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?

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

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

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

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 this shape. How would you describe it?

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 the chairs?

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 the rocket?

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 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 these rabbits?

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

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

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

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

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

Can you visualise what shape this piece of paper will make when it is folded?

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

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

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

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

Can you logically construct these silhouettes using the tangram pieces?

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

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?

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?

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

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

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

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?

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

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

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

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

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 these convex shapes?

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

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

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?

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

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

Use the tangram pieces to make our pictures, or to design some of your own!