Shapes and Volume

Lesson 7

Math

Unit 3

5th Grade

Lesson 7 of 16

Objective


Solve more complex real-world and mathematical problems involving volume.

Common Core Standards


Core Standards

  • 5.MD.C.5 — Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

Foundational Standards

  • 4.MD.A.3
  • 5.NBT.B.5
  • 5.NBT.B.6

Criteria for Success


  1. Find the height of a figure given the area of its base and its volume in a contextual problem (MP.4). 
  2. Find the area of the base of a figure given its height and volume in a contextual problem (MP.4).
  3. Find a dimension of a figure given its volume and the two other dimensions in a contextual problem (MP.4). 
  4. Find possible dimensions of a figure given its volume in a contextual problem (MP.4). 
  5. Find the volume of a figure given modifications to an existing figure in a contextual problem (e.g., “a container’s length is doubled, what is its new volume?”) (MP.4). 
  6. Find how many rectangular prisms can fit inside a larger rectangular prism given the dimensions of each in a contextual problem (MP.4). 
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Anchor Tasks


Problem 1

Hassan bought a trashcan for his bathroom. The base of the trashcan has an area of 32 square inches and a volume of 288 cubic inches. Hassan is hoping the trashcan can fit under his sink which has a height clearance of 8 inches. Will his trashcan fit? Explain.

Guiding Questions

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Problem 2

A rectangular prism has a volume of 84 cubic feet. What could be its length, width, and height?

Guiding Questions

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Problem 3

a.   Find the volume of a rectangular prism that measures 3 units by 3 units by 3 units.

b.   Without calculating, about how much larger would you expect a 4 unit by 4 unit by 4 unit rectangular prism to be? Explain.

c.   Find the actual volume of the 4 unit by 4 unit by 4 unit rectangular prism. Was you prediction in Part (b) reasonable? Why or why not?

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • Look at #3b. What were the dimensions of the different fish tanks you made for Cari?
  • How many more cubes are needed to fill the figure in #5? What made this problem difficult? 
  • Look at #6. Can Tim's fridge fit? Why or why not?
  • What is the volume of Prism Y in #7? What could Prism Y’s dimensions be? How did you figure that out? 
  • How did you find the volume of the smaller rectangular prism in #8? 
  • Look at #9. How much will Shelly have to pay? How did you figure that out? 
  • Look at #10. How much clay can the second box hold? How did you figure that out? Why is it not 6 times as much clay?
  • Look at #11, Part A. How many books fit in the container? 

Target Task


A rectangular prism has a volume of 728 cubic yards. The length is 13 yards. The width is 7 yards. What is the height, in yards?

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 6

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Lesson 8

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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