Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

What is the least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?

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?

Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

How can we decide what the 'best' solution to this problem is? Take a look at these and make up your own mind!

This article is based on some of the ideas that emerged during the production of a book which takes visualising as its focus. We began to identify problems which helped us to take a structured view of the purposes and skills of visualising.

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.