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

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?

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.

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?

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

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

Which of these pocket money systems would you rather have?