A game in which players take it in turns to choose a number. Can you block your opponent?

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

Use the tangram pieces to make our pictures, or to design some of your own!

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

A game to make and play based on the number line.

Factors and Multiples game for an adult and child. How can you make sure you win this game?

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

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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

In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .

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

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

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.

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

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?

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

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Can you make the birds from the egg tangram?

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

These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.

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

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

Exploring balance and centres of mass can be great fun. The resulting structures can seem impossible. Here are some images to encourage you to experiment with non-breakable objects of your own.

It might seem impossible but it is possible. How can you cut a playing card to make a hole big enough to walk through?

Make a mobius band and investigate its properties.

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

Make some celtic knot patterns using tiling techniques

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

Surprise your friends with this magic square trick.

Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.

Did you know mazes tell stories? Find out more about mazes and make one of your own.

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

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 Little Fung at the table?

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

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

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

You could use just coloured pencils and paper to create this design, but it will be more eye-catching if you can get hold of hammer, nails and string.

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 this junk?

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

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

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

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

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

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

Follow these instructions to make a three-piece and/or seven-piece tangram.

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

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