Origami is a good way to look at reflection and rotation symmetry. Here are four origami pieces that showcase symmetry.
1) “Frisbee/Magic Star”, from Action Origami. This is a really fun model that produces a great contrast between reflection and rotation symmetry – in “magic star” form, it has rotation symmetry but not reflection symmetry; in “Frisbee” form, it’s a regular octagon with 8 lines of symmetry. The model needs 8 pieces of paper; the individual pieces are very easy to fold; putting the pieces together is OK but needs a little attention to the orientation of the pieces.
2) “Throwing Star”, in Easy Origami. Another “windmill” design with rotation but not reflection symmetry. A little harder to fold and might result in kids throwing stars around the room, so beware!
3) “Curly Box”, in World’s Best Origami. This is a really nice design; it’s the hardest to fold but the result is worth it.
4) Untitled Hexagonal Flowery Thing – What’s really nice about this is that when the “petals” are closed it has rotation but not reflection symmetry, and with the petals open it has six lines of symmery.