Today we were working on writing linear and non-linear functions from Brad Fulton’s book, The Pattern and Function Connection. There are 52 patterns, labeled A-Z and then AA-ZZ. Of course, when any group began working on Function PP I heard them snicker and giggle. I get it. It’s kind of funny even for me (teaching middle school is easier if your sense of humor is closer to theirs). Anyways, I was with one group who got Function PP and began giggling, to which I sarcastically laughed and said, “OK, get it out of your system.” Without missing a beat, one of my funnier 8th graders replied with, “Pun intended.” It was brilliant. So quick. So perfectly timed. I was jealous I didn’t think of it first! I couldn’t help but laugh out loud. I love it when that happens.
Earlier this year in geometry we looked at examples and non-examples of different figures in order to let students develop their own definitions for the figures. I really enjoyed the process and felt like it was great for students, so I tried it again today when introducing functions to my 8th graders. I gave them one function and one non-function, and let them compare the two and try to figure out what distinguished the one as a function. After having the student discuss in their groups and then share out, I put another example of each up, which contradicted their first conjectures. For example, the first function I put up was linear, so a lot of students guessed that functions were linear. But then I put up a parabola, which threw that off. This went on for a while and I started putting up input/output tables and sets of coordinates. Finally, in both classes students began noticing that each x value, or input was only used once in the functions, and some were used twice in the non-functions. It was a great letting the students develop their own definition for functions based on exploration and discussion, rather than me just telling them what a function was. I want to do this more often.
Once again (for at least the 4th time in the past few weeks), I found a great task from Math Projects Journal to use with my geometry students today. It involves robotic characters at Disneyland and midpoints, distance formula, parallel and perpendicular lines, centers of a triangle, all sorts of good stuff. Students were fully engaged and the discussions happening were great. One of my favorite moments of the day though came as I was approaching a group to check in with their progress and student A had just finished asking student E if he could solve one of the problems a certain way (I didn’t catch which one). Student E looked at him and responded, “That’s not how it works. That’s not how any of this works.” ( a la this Esurance commercial). It produced yet another “Mr. M laughs hysterically in the middle of class” moment. Those are always fun.
We’re in the middle of our coordinate geometry unit and today I gave the students a few problems from the Open Middle geometric properties section, the awesome website put together by Robert Kaplinsky, Nanette Johnson, and Bryan Anderson. While the problems all involved concepts we’d been discussing (parallel and perpendicular lines, distance, etc.), they were definitely a higher DOK level than we’ve been using. That’s one of the reasons I wanted to give these problems to the students, because they need to practice with these types of problems. Students jumped right in and started trying a bunch of different strategies while trying to work the problems out. At one point one of my students sighed and said, “This is SO frustrating.” To which I of course replied, “Good. It’s good to be frustrated sometimes.” I need to be better about finding these types of rich problems, that are accessible but “frustrating,” and giving them to my students on a more regular basis. Thanks for the great work Open Middle!
Today for a warm-up I gave my classes one of John Stevens’ awesome Would You Rather prompts: Would you rather receive 500 pounds of pennies or 40 pounds of quarters? The discussion was great. Most students wanted to figure out which one was worth more, so I threw that out to them as a bonus question. I had them think for a minute and then move to opposite sides of the room, a la Brad Fulton. My favorite part ended up being one student who kept bouncing back and forth from one side to the other as she changed her mind. Her reasoning at different times included thoughts like:
“Well the pennies weigh 12 and a half times more than the quarters.”
“But one quarter is worth 25 times more than a penny.”
“But I think it takes about 2 pennies to weigh the same as one quarter.”
The discussion was great. Most couldn’t believe that the prompt was based on a true story. I ended up showing them the article linked on the WYR website. Middle schoolers ALWAYS need proof.
So we’re beginning our coordinate graphing unit in geometry and we’ve been reviewing things like different forms of linear equations, parallel and perpendicular lines, etc. Today I gave students an activity, based on the old TV show “The X-Files,” to work on out of Chris’ awesome Math Project Journal’s Ultimate Math Lessons book (which I love BTW). The thing about this activity is that it’s so far fetched that as hard as I tried, I couldn’t read the scenario without cracking up. It involves the President being kidnapped by aliens and them organizing a hostage exchange between themselves and Mulder who had captured one of their alien buddies. Anyways, both myself and the students got a good laugh, and they enjoyed the task itself. BTW, I’m sorry to report that based on our findings the President has been taken to a galaxy far far away. But now we have an alien on Earth, so…
You’ve been to Christopher Danielson’s awesome site Talking Math With Your Kids, right? Of course you have. And you’ve downloaded his awesome new shapes book, “Which one doesn’t belong?”, right? Of course you have. Well I have too, and over the past few weeks I’ve been using it with my 8th grade classes as a warm-up once a week. When I showed them the first set of shapes and asked them which one didn’t belong, there was obviously some disagreement and some outrage that there seemed to be a reason why any of them wouldn’t belong, but I was forcing them to choose ONE.
Now, 8th graders NEED resolutions to situations like this, so I had to give them an answer. Obviously, if I told them that any could “not belong” depending how you look at it, that would’ve been the end of it. So instead, on the spot, I just decided to pick the shape that the least amount of students thought didn’t belong. But here’s the best part: I didn’t tell them WHY. Instead, I told them that I’d show them 4 new shapes next week and they could use the information gathered from today to make their decision next week. This has happened for the last 4 weeks. Every week I tell them that there is a pattern to figuring out the shape that doesn’t belong, and a few have mentioned, in jest, that I just pick the shape with the least people.
But the shape I choose is clearly not the point. The point is the discussions. They are great discussions with students analyzing side lengths, angle measures, polygon properties, and polygon dissection. The discussions are rich with geometric reasoning and several students always change their minds during the course of discussion, when another students brings up a point they hadn’t thought of. I’m going to do this for at least one more week, and if they’re lucky, I just MIGHT tell them how I’ve been choosing the shapes. Maybe.
After taking 2 weeks off, I’m back! We just came back to school yesterday after a 4 day weekend, and if you’re anything like me, the “short” weeks always feel like the longest! I’ve been confused about what day it is, what classes I see each day, etc. That leads into what happened today.
So today we were talking about my favorite infinite sum (1+2+3+4+5…) with geometry (we’ve been discussing these once a week as a warm-up because they really get into them). Before we discuss, I have each student write their initial guess on a small piece of paper and collect them, then I write all of their answers anonymously on the board. So today I collected the papers, walked up to the board, and looked at the first one. 8. 8? Really? I was confused but I write all answers on the board so I wrote it and looked at the next paper. 8. Seriously?!!! So I put a check next to the first 8 and looked at the next paper. 8?!!! You’ve got to be kidding me!!! I was really confused about how multiple students all came up with 8 as an answer. Then one girl said, “Mr. M, are you sure that’s not infinity?” I proceeded to have one of those moments where I realized what had just happened and then couldn’t do anything but laugh. The rest of the discussion, anytime I referred to infinity, I called it 8. The students, of course, thought the whole situation was hilarious!
Today we were exploring congruency shortcuts for triangles using this lesson recommended by Elissa here. It went really well. Students were having great discussions in their groups and exploring conditions using Anglegs. I can’t tell you how much I’m enjoying my geometry classes this year. Almost everyday is class I am impressed with the amount of thoughtfulness and effort that they put into our explorations. I somewhat expected this coming into this year, as these are 8th graders who are 2 years ahead in math, but I wasn’t expecting this level of engagement. I want to make sure I keep challenging and pushing them, as they seem to be rising to every expectation I put forward. I’m having a great time teaching these kids this year.
Today we had a half day with professional development in the afternoon. This year for our PD days, different members of the staff are presenting sessions and we all choose which ones we want to attend, like at a conference. Today my session was about a bunch of the awesome resources that members of the MTBoS have created. I only had 45 minutes, so I showed them Estimation 180, Visual Patterns, Math Talks, Would You Rather, and Math Arguments 180. The teachers seemed really excited about these resources and the ways I explained how they engage students and provide great discussions. I’m excited to see how they’re implemented in their classrooms. HUGE shout outs to Andrew Stadel, Fawn Nguyen, John Stevens, and @MathCurmudgeon for all of their hard work putting these sites together for the rest of us to use.