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

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

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

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

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

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

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 this plaque design?

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

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

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 goat and giraffe?

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

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 use the interactive to complete the tangrams in the shape of butterflies?

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.

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 candle and sundial?

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

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

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

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 this telephone?

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

Can you logically construct these silhouettes using the tangram pieces?

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 these convex shapes?

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

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?

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

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?

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

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

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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 the child walking home from school?

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

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

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 outlines of Mai Ling and Chi Wing?

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 the workmen?

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

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