When you’re going over the homework, talk for a while about the throwing-a-ball-into-the-air scenario. It will come up again, and I really want people to understand it. The particular point I try to make is how the math reflects the reality. You have a function
On the other hand, suppose you ask “When will it be at –3 ft?” (That is, under the ground.) You might expect no answer at all, since the ball never is under the ground. But the math doesn’t know that—it thinks the ball is following the same function forever. So you get two answers. One is after the ball hits the ground. The other is before it left—a negative time! This is where you have to use common sense to find the “real” answer, as distinct from the answer the math gave you.
I spend a good half-period, at least, talking through this. I think it is an incredibly important point about the way we use math to model the world. See this webpage for an exercise you can use just on this.
Anyway, onward…the assignment “Completing the Square” pretty much speaks for itself. Probably the only preamble you need is to point out that many quadratic equations, which do have solutions, cannot be factored. So we are going to learn another technique which has the advantage that it can always be used. (Factoring is still easier and faster when it works.)
Now you can just get them started on it, and then wander around and help. Just make sure that before the class is done, everyone gets the technique. You may also want to point out to them that they already did this on yesterday’s assignment.
On #4 make sure they get two answers, not just one!
“Homework: Completing the Square”. The hard ones here, that you will get questions on the next day, are #9 and #10. Note that, on #9, I am not looking for the discriminant and the quadratic formula and stuff; just the obvious fact, based on completing the square, that if
"This is the "teacher's guide" book in Kenny Felder's "Advanced Algebra II" series. This text was created with a focus on 'doing' and 'understanding' algebra concepts rather than simply hearing […]"