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.

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

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?

An interactive activity for one to experiment with a tricky tessellation

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

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?

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

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. . . .

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?

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.

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

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

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

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

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

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

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?

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

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?

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.

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

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

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 outline of Little Ming playing the board game?

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

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

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 fit the tangram pieces into the outlines of these people?

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

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

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

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 this shape. How would you describe it?

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!

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

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 outline of this telephone?