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!

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

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

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

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

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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?

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

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

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

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

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

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

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

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

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

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

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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?

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

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

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

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

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

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?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

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

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 make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

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

Use the interactivity or play this dice game yourself. How could you make it fair?

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?

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?

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

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 outlines of the watering can and man in a boat?

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 Little Ming playing the board game?

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

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.