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?

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?

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

How efficiently can various flat shapes be fitted together?

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

Use this interactivity to sort out the steps of the proof of the formula for the sum of an arithmetic series. The 'thermometer' will tell you how you are doing

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

Make some celtic knot patterns using tiling techniques

Can Jo make a gym bag for her trainers from the piece of fabric she has?

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

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

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

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

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

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.

Learn about Pen Up and Pen Down in Logo

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

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

Try ringing hand bells for yourself with interactive versions of Diagram 2 (Plain Hunt Minimus) and Diagram 3 described in the article 'Ding Dong Bell'.

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

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

What happens when a procedure calls itself?

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

Turn through bigger angles and draw stars with Logo.

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

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

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

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