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

Exchange the positions of the two sets of counters in the least possible number of moves

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

An interactive activity for one to experiment with a tricky tessellation

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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 the chairs?

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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

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

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

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

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 these clocks?

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

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

Stop the Clock game for an adult and child. How can you make sure you always win this game?

Train game for an adult and child. Who will be the first to make the train?

Can you work out what is wrong with the cogs on a UK 2 pound coin?

Complete the squares - but be warned some are trickier than they look!

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 outlines of these people?

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

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

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

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

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

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

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

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

Can you put these shapes in order of size? Start with the smallest.

What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

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