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.

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

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 outlines of these clocks?

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

An interactive activity for one to experiment with a tricky tessellation

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

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

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. . . .

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 chairs?

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.

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?

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 lobster, yacht and cyclist?

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

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

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

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!

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?

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

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

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.

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 Little Fung at the table?

Use the interactivity or play this dice game yourself. How could you make it fair?

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

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

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

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

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

Stop the Clock game for an adult and child. How can you make sure you always win this game?

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

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

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

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?

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?

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

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.

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