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

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

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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

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?

Sort the houses in my street into different groups. Can you do it in any other ways?

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?

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.

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.

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 outlines of these people?

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

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?

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

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

An interactive activity for one to experiment with a tricky tessellation

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

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?

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!

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

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

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

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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

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?

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

Make one big triangle so the numbers that touch on the small triangles add to 10.

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

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

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

Twenty four games for the run-up to Christmas.

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

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

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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

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

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

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

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

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