Pythagorean Theorem
The goal of my presentation was to create a sketch that explores the Pythagorean Theorem. Specifically, I wanted to look at what happens to each square when the sides of the triangle changes. The basic sketch works by first drawing a triangle using a line segment and a semicircle. Then, using perpendicular lines, create the squares from each side of the triangle.
The main way that this drawing is different from a paper and pencil drawing is that it enables be to show how the theorem works. That is, I can prove that the sides of the triangle squared equals the side of the hypotenuse squared, for any length of sides a and b.
Based on math practice #5, I used GeoGebra tools to create three squares with side lengths equal to each of the three sides of the blue right triangle. I also used math practice #1, make sense of problems and persevere in solving them, because the sketch allows students to play with the drawing and prove to themselves that the theorem works. They can physically see how the theorem works, and therefore, they can learn from it. I also used math practice #8, look for and express regularity in repeated reasoning, because it proves the Pythagorean theorem, which students can use to solve other problems in which the theorem can be used.
The thing I best liked about my project is that it shows that the Pythagorean theorem works with any right triangle, and it allows students to physically see why the theorem works and how to use it for other mathematical problems.