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.
In abstract and computer generated art, a real object can be represented by a simplified set of lines. Can you create a picture using mathematical instructions?
Four vehicles travelled on a road. What can you deduce from the times that they met?
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?
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?
Collect as many diamonds as you can by drawing three straight lines.
Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.
Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?
Drawing a triangle is not always as easy as you might think!
This task requires learners to explain and help others, asking and answering questions.
How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?
Can you make sense of the three methods to work out the area of the kite in the square?
Can you find sets of sloping lines that enclose a square?