We did an awesome project today inspired by Fawn. Coming up on area of composite shapes, I needed a way for students to practice the composite-ness and the “splitting up” skill. A popular text book problem asks about pools and tiling/grass/etc around the pool in the yard, so I thought about having them draw a pool and do all that jazz, but I couldn’t really get that idea together.
A popular text book problem asks about pools and tiling/grass/etc around the pool in the yard, so I thought about having them draw a pool and do all that jazz, but I couldn’t really get that idea together. As it turns out, there’s this kinda big holiday called
Easter Spring coming up, in which Hallmark has secularized another Christian holiday for a profit. So I had my kids make greeting cards at the end of class yesterday (after they worked on a “traditional” worksheet on area of composite shapes in groups) and photocopied them after school. I was pretty vague about what we would be using them for on purpose, which drove my students a little nuts. Some of the kids even came up to me after school yesterday to ask what the cards were for. Mostly, though, they liked the elementary school throwback to arts and crafts.
Today, the entirety of the class was devoted to this one question: How much of your card is left uncovered?
Here’s what my awesome students came up with:
- Different ways of seeing- most students broke up the shapes and then subtracted those areas from the card area, but some broke up the non-covered areas to calculate it directly.
- Differentiation!!!!!!!!! Some students took a long time to figure out how to split their shapes, some students were able to do some but not all calculations, some were ready to start splitting into smaller shapes to be more precise, and some students were even able to finish all calculations and write a paragraph to explain their reasoning
- Foreshadowing of calculus: the smaller we split our shapes/the more shapes we calculate, the closer we can get to the actual area
- Using the document camera after about 5-10 minutes of work to show classmates’ examples helped tremendously
- I was able to have some students put fewer shapes on their card and other students put more shapes on (more differentiation!)
- Copy the cards! So helpful to have a paper version to draw on so they could still use their cards as cards
- Most students engaged
- Some students had a hard time getting started- I ended up suggesting that they start by finding the covered area instead but a lot of them still didn’t understand what to do until their classmates presented their beginnings. Is this a problem? What other scaffolded questions could I ask to help students get started?
- How can I/ should I make the connection to calculus more explicit?
Go to the dollar store. Not Target.
- Coloring supplies
- Colored notecards
- Foam sticky shapes
Teaching ACT Math this semester is actually really fun- I get a chance to dabble in teaching all kinds of math. The main difficulty with it is that I teach 9th graders. Who are very interested in college, but the ACT is just so far away…
I try to incorporate sample problems into the Warmup/Do Now/Bellringer/pickyourflavor. Today’s was an especial gem that led to a lot of rich conversation.
We talked about drawing a picture and then some kids admitted they were stuck. One student volunteered that she split the clock into 4 90˚ chunks, and then split that in half to get 45˚ but she still wasn’t sure of the answer. Another student took that idea and said he split the 90˚ into 3 chunks since there were 3 hours so each hour is 30˚. Since we were looking for 1 o’clock, he reasoned, it is one 30˚ angle (choice B)
Then another student volunteered that instead of splitting into 4, she split the 360˚ circle into 12 and got 30˚. She had a hard time coming up with a reason for why it was 30 and not some other multiple of 30 when I had asked her earlier, though.
Finally, I introduced the idea of proportions (1/12 = ? / 360) and showed how it was just like what they had done.
We were really riding a high as a class, one girl was like everyone in here is so smart, and I was like, maybe I we can just take this gig a little further. So then I asked them what time each of the other answer choices would show. They told me 45˚ would be 1:30 because “it’s a whole 30˚ plus 15˚, which is 1 hour plus half an hour”. This was my proudest moment of the day today- maybe my constant number sense modeling (a la Jo Boaler) is finally taking root in their freshman brains!
NCTM 2014 left me ON FIRE. (Almost literally, it was so hot walking around on Saturday.) But seriously, it left me hungry for more: more PrBL in my classroom, more student conversations, more teacher online collaboration, more ed conversations, more all of it.
One conversation that I am glad to see continuing is the one centered around getting younger teachers in the classroom to participate in NCTM. An NCTM rep said the average member of NCTM is 57. Whether or not that statistic is true, here is what I’m interested in exploring from that conversation.
A lot of young teachers I personally tried to cajole/blackmail/etc into coming to NCTM wanted to come, but couldn’t find the $$$. So, how can we make that more accessible to them? Give a “new teacher” discount” a la student discount (how do you define/prove “new teacher”)? Give a first-time attender discount? Give scholarships? A quick look at the NCTM page gave this single conference scholarship for first-time attenders as well as a similar one for prospective teachers. There’s also some other grants and scholarships but most of them have a requirement that you have to have been teaching for at least 3 years (which disqualifies me until next year). What if MTBoS banded together to come up with a scholarship or 2? I’d be willing to chip in a few bucks.