Move just three of the circles so that the triangle faces in the opposite direction.

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

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?

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?

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

Play this well-known game against the computer where each player is equally likely to choose scissors, paper or rock. Why not try the variations too?

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.

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

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

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

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

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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

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

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

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.

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

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

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. . . .

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?

You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?

An interactive activity for one to experiment with a tricky tessellation

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

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

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

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!

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?

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

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

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

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

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 the child walking home from school?

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.

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 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 outline of Little Fung at the table?

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

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

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?