The equation of a line, and of a circle: Focusing on change
Here is sliders which change the parameters of a circle, and sliders which change the parameters of a straight line.
Below are a list of questions, specifically linked to change and variation:
Questions to ask:
What do we expect to happen if we change the value of m?
How many times is the line currently intersecting the circle?
The following can be asked on mini-whiteboards, and then you can check and discuss the various students answers:
Can you change one, and only one, aspect of the line y=mx+c above, so that there are no intersections?
Can you change one aspect of the circle so that there are no intersections?
Is it possible to change one aspect of the circle, so that there is exactly one intersection?
Do additional aspects need to be changed for this? If not, why not?
Appropriate for: GCSE (If centred at the origin only), L2 Further maths, and AS Level maths.