Geometry

Lesson 16

Objective

Identify and describe two-dimensional figures that result from slicing three-dimensional figures.

Common Core Standards

Core Standards

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  • 7.G.A.3 — Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Foundational Standards

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  • 5.G.B.3

  • 5.MD.C.3

Criteria for Success

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  1. Understand that a three-dimensional figure can be sliced in various ways that result in a two-dimensional cross-section
  2. Understand that a slice through a right pyramid or prism, parallel to the base, will have the same shape as the base.
  3. Identify the two-dimensional figures that result from various slices through right pyramids and prisms. 

Tips for Teachers

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Visualizing the two-dimensional figures that result from slicing a three-dimensional figure can be challenging for some students. The following are two visual supports:

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Anchor Problems

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Problem 1

Justine has a block of cheese in the shape of a square prism, as shown below.

She cuts the block in half. 
What are two different two-dimensional faces that could result from Justine slicing the cheese in half?

Guiding Questions

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Problem 2

A right rectangular pyramid is shown below.


Describe how the following two-dimensional figures can be created by slicing the pyramid. 

  • rectangle
  • triangle
  • trapezoid

Guiding Questions

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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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Misha has a cube and a right-square pyramid that are made of clay. She placed both clay figures on a flat surface. 

Misha will make slices through each figure that are parallel and perpendicular to the flat surface. Which statements are true about the two-dimensional plane sections that could result from one of these slices?

Select all that apply.

  1. A plane section that is triangular could result from one of these slices through the cube.
  2. A plane section that is square could result from one of these slices through the cube.
  3. A plane section that is rectangular but not square could result from one of these slices through the cube.
  4. A plane section that is triangular could result from one of these slices through the pyramid.
  5. A plane section that is square could result from one of these slices through the pyramid.
  6. A plane section that is rectangular but not square could result from one of these slices through the pyramid.

References

PARCC Mathematics Practice Tests Grade 7 Paper-Based Practice TestQuestion #20

Grade 7 Paper-Based Practice Test from Mathematics Practice Tests is made available by Partnership for Assessment of Readiness for College and Careers. © Copyright 1998 - 2015 Pearson Education, Inc. or its affiliate(s). All rights reserved. Accessed March 10, 2018, 2:31 p.m..

Mastery Response

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