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?

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?

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?

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

Delight your friends with this cunning trick! Can you explain how it works?

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?

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

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?

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.

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?

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

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

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

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

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.

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

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?

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

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

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

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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

Turn through bigger angles and draw stars with Logo.

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.

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

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. . . .

Make some celtic knot patterns using tiling techniques

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

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

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

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

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

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

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?

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

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

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

What shape would fit your pens and pencils best? How can you make it?

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

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

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.

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

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

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?

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

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