My name is Keli, and I love to teach math. One of my New Year's Resolutions is to start a teaching blog, since teaching is something I could go on about forever. Today felt like a good day, and I figured if I got started early on my blogging, I'd be all set for New Year's.
It was a good day... Today was one of those days that makes teaching worth it. The amazing thing about today was that today's lesson wasn't something I planned for hours, reinventing the wheel, but something simple. I have to give credit to Dan Meyer. I follow his blog religiously (check it out at http://blog.mrmeyer.com/), and love his website 101 Questions. So my lesson came from his post/lesson called Super Bear. We're learning about proportions this unit and so far they've learned how to solve proportions but not how to apply them. I decided to spend several days on the application part and this was our starting point.
If a lesson could be described as beautiful, this would be it. First of all, the students were engaged. They wanted to eat the super bear. Do you have a super bear? Will you bring us one? Can we have gummy bears? Yeah, I know these questions have nothing to do with math, but it got them talking. We watched the first video in the lesson, then I posed the question how many regular gummy bears will it take to make one super gummy bear? Before we solve, we discuss: what do you need to know? How can you get this information? Make an estimate that you know is too high and an estimate that you know is too low. We discuss accuracy and precision. Then I give them the info they need, and they solve.
We did this particular problem together. Why? Mainly, I wanted them to get it wrong. Wrong?! Yes, you read that right, I wanted them to fail this problem... the first time. I chose a student that I knew had set the problem up wrong, had them solve it and then we discussed the answer. The wrong answer was somewhere around 5,000 regular gummy bears per 1 super bear. "Does this seem reasonable?" I asked. Most students thought it was. So to get to this point, it took about an hour (we have a 90 minute math block each day), and I wanted them to realize they were wrong without telling them so we made a table showing number of regular gummy bears and total mass. We compared numbers and magically Sam, a student in class said, "something isn't right. In the table when we got to 1,000 regular bears it had a bigger mass than the super bear. But the answer we got was 5,000." We discussed more and someone brought up the point about unit rates.
And here was my jumping off point. Let's do a unit rate for regular gummy bears since you guys are so good at finding them. We started with the mass of 10 gummy bears and found the mass of one gummy bear, then compared the two rates. What do we notice about the rates versus our problem. And like that, they got it, and here is where I introduced today's lesson about proportions: when you set up proportions they have to have the same units equal the same units. For example if you are using miles per hour and set up a proportion it needs to look like:
It was so effortless and natural feeling and I counted myself lucky to be teaching such a wonderful group of students. Will they truly understand this problem? I bet most of them will if not today, then by tomorrow. Did I really spend an entire class period on one problem? Yes, I spend lots of days like this so the students can really dive into the concepts instead of relying on rote memorization.
