Learn about Pen Up and Pen Down in Logo

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

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

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

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

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.

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

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.

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?

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

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

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.

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

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

Make a mobius band and investigate its properties.

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

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. . . .

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

Make some celtic knot patterns using tiling techniques

This package contains hands-on code breaking activities based on the Enigma Schools Project. Suitable for Stages 2, 3 and 4.

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

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

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

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

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

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.

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.

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?

What happens when a procedure calls itself?

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

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

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?

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

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

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?

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?

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

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

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