I was in a collaboration meeting this morning with the rest of the 8th grade teachers and before the meeting I was putting some problems together for my geometry class to work on. I made an angle chasing problem involving a triangle and a couple parallel lines, but I didn’t feel like making up equations for unknown angles, so I opened up our textbook, pulled out a couple equations that I knew had integer answers from two different problems, and just wrote them into a couple of the missing angles. When I got back to my class I glanced at the problems to see how students did with them and was immediately shocked to see that they had labeled one of the angles in the diagram as having a measure of -18 degrees. Confused, I did the calculations in my head for that part of the diagram (which involved a straight angle made up of 3 adjacent angles) and discovered that one of the equations I pulled resulted in one of the angles being 135 degrees, and another being 63 degrees, which of course, would mean that the third angle had a measure of -18 degrees. WHOOPS! I couldn’t help but start laughing. I can only imagine my class, with a substitute in the room, when they discovered this. I’m sure they were incredibly confused and tried the problem a bunch of times, sure that they were doing it right but not sure why their answer was off. I owe them an apology when I see them again on Thursday. I’m sure some of them were mad at me, but I definitely got a good laugh out of it.
Yesterday when there was a sub in my class I gave my geometry students a few pretty challenging angle chasing problems involving parallel lines and transversals. As expected, many of them found them difficult, but some were able to solve them correctly, with many other getting a good start but just hitting a point where they weren’t sure where to go from there. That said, my favorite part of discussing the solutions was when students suggested ways to solve the problems that I hadn’t initially thought of. My way of solving the problems was very different than some of theirs, but we all ended up at the same place. It’s a nice reminder that students sometimes see and think about things in very different ways than us teachers, and we all have a lot to learn from each other.
Today with my 8th graders we did Robert’s “How Many Stars Are There in the Universe?” lesson. My students really enjoyed it. I began class with them estimating how many stars are in the universe, and it led to a great discussion about huge numbers. When I showed them the video with the numbers blacked out and the answer bleeped out, they started cracking up laughing. There’s just long enough before the bleep to hear a slight “f” sound, which of course when it’s followed by a bleep, a room full of middle school students immediately think only one thing. It was pretty funny. After we did the stars calculation I asked them the follow up question about grains of sand and they all picked which one they thought there was more of. Most picked grains of sand and were shocked when it turned out there are about 10 times as many stars. All-in-all it was a great lesson and the students really seemed to enjoy the discussions.
Today in geometry, to get students thinking about the concept of transversals, we did Andrew’s “Transversals, Tape, and Stickies” investigation. Simply put, it was fantastic. The discussions it elicited between students were great, and they all were able to solve both problems. They got really excited when they solved the one with the 3 intersecting lines, since it took them all several attempts to figure it out. Once they began finishing, I tasked them with creating their own puzzles and trading them with other groups. They got really into this too and were totally engaged and enthusiastic for the entire period. It was a lot of fun.
When I logged on to my reassessment form this morning to see who was coming in to reassess tomorrow, I was pleasantly surprised at the number of students who had signed up. Then I realized that, along with my regular study hall class, I don’t have anywhere near enough desks to accommodate all those kids. I’m going to have to play this one by year and figure it out on the fly. I’d rather have too many students wanting to reassess than none. I see it as a sign that students are valuing the learning and not point getting for a grade. It’s nice to see.
OK, so I know it’s a little mean but I just can’t help myself sometimes. Today as a warm-up I asked my geometry classes what zero divided by zero was. A lively debate ensued, with students making arguments for 0, 1, undefined, infinity, and “new stuff” which meant something they didn’t know about yet. I got them all ready to hear the answer, and I said, “The answer to zero divided by zero IS…something we’ll talk about on Monday.” Both classes sent up a roar of frustration and started moaning and groaning. I couldn’t help but laugh. I crack myself up sometimes.
Both of my Math 8 classes have been on fire this week. We’ve been working on exponent properties and I’m embarrassed to say that the lessons have been less than stellar, but that hasn’t stopped them. They have really gotten into simplifying expressions with exponents. I think they get a real sense of satisfaction because the expressions look so formidable at first sight. One of my classes in particular, has many students who have not been successful in math in the past. This class has put forth a tremendous amount of effort this week, so much so that I really took notice and couldn’t help but gush a little bit about it to them at the end of the period today. I am so proud of them and hope that this kind of enthusiasm and effort continue throughout the year.
A couple of my former students came by to visit after school today. They told me all about high school and how crazy it was, and how they missed my class. It was really nice. You always hope you’re connecting with your students, and moments like this let you know that you are. Before they left, one of them wrote this message on the board. How could this NOT be the highlight of my day?
Twelve students came in during study hall today to reassess on one or more learning targets from the past week. They ALL improved their scores from the first assessment. I hope this trend continues throughout the year.
We’re working on exponent properties in my 8th grade class and were talking about multiplying expressions with exponents and students had just generalized a rule by examining examples and non-examples. I gave students a few basic problems first, then told them we were going to step the difficulty up, which a lot of them got really excited about. They wanted a challenge. So I put a few problems on the board that at first glance freaked some of the students out, but they started working on them. This year I’m focusing on having students work individually first, then share with their groups. As I circulated while they shared with their groups, one of my students (who I have known since she was in 5th grade and has always struggled with math) had a big smile on her face. When I checked in with her group, it turns out she had simplified one of the expressions and her answer matched the rest of her group’s answers, which they had determined was correct. She was really excited about it and said to me, “Look Mr. M, I did it!” I felt great for her.