Tilings and Symmetry

This week we've been making tilings, also known as tessellations. A tiling is what you get when you lay a bunch of shapes edge-to-edge to cover a flat space. The shapes aren't allowed to overlap, and you aren't allowed to leave gaps.

I gave the kids stencils for squares and equilateral triangles whose sides were 1 inch long, and told them to either trace them onto paper to make a tiling, or cut out tiles from construction paper and glue them down to make a tiling. They could use the squares and triangles to make different shapes, like bigger triangles, or "house-shaped" pieces.

We got some very nice tilings, and also some nice pictures made of tiles that weren't tilings because they had overlapping tiles or gaps.

Today we used the tilings to talk about reflectional and rotational symmetry. Reflectional symmetry is when you can draw a line (called the "line of symmetry") through the middle of a picture and the two sides of the picture look the same. Rotational symmetry is when you can rotate the picture and it looks the same after rotation as it did before (for example, take a square and turn it one-quarter turn). We drew some lines of symmetry for squares and triangles, then looked at the types of symmetry in our tilings.

We also looked at pictures from this website, which has pictures of ancient tilings including ones that are Egyptian, Persian, Arabian, and Moresque. When we look at symmetries, all those tilings can be clumped into 17 groups. We talked about some of those groups and the funny names they have.