This article for pupils gives an introduction to Celtic knotwork
patterns and a feel for how you can draw them.
This article for students gives some instructions about how to make some different braids.
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.
Make an equilateral triangle by folding paper and use it to make
patterns of your own.
Make some celtic knot patterns using tiling techniques
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
More Logo for beginners. Now learn more about the REPEAT command.
Make a clinometer and use it to help you estimate the heights of
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 practical activity involves measuring length/distance.
Make a cube out of straws and have a go at this practical
Write a Logo program, putting in variables, and see the effect when you change the variables.
What happens when a procedure calls itself?
Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.
Turn through bigger angles and draw stars with Logo.
Learn about Pen Up and Pen Down in Logo
What do these two triangles have in common? How are they related?
Learn to write procedures and build them into Logo programs. Learn to use variables.
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Exploring and predicting folding, cutting and punching holes and
Ideas for practical ways of representing data such as Venn and
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
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?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
The triangle ABC is equilateral. The arc AB has centre C, the arc
BC has centre A and the arc CA has centre B. Explain how and why
this shape can roll along between two parallel tracks.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
An activity making various patterns with 2 x 1 rectangular tiles.
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Here's a simple way to make a Tangram without any measuring or
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
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 make the birds from the egg tangram?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?