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

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

Learn about Pen Up and Pen Down in Logo

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

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

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

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.

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

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

What happens when a procedure calls itself?

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

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?

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

Make a mobius band and investigate its properties.

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

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

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

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. . . .

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

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.

Turn through bigger angles and draw stars with Logo.

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?

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

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.

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.

Surprise your friends with this magic square trick.

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

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.

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

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

Make some celtic knot patterns using tiling techniques

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

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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?

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

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

Here are some ideas to try in the classroom for using counters to investigate number patterns.

Here's a simple way to make a Tangram without any measuring or ruling lines.

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

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