But let's start with yesterday's lessons, though, since I really want to discuss how I taught Geometry on this Geometry blog. As I mentioned during last week's Thanksgiving break posts, I began with CPM Lesson 3.1.1, which introduces reflections. The students sort of figured out what it means to reflect a polygon across a mirror. But while I tried to adjust the lesson throughout the day, the result was the same -- the students struggled with the coordinates part of the lesson.
This is to be expected -- many of the problems we had in Chapter 2 ultimately go back to the fact that they aren't completely comfortable with a coordinate plane. But hold on a minute -- there's not even supposed to be a coordinate plane in our intro to reflections! This idea goes all the way back to David Joyce, a mathematician whom I described on the blog in the early days. (Joyce wouldn't completely agree with transformation-based Geometry, but he does state that a coordinate plane should be avoided until synthetic geometry is taught.) And in fact, the original CPM problems don't contain a coordinate plane either -- there is a grid in the background, but neither the vertices nor the mirror line are labeled with x- or y-coordinates.
So where did the coordinates come from? Apparently, one of my colleagues created this worksheet and just added the coordinate section himself (or herself). While I can understand why we might want coordinates here, I've established myself (here on the blog) as the transformations expert, so I shouldn't blindly follow what the other teachers do.
By the time I reached sixth period yesterday, I decided to emphasize the first part of the worksheet where the students draw the reflections and save the coordinates for the end. A few students still had drawings that weren't exact, though. Perhaps this would have been a good time for me to turn on the Promethean and use its Whiteboard grid to emphasize the importance of being exact in the drawings.
That takes us to today -- Giving Tuesday, the last day of the Thanksgiving week in which almost every day has a special name. I'm almost tempted to write this as "A Day in the Life" with the weird things happening in second and fourth period, but I won't.
I already mentioned how Transformation Golf has already been set up in Desmos. In second period, I set up the Desmos and leave it for the students to work on after I leave for the meeting.
As for fourth period, I hadn't been planning to show a livestream of the USA soccer match -- instead, I was just going to show them the score from time to time. It's my neighbor teacher, showing her own class the game during third and fourth period, who convinces me that the quadrennial event is going to be a distraction anyway, so I might as well do something simple, like the same Desmos that I'd already left for second period.
Of course, the timing of the World Cup couldn't have been any worse. The big primetime matches in Qatar's time zone end up at 11 AM Pacific time -- and since it's in November-December due to the Qatari heat, it's during the school year. I should be fortunate that the first two USA matches were during Thanksgiving break.
(In 2018 and 2014, the World Cup began on Day 180 in the respective school districts where I was subbing at the time, so it wasn't much of a distraction. The last time the Cup affected me at a school was all the way back in 2010 -- back when schools still started after Labor Day and so the last day of school was deep into June. The first semester of 2009-2010 was my student teaching, but I was subbing in my district during the second semester.)
Moreover, my neighbor teacher is also one of the two teachers writing the Math I final exam. In her own class, she decides to jump to Section 3.3 on distributive property and solving equations, and informs me that there might not be much transformations on the final. As much as I want to teach the Geometry lessons, the priority must be preparing the students for the final exam.
Indeed, tomorrow in fourth period will be even more distracting than today. The majority of my students are Hispanic, and so they might be interested in Team Mexico as they play Saudi Arabia. And moreover, Mexico (unlike Team USA) doesn't control its own destiny -- it also needs a favorable result in the Argentina vs. Poland match in order to advance. Furthermore, some of my students care about Argentina not because of Mexico's group, but due to the presence of the famous Lionel Messi. (At least USA's match vs. the Netherlands will be on Saturday, not a school day -- and I believe that Mexico, if they advance, will play on the weekend as well.)
So the last thing I want to do is teach Lesson 3.1.3 on slopes of parallel and perpendicular lines -- my kids already have lots of trouble with slope, and then I'd be teaching that when there are two matches competing for their attention. Thus instead, I might likewise jump to 3.3 like the other Math I teachers, though I'll still do Transformation Golf with sixth period tomorrow.
And so, unless it's announced that more of 3.1 will be on the final, that's the sum total of the Geometry that I'm teaching this semester -- in a chapter that's delayed because we kept extending Chapters 1-2, then taught when there are special ed meetings and World Cup distractions, and then compressed because it's almost winter break.
I look forward to teaching the next Geometry chapter, namely Chapter 7. But who's to say that this chapter won't suffer the same fate -- Chapters 4-6 get extended, then we're up against spring break so the other teachers say, let's cut out the Geometry again?
And all of this ruined my song as well, since I don't perform during the soccer match.
I'll still post the Mocha code for this song:
https://www.haplessgenius.com/mocha/
Don't forget to click Sound before you RUN the program.
The chord riffs are Am-D for the verses, Am-C for the pre-chorus, and E(7)-Am for the chorus. The chorus melody is E-(low)A-B-E-(high)A, with the B representing Degree 11.
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