A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

Use the blue spot to help you move the yellow spot from one star to the other. How are the trails of the blue and yellow spots related?

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 Mai Ling?

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

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 outlines of the candle and sundial?

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 junk?

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

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 the child walking home from school?

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

These interactive dominoes can be dragged around the screen.

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

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

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 Little Fung at the table?

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 Little Ming?

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.

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

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

Work out the fractions to match the cards with the same amount of money.

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

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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?

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?

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

Can you create a story that would describe the movement of the man shown on these graphs? Use the interactivity to try out our ideas.

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?

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

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?

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 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?

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

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

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