Shapes and Volume

Lesson 3

Math

Unit 3

5th Grade

Lesson 3 of 16

Objective


Find the volume of a right rectangular prism by thinking about its layers.

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.

Criteria for Success


  1. Look for and make use of the structure of rectangular prisms to find their volume by counting the number of cubes in a layer and the number of layers (MP.7). 
  2. Look for and make use of structure to understand that rectangular prisms can be decomposed into layers in different ways (MP.7). 
  3. Write repeated addition or multiplication expressions to represent the number of cubes in a prism based on the number of layers and the number of cubes in each layer. 

Tips for Teachers


  • Using cardstock, Net D, and tape, create at least one open-top container (which measures 3 cm x 3 cm x 6 cm) by printing out the template on cardstock, cutting it out along the solid lines, folding along the dotted lines, and taping it to create an open-top container. 
  • You might want to construct multiple open-top containers so that students can explore volume in small groups in a more hands-on way rather than the figures being presented at the front of the class.
  • In Anchor Task 1, students need exactly 14 centimeter cubes and no more, but they may want to use centimeter cubes in later tasks in which case they'll need more cubes. You might choose to put 14 cubes in individual baggies for Anchor Task 1, then make more cubes available to students if needed in later Anchor Tasks.

Lesson Materials

  • Net D (1 per student or small group) — See Tips for Teachers for how to prepare this material before the lesson.
  • Optional: Cardstock (1 sheet per student or small group) — See Tips for Teachers for more information.
  • Tape (1 per teacher) — See Tips for Teachers for more information.
  • Centimeter cubes (About 50 per student or small group) — See Tips for Teachers for more information.
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Anchor Tasks


Problem 1

What is the volume, in cubic units, of this figure?

(Teachers: Present students the open-top containers constructed from the net of the figure from Net D as well as no more than 14 centimeter cubes per student/group.)

Guiding Questions

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Problem 2

How many layers are there in the following figure? How many cubes are in each layer? What is the volume of the figure?

Find another way to think of the layers in the figure.

Guiding Questions

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Problem 3

a.   Explain or show how the expression $$5\times24$$ represents the volume of this rectangular prism.

b.   Explain or show how the expression $$6\times20$$ represents the volume of this rectangular prism. 

c.   Find a different way to calculate the volume of this rectangular prism. Explain or show your thinking.

d.   Write an expression to represent the way you calculated the volume.

Guiding Questions

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References

Illustrative Mathematics Grade 5 Unit 1 Lesson 4 Activity 2

Grade 5 Unit 1 Lesson 4 Activity 2, accessed on Jan. 5, 2022, 9:38 a.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.

Modified by Fishtank Learning, Inc.

Problem Set


Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

  • In #1, how did you decide how to go about decomposing the prisms? Is there a different way or order in which you could have done it?
  • What was Josh having a hard time visualizing in #2? Which layers are easier for you to visualize? Which are the hardest? How can you make the hardest layers easier to see?
  • How did you determine the volume of the prism in #3 only knowing what one layer looked like?
  • What mistake did Mauro make in #4? What was the volume of the prism?

Target Task


Use the figure below to answer the following questions.

a.   Sasha says she sees 2 layers with 9 cubes in each layer the prism above. Draw lines on the prism to show the layers Sasha sees.

b.   Yaritza says she sees 3 layers of 6 cubes in each layer in the prism above. Do you agree or disagree that there are 3 layers with 6 cubes in each layer in the prism? Explain.

c.   Find the volume of the prism.

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

Answer Keys

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 2

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Lesson 4

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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