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.

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.

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

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

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.

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

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

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

Explore the relationship between simple linear functions and their graphs.

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

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

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 ?

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.

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