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

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?

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?

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

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

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

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.

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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

Can you explain why it is impossible to construct this triangle?

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

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

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

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

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

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

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

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?

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?

Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees.

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?

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

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

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?

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

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?

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

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

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

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?

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

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

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

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

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

Which of these triangular jigsaws are impossible to finish?

If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?

Using the interactivity, can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

Jennifer Piggott and Charlie Gilderdale describe a free interactive circular geoboard environment that can lead learners to pose mathematical questions.

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

Two right-angled triangles are connected together as part of a structure. An object is dropped from the top of the green triangle where does it pass the base of the blue triangle?

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.

Make an equilateral triangle by folding paper and use it to make patterns of your own.