Today was the first day of the second week of class. Last night I lay awake, worrying that this 'no textbook' thing was scary. (I'm not using a textbook during class. I've required them to get a textbook, but it doesn't have to be a new one. I've helped a few of them buy $4 copies of the older edition of our department's required text.) Are they doing their homework (that I'm not collecting)? Do they have any idea how to find good problems to practice on? What was I thinking?!
I asked today in class. Probably less than half of them have been doing their homework. I think I'll ask to look over some of the homework binders, so I can get a sense of how well they're choosing problems.
I'm teaching 3 sections of Beginning Algebra; they need review on fractions, integers, distributive property, and order of operations, which I'm now calling FIDO (instead of 'chapter one'). Last week on day two I gave them a problem I've given for years now. You've bought 3 lots at a campground with your partner. You've broken up. You now own 1 1/2 lots. Each lot is 2 1/3 acres. How much acreage do you own? I require them to start out by drawing a picture, and they work in groups of 4. We get to think carefully about fractions.
We did some more fraction stuff last week, and today's warmup was a nested fraction challenge problem:
[Yeay, I did that by using print in word, then saving as pdf, then saving that as jpeg, then cropping. Way easier than using online equation thingies.]
Can you all guess the most popular error? I hadn't seen it coming, but I should have... Lots of students wanted to cancel the 1's. When that was the first suggestion of how to start, I started to say something, and caught myself. I think not many noticed.
We talked about what belonged on top if the 1 was canceled. A zero? No... And it looked pretty strange with nothing on top... The first class had someone tell me that the problem was with the addition. I have in the past explained about not canceling when there's addition and subtraction in the fraction, but students all the way up through calculus keep doing it. Way too tempting... Perhaps the fact that they were trying to figure this out together will help them resist temptation? In the second class, when no one could tell me what was going on, I left it on the board for us to ponder. I did not give them the 'answer' (that the addtion is why you can't cancel). We finally got it.
I was excited about how it went today. We spent so much time on this weird problem that we didn't get much time for integers. There will be time tomorrow.