Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

How many different shapes can you make by putting four right- angled isosceles triangles together?

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?

In the diagram the radius length is 10 units, OP is 8 units and OQ is 6 units. If the distance PQ is 5 units what is the distance P'Q' ?

In the diagram the point P' can move to different places along the dotted line. Each position P' takes will fix a corresponding position for P. If P' moves along a straight line what does P do ?

In the diagram the point P can move to different places around the dotted circle. Each position P takes will fix a corresponding position for P'. As P moves around on that circle what will P' do?

Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?

Why are there only a few lattice points on a hyperbola and infinitely many on a parabola?

Find a quadratic formula which generalises Pick's Theorem.

Children from Herman First School found lots of ways to sort the houses, but perhaps there are more?

There are an infinite number of ways in which Mr McGregor can ensure that all his gardens have the same number of plants.

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.

An introduction to groups using transformations, following on from the October 2006 Stage 3 problems.