What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

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

How much do you have to turn these dials by in order to unlock the safes?

Can you describe the journey to each of the six places on these maps? How would you turn at each junction?

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

This problem shows that the external angles of an irregular hexagon add to a circle.

This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.