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.
What shapes can you make by folding an A4 piece of paper?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
Follow these instructions to make a three-piece and/or seven-piece
Make a mobius band and investigate its properties.
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
Surprise your friends with this magic square trick.
Using these kite and dart templates, you could try to recreate part
of Penrose's famous tessellation or design one yourself.
Make a clinometer and use it to help you estimate the heights of
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!
Did you know mazes tell stories? Find out more about mazes and make
one of your own.
Make an equilateral triangle by folding paper and use it to make
patterns of your own.
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?
How can you make a curve from straight strips of paper?
What is the largest number of circles we can fit into the frame
without them overlapping? How do you know? What will happen if you
try the other shapes?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
These practical challenges are all about making a 'tray' and covering it with paper.
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?
What do these two triangles have in common? How are they related?
How many triangles can you make on the 3 by 3 pegboard?
Ideas for practical ways of representing data such as Venn and
How many differently shaped rectangles can you build using these
equilateral and isosceles triangles? Can you make a square?
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
What happens to the area of a square if you double the length of
the sides? Try the same thing with rectangles, diamonds and other
shapes. How do the four smaller ones fit into the larger one?
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?
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?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Here's a simple way to make a Tangram without any measuring or
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Can you fit the tangram pieces into the outline of Granma T?
An activity making various patterns with 2 x 1 rectangular tiles.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
Can you fit the tangram pieces into the outline of this telephone?
Can you describe what happens in this film?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
Can you fit the tangram pieces into the outline of this junk?
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?
Learn about Pen Up and Pen Down in Logo
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?