Visualising and representing

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

How efficiently can you pack together disks?

Use functions to create minimalist versions of works of art.

When dice land edge-up, we usually roll again. But what if we didn't...?

Move just three of the circles so that the triangle faces in the opposite direction.

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?