## Rewriting a messy conic section

I tried my best to make this as clear as possible. Any comments would be appreciated.

### 7 Responses

1. Thanks for your advice on the parabola paper folding activity. I see how that would be an improvement, so I’ll make a note in my plans to try it next time.

I like your completing the square slide. The underlining and arrows and boxes of explanation with different colors make it clear what the flow is. I have 2 suggestions and 1 comment on what I do differently (and I don’t know that it’s better).

1. I would have the problem end up where one of the x or y has a “+” and one a “-“, so the students wouldn’t think it’s always minus. For example ending up with (x + 3)^2 and (y – 2)^2.

2. I would also change the numbers so it’s not 4 that ends up being squared then added for both the x and y parts.

My difference: When I complete the square, I automatically adjust the other side of the = sign instead of doing it in place (+16 -16) as you do. I don’t know if that’s better or worse or just different.

Otherwise, cool.

2. Comment 1 & 2: Both things I’m unhappy about. I realized it after I already had the layout, but I pretty much have to start from scratch to fix this. (Maybe next year!)

Last year when I taught this I automatically adjusted the other side of the = sign. The students were so befuddled I decided to slow the process down. The main issue is the distribution, where doing a “partial distribution” when pulling -16 out of the parenthesis is one extra math concept tossed in the mix.