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 semi-pure 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 non-regular polygon and "Escher-like" tessellations.

Mathematics: Students will use translations, rotations, and reflections to create tessellations. Moreover, the students will investigate the following theorems:

• Equilateral triangles, squares, and hexagons are the only three regular polygons that create pure tessellations.
• There are eight different semi-regular tessellations.
• Any scalene triangle or quadrilateral will create a pure tessellation.

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 semi-pure regular tessellations described in the activity.