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

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

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

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.

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

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

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.

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

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

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?

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

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 ?

Charlie has created a mapping. Can you figure out what it does? What questions does it prompt you to ask?

Explore the relationship between resistance and temperature

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

Explore the relationship between simple linear functions and their graphs.

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

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.

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

Two cyclists, practising on a track, pass each other at the starting line and go at constant speeds... Can you find lap times that are such that the cyclists will meet exactly half way round the. . . .

Can you adjust the curve so the bead drops with near constant vertical velocity?

When I park my car in Mathstown, there are two car parks to choose from. Which car park should I use?

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. . . .

Here are some more quadratic functions to explore. How are their graphs related?

Explore the two quadratic functions and find out how their graphs are related.

Explore the relationship between quadratic functions and their graphs.

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.

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

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

Knowing two of the equations find the equations of the 12 graphs of cubic functions making this pattern.

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

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

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

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

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.

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

Alison has created two mappings. Can you figure out what they do? What questions do they prompt you to ask?

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