So yesterday we were learning to factor trinomials of the form ax^2 + bx + c in my math models class. I've taught this topic so many ways, but I have come to realize all of the little "tricks" to help them are useless, because the following year, they can't remember the "tricks". So in order to help them really understand the process, we are doing good old fashioned guess and check. This process was murder for my MMA kids because if they can't arrive at an answer within a few steps, they immediately proclaim "This is way too much work miss, " and you lose them for the rest of the lesson.
Anyway, on each problem, I would write out the possible factorizations and I was getting each row to check a different possibility. The first example went well and our second answer choice was the correct answer. On example two, the first answer choice ended up being the correct answer and I proclaimed, "wow, it's my lucky day!" "I can't believe I picked the right answer on my first try!" Then on example 3, I accidently did the same thing, I picked the correct factorization as my first guess (even though I really didn't want to). I then proclaimed in a very dramatic voice (because I was trying to keep their attention) "I can't believe I got lucky twice in one day!" A hush fell over the room and then laughter ensued. The whole class was beside themselves with laughing. It took me a few minutes to figure out what in the world was so funny. Then one brave student said, "Miss, think about what you just said."
I'm not sure how much they really learned yesterday about factoring. I can see that I will need to spend several more days on the topic. I'm going to try a little group activity today to avoid another "boring" lecture and hopefully more slips of the tongue.
I do the same thing. I just show them a couple of examples, and how if the last sign is + then both signs must be either ++ or --, and if the last sign is -, then signs must be +- or -+.
ReplyDeleteThe problem I have is that kids cannot FOIL in their heads. This is a huge time saver for the kids that can do it.
Ha! You can't help that their minds are thinking that way.
ReplyDeleteThis morning, I took a bunch of third-graders to the Harvard Museum of Natural History. As went around looking at the stuffed animals, what do you think the eight and nine-year-olds noticed? Penises. They spent much of the time pointing and giggling.
I wonder what their answers will be to questions at home, What did you learn today?"
Have you tried algebra tiles at all? Just wondering if this would be worth a try. I taught my 8th graders factored/expanded form last year and introduced it using the tiles.. seemed like it stuck with them for the time being, but I'm doubtful they've still got it.
ReplyDeleteI teach factoring by using the factors of a*c that add up to be b. Then substitute them back into the problem and then factor by grouping. I tried the short cut way with the coefficient of x^2 being 1 and all of that, but they got confused.
ReplyDeleteI have been doing it this way for about 5 years now and for the most part they get it .
BTW, I have said worse things in my class. Maybe it's cause I am male, I just laugh it off. Sounds like you have a super class there.