Explore the lattice and vector structure of this crystal.

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

Can you describe this route to infinity? Where will the arrows take you next?

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

In a three-dimensional version of noughts and crosses, how many winning lines can you make?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?