The Pythagorean Theorem states, for a right triangle with legs a and b and hypotenuse c, a^2 + b^2 = c^2.
The activity goes as follows:
Step 1: Begin with a square piece of paper.
Step 2: Fold it in half once and then once again to have a smaller square. Then fold it again to create a triangle.
In reference to her question at the end, "how do you know the hypotenuse "square" is mathematically a square?" We began working with a square piece of paper and to create the square with each side as the hypotenuse. Then, we had to fold the same amount of paper on each side, which resulted in the same length sides. Thus, we can conclude that the hypotenuse "square" is mathematically a square.
I was confused at first while attempting this activity, but I found it very useful and once I was able to get the folding down correct I received accurate results that made sense. I believe that this is a great way to have students see how the Pythagorean Theorem works without even realizing that it was a proof.