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

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

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?

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

Learn about Pen Up and Pen Down in Logo

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

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

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

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

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

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.

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

Turn through bigger angles and draw stars with Logo.

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.

What happens when a procedure calls itself?

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

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

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?

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

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.

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

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

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

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

Use the tangram pieces to make our pictures, or to design some 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.

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?

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?

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

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?

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

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?

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

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?

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

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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

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

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

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?

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

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

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

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

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

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?