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

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

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

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

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. . . .

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.

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

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

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

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?

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?

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

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

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

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

Learn about Pen Up and Pen Down in Logo

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

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

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.

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

Make a mobius band and investigate its properties.

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

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

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

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

What shape and size of drinks mat is best for flipping and catching?

Surprise your friends with this magic square trick.

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

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

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

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

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

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

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?

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

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

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

You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

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?

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?

How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.