# Intersecting Planes - Origami

2 Steps
This is a great way for students to visualize intersecting planes in 3-D space.
It also very hands-on and does not require a lot of time.

Materials:
6 sheets of paper (3 different colors x 2 sheets each)

Prep:
I buy colorful reams of paper and take them to Kinkos (a copy shop) and have them cut off one end of each ream.
Turn the 8.5" x 11" paper into 8.5 "x 8.5" squares.
They usually charge a dollar or two per ream.

You could also do this yourself if you have a big paper cutter.  It just takes longer since you have to cut 4-10 sheets at a time.

Groups:
I usually pair up my students.  It makes the folding go quicker and it is much easier to put together if you have 4 hands working and holding pieces.

Objective:
My students are good at seeing Points and Lines and intersections in 2D.  But when I introduce Planes in 3D space, they have a hard time visualizing it in their head.  So I do this activity to give them a physical object that represents Intersecting Planes in 3D space.  It is important to have the 3 colors, as these represent the 3 different planes.  This is not a perfect example, but the kids really seem to get into it and they have a much better grasp on 3D space.

Extension:
You could also extend this later to include Concave Polyhedrons.

2 Parts:

Folding the Paper

Putting it Together

Credit:
I did not create this lesson.  I was taught it in a training seminar.  I do not remember the presenter or even the name of the seminar.  It was shared freely with me, and you should share it with others :-)
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## Step 1: Folding the Paper

Steps:
1) Fold the square in half each direction
2) Flip the paper over
3) Fold the square in half diagonally each direction
4) Form a pyramid with the paper
5) Repeat steps #1-4 for each square

Why this process:
There are simpler ways to fold the paper to get all the creases you need.  But, I fold them this way to make the paper naturally form the pyramid.

Common Error:
A common error of my students it to make a Diamond instead of the Pyramid.  To fix this, just flip the Diamond inside-out.

demonfox says: Feb 2, 2012. 12:22 PM
I used to love making these as a kid.
If you hold one loosely between your palms and blow on the tip it spins :)