Position and Direction

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?

In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

Create a pattern on the small grid. How could you extend your pattern on the larger grid?

What patterns can you make with a set of dominoes?

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

Can you design your own version of the Olympic rings, using interlocking squares instead of circles?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?