Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.
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?
How can you make an angle of 60 degrees by folding a sheet of paper
Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
These are pictures of the sea defences at New Brighton. Can you
work out what a basic shape might be in both images of the sea wall
and work out a way they might fit together?
A description of how to make the five Platonic solids out of paper.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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?
Turn through bigger angles and draw stars with Logo.
You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.
What shape and size of drinks mat is best for flipping and catching?
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.
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 tangram pieces to make our pictures, or to design some of
This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
Make an equilateral triangle by folding paper and use it to make
patterns of your own.
Make a clinometer and use it to help you estimate the heights of
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?
Delight your friends with this cunning trick! Can you explain how
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?
This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.
A game to make and play based on the number line.
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?
A jigsaw where pieces only go together if the fractions are
A game in which players take it in turns to choose a number. Can you block your opponent?
Here is a chance to create some Celtic knots and explore the mathematics behind them.
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?
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
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.
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
Can Jo make a gym bag for her trainers from the piece of fabric she has?
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.
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Can you describe what happens in this film?
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
What shape would fit your pens and pencils best? How can you make it?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
How many differently shaped rectangles can you build using these
equilateral and isosceles triangles? Can you make a square?
Make a spiral mobile.
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 pupils gives an introduction to Celtic knotwork
patterns and a feel for how you can draw them.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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