# Illustrative Mathematics Grade 7, Unit 7, Lesson 11: Slicing Solids

Learning Targets:

• I can explain that when a three dimensional figure is sliced it creates a face that is two dimensional.
• I can picture different cross sections of prisms and pyramids.

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Illustrative Math

#### Lesson 11: Slicing Solids

Let’s see what shapes you get when you slice a three-dimensional object.

Illustrative Math Unit 7.7, Lesson 11 (printable worksheets)

#### Lesson 11 Summary

The following diagrams show how a cross section is formed when we slice through a three-dimensional figure.

#### Lesson 11.1 Prisms, Pyramids, and Polyhedra

Describe each shape as precisely as you can. Click on the applet and drag the mouse to show the object turning in 3D.

Open Applet

Open Applet

Open Applet

#### Lesson 11.2 What’s the Cross Section?

Here are a rectangular prism and a pyramid with the same base and same height. Drag the large red point up and down to move the plane through the solids.

Open Applet

1. If we slice each solid parallel to its base halfway up, what shape cross sections would we get? What is the same about the cross sections? What is different?
2. If we slice each solid parallel to its base near the top, what shape cross sections would we get? What is the same about the cross sections? What is different?

#### Are you ready for more?

Describe the cross sections that would result from slicing each solid perpendicular to its base.

#### Lesson 11.3 Card Sort: Cross Sections

Your teacher will give you a set of cards. Sort the images into groups that make sense to you. Be prepared to explain your reasoning.

#### Lesson 11.4 Drawing Cross Sections

Use the applet to draw each cross section and describe it in words.

1. Here is an applet with a rectangular prism, 4 units by 2 units by 3 units.
a. A plane cuts the prism parallel to the bottom and top faces.
b. The plane moves up and cuts the prism at a different height.
c. A vertical plane cuts the prism diagonally.

Open Applet

1. A square pyramid has a base that is 4 units by 4 units. Its height is also 4 units.
a. A plane cuts the pyramid parallel to the base.
b. A vertical plane cuts the prism.

Open Applet

1. A cube has an edge of length 4.
a. A plane cuts off the corner of the cube.
b. The plane moves farther from the corner and makes a cut through the middle of the cube.

Open Applet

#### Lesson 11 Practice Problems

1. A cube is cut into two pieces by a single slice that passes through points A, B, and C. What shape is the cross section?
2. Describe how to slice the three-dimensional figure to result in each cross section.
3. Here are two three-dimensional figures. Describe a way to slice one of the figures so that the cross section is a rectangle.
4. Each row contains the degree measures of two supplementary angles. Complete the table.
5. Two months ago, the price, in dollars, of a cell phone was c.
a. Last month, the price of the phone increased by 10%. Write an expression for the price of the phone last month.
b. This month, the price of the phone decreased by 10%. Write an expression for the price of the phone this month.
c. Is the price of the phone this month the same as it was two months ago? Explain your reasoning.

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

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