we learned?” (We can show equations and representations.)

If you did not teach the previous optional lesson, ask: “What did you learn about division today? How can we show examples of what we learned?” Record responses on a poster to be used in future lessons.

“What do you still wonder about division?” (Can you divide fractions? When would you ever need to divide a fraction? Does the answer get smaller or bigger when you divide fractions?)

Record student responses for all to see. Keep the display visible. Refer back to it in future lessons.

13 of 15

Share Macaroni and Cheese

Cool-Down

14 of 15

Cool Down: Share Macaroni and Cheese

15 of 15

Image Citations

Photo by Priyanka Aggarwal on Unsplash

Photo by Tina Witherspoon on Unsplash

Photo by Hermes Rivera on Unsplash

Photo by Mariana Ibanez on Unsplash

Photo by Alex Haney on Unsplash

Creative Commons BY-NC-SA

Download, adopt, and adapt this Open Educational Resource for your students' needs