Exploring balance and centres of mass can be great fun. The resulting structures can seem impossible. Here are some images to encourage you to experiment with non-breakable objects of your own.

Make some celtic knot patterns using tiling techniques

This article for students gives some instructions about how to make some different braids.

Follow these instructions to make a three-piece and/or seven-piece tangram.

More Logo for beginners. Now learn more about the REPEAT command.

This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.

You could use just coloured pencils and paper to create this design, but it will be more eye-catching if you can get hold of hammer, nails and string.

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

Make an equilateral triangle by folding paper and use it to make patterns of your own.

It might seem impossible but it is possible. How can you cut a playing card to make a hole big enough to walk through?

Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.

Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.

How can you make a curve from straight strips of paper?

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?

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

Which of the following cubes can be made from these nets?

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

Make a mobius band and investigate its properties.

Surprise your friends with this magic square trick.

A description of how to make the five Platonic solids out of paper.

Galileo, a famous inventor who lived about 400 years ago, came up with an idea similar to this for making a time measuring instrument. Can you turn your pendulum into an accurate minute timer?

Did you know mazes tell stories? Find out more about mazes and make one of your own.

This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.

In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .

Learn about Pen Up and Pen Down in Logo

Can you each work out the number on your card? What do you notice? How could you sort the cards?

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

A game in which players take it in turns to choose a number. Can you block your opponent?

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

Follow these instructions to make a five-pointed snowflake from a square of paper.

Here are some ideas to try in the classroom for using counters to investigate number patterns.

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?

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

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?

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

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

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

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

How can you put five cereal packets together to make different shapes if you must put them face-to-face?