Origami is not simple paper folding anymore, scientists are using the mathematics behind origami to build a 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.

1) Hand 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) Ask students to brainstorm more uses for origami and folding in math and science. Ask the students how do math and origami relate?

3) Now test out the students understanding. Hand out several pieces of square paper to each student.

4) Ask your students to first fold the square to produce a 30◦-60◦-90◦ triangle inside it. Hint: you want your folds to make the hypotenuse twice as long as one of the sides. Keep trying!

5) Ask the students to write down their explanation of why it works. Have a few students read their explanations to the class.

6) Pair students up in teams of 2 or 3 and ask them to use what they did in Question 1 to fold an equilateral triangle inside a square. (Allow time for students to make many attempts, one solution is here.)

Follow-up: If the side length of your original square is 1, what is the length of a side of your equilateral triangle? Would it be possible to make the triangle’s side length bigger?