Origami is not simple paper folding anymore, scientists are now using the mathematics behind origami to build folding telescope that could deploy in space and new folding devices to treat congestive heart failure. In this lesson students will learn about some of the practical uses for origami and then begin to use some of the mathematical principles themselves.

Students will use mathamatical folding as well

1) First print out the NewsHour Science Report: In Paper Folding, Art and Science Align. Have students individually read the article underlining anything that is surprising to them. Ask students to share what they found surprising and write it on the board.

2) Now students will see some of the practical implcations of origami. Students will need a square piece of paper. It is not necessary to have official origami paper. Cutting standard 8.5 by 11 paper into a square works fine. Have the class fold a samurai hat from a single piece of square paper. Look here for instructions on how to fold this. Allow time for students to attempt the hat several times.

3) The overall shape of this hat is a triangle. The goal is to have students analyze the dimensions of this shape and how they relate to the original size of the unfolded paper square. Ask the class how large a piece of paper would be necessary to fold a hat that they could actually wear? Write all of the theories on the board. Ask the students how they came up with that number.

4) Have students color in the triangle which makes up the back side of the samurai hat then unfold the hat to examine the crease pattern.

5) The students should trace out all the crease lines used to make the hat with a black marker. Make sure they do this on the side of the paper that has the colored in part from the back of the hat. See figure 1 for what the unfolded and marked crease pattern should look like.

Figure 1: The Crease Pattern for the Samurai Hat

6) Now ask the students to find the dimension of this triangle given the dimensions of the entire paper. (You can either tell students the length of one side of the square piece of paper or have them measure the paper themselves.) For students who are comfortable with algebra, they could let s represent the length of the side of the square paper.

7) Have students guess how large the bottom of the hat (the hypotenuse of the colored triangle) would need to be to fit their own head. Write these answers on the board.

8) Ask the students to calculate how big the original piece of paper would need to be to make this size hat. Have them test their theories. If newspapers or other large sources of paper are available they can check their calculations and see if it does make a life size hat!

For a slightly more complicated fold and geometric analysis, have students fold a masu box. See here for example. Then have them calculate how the dimensions of the finished box relate to the dimensions of the original paper.