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

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

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

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

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 this sports car?

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

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

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 the lobster, yacht and cyclist?

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 the chairs?

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

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 Little Fung at the table?

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?

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 these rabbits?

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 goat and giraffe?

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?

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

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 these convex shapes?

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 Wai Ping, Wah Ming and Chi Wing?

Can you logically construct these silhouettes using the tangram pieces?

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

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

Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.

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

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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?

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

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

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

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

Can you make the birds from the egg tangram?

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 ...

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

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?

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

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

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!