Learn about Pen Up and Pen Down in Logo

You can use a clinometer to measure the height of tall things that you can't possibly reach to the top of, Make a clinometer and use it to help you estimate the heights of tall objects.

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

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

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

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

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?

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?

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

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

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

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

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

Surprise your friends with this magic square trick.

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.

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

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

Make a mobius band and investigate its properties.

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

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.

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.

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

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

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

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

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

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. . . .

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

What happens when a procedure calls itself?

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

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

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

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.

Can you each work out what shape you have part of on your card? What will the rest of it look like?

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

This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

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?

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?

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