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 tangram.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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.
It might seem impossible but it is possible. How can you cut a playing card to make a hole big enough to walk through?
More Logo for beginners. Now learn more about the REPEAT command.
A game to make and play based on the number line.
Make a mobius band and investigate its properties.
Make a spiral mobile.
Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.
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 tall objects.
Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.
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 to write procedures and build them into Logo programs. Learn to use variables.
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?
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.
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?
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.
Did you know mazes tell stories? Find out more about mazes and make one of your own.
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
Turn through bigger angles and draw stars with Logo.
Learn about Pen Up and Pen Down in Logo
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. . . .
Surprise your friends with this magic square trick.
Make a ball from triangles!
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.
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.
Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.
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.
Can you describe what happens in this film?
It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!
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.
What happens when a procedure calls itself?
This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.
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.
What shapes can you make by folding an A4 piece of paper?
Ideas for practical ways of representing data such as Venn and Carroll diagrams.
How do you know if your set of dominoes is complete?