What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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 Little Ming?

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

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 rocket?

Can you sort these triangles into three different families and explain how you did it?

Can you fit the tangram pieces into the outline of this goat and giraffe?

Can you fit the tangram pieces into the outline of the telescope and microscope?

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

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

Sort the houses in my street into different groups. Can you do it in any other ways?

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 junk?

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

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

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?

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

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 the lobster, yacht and cyclist?

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

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

Take it in turns to make a triangle on the pegboard. Can you block your opponent?

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

Can you fit the tangram pieces into the outline of these rabbits?

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

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 shape. How would you describe it?

Can you fit the tangram pieces into the outline of these convex shapes?

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?

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 outline of Little Ming and Little Fung dancing?

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

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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 put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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

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

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?

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?

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

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

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

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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