Shapes and Volume

Lesson 5

Math

Unit 3

5th Grade

Lesson 5 of 16

Objective


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.

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

Criteria for Success


  1. Understand that the base of a rectangular prism is one of its faces, often the one on which it rests, and that the height of a rectangular prism is the number of layers of unit cubes are stacked from the base to the top.
  2. Calculate the volume of a pictured rectangular prism using the formula $$V = b \times h$$.
  3. Calculate the volume of a pictured rectangular prism using the formula $$V = l \times w \times h$$.

Tips for Teachers


Lesson Materials

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Anchor Tasks

25-30 minutes


Problem 1

a.   Match each rectangular prism (cut out from page 1 of Rectangular Prisms Template) with the expression(s) (cut out from pages 2 and 3 of Rectangular Prisms Template) that represents its volume in cubic units. Be prepared to explain your reasoning.

b.   For each prism write one additional expression, not in the card sort, that represents its volume in cubic units.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Illustrative Math Grade 5 Unit 1 Lesson 6

Illustrative Math Grade 5 Unit 1 Lesson 6 Activity 1, accessed on Jan. 5, 2022, 2:29 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

a.   Work with a partner to complete the tables. One partner completes Table 1 and the other completes Table 2.

Prism A Prism B

Table 1

  length (units) width (units) height (units) volume (cubic units)
Prism A        
Prism B        

Table 2

  area of the base (square units) height (units) volume (cubic units)
Prism A      
Prism B      

b.   Compare your tables and discuss:

  1. What do the tables have in common?
  2. What is different about the tables?

Guiding Questions

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Student Response

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References

Illustrative Mathematics Grade 5 Unit 1 Lesson 6 Activity 2

Grade 5 Unit 1 Lesson 6 Activity 2, accessed on Jan. 7, 2023, 3:51 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 Set

15-20 minutes


Discussion of Problem Set

  • If you’re given the area of the base of a prism and its height, how can I find its volume?
  • What are the three dimensions of a prism? How can I use them to find its volume?
  • How are these two ways of thinking about computing the volume of a rectangular prism related to how cubic units fit into it?

Target Task

5-10 minutes


Select the three expressions that can be used to find the volume of the prism below.

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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

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.

Lesson 6
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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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