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.

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?

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 Mai Ling and Chi Wing?

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 outline of Little Ming?

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 outlines of the workmen?

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 outline of the rocket?

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

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

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

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 these rabbits?

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

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

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

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

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

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

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 plaque design?

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?

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?

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

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

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?

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 Little Ming playing the board game?

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

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?

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

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

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

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

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

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?

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

Can you fit the tangram pieces into the outline of Little Fung at the table?

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?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?