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

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

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.

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

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

Here are several equations from real life. Can you work out which measurements are possible from each equation?

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

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 ?

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

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

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

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.

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 the distance it travels at each stage.

Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.

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

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

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

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

This is a beautiful result involving a parabola and parallels.

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.

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.

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

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?

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?

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

Several graphs of the sort occurring commonly in biology are given. How many processes can you map to each graph?

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

Which line graph, equations and physical processes go together?

Which curve is which, and how would you plan a route to pass between them?

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

What biological growth processes can you fit to these graphs?

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

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

Use the interactivity to move Mr Pearson and his dog. Can you move him so that the graph shows a curve?

Can you create a story that would describe the movement of the man shown on these graphs? Use the interactivity to try out our ideas.

Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.

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. . . .

Explore the hyperbolic functions sinh and cosh using what you know about the exponential function.

Sketch the graphs of y = sin x and y = tan x and some straight lines. Prove some inequalities.

Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.

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

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

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.

Prove that the graph of f(x) = x^3 - 6x^2 +9x +1 has rotational symmetry. Do graphs of all cubics have rotational symmetry?