## Introduction: Intersecting Planes - Origami

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.

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

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.

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.

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.

You could also extend this later to include Concave Polyhedrons.

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 :-)

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****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 :-)

## 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.

## Step 2: Putting It Together

This is where an extra set of hands is really beneficial.

I will show this based on the colors

1) Have one student take a Orange Pyramid and hold it upside-down

2) Have the other student pick up the 2 Blue Pyramids

3) Put the 2 Blue Pyramids inside the Orange Pyramid facing each other.

4) Since the Blue is inside Orange, put the Green outside the Orange.

5) Put the Green inside the Blue.

6) Repeat this for the other side of the Green.

- Blue inside Orange

- Orange inside Green

- Green inside Blue

7) You should have one Orange left to cap off the origami. Feed the top Orange to match the bottom Orange.

I will show this based on the colors

**Steps:**1) Have one student take a Orange Pyramid and hold it upside-down

2) Have the other student pick up the 2 Blue Pyramids

3) Put the 2 Blue Pyramids inside the Orange Pyramid facing each other.

4) Since the Blue is inside Orange, put the Green outside the Orange.

5) Put the Green inside the Blue.

6) Repeat this for the other side of the Green.

- Blue inside Orange

- Orange inside Green

- Green inside Blue

7) You should have one Orange left to cap off the origami. Feed the top Orange to match the bottom Orange.

**Watch the video to see it in action.**