Exploring the algebraic properties and concepts that is the framework behind the idea of Pythagorean triples and quadruples is a difficult and complex topic, especially for high school algebra students. Which, as a future high school math teacher, is my targeted audience. As some students are visual learners, there is a visual method to finding Pythagorean triples and quadruples easily, where students are able to give as many integer solutions to these well-known equations in a colorful way. We will explore the visual method to finding multiple solutions to the common equations for triples and quadruples and from this creating an algebraic representation of this visual method. We will then look at a technique that produces solutions to any equation in which a perfect square is set equal to the sum of a specified number of perfect squares. Most of my research came from the article Visualizing Pythagorean Triples and Beyond by David A. Booze, J. Kevin Colligan, Dan Kalman, Virginia Stallings and Jeffrey Wanko from the December 2010/January 2011 issue of The Mathematics Teacher. I look forward to showing you this method which I actually find kind of fun! See you Wednesday, Lizzie