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.

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

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

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

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 make the birds from the egg tangram?

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

These pictures show squares split into halves. Can you find other ways?

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

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

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

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 the child walking home from school?

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

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

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

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

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

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

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

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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

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

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

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 these rabbits?

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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

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

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

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 this shape. How would you describe it?

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

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?

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

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

An activity making various patterns with 2 x 1 rectangular tiles.

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

Explore the triangles that can be made with seven sticks of the same length.

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

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 Little Ming playing the board game?

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

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

Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?