Follow these instructions to make a three-piece and/or seven-piece tangram.
Learn about Pen Up and Pen Down in Logo
Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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.
Surprise your friends with this magic square trick.
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.
It might seem impossible but it is possible. How can you cut a playing card to make a hole big enough to walk through?
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 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.
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?
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. . . .
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.
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.
More Logo for beginners. Now learn more about the REPEAT command.
Turn through bigger angles and draw stars with Logo.
Did you know mazes tell stories? Find out more about mazes and make one of your own.
A game to make and play based on the number line.
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.
Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.
Can you describe what happens in this film?
This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.
How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
Here are some ideas to try in the classroom for using counters to investigate number patterns.
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?
This article for students gives some instructions about how to make some different braids.
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
Follow these instructions to make a five-pointed snowflake from a square of paper.
This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.
Here's a simple way to make a Tangram without any measuring or ruling lines.
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?
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.
What happens when a procedure calls itself?
Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?
How is it possible to predict the card?