Bringing together the young artists and the young organizers in your class, this instructional activity takes that popular topic of tessellations and gives it algebraic roots. After covering a few basic properties and definitions, learners attack the task of determining just which regular polygons actually can tessellate. Spiraling in algebraic concepts of solving inequalities and interpreting the results really drives home those links between geometry and algebra. A novel twist to add to your standard tessellating a plane repertoire.