
The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

A triangle ABC resting on a horizontal line is "rolled" along the line. Describe the paths of each of the vertices and the relationships between them and the original triangle.

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. Can you predict how many of the faces of the smaller cubes will remain red?

Can you explain what is happening and account for the values being displayed?