# Geometry

## Objective

Solve real-world and mathematical problems involving volume.

## 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.

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• 6.G.A.2

• 5.MD.C.5

## Criteria for Success

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1. Use the formulas for volume of prisms and pyramids to solve multi-step real-world problems.

## Tips for Teachers

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Lessons 20 and 21 engage students in finding the volume of prisms and pyramids. Students use their equation skills to manipulate the volume formula to find missing measurements. Lesson 20 focuses on solving real-world problems. In Lesson 21, students will compare volume to surface area in real-world contexts.

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## Anchor Problems

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### Problem 1

Owen is building a small wooden birdhouse. The bottom of the birdhouse is a rectangular prism that opens up to a roof in the shape of a rectangular pyramid. (Diagram is not drawn to scale.)

How much space is inside Owen’s birdhouse?

#### Guiding Questions

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### Problem 2

The seventh graders at Sunview Middle School were helping to renovate a playground for the kindergartners at a nearby elementary school. City regulations require that the sand underneath the swings be at least 15 inches deep. The sand under both swing sets was only 12 inches deep when they started.

The rectangular area under the small swing set measures 9 feet by 12 feet and required 40 bags of sand to increase the depth by 3 inches. How many bags of sand will the students need to cover the rectangular area under the large swing set if it is 1.5 times as long and 1.5 times as wide as the area under the small swing set?

#### Guiding Questions

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#### References

Illustrative Mathematics Sand Under the Swing Set

Sand Under the Swing Set, accessed on July 5, 2016, 10:02 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.

### Problem 3

7.2 L of water are poured into a container in the shape of a right rectangular prism. The inside of the container is 50 cm long, 20 cm wide, and 25 cm tall. How far from the top of the container is the surface of the water? ( $1 \space \mathrm{L} = 1,000 \space \mathrm{cm^3}$)

#### Guiding Questions

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#### References

EngageNY Mathematics Grade 7 Mathematics > Module 3 > Topic C > Lesson 24Example 2

Grade 7 Mathematics > Module 3 > Topic C > Lesson 24 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..

## 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.

• Challenge: Twelve 2" by 2" by 2" ice cubes are put in a square prism vase, measuring 4" by 4" for the base and 8" tall. Once the ice cubes melt, how high up will the water reach in the vase?