What shape and size of drinks mat is best for flipping and catching?

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

What shape would fit your pens and pencils best? How can you make it?

Can Jo make a gym bag for her trainers from the piece of fabric she has?

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

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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

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

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.

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

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

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

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. . . .

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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

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

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

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

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.

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

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.

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 some celtic knot patterns using tiling techniques

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

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

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

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

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?

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

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

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?

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

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.

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

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

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?

Turn through bigger angles and draw stars with Logo.

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

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

Learn about Pen Up and Pen Down in Logo

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?

What happens when a procedure calls itself?

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

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

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.

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