What happens when you try and fit the triomino pieces into these two grids?

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

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Our 2008 Advent Calendar has a 'Making Maths' activity for every 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?

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 candle and sundial?

Can you find all the different ways of lining up these Cuisenaire rods?

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 the rocket?

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 Mai Ling?

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 Wai Ping, Wah Ming and Chi Wing?

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

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

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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

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

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 brazier for roasting chestnuts?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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

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

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

How many different rhythms can you make by putting two drums on the wheel?

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

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

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

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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?

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 these rabbits?

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