Learn about Pen Up and Pen Down in Logo

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

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?

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

Turn through bigger angles and draw stars with Logo.

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.

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

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?

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

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

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

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

Surprise your friends with this magic square trick.

Make a mobius band and investigate its properties.

Make some celtic knot patterns using tiling techniques

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

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

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

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.

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. . . .

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

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

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

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?

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

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

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?

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

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?

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

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

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

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

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

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

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.

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

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

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?

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