Geometry

Lesson 21

Objective

Distinguish between and solve real-world problems involving volume and surface area.

Common Core Standards

Core Standards

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  • 7.G.B.6 — Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Foundational Standards

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  • 6.G.A.2

  • 6.G.A.4

Criteria for Success

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  1. Determine if a real-world situation describes surface area or volume. 
  2. Solve multi-step real-world problems involving volume and surface area of three-dimensional figures. 

Tips for Teachers

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This lesson brings together students’ skills in working with 3-D figures, distinguishing between contexts that call for volume vs. those that call for surface area.

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Anchor Problems

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Problem 1

Determine if each situation below would be solved by finding the surface area or the volume of the object. Explain your reasoning.

  1. How much wrapping paper is needed to wrap a present?
  2. How much water will fill a fish tank?
  3. How much cardboard is needed to create an open box?
  4. How many cubic inches of dirt will a box hold?
  5. How much snow is covering a driveway?

Guiding Questions

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Problem 2

At a daycare, Kiran sees children climbing on this foam play structure.

Kiran is thinking about building a structure like this for his younger cousins to play on.

  1. The entire structure is made out of soft foam so the children don’t hurt themselves. How much foam would Kiran need to build this play structure?
  2. The entire structure is covered with vinyl so it is easy to wipe clean. How much vinyl would Kiran need to build this play structure?
  3. The foam costs $$1¢$$ per $$\mathrm{in^3}$$. The table below lists the costs for different amounts of vinyl. What is the total cost for all the foam and vinyl needed to build this play structure?
  Vinyl ($$\mathrm{in^3}$$) Cost ($)
Row 1 75 0.45
Row 2 125 0.75

Guiding Questions

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References

Open Up Resources Foam Play Structure

Foam Play Structure is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed March 10, 2018, 1:39 p.m..

Modified by The Match Foundation, Inc.

Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

Target Task

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Melody is planning a raised bed for her vegetable garden.

  1. How many square feet of wood does she need to create the bed? 
  2. She needs to add soil. Each bag contains 1.5 cubic feet. How many bags will she need to fill the vegetable garden?

References

EngageNY Mathematics Grade 7 Mathematics > Module 3 > Topic C > Lesson 25Exit Ticket

Grade 7 Mathematics > Module 3 > Topic C > Lesson 25 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Mastery Response

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