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

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

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.

Explore the relationship between simple linear functions and their graphs.

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

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

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.