With paper and pencil:
- Construct grids using compass and straight edge (ruler). Using colored pencils, make a design and repeat it within the grid.
- Using dot paper or graph paper, encourage students to make a design and then repeat it using only one basic symmetry. Then choose another of the four basic symmetry operations, and repeat it using the same design. Does it make a different pattern? Try this exercise using each of the four basic symmetries.
- Using graph paper and colored pencils, ask students to design their own carpets, taking into account symmetry, asymmetry, and symmetry-breaking.
With other classroom tools:
- Try out a computer program for making tessellations.
- We like to use TesselMania!.
- ... or follow Suzanne Alejandre's fantastic Tessellation Tutorials using Claris Works, HyperCard, HyperStudio, or LogoWriter.
- Experiment with rug patterns using Geometer's Sketchpad.
- Make patterns with colored rubberbands on geoboards (peg boards).
- Make patterns using pattern attribute blocks of different colors. Try the same exercise with a mirror for reflection.
- Using three mirrors at right angles to one another, try the previous exercise again.
- Use cardboard or plastic cut-out shapes to make tessellations. Try alternating two colors and see what happens.