What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

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

What do these two triangles have in common? How are they related?

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?

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?

Make a flower design using the same shape made out of different sizes of paper.

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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?

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

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

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?

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

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

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.

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

Can you each work out what shape you have part of on your card? What will the rest of it look like?

Here is a selection of different shapes. Can you work out which ones are triangles, and why?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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

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.

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?

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

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

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 shapes?

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

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

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?

How would you move the bands on the pegboard to alter these shapes?

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?

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

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?

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?

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

Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?

How many different triangles can you make on a circular pegboard that has nine pegs?

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 interactivity allows you to sort logic blocks by dragging their images.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

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

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.