Grade Levels: 3 - 6INTRODUCTION
The connections between art and math are strong and frequent, yet few students are aware of them. This geometry lesson is integrated with history and art to engage even the most math resistant of your students and to enlighten everyone about M. C. Escher's work in tessellations.
SUGGESTED TIME ALLOWANCE
1. Introduce key vocabulary words: tessellation, polygon, angle, plane, vertex and adjacent. Ask students to tell you what they know about the word tessellation. Discuss the three basic attributes of tessellations:
First, they are repeated patterns. Ask students to find examples of repeated patterns in the room. Generate a list of the words one could use to describe these patterns. Tell students that while those are repeated patterns, only some are tessellations because tessellations are a very specific kind of pattern. Second, tessellations do not have gaps or overlaps. If students have pointed to a pattern in the room that has a gap or an overlap in it, point out that it does not fit the definition of a tessellation. Third, tessellations can continue on a plane forever. Define plane (use a concrete example in the room) and show students how the pattern could continue on that plane if it were to go on beyond the confines of the building (e.g., it could continue as a pattern on the ceiling without any gaps or overlaps even if the ceiling were to continue forever, far beyond the walls of your school).
2. Provide students with the Shapes worksheet within the Tessellations packet, which has a copy of a square, a rectangle,a rhombus, and a hexagon on it. (These were chosen because each tessellates.) Using the Student Directions worksheet, demonstrate how to transform a shape into something that will also tessellate.
Enter your class in one of several online tessellation contests.
Look at American folk art that uses tessellations (such as quilts).
Tessellations were popularized by M. C. Escher.
Research M. C. Escher, Penrose, and other "Recreational mathematicians."