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

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 outlines of these clocks?

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

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 the child walking home from school?

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

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

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

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 Ming playing the board game?

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

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

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 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 this plaque design?

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

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

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

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

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 candle and sundial?

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

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 telephone?

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

Can you logically construct these silhouettes using the tangram pieces?

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

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?

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

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

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

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 outline of Granma T?

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

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

Reasoning about the number of matches needed to build squares that share their sides.

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

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?

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

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

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

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

Make a flower design using the same shape made out of different sizes of paper.

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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