Today was one of those days, big time.
We've been multiplying and dividing rational expressions for several days. Longer than I'd planned, actually, but with me being observed and then being out for one class on one day, they dragged on and on. Today was the intro to adding and subtracting.
I thought it would be ok. I know that the idea of finding common denominators to kids who aren't super familiar with their multiplication tables (really!) is tough. But I thought we could reason through it.
Unfortunately, that wasn't quite the case for my first class. Maybe it wasn't as bad as I thought. Maybe I'm letting the girl who was super frustrated (and then got upset) influence my memory. But I took the 10 minutes between classes (because homeroom) to write up a new set of notes for my next class and things were fine. One of the kids even said he thought that adding was so much easier than multiplying. (Though we haven't gotten to the real meat of the problems yet.)
I broke it down for my 2nd period class. I laid out two problems side by side. Same numbers in both but included variables the second time around.
We found one answer then went to the second. Is there a difference in method? Nope. Just have some extra n's hanging out.
Did a couple more like that, then I threw in some variables in the denominator. Big deal? Nope. Just need to include an x in the common denominator.
So now what if the variables on the denominator have some exponents? We discussed how we can build up denominators by multiplying (so make them bigger), and that includes the exponents.
We're working up to the idea of including binomial factors. But it's definitely doable.
Let's contrast that with the problems I did in my 1st class. I think I'd be crying too.
I'm supposed to be out tomorrow for a PD; I'm actually considering going late so that I can stay and work with my 1st period class again. I think I owe them that much.