This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.
Build a scaffold out of drinking-straws to support a cup of water
This article for students gives some instructions about how to make some different braids.
Follow these instructions to make a three-piece and/or seven-piece tangram.
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?
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
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. . . .
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?
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
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?
Make an equilateral triangle by folding paper and use it to make patterns of your own.
Here is a chance to create some Celtic knots and explore the mathematics behind them.
Make a clinometer and use it to help you estimate the heights of tall objects.
Make a spiral mobile.
A game to make and play based on the number line.
Learn to write procedures and build them into Logo programs. Learn to use variables.
More Logo for beginners. Now learn more about the REPEAT command.
A description of how to make the five Platonic solids out of paper.
What happens when a procedure calls itself?
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?
How is it possible to predict the card?
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.
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
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.
Which of the following cubes can be made from these nets?
How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?
Turn through bigger angles and draw stars with Logo.
Learn about Pen Up and Pen Down in Logo
Write a Logo program, putting in variables, and see the effect when you change the variables.
This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.
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 is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.
Can you describe what happens in this film?
Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.
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?
Use the tangram pieces to make our pictures, or to design some of your own!
Surprise your friends with this magic square trick.
How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.
Make a mobius band and investigate its properties.
Did you know mazes tell stories? Find out more about mazes and make one of your own.
Make a ball from triangles!
How can you make a curve from straight strips of paper?
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.
Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?
What shape and size of drinks mat is best for flipping and catching?