Visualising and representing

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes and the small cubes that would fit inside each one.

What would happen if we lost all the nines in our number system?