I cut this square into two different shapes. What can you say about
the relationship between them?
Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
How many different triangles can you make on a circular pegboard
that has nine pegs?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
How many triangles can you make on the 3 by 3 pegboard?
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?
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?
You have pitched your tent (the red triangle) on an island. Can you
move it to the position shown by the purple triangle making sure
you obey the rules?
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
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?
This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?
Can you find all the different triangles on these peg boards, and
find their angles?
The graph below is an oblique coordinate system based on 60 degree
angles. It was drawn on isometric paper. What kinds of triangles do
these points form?
Explore the triangles that can be made with seven sticks of the
Using a loop of string stretched around three of your fingers, what
different triangles can you make? Draw them and sort them into
What shapes can you make by folding an A4 piece of paper?
The large rectangle is divided into a series of smaller
quadrilaterals and triangles. Can you untangle what fractional part
is represented by each of the ten numbered shapes?
This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.
What does the overlap of these two shapes look like? Try picturing
it in your head and then use the interactivity to test your
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
Draw three straight lines to separate these shapes into four groups
- each group must contain one of each shape.
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.
Take it in turns to make a triangle on the pegboard. Can you block
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
Can you sort these triangles into three different families and explain how you did it?
This challenge invites you to create your own picture using just
straight lines. Can you identify shapes with the same number of
sides and decorate them in the same way?
Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?
Use the interactivity to make this Islamic star and cross design.
Can you produce a tessellation of regular octagons with two
different types of triangle?
Watch this "Notes on a Triangle" film. Can you recreate parts of
the film using cut-out triangles?
A group activity using visualisation of squares and triangles.
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Can you help the children in Mrs Trimmer's class make different
shapes out of a loop of string?
Liethagoras, Pythagoras' cousin (!), was jealous of Pythagoras and came up with his own theorem. Read this article to find out why other mathematicians laughed at him.