Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.
Make an equilateral triangle by folding paper and use it to make patterns of your own.
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
Turn through bigger angles and draw stars with Logo.
Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.
Make a clinometer and use it to help you estimate the heights of tall objects.
How is it possible to predict the card?
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?
What happens when a procedure calls itself?
Make a spiral mobile.
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.
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. . . .
More Logo for beginners. Now learn more about the REPEAT command.
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?
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.
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.
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?
This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.
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.
Which of the following cubes can be made from these nets?
A game to make and play based on the number line.
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?
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.
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.
Can you describe what happens in this film?
A jigsaw where pieces only go together if the fractions are equivalent.
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
A description of how to make the five Platonic solids out of paper.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Follow these instructions to make a three-piece and/or seven-piece tangram.
I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?
Build a scaffold out of drinking-straws to support a cup of water
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?
I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Did you know mazes tell stories? Find out more about mazes and make one of your own.
Surprise your friends with this magic square trick.
Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?
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.
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?
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.