# The Pythagorean Theorem

Conjecture

Proof

Probability

Applications

Summary

Summary

Summary

Lesson

Lesson

Files

Files

Files

#### Overview

Summary

In this unit, which is designed for a Math 1 class, students will explore the Pythagorean Theorem—its statement, converse, extensions, and applications.  In the first lesson, students use GSP to make a conjecture about the relationship between a2 + b2 and c2 in acute, obtuse, and right triangles.  In the second lesson, students work in groups to explore dynamic diagrams, then generate a proof of the Pythagorean Theorem.  In the third lesson, students perform simulations with Fathom to further investigate the conjectures they made about acute and obtuse triangles in the first lesson.  Finally, in the fourth lesson, students apply the Pythagorean Theorem in three ways: in coordinate geometry to develop the distance formula, in Excel to generate Pythagorean triples, and in GSP with shapes other than squares on a right triangle's three sides.

Throughout the unit, technlogy is used to give students a deeper understanding of the Pythagorean Theorem.  GSP gives students the opportunity to investigate the theorem in a dynamic environment, Fathom quickly creates large sets of data for analysis, and Excel allows students to easily generate Pythagorean triples.  In designing the unit's lessons, I initially had trouble incorporating technology other than GSP, as I considered this to be a largely geometry-centered unit.  However, as I developed the unit further, noting important applications and extensions of the theorem, it became clear that Fathom and Excel would also be useful.  By forcing myself to "think outside the box" and look for non-geometric applications of the Pythagorean Theorem, I not only incorporated more types of technology into the unit, but also made the unit as a whole more mathematically rich and better aligned with the Georgia Performance Standards.  Technology allowed me to create lessons that investigated the Pythagorean Theorem from both a geometric and a non-geometric standpoint, so students can see the connections among various branches of mathematics while learning more about the theorem.

Time Required

 Lesson Number of 50-min. periods Number of 90-min. blocks 1 1 ½ 2 2 1 (two halves) 3 1 to 2 ½ to 1 4 1 to 3 ½ to 1½ Total 5 to 8 2½ to 4

Continue to Lesson 1 - Summary