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
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
What shape would fit your pens and pencils best? How can you make it?
This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.
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.
Can Jo make a gym bag for her trainers from the piece of fabric she has?
This article for students gives some instructions about how to make some different braids.
This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.
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?
Make a mobius band and investigate its properties.
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?
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?
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.
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.
Make a spiral mobile.
Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.
Make a clinometer and use it to help you estimate the heights of tall objects.
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.
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. . . .
Use the tangram pieces to make our pictures, or to design some of your own!
Follow these instructions to make a three-piece and/or seven-piece tangram.
More Logo for beginners. Now learn more about the REPEAT command.
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.
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?
A description of how to make the five Platonic solids out of paper.
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
Write a Logo program, putting in variables, and see the effect when you change the variables.
Learn about Pen Up and Pen Down in Logo
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.
How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?
Make a ball from triangles!
Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?
Turn through bigger angles and draw stars with Logo.
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
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.
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?
Here is a chance to create some Celtic knots and explore the mathematics behind them.
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.
Which of the following cubes can be made from these nets?
How can you make a curve from straight strips of paper?
A game in which players take it in turns to choose a number. Can you block your opponent?