Write a Logo program, putting in variables, and see the effect when you change the variables.
Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
Learn about Pen Up and Pen Down in Logo
Turn through bigger angles and draw stars with Logo.
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.
What happens when a procedure calls itself?
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.
This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.
It might seem impossible but it is possible. How can you cut a playing card to make a hole big enough to walk through?
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.
How is it possible to predict the card?
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?
A game to make and play based on the number line.
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. . . .
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
Build a scaffold out of drinking-straws to support a cup of water
Make a spiral mobile.
This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.
Which of the following cubes can be made from these nets?
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.
Use the tangram pieces to make our pictures, or to design some 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?
A description of how to make the five Platonic solids out of paper.
Make a clinometer and use it to help you estimate the heights of tall objects.
Make some celtic knot patterns using tiling techniques
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.
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 an equilateral triangle by folding paper and use it to make patterns of your own.
Can you describe what happens in this film?
This article for students gives some instructions about how to make some different braids.
How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?
Here is a chance to create some Celtic knots and explore the mathematics behind them.
What shape and size of drinks mat is best for flipping and catching?
What shape would fit your pens and pencils best? How can you make it?
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
Can Jo make a gym bag for her trainers from the piece of fabric she has?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
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?
Delight your friends with this cunning trick! Can you explain how it works?
The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.
Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
How can you make an angle of 60 degrees by folding a sheet of paper twice?
Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?