Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.
Learn about Pen Up and Pen Down in Logo
Follow these instructions to make a three-piece and/or seven-piece tangram.
Learn to write procedures and build them into Logo programs. Learn to use variables.
Make a mobius band and investigate its properties.
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?
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
Make a ball from triangles!
Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.
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.
A game to make and play based on the number line.
Surprise your friends with this magic square trick.
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?
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.
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?
Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
Make an equilateral triangle by folding paper and use it to make patterns of your own.
More Logo for beginners. Now learn more about the REPEAT command.
Turn through bigger angles and draw stars with Logo.
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.
Make a spiral mobile.
This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.
How can you make a curve from straight strips of paper?
Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.
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?
Follow these instructions to make a five-pointed snowflake from a square of paper.
Use the tangram pieces to make our pictures, or to design some of your own!
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.
This practical activity involves measuring length/distance.
Make some celtic knot patterns using tiling techniques
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?
It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!
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?
This article for students gives some instructions about how to make some different braids.
How do you know if your set of dominoes is complete?
What happens when a procedure calls itself?
How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?
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.
This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.
This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.
Ideas for practical ways of representing data such as Venn and Carroll diagrams.