Observing Symmetry

1. Have your students observe and analyze patterns in brickwork, pavements, wallpapers around the school building or at home.

2. Go on a "tessellation" walk. Tally which shapes tessellate and where. (hint: check out tile floors, ceiling tiles, radiator vents, window grills, roof tiles).

3. Use a kaleidoscope to make and observe patterns (used reflection).

4. Prepare a set of laminated grids through which to observe and analyze patterns.

5. Fold and cut paper to make patterns; notice how different folds may make different symmetries.

6. What kinds of symmetries and patterns can you find in the clothing you are wearing?

7. Using an overhead projector, arrange pennies so that the centers form a square grid; arrange them again with tighter packing so that the centers form a triangular grid. Have the students use the triangular grid to locate a rhomboid grid, and a hexagonal grid. Are there any other ways to tight pack the pennies? What are the implications of this for pattern-making?