Shapes and Volume

Lesson 6

Math

Unit 3

5th Grade

Lesson 6 of 16

Objective


Understand standard units for measuring volume, including cubic inches, cubic centimeters, cubic feet, and cubic meters. Solve real-world and mathematical problems involving these various units.

Common Core Standards


Core Standards

  • 5.MD.C.4 — Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
  • 5.MD.C.5.B — Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

Criteria for Success


  1. Understand that cubic centimeters, cubic inches, cubic feet, and cubic yards are standard measurement units for measuring volume, each of which has side lengths of 1 centimeter, inch, foot, or meter, respectively.
  2. Develop benchmarks for cubic centimeters, cubic inches, cubic feet, and cubic yards.
  3. Identify the most appropriate unit to use to measure the volume of a particular object, such as a box of playing cards.
  4. Find the volume of a rectangular figure given the area of its base and its height in a contextual problem (MP.4).
  5. Find the volume of a figure given its dimensions in a contextual problem (MP.4).

Tips for Teachers


The standards do not specify whether students need to be familiar with the exponential notation for volume, namely units$$^3$$, cm$$^3$$, in$$^3$$, etc, in Grade 5. Thus this notation is not included in tasks but it’s at the teacher’s discretion to introduce it or not. If you choose to introduce the notation, you can eventually relate it to the idea of units being repeatedly multiplied together and therefore the notation representing that idea (e.g., a prism with measurements 2 cm, 3 cm, and 4 cm has a volume of 2 cm × 3 cm × 4 cm, or (2 × 3 × 4) (cm × cm × cm), or 24 cm$$^3$$).

Lesson Materials

  • Optional: Centimeter cubes (1 per teacher)
  • Optional: Ruler (1 per teacher)
  • Optional: Inch cube (1 per teacher)
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Anchor Tasks


Problem 1

a.   What do you notice? What do you wonder?

b.   The small cube is a cubic foot. The large cube is a cubic yard. What kinds of volumes would make sense to measure with cubic feet? What about cubic yards?

Guiding Questions

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References

Illustrative Mathematics Grade 5 Unit 1 Lesson 7 Warm-Up

Grade 5 Unit 1 Lesson 7 Warm-Up, accessed on Jan. 7, 2023, 8:40 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem 2

For each object, choose the cubic unit you would use to measure the volume: cubic centimeter, cubic inch, or cubic foot. Be prepared to explain your reasoning.

a.   The volume of a moving truck

b.   The volume of a freezer

c.   The volume of a juice box

d.   The volume of a classroom

e.   The volume of a dumpster

f.   The volume of a lunch box

Guiding Questions

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References

Illustrative Mathematics Grade 5 Unit 1 Lesson 7 Activity 1

Grade 5 Unit 1 Lesson 7 Activity 1, accessed on Jan. 7, 2023, 8:45 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem 3

a.   Natasha needs to buy a terrarium for her pet lizard that is at least 1,155 cubic inches. She’s considering buying a terrarium that has a length of 12 inches, a width of 8 inches, and a height of 10 inches. Will this terrarium be large enough for her lizard? Explain. 

b.   Geoffrey buys a smoke alarm for his kitchen, which is can detect smoke in spaces no larger than 1,000 cubic feet. His kitchen covers an area of 160 square feet and the ceilings in the kitchen are 8 feet tall. Did Geoffrey buy the right smoke alarm? Explain.

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • In #1, I think Prism C has the greatest volume because it’s the only one with a dimension of 12 inches. Do you agree or disagree?
  • How did you choose the units with which you’d measure the objects you found in #4?
  • What equation represents the volume of the prism in #5? What about #6?
  • How did you decide which cube is a cubic centimeter versus a cubic inch in #7?

Target Task


Problem 1

A vending machine measures 6 feet tall, 4 feet wide, and 2 feet deep. What is the volume, in cubic feet, of a vending machine?

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Problem 2

A vase is in the shape of a rectangular prism. The base of the vase has an area of 25 square inches. The height of the vase is 16 inches. What is the volume, in cubic inches, of the vase?

Student Response

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Additional Practice


The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 5

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Lesson 7

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Volume of Three-Dimensional Figures

Topic B: Classification of Two-Dimensional Shapes

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