Transformations of shapes is an important part of any Geometry class. It is essential to helping us visualize and learn the algebraic equations that students will work with in the future, and for understanding all of the visual representations of data that are becoming increasingly important in our lives. This project, inspired by Islamic tile art, aimed to help students learn the concepts of geometric transformations (translations, reflections, rotations), as well as foundational understandings of lines (parallel, perpendicular) and angles (acute, obtuse, right, straight). It also aimed to have them demonstrate their understanding in a way that supports student ownership.
Students were given minimum requirements: a set of parallel lines, 1 triangle, 1 semicircle, 1 quadrilateral, and a pair of intersecting lines. They were to draw these things on 1 tile (patty paper). The rest was up to them, they could add any lines, angles, shapes they wanted. When their tile was complete, they used geometric transformations to change their single tile into the large pattern design you see here by rotating, reflecting, translating their tile in different ways.
