Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.

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?

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.

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?

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

Explore the triangles that can be made with seven sticks of the same length.

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

Take it in turns to make a triangle on the pegboard. Can you block your opponent?

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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?

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?

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

Can you sort these triangles into three different families and explain how you did it?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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?

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?

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?

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?

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?

This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.

Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.

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?

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

I cut this square into two different shapes. What can you say about the relationship between them?

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.