We (along with most of the area, it seems) headed back to school today. We have 3 days of regular classes to finish up the semester and then exams next week. You know how kids have trouble remembering things over a weekend? Try a 2-week break and then an exam over a semester's worth of material. Sometimes it gets ugly.

With three days this week, I didn't want to give my precalc kids that much free time to work on exam reviews. We'd finished up before our break with law of sines/cosines, so I'm taking two of these days to work on area of triangles. It's a nice way to ease back into school, I think.

I started out by giving them these two triangles and asked them to find the area.

They whipped through the first one easily and most kids automatically drew an altitude for triangle #2, found its length, and used that for the area of the triangle.

In 3rd period (my second time through) I then gave them this and asked them to find the area. (Assuming that A, b, and c were known values)

Despite having just done this (with numbers) some of them were a little unsure. I advised them to repeat what they'd done in #2 but leave the letters. I have to admit - I'd never done this myself before to derive the area formula. I'm embarrassed at how easy it was and how I should've made them do this years ago!

If you work through it, the altitude has length of csinA, so when you plug it in to the 1/2bh formula, you get an area of 1/2 bcsinA. Voila!

The second area formula (Heron's) isn't so easily derivable (though I tried on my own). But at least we got one in!

I usually like to spend a few days working on some area problems after we talk about the formulas, but with my limited time for the next couple of days I can't do that this year. Instead, I'm going to give the kids the 6 problems I normally hand out for them to work individually and have them work them as table groups. I don't want to take a lot of time to grade them, so I copied a spinner with 7 sections (because I threw in a toughie at the end) and am going to have them write their answer in the 7 blocks. That way I'll be able to see all of their answers at a quick glance.

I'm wondering if I can get even lazier and make this even easier on myself. :)

I'm trying to improve at letting my kids work independently because I'm tempted to explain at the board or have every minute accounted for. My headmaster recommended that I let them try to interpret for 5-10 minutes (telling them that I will explain in 5-10 minutes) before explaining. How do you handle the independent work time?

ReplyDeleteIt's kind of funny, because I felt like under previous school administration we had to do exactly that - teach to the bell. And that's so not how I like to do things. I've been lucky this year in that the kids really do work well when I give them time to do so. And really, I think that setting up the groups for them to sit in have helped a lot. If they're just goofing around and talking I make sure they know that they need to be on task, but it rarely comes to that.

ReplyDeleteIs independent work time something that _you_ have a problem with because you feel like you should be talking? Or is it that the kids can't handle it?

If it's you, I'd suggest adapting Dan Meyer's mantra of "Be Less Helpful." I have it framed on my desk. Let them struggle through things! Even if it's only for a few minutes.

If the kids are struggling with staying on task or working without direct guidance all of the time, maybe you could set a timer. Tell them they have to work for that allotted amount of time before you'll answer questions. Or have a scaffolding of questions so that they can work up to what it is you really want them to do. Or go with the "Ask 3, then me" attitude, where they have to consult with each other before they approach you.

Just a few thoughts. :)