This post will describe my afternoon at a local high school, trying learning through problem solving lessons all day. The morning is described in part 6.
Class #4 – Math 10-4 Math 10-4 is a Knowledge and Employability math course. It is intended for students with low IQ’s, who are unable to complete our regular math program. Students who go this route in High School receive a certificate of achievement, rather than a high school diploma.
LTPS – Bucky the Badger
I got the Bucky the Badger video from Dan Meyer when he did a session in Edmonton in March. It’s a funny video, and the math involved is not complicated. I thought it would be perfect for this class.
I followed the same process, whereby I played my altered question video. I asked them what they wondered about. They were all over the place. They wondered why he had such poor pushup form. They wondered why that mascot costume was so ugly. It was taking every ounce of patience I had for wait time, because I was starting to think they were never going to get to any kind of mathematical question. Eventually, they decided they might be a bit interested in how many pushups the mascot did. Several were sure it was 83, so I explained the process of doing the pushups again to them.
If Wisconsin scores a touchdown, he does 7 push-ups because their score is now 7. If they follow that up with a field goal, he does 10 push-ups, because their score is now 10. At this point he has done 17 push-ups in total. Then if they score a touchdown, Bucky does 17 push-ups, because their score is now 17, bringing his push-up total to 34. Then I asked them again how many they thought he did. Guesses ranged from 83 to 300. I couldn’t get them over 300 as a guess, so I let them loose, thinking I’d explain it later.
I asked them what further information they required. They said they needed to know how the Badgers got to 83 points. I gave them TD, FG, TD, TD, TD, TD, TD, TD, TD, FG, TD, TD, TD.
They needed much help. This was my first experience in a Math 10-4 class and I have no special education training. They were, however, engaged and trying hard with it. They were neat kids. Some started by building the chart from the video on the board. Many began to get answers in the ballpark of the correct answer.
One group was done, and had it right. I gave them the extension: Does it matter where the two field goals occur? They concluded it did. So I asked them to figure out where to put the two field goals so that Bucky ended up doing the most possible pushups. They concluded that the two field goals should come at the end. I thought they were wrong, not because I had done the question before, but because a group of teachers told me that when I gave them the same extension in a session I did. I told the kids they were wrong for that very reason. They proved to me that they were right, and were pretty proud to have bested some math teachers. I showed the class the answer video, and they were pleased to have been right.
The biggest success here was a girl who initially asked, “who cares?” when we came up with the question. She appeared totally disengaged. During the activity, however, she noticed that a pair of boys had made an error in a chart they were producing on the whiteboard. She came up, grabbed the marker from their hands, fixed the error, and went back to her desk. She accidentally got engaged in the problem. It was a major success.
Curricular Fit: 100% – Pattern Extension is in Math 10-4. This activity could also be used as an introductory activity in Math 20-1 Sequences and Series.
Class #5 – Math 20 Honors This class was an honors level grade 11 math course. Most of these kids will go on to AP Calculus next year. They are currently on our old curriculum, so they are following our Math 20 Pure course.
LTPS – Spider and Grasshopper
I used the spider and grasshopper question I found on Andrew Shores’ blog. I started by giving them this image.
This group was astute enough to point out that I was manipulating them because there really was only one question they could ask here. They humored me, though, and got to work on figuring out when the grasshopper would meet his demise.
They worked hard on it. I had groups making charts, others trying a logical proof. Some groups were trying to find and solve a system of equations. What they all realized eventually, of course, is that the grasshopper never hits a spider web. I was quietly telling some groups to prove this. Then I made a mistake. I got the whole class’s attention and pointed out (without allowing them to discuss it) that there was no answer, and therefore the question had shifted from being “find out when they meet” to being “prove that they never meet”. This was far too teacher directed, and some quit on me after hearing it.
What went well: Several students were working hard on a general proof, and enjoying it. A few of them had it generalized nicely.
What I could have done better: Lots. I should have stopped them and let them have a discussion whereby they could have discovered that they were all finding no intersection. That discussion would have led to the next question, rather than me giving it to them. I also wrote my general proof on the board at the end, rather than having one of them do it. That’s one place where this whole process tends to fall apart for me. I fall back on my old habits of wanting to do too much that is teacher directed. I need to remember to turn more over to the students.
Curricular Fit: 100% – Logic, reasoning, and proofs are in Math 20 Pure. This will also have good fit in Math 20-2 under the new curriculum, where logic and reasoning are major topics.
Class #6 – Math 20 Pure This was a regular Math 20 Pure class. These are our pre-calculus students at the 11th grade level. Most will go on and take calculus in grade 12.
LTPS – Mozart’s Dice Game
I used the Mozart’s Dice Game, as described in an earlier post on my blog. We created and listened to a minuet using the site linked in that previous post. Then I told them that I was pretty sure that no one had ever heard that minuet before. I asked them why I was so confident. They suggested that there must be a lot of them. I asked them how many. They didn’t know, so I suggested they figure it out. We had a hard time with the part of the process whereby they are to come up with a guess, because the number is unfathomable. The correct answer is 129 octillion, 629 septillion, 238 sextillion, 163 quintillion, 50 quadrillion, 258 trillion, 624 billion, 287 million, 932 thousand and 416 (Thanks Wolfram). In the end, their guess of “lots” was pretty accurate.
They got to work, and most made really nice progress and ended up inventing the fundamental counting principle themselves.
What went well: This class enjoyed the problem, and made really nice progress with it.
What I could have done better: One student had answered the question before the rest of the class had even had time to figure out what the question was. Some quit because they knew someone else had already done it. I should have given him an extension (how long would it take for the whole world to listen to these, if we divide it up equally) to keep him quiet and busy.
Curricular Fit: 0% – this does not fit in Math 20 Pure. This can be used in our curriculum, however, since the fundamental counting principle is in Math 30 Pure, Math 30-1, Math 30 Applied and Math 30-2.