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

Learn about Pen Up and Pen Down in Logo

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

Turn through bigger angles and draw stars with Logo.

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

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

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

Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.

More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.

What happens when a procedure calls itself?

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

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?

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.

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

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 some celtic knot patterns using tiling techniques

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. . . .

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

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?

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

Here is a chance to create some Celtic knots and explore the mathematics behind them.

Make a clinometer and use it to help you estimate the heights of tall objects.

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

Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.

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

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

Build a scaffold out of drinking-straws to support a cup of water

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

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

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

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

As part of Liverpool08 European Capital of Culture there were a huge number of events and displays. One of the art installations was called "Turning the Place Over". Can you find our how it works?

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.

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.

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

Make a mobius band and investigate its properties.

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

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

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

I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour?

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?

Design and construct a prototype intercooler which will satisfy agreed quality control constraints.

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

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.