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

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

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?

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!

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

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

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

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

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

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 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 outlines of the chairs?

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

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?

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

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

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

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.

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

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

An interactive activity for one to experiment with a tricky tessellation

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

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?

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

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.

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

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. . . .

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.

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

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?

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

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?

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 Ming playing the board game?

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

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 workmen?

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 outlines of these people?