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

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

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

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

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

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

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

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 a mobius band and investigate its properties.

Make some celtic knot patterns using tiling techniques

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Surprise your friends with this magic square trick.

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

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. . . .

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?

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

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.

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

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

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

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

You can use a clinometer to measure the height of tall things that you can't possibly reach to the top of, Make a clinometer and use it to help you estimate the heights of tall objects.

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

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?

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?

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

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

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

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

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

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

Learn about Pen Up and Pen Down in Logo

Turn through bigger angles and draw stars with Logo.

This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.

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

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.

I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?

Write a Logo program, putting in variables, and see the effect when you change the variables.

Learn to write procedures and build them into Logo programs. Learn to use variables.

Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.

What happens when a procedure calls itself?

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

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