The Pythagorean Theorem is one of the foundational studies in the secondary years. It is one of the mathematical formulas that many people remember from their mathematical journey in school. Even the Scarecrow in The Wizard of Oz took a stab at the Pythagorean Theorem when he got his diploma. The Pythagorean Theorem, once introduced in middle school, serves as the foundation for the distance formula, the special right triangle ratios, as well as the unit circle in Trigonometry.
Typically students are simply given the formula and told to use it. In this study, students investigate and discover the relationships for themselves. A different approach to a proof is offered. It is a dissection proof. Other famous historical proofs are referenced as well, even one from a Unites States President! In this 30+ page packet (plus powerpoint) there are two different literacy connections, opportunities for writing, two different investigations for discovery of the Pythagorean Theorem, a dissection proof, activities for vocabulary, a graphic organizer for students to organize their findings in, several tasks that allow students to think deeper about ideas, and three application probes. Directions for performing the dissection proof on Geometer’s Sketchpad® is included but can be easily adapted for the TI-Nspire®. Centimeter paper, engineering graph paper, and color masters for the dissection proof are also included. A powerpoint for classroom use during the study of this topic is also included. This collection of activities and investigations can be used from middle school through review for Advanced Algebra and Trig.