Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.
Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
A description of how to make the five Platonic solids out of paper.
Turn through bigger angles and draw stars with Logo.
This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.
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?
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.
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.
This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.
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
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?
This article for pupils gives an introduction to Celtic knotwork
patterns and a feel for how you can draw them.
Here is a chance to create some Celtic knots and explore the mathematics behind them.
What happens when a procedure calls itself?
More Logo for beginners. Now learn more about the REPEAT command.
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?
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
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?
Can you describe what happens in this film?
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.
This article for students gives some instructions about how to make some different braids.
Make some celtic knot patterns using tiling techniques
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
A game to make and play based on the number line.
Make a spiral mobile.
How can you make an angle of 60 degrees by folding a sheet of paper
Make a clinometer and use it to help you estimate the heights of
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. . . .
It might seem impossible but it is possible. How can you cut a
playing card to make a hole big enough to walk through?
What shape and size of drinks mat is best for flipping and catching?
This package contains hands-on code breaking activities based on
the Enigma Schools Project. Suitable for Stages 2, 3 and 4.
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
Use the tangram pieces to make our pictures, or to design some of
Build a scaffold out of drinking-straws to support a cup of water
Can Jo make a gym bag for her trainers from the piece of fabric she has?
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Here is a chance to create some attractive images by rotating
shapes through multiples of 90 degrees, or 30 degrees, or 72
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
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.
What shape would fit your pens and pencils best? How can you make it?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
Delight your friends with this cunning trick! Can you explain how
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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.