Unit 4, Lesson 15: Volume of Prisms

15.1: A Box of Cubes (5 minutes)

Setup: 2–3 of quiet work time, followed by a whole-class discussion.

Lesson GoalsDetermine volume of a prism by packing unit cubes of fractional lengths and bymultiplying all the edge lengths.Solve volume problems involving fractional lengths.

Required Materials•

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GRADE 6 MATHEMATICS

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Unit 4: Dividing Fractions, Lesson 15: Volume of Prisms 1

Student task statement1. How many cubes with an edge length of 1 inch fill this box?

2. If the cubes had an edge length of 2 inches, would more or fewer cubes be needed to fill the box? Explainhow you know.

3. If the cubes had an edge length of inch, would more or fewer cubes be needed to fill the box? Explain

how you know.

Possible responses

1. 120

2. Fewer

3. More

GRADE 6 MATHEMATICS

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Unit 4: Dividing Fractions, Lesson 15: Volume of Prisms 2

15.2: Cubes with Fractional Edge Lengths (20 minutes)

Setup:

Students in groups of 3–4. 8–10 minutes of quiet work time, followed by 5 minutes of group discussion. Encourage students to draw asketch, if needed.

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Unit 4: Dividing Fractions, Lesson 15: Volume of Prisms 3

Student task statement1. Diego correctly points out that 108 cubes with an edge length of inch are needed to fill a rectangular

prism that is 3 inches by 1 inch by inch. Explain or show how this is true. Draw a sketch, if needed.

2. What is the volume, in cubic inches, of the rectangular prism? Show your reasoning.

3. Lin and Noah are packing small cubes into a cube with an edge length of inches. Lin is using cubes

with an edge length of inch, and Noah is using cubes with an edge length of inch.

a. Who would need more cubes to fill the -inch cube? Show how you know.

b. If Lin and Noah use their small cubes to find the volume of the -inch cube, would they get the

same value? Explain or show your reasoning.

Possible responses

1. Explanations vary.

2. 4 in3

3. a. Noah would need more cubes.

b. Yes, they would get the samevolume.

Anticipated misconceptions

If students have trouble getting started,ask them to revisit their work with

-inch cubes from a previous lesson.

Remind them that a cube with -inch

edge length has a volume of in3

(because we can fit 8 of such cubes in a1-inch cube). Ask them to think abouthow many -inch cubes can fit into a

1-inch cube, or think about what thevolume of a -inch cube is in cubic

inches.

Some students may not be able tovisualize and keep track of the

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Unit 4: Dividing Fractions, Lesson 15: Volume of Prisms 4

measurements of the boxes in this task.Encourage students to draw and labelthe measurements of the boxesdescribed in these questions.

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Unit 4: Dividing Fractions, Lesson 15: Volume of Prisms 5

15.3: Fish Tank and Baking Pan (Optional, 20 minutes)

Setup:

Students in groups of 3–4. 5 minutes of quiet work time for the first question and 2–3 minutes of group discussion, followed by time tocomplete the second question.

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Unit 4: Dividing Fractions, Lesson 15: Volume of Prisms 6

Student task statement1. A fish tank in a nature center has the shape of a rectangular prism. The tank is 10 feet long, feet wide,

and 6 feet tall.

b. The caretaker of the center filled of the tank with water. What was the volume of the water in the

tank in cubic feet? What was the height of the water in the tank? Explain or show your reasoning.

c. One day, the tank was filled with 330 cubic feet of water. The height of the water was what fractionof the height of the tank? Show your reasoning.

2. Clare’s recipe for banana bread won’t fit in her favorite pan. The pan is inches by 11 inches by 2

inches. The batter fills the pan to the very top, and when baking, the batter spills over the sides. To avoidspills, there should be about an inch between the top of the batter and the rim of the pan. Clare hasanother pan that is 9 inches by 9 inches by inches. If she uses this pan, will the batter spill over during

baking?

a. What is the volume of the tank in cubic feet? Explainor show your reasoning.

Possible responses

1. a. 495 ft3

b. 396 ft3. The water is feet

deep.

c. of the height of the tank

2. Yes, it would spill. Explanationsvary.

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Unit 4: Dividing Fractions, Lesson 15: Volume of Prisms 7

Lesson Synthesis (5 minutes)How is finding the volume of a prism with fractional edge lengths like and unlike finding the volume of a prism with whole-number edgelengths? How do we find an unknown length of a rectangular prism if we know its volume and the other two edge lengths?

15.4: Storage Box (Cool-down, 5 minutes)

Setup: None.

Are you ready for more?1. Find the area of a rectangle with side lengths and .

2. Find the volume of a rectangular prism with side lengths , , and .

3. What do you think happens if we keep multiplying fractions ?

4. Find the area of a rectangle with side lengths and .

5. Find the volume of a rectangular prism with side lengths , , and .

6. What do you think happens if we keep multiplying fractions ?

Possible Responses

1.

2.

3. Approach the value of 0

4. 2

5.

6. Approach the value of 1

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Unit 4: Dividing Fractions, Lesson 15: Volume of Prisms 8

Student task statementA storage box has a volume of 56 cubic inches, and the base of the box is 4 inches by 4 inches.

1. What is the height of the box? 2. Lin’s teacher uses the box to store her set of cubes withan edge length of inch. If the box is completely full,

how many cubes are in the set?

Possible responses

1. inches

2. 448 cubes

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Unit 4: Dividing Fractions, Lesson 15: Volume of Prisms 9