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.

A game in which players take it in turns to choose a number. Can you block your opponent?

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

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?

Factors and Multiples game for an adult and child. How can you make sure you win this game?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

Can you cut up a square in the way shown and make the pieces into a triangle?

Can you fit the tangram pieces into the outline of the rocket?

Can you fit the tangram pieces into the outline of the telescope and microscope?

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

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

Can you fit the tangram pieces into the outline of these rabbits?

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

Can you split each of the shapes below in half so that the two parts are exactly the same?

Can you put these shapes in order of size? Start with the smallest.

Make a cube out of straws and have a go at this practical challenge.

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Can you make the birds from the egg tangram?

Here's a simple way to make a Tangram without any measuring or ruling lines.

Exploring and predicting folding, cutting and punching holes and making spirals.

Can you fit the tangram pieces into the outline of Mai Ling?

Can you fit the tangram pieces into the outline of this plaque design?

Can you fit the tangram pieces into the outline of Little Ming?

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

Here is a version of the game 'Happy Families' for you to make and play.

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 Little Fung at the table?

Can you fit the tangram pieces into the outline of these convex shapes?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

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 telephone?

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 outline of this junk?

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

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

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

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

Can you fit the tangram pieces into the outlines of the candle and sundial?

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?

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

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 the child walking home from school?