If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

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?

The challenge for you is to make a string of six (or more!) graded cubes.

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

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

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

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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 this plaque design?

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

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

An activity making various patterns with 2 x 1 rectangular tiles.

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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 Little Ming?

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.

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.

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 Wai Ping, Wah Ming and Chi Wing?

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 these people?

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 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 these rabbits?

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.

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

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

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 Mai Ling and Chi Wing?

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?

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

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

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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 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 these convex shapes?

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.