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

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.

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

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

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

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

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

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

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. . . .

An interactive activity for one to experiment with a tricky tessellation

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 chairs?

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

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?

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

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.

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

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

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?

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

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!

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 outlines of these people?

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?

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

How many different triangles can you make on a circular pegboard that has nine pegs?

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 Little Fung at the table?

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

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

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

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

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

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?

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

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?

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?

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

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?