Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
Follow these instructions to make a three-piece and/or seven-piece
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
What happens when a procedure calls itself?
Make an equilateral triangle by folding paper and use it to make
patterns of your own.
Learn to write procedures and build them into Logo programs. Learn to use variables.
Make a mobius band and investigate its properties.
It might seem impossible but it is possible. How can you cut a
playing card to make a hole big enough to walk through?
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.
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.
Make a clinometer and use it to help you estimate the heights of
Using these kite and dart templates, you could try to recreate part
of Penrose's famous tessellation or design one yourself.
Surprise your friends with this magic square trick.
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!
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. . . .
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?
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
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.
Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.
Write a Logo program, putting in variables, and see the effect when you change the variables.
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.
More Logo for beginners. Now learn more about the REPEAT command.
Turn through bigger angles and draw stars with Logo.
Learn about Pen Up and Pen Down in Logo
Did you know mazes tell stories? Find out more about mazes and make
one of your own.
Make a spiral mobile.
Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.
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.
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
Can you describe what happens in this film?
How many differently shaped rectangles can you build using these
equilateral and isosceles triangles? Can you make a square?
This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.
Here are some ideas to try in the classroom for using counters to investigate number patterns.
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
Follow these instructions to make a five-pointed snowflake from a
square of paper.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
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.
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?
Kaia is sure that her father has worn a particular tie twice a week
in at least five of the last ten weeks, but her father disagrees.
Who do you think is right?
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
A description of how to make the five Platonic solids out of paper.
Here's a simple way to make a Tangram without any measuring or
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.