Clarifying Activity Students use pattern blocks to investigate tessellations of the plane. Once the students feel confident they have found all the possible tilings, they should justify why these shapes are, in fact, the only regular polygons which tile the plane. Students investigate non-regular polygons that will tile the plane. The student uses properties of transformations and their compositions to make connections between mathematics and the real world in applications such as tessellations or fractals. Clarifying Activity Based on the exploration of regular polygons that tile the plane in the Clarifying Activity in c.1, students look for examples of regular tessellations in the world around them and discuss the strengths or benefits of various tessellations.
Triangles are structurally rigid and are often used as supports.
Bee's honeycombs are tessellations of hexagons. Since these are used to store honey, the hexagon provides a large area while still having the efficiency of a regular tessellation. Clarifying Activity Students investigate a miniature golf problem like the one below. Below is a diagram of a miniature golf hole as seen from above. Find a path that will get the ball in one shot from the tee to the hole.