Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

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

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

Can you make the birds from the egg tangram?

Here is a version of the game 'Happy Families' for you to make and play.

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

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 telephone?

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

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

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?

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

Can you cut up a square in the way shown and make the pieces into a triangle?

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

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

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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

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

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

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 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 chairs?

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

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

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 workmen?

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 brazier for roasting chestnuts?

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 Little Ming playing the board game?

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

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

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?

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 the rocket?

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

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

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

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

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

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

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

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?

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?

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

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