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Exploring
and Creating Tessellations


 
This activity has students explore and construct several different types of tessellations. The first part of the activity uses only regular polygons to create pure and semipure tessellations; therefore, you will need scripts for the constructions of an equilateral triangle, a square, and a regular hexagon. The second part extends the notion of tessellations to create nonregular polygon and "Escherlike" tessellations. Mathematics: Students will use translations, rotations, and reflections to create tessellations. Moreover, the students will investigate the following theorems:
Mathematical Thinking: In this activity, students will be asked to conjecture about the construction of possible tessellations. Technology: This activity uses several Sketchpad commands and features such as: Script, Translate, Rotate, Reflect, Mark Center, Mark Mirror, Mark Vector, and Mark Angle. The following sketches illustrate the three regular polygons that tessellate the plane, and five of the eight semipure regular tessellations described in the activity. 

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