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.

Turn through bigger angles and draw stars with Logo.

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

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

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

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

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

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

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.

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

What happens when a procedure calls itself?

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.

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

Surprise your friends with this magic square trick.

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

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

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

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 a mobius band and investigate its properties.

Make some celtic knot patterns using tiling techniques

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.

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

Learn about Pen Up and Pen Down in Logo

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

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

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

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?

Follow these instructions to make a five-pointed snowflake from a square of paper.

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

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.

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?

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.

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.

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

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

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

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?

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

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

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

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

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