Curriculum  /  Math  /  5th Grade  /  Unit 3: Shapes and Volume  /  Lesson 4

Shapes and Volume

Lesson 4

Math

Unit 3

5th Grade

Lesson 4 of 16

Objective

Find the volume of a right rectangular prism using its side lengths.

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

  • 3.OA.B.5

Criteria for Success

  1. Look for and make use of structure to find the volume of concrete rectangular prisms by finding the number of cubes in a layer by multiplying its length times width, then multiplying by the number of layers (MP.7). 
  2. Reason abstractly and quantitatively to see that the dimensions can be multiplied together in any order and the volume will remain the same (MP.2).
  3. Write multiplication expressions to represent the number of cubes in a prism based on the number of rows and columns of a layer and the number of layers of unit cubes.

Tips for Teachers

  • Using cardstock, Net E, and tape, create at least one open-top container (which measures $$3$$ cm $$\times\:3$$ cm $$\times\:6$$ 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.

Lesson Materials

  • Net E (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 (13 per student or small group) — Students need exactly this many centimeter cubes and no more. See Anchor Task 1 for more information.
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Anchor Tasks

25-30 minutes

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 E, as well as no more than 13 centimeter cubes per student/group.)

Guiding Questions

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Student Response

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Problem 2

These are answers to questions about the prism above. Read each answer and determine what question it is answering about the prism.  

a.   3 is the answer. What is the question?

b.   5 is the answer. What is the question?

c.   $$3\times4=12$$. The answer is 12. What is the question?

d.   $$12\times5=60$$. The answer is 60 cubes. What is the question?

e.   3 by 4 by 5 is the answer. What is the question?

Guiding Questions

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Student Response

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References

Illustrative Mathematics Grade 5 Unit 1 Lesson 5 Activity 3 — What is the Question?

Grade 5 Unit 1 Lesson 5 Activity 3, accessed on Jan. 5, 2022, 11:27 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 3

Akiko and Philip are finding the volume of the following rectangular prism. 

Philip says that you have to multiply length by width by height, so you have to multiply $$6 \times 9 \times 5$$ in that order. Akiko says the computation will be easier if you multiply $$6 \times 5$$ first and then multiply by 9. 

a.   Is Philip correct? Must the dimensions be multiplied in that order? Show or explain your thinking. 

b.   Why do you think Akiko thinks that multiplying $$6 \times 5 \times 9$$ will be an easier computation? Show or explain your thinking. Then use Akiko's expression to find the volume of the prism.

c.   Use what you’ve concluded from Parts (a) and (b) to explain how you would calculate the volume of a rectangular prism whose length is 4 feet, width is 7 feet, and height is 15 feet. 

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • How did you find the volume of the rectangular prism in #4, despite not being given its dimensions or being fully packed with cubes?
  • Compare your earlier strategies for finding volume to the method we learned today. How do you use the number of cubes in the rows and columns of a layer and the number of layers to find the volume of a rectangular prism?

Target Task

5-10 minutes

Explain or show how the expression $$2\times3\times4$$ represents the volume of the prism below.

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.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

Represent volume using expressions related to the formulas $$V = b \times h $$ and $$V = l \times w \times h$$. Use these formulas to find the volume of pictorial rectangular prisms.

Lesson 5
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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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