Visualising and representing

Choose any three by three square of dates on a calendar page...

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Reasoning about the number of matches needed to build squares that share their sides.

Make a cube out of straws and have a go at this practical challenge.