Position and Direction

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

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

This ladybird is taking a walk round a triangle. Can you see how much she has turned when she gets back to where she started?

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?

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?

Can you cover the camel with these pieces?

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

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

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

How many possible symmetrical necklaces can you find? How do you know you've found them all?

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

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

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?