Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

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.

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 describe this route to infinity? Where will the arrows take you next?

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

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

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

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

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.

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

Can you sketch graphs to show how the height of water changes in different containers as they are filled?

How many lattice points are there in the first quadrant that lie on the line 3x + 4y = 59 ?

Can you find the area between this graph and the x-axis, between x=3 and x=7?

Find the point on the line segment AB that is twice as far from B as it is from A.