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All Kinds of Prisms

Grade 5: Unit 1: Lesson 11

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Lesson Purpose

The mathematical purpose of this lesson is for students to apply what they have learned about finding the volumes of right rectangular prisms and figures composed of right rectangular prisms to solve real-world problems.

Lesson Narrative

In previous lessons, students learned to find the volume of a right rectangular prism by multiplying the number of cubes in a layer by the number of layers. They found the volumes of rectangular prisms with and without the unit cubes showing. They used the associative property of multiplication to represent threefold whole-number products as volumes and learned to find the volume of rectangular prisms with whole-number side lengths by multiplying the length by the width by the height and multiplying the area of the base times the height. They also understand volume as additive. They found volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts. In this lesson, students apply these understandings to solve real-world problems.

Learning Goals

•Solve real-world and mathematical problems involving volume.

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Let’s find the volume of all different kinds of prisms.

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Which One Doesn’t Belong: Many Prisms

Warm-Up

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Which one doesn’t belong?

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What do Figures A, C, and D have in common?

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Prism Palooza

Activity 1

MLR6: Three Reads

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For each problem, explain or show your reasoning.

a. Han is filling a box with cubes. Shown is a diagram of the box. How many cubes can fit in the box if Han completely packs it, without gaps between cubes?

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b. Clare brought a storage container for her art supplies. The storage container was 4 feet wide, 9 feet long, and 5 feet high. What is the volume of her container?

Launch

•Groups of 2

Student Work Time

•8 minutes: individual work time

•2 minutes: partner discussion

•Monitor for students who find the volume in different ways, either using different bases or using 3 measurements for the length, width, and height.

Student Responses

300 cubes
180 cubic feet
270 cubic feet

Activity Synthesis

•Ask selected students to share their solutions for the second problem.

•“How are the strategies the same? How are they different?”

They both got the same solution, but one person multiplied to get the area of the base and then multiplied the result by 5, but the other person chose to multiply first.

•“How is the third problem different from the first two?”

It does not give us the length and width of the closet. It just gives the area of the floor.

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C. Mai’s new bedroom has a walk-in closet with a floor that measures 30 square feet. Her closet ceiling is 9 feet from the floor. What is the volume of her closet?

Launch

•Groups of 2

Student Work Time

•8 minutes: individual work time

•2 minutes: partner discussion

•Monitor for students who find the volume in different ways, either using different bases or using 3 measurements for the length, width, and height.

Student Responses

300 cubes
180 cubic feet
270 cubic feet

Activity Synthesis

•Ask selected students to share their solutions for the second problem.

•“How are the strategies the same? How are they different?”

They both got the same solution, but one person multiplied to get the area of the base and then multiplied the result by 5, but the other person chose to multiply first.

•“How is the third problem different from the first two?”

It does not give us the length and width of the closet. It just gives the area of the floor.

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Problem Solving with Figures

Activity 2

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This type of garden is called a raised bed garden because the plants are not in the ground.
If we planted a garden at our school, what vegetables would you want to grow?

Launch

•Display the picture of the garden from the student workbook:

Student Work Time

• 5 minutes: individual work time

• 5 minutes: partner discussion

• Monitor for students who break the garden into two rectangular prisms, finding the volume of

each, and for students who put them together to form a single rectangular prism.

Student Responses

216 cubic feet
(3 x 8 x 4) + (3 x 10 x 4) with factors in any order.
Sample response: 3 x 4 x 18
Sample response: I like my garden better because it looks more like a square.

Activity Synthesis

•Display the diagram of the garden from the task.

•Invite students to share how they found its volume.

•“What do the two parts of the garden have in common?”

They are both 4 feet tall and 3 feet wide.

•“What is different about the two parts of the garden?”

The length. One piece is 10 feet long and the other piece is 8 feet long.

•“How could you put the pieces together to make a single rectangular prism?”

The sides that are 3 feet by 4 feet fit together and the length would be 18 feet.

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The elementary school is going to build a raised bed garden like the one in the picture, but they will use a different design. Here is a

diagram that shows the side lengths of the garden the school will build.

Launch

•Display the picture of the garden from the student workbook:

Student Work Time

• 5 minutes: individual work time

• 5 minutes: partner discussion

• Monitor for students who break the garden into two rectangular prisms, finding the volume of

each, and for students who put them together to form a single rectangular prism.

Student Responses

216 cubic feet
(3 x 8 x 4) + (3 x 10 x 4) with factors in any order.
Sample response: 3 x 4 x 18
Sample response: I like my garden better because it looks more like a square.

Activity Synthesis

•Display the diagram of the garden from the task.

•Invite students to share how they found its volume.

•“What do the two parts of the garden have in common?”

They are both 4 feet tall and 3 feet wide.

•“What is different about the two parts of the garden?”

The length. One piece is 10 feet long and the other piece is 8 feet long.

•“How could you put the pieces together to make a single rectangular prism?”

The sides that are 3 feet by 4 feet fit together and the length would be 18 feet.

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What is the volume of the garden? Explain or show your reasoning.

Write an expression to represent the volume of the garden.

Launch

•Display the picture of the garden from the student workbook:

Student Work Time

• 5 minutes: individual work time

• 5 minutes: partner discussion

• Monitor for students who break the garden into two rectangular prisms, finding the volume of

each, and for students who put them together to form a single rectangular prism.

Student Responses

216 cubic feet
(3 x 8 x 4) + (3 x 10 x 4) with factors in any order.
Sample response: 3 x 4 x 18
Sample response: I like my garden better because it looks more like a square.

Activity Synthesis

•Display the diagram of the garden from the task.

•Invite students to share how they found its volume.

•“What do the two parts of the garden have in common?”

They are both 4 feet tall and 3 feet wide.

•“What is different about the two parts of the garden?”

The length. One piece is 10 feet long and the other piece is 8 feet long.

•“How could you put the pieces together to make a single rectangular prism?”

The sides that are 3 feet by 4 feet fit together and the length would be 18 feet.

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Lesson Synthesis

In this unit, you did a lot of work with prisms and volume. What are some things you know about volume and rectangular prisms?

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Talk to your neighbor. Discuss which part of the unit was your favorite and why.

How did working with the cubes help you with the rest of the volume work in the unit?

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The Volume of a Sandbox

Cool-Down

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Cool Down: A preschool is building a sandbox. Below is a diagram that shows the side lengths of the sandbox.

What is the volume of the sandbox? Explain or show your reasoning.

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Image Citations

https://pixabay.com/photos/wooden-cubes-abc-cubes-letters-473703/

Creative Commons BY-NC-SA

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