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

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

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.

Turn through bigger angles and draw stars with Logo.

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

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

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

Learn about Pen Up and Pen Down in Logo

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

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?

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

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

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

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.

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

Write a Logo program, putting in variables, and see the effect when you change the variables.

Surprise your friends with this magic square trick.

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

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. . . .

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.

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?

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

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.

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

What happens when a procedure calls itself?

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

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

Make some celtic knot patterns using tiling techniques

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

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

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?

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

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

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?

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

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

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

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

Can you cut up a square in the way shown and make the pieces into a triangle?

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

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

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?

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?