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

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?

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

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

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

Can you fit the tangram pieces into the outline of the child walking home from school?

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

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

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

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?

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 Little Fung at the table?

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

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

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

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 Mai Ling?

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

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

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

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

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 outline of this goat and giraffe?

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

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

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

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

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

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 the candle and sundial?

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

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 outline of this sports car?

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.

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

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

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

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Can you make five differently sized squares from the tangram pieces?

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

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

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

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?