Parallel and Perpendicular Cross Sections

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Students will be able to describe polygons formed when 3D figures are cross sectioned both parallel and perpendicular to the base.

Big Idea

This lesson is awesome because it allows students to apply what they have learned and create some 3D figures and cut them apart to see the cross section. Students will also have an opportunity to review vocabulary in this lesson.


5 minutes
  • POD

As student enter the room, they will have a seat, take out their Problem of the Day (POD) sheet and begin to work on the question on the SMARTboard. The POD also allows students to use MP 3 continually based on the discussions we have about the problem each day. Using a scale of 1 to 10 describe how comfortable you are with explaining the difference between the cross sections of a rectangular prism cut parallel to the base and cut perpendicular to the base. Identify where you need help.

  • Learning Target

The target for the day is also on the SMARTboard each day when students enter the room.  The target for today’s lesson is for students to describe the polygons formed when 3D figures are cross sectioned both parallel and perpendicular to the base.



25 minutes

Using the Net Works sheet and several sheets of grid paper, have students create as many nets as possible for their figure.  As they are working, have students focus on the cross sections made or that can be potentially made on each net. Students need to be able to see the different polygons that can be made. Ask students to prove that their nets are accurate. They can give an oral or written explanation. If they still need to cut the net out and fold it to determine if it is accurate, follow up with questions about how the net needs to change to work. Put students into groups and have them create a poster with a different net for each figure and the polygon that would represent the cross section of the figure (MP2). Groups will represent their findings to the class. They should attach the original net to the poster. Groups should be able to explain why some nets work and others do not.


5 minutes

Have students watch the video, 3D Shapes: Names, Nets, and Cross sections to review the material. 

When students finish the video, have them respond to the exit ticket prompt: Is there a difference between the polygon that results when a right rectangular prism is cut parallel to the base and a right rectangular pyramid that is cut parallel to the base? If so, describe the difference. If not, explain the similarity.