Follow these instructions to make a three-piece and/or seven-piece
Make an equilateral triangle by folding paper and use it to make
patterns of your own.
Learn about Pen Up and Pen Down in Logo
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 to write procedures and build them into Logo programs. Learn to use variables.
Make a clinometer and use it to help you estimate the heights of
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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?
Turn through bigger angles and draw stars with Logo.
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.
More Logo for beginners. Now learn more about the REPEAT command.
Make a cube with three strips of paper. Colour three faces or use
the numbers 1 to 6 to make a die.
Make a ball from triangles!
Using these kite and dart templates, you could try to recreate part
of Penrose's famous tessellation or design one yourself.
Make a spiral mobile.
Surprise your friends with this magic square trick.
Did you know mazes tell stories? Find out more about mazes and make
one of your own.
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
Ideas for practical ways of representing data such as Venn and
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.
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
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?
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. . . .
This package contains hands-on code breaking activities based on
the Enigma Schools Project. Suitable for Stages 2, 3 and 4.
What happens when a procedure calls itself?
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
A game to make and play based on the number line.
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.
How can you make a curve from straight strips of paper?
This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.
Use the tangram pieces to make our pictures, or to design some of
Can you describe what happens in this film?
This article for students gives some instructions about how to make some different braids.
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
Can you make the birds from the egg tangram?
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 are some ideas to try in the classroom for using counters to investigate number patterns.
Follow these instructions to make a five-pointed snowflake from a
square of paper.
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
This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
What shapes can you make by folding an A4 piece of paper?
This article for pupils gives an introduction to Celtic knotwork
patterns and a feel for how you can draw them.
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.