Definitions of tessellation can be found in any Geometry book and if you teach like most teachers, you would most likely write it on the board and go through the exercises in the section. In fact, Glencoe (2001) defines a tessellation as a plane with repeating figures so there is no overlapping or empty spaces. Given the new reform movements in mathematics and NCTM standards students need to be engaged in mathematics which requires exploration, communication, reasoning, connections, proof, and representation (NCTM, 2000).
So, the following is a suggestion which uses reform- based pedagogy to teach tessellations.
First: Bring in samples such as woven rugs, quilts, flooring, or even pottery which represent tessellations naturally. In my eight years of teaching, if there is a separate section for tessellations, it follows the sections on polygons and regular polygons, as well as transformations. So the students experience with these sections can be used to build there knowledge about tessellations.
Once you have given students examples of tessellations using real-life applications and those that students may suggest, get a working definition. Use their definition , probing, possibly counter-examples to help student arrive at the correct definition. Then I would suggest the activity below.
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