Use the clues about the symmetrical properties of these letters to place them on the grid.

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

Use the blue spot to help you move the yellow spot from one star to the other. How are the trails of the blue and yellow spots related?

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

See the effects of some combined transformations on a shape. Can you describe what the individual transformations do?

Does changing the order of transformations always/sometimes/never produce the same transformation?

How many different transformations can you find made up from combinations of R, S and their inverses? Can you be sure that you have found them all?

This article for students and teachers tries to think about how long would it take someone to create every possible shuffle of a pack of cards, with surprising results.