This problem is intended to get children to look really hard at something they will see many times in the next few months.

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?

Investigate these hexagons drawn from different sized equilateral triangles.

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

Use the isometric grid paper to find the different polygons.

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

Can you fill in the empty boxes in the grid with the right shape and colour?

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.

Look at the mathematics that is all around us - this circular window is a wonderful example.

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

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?

Can you reproduce the Yin Yang symbol using a pair of compasses?

Make an estimate of how many light fittings you can see. Was your estimate a good one? How can you decide?

How could you find out the area of a circle? Take a look at these ways.

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

What shape and size of drinks mat is best for flipping and catching?

Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

This LOGO challenge starts by looking at 10-sided polygons then generalises the findings to any polygon, putting particular emphasis on external angles

This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.

Can you use LOGO to create this star pattern made from squares. Only basic LOGO knowledge needed.

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

This article for pupils gives some examples of how circles have featured in people's lives for centuries.

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?

Read all about the number pi and the mathematicians who have tried to find out its value as accurately as possible.

An environment that enables you to investigate tessellations of regular polygons