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 jigsaw where pieces only go together if the fractions are equivalent.

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

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

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 fit the tangram pieces into the outlines of these clocks?

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 telephone?

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 Little Fung at the table?

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

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

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 goat and giraffe?

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?

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

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 this junk?

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 shape. How would you describe it?

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

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

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

What shape is made when you fold using this crease pattern? Can you make a ring design?

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

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

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

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

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

Our 2008 Advent Calendar has a 'Making Maths' activity for every 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!

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

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

A game to make and play based on the number line.

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

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

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?

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

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

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

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

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

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?