Shapes and Volume

Lesson 10

Math

Unit 3

5th Grade

Lesson 10 of 16

Objective


Understand that volume is additive. Find the volume of composite solid figures when not all dimensions are given and/or they must be decomposed.

Common Core Standards


Core Standards

  • 5.MD.C.5.C — Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

Foundational Standards

  • 4.MD.A.3
  • 3.OA.B.5

Criteria for Success


  1. Find the volume of a composite solid figure made up of rectangular prisms in which some dimensions are not labeled. 
  2. Find the volume of a composite solid figure made up of rectangular prisms in which the figure is not decomposed into its parts, so some interpretation must be done. 
  3. Write an equation to represent the volume of a composite solid.

Tips for Teachers


Lesson Materials

  • Markers or crayons (2 per student)
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Anchor Tasks


Problem 1

a.   John was finding the volume of this figure. He decided to break it apart into two separate rectangular prisms. John found the volume of the solid below using this expression: (4 × 4 × 1) + (2 × 4 × 2).

Decompose the figure into two rectangular prisms and shade them in different colors to show one way John might have thought about it.

b.   Phillis also broke this solid into two rectangular prisms, but she did it differently than John. She found the volume of the solid below using this expression: (2 × 4 × 3) + (2 × 4 × 1).

Decompose the figure into two rectangular prisms and shade them in different colors to show one way Phillis might have thought about it.

Guiding Questions

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References

Illustrative Mathematics Breaking Apart Composite Solids

Breaking Apart Composite Solids, accessed on Feb. 5, 2018, 12:04 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

Find the volume of the following figure.

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • Compare your approach to solving #3 with that of the person sitting next to you. How is your thinking alike? How is it different? 
  • Look at #5. What were the two ways you could decompose the figure? Which one was easier for you to compute with? 
  • What advice would you give to a friend who was having trouble picturing the dimensions on a composite figure? What helps you to figure out missing dimensions? 
  • How much will the packing material cost in #7, Part C? How did you solve?

Target Task


Raju has a solid brass bookend, shown below. How much brass, in cubic centimeters, is the bookend made of?

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 9

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Lesson 11

Lesson Map

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Topic A: Volume of Three-Dimensional Figures

Topic B: Classification of Two-Dimensional Shapes

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