These pattern blocks can be fit together in a number of arrangements such that they tessellate the plane. The angle measurement around any point is 360 degrees. Many interesting tessellations can be made from triangles and squares. For example, if you cut a shape out of one side of a square and translate that shape to the other side, you create a new polygon that will tessellate the plane. Similarly, if you cut a shape out of one side of a triangle and rotate the shape to the other side, you get a figure that tessellates the plane.
Tessellations have many uses for both mathematicians and scientists.
A chemist may study tessellations to experiment with how crystals and crystalline structures are formed in nature. You can do your own research to find out more about Penrose tiles. Introduce the concept of a tessellation and have studenst identify examples found in natureand in architecture and design. Discuss other types of optical illusions.