Here is a solitaire type environment for you to experiment with. Which targets can you reach?

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

How can you make an angle of 60 degrees by folding a sheet of paper twice?

Can you fit the tangram pieces into the outline of these convex shapes?

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?

Can you fit the tangram pieces into the outline of Mai Ling?

Can you fit the tangram pieces into the outline of this plaque design?

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

Can you fit the tangram pieces into the outline of this sports car?

What is the greatest number of squares you can make by overlapping three squares?

Can you fit the tangram pieces into the outlines of the chairs?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you fit the tangram pieces into the outline of the child walking home from school?

Can you fit the tangram pieces into the outline of Little Ming?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Can you fit the tangram pieces into the outlines of the candle and sundial?

Can you fit the tangram pieces into the outline of the rocket?

Can you fit the tangram pieces into the outlines of these clocks?

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?

Can you fit the tangram pieces into the outline of this goat and giraffe?

Can you fit the tangram pieces into the outline of this telephone?

Can you fit the tangram pieces into the outline of Granma T?

Can you fit the tangram pieces into the outlines of the workmen?

How many models can you find which obey these rules?

Can you fit the tangram pieces into the outline of this junk?

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

Can you fit the tangram pieces into the outline of these rabbits?

Can you fit the tangram pieces into the outline of the telescope and microscope?

Can you fit the tangram pieces into the outline of Little Fung at the table?

Can you fit the tangram pieces into the outlines of these people?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

Delight your friends with this cunning trick! Can you explain how it works?

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

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

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Here's a simple way to make a Tangram without any measuring or ruling lines.

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

Can you make the birds from the egg tangram?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.