Make some celtic knot patterns using tiling techniques

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

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

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

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

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

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

What happens when a procedure calls itself?

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. . . .

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

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?

Learn about Pen Up and Pen Down in Logo

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?

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

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

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

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

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

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.

Turn through bigger angles and draw stars with Logo.

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

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?

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

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

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

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

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

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

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

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

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

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

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

Make a mobius band and investigate its properties.

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

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

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

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

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

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

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.

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

How can you make an angle of 60 degrees by folding a sheet of paper twice?