The illustration shows the graphs of twelve functions. Three of them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations of all the other graphs.

Here is a pattern composed of the graphs of 14 parabolas. Can you find their equations?

The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.

Quadratic graphs are very familiar, but what patterns can you explore with cubics?

Here is a pattern for you to experiment with using graph drawing software. Find the equations of the graphs in the pattern.

Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

Can you work out which processes are represented by the graphs?

What biological growth processes can you fit to these graphs?

Can you find the lap times of the two cyclists travelling at constant speeds?

Explore the relationship between resistance and temperature

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

Various solids are lowered into a beaker of water. How does the water level rise in each case?

Can you draw the height-time chart as this complicated vessel fills with water?

Four vehicles travel along a road one afternoon. Can you make sense of the graphs showing their motion?

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Collect as many diamonds as you can by drawing three straight lines.

This set of resources for teachers offers interactive environments to support work on graphical interpretation at Key Stage 4.

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?

Four vehicles travelled on a road. What can you deduce from the times that they met?

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

Looking at the graph - when was the person moving fastest? Slowest?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.