Friday, March 17, 2023

Lesson 6.3.3: Solving Systems by Elimination, Continued (Days 131-132)

Today is the seventeenth, and so this is my monthly "A Day in the Life" post for March. It is Friday, often a day for department or other meetings. But there is no such meeting today.

Of course, today is also St. Patrick's Day. I used to have a St. Paddy's Day pencil giveaway, but no such pencils are sold in stores these days. Thus I no longer have one.

8:30 -- First period arrives. This is the first of two Math III classes.

This is the second day of SBAC Prep Boot Camp. According to the pacing guide, today's task is to answer fifteen practice test questions on Illuminate. This platform is mentioned in the song I perform yesterday -- it's always used for district Benchmarks, but non-Benchmark tests can be taken there as well. Indeed, last year I used it for some Calculus and Trig tests, and this year another teacher has set up a practice SBAC there on Illuminate.

The pacing guide also states that the Chapter 8 DeltaMath test corrections are assigned as homework, which is atypical for me. But the other teachers want to make sure that the corrections don't take an extra day away from the SBAC Prep Boot Camp.

The Exit Pass question comes from a SBAC question. Eva wants to buy a bike for $240, but she only has $42 in the bank. If Eva is paid $12 per hour as a babysitter, then how many hours must she work in order to afford the bike? The correct answer is 16.5 hours -- but for the Exit Pass, I have the students round off the answer to 17 hours, because today's date is the seventeenth. After the Exit Pass, the students turn in their notebooks, since Chapter 8 is essentially over.

9:25 -- First period leaves for nutrition.

9:40 -- Second period arrives. This is the first of three Math I classes.

Normally, I give some sort of quiz or assessment every Friday in Math I. But this week, I'm leaning towards counting the poster project as this week's quiz. So instead I try to give a lesson -- unfortunately, there are several problems with today's lesson.

I'm labeling today's post as Lesson 6.3.3, but I'm torn between an extra of 6.3.2 and starting 6.3.3. Here the CPM lesson numbers refers to the three levels of the elimination method as defined by DeltaMath -- Level 1 is for pure addition or subtraction, Level 2 is where one of the equations must be scaled, and Level 3 means that both equations are scaled.

Today is Sixday on the Eleven Calendar:

Resolution #6: We implement all parts of our projects.

Yesterday was the first day of Lesson 6.3.2. As I explained in my last post, I decided to go over the DeltaMath questions on guided elimination last time and save Desmos for today (especially since the Desmos questions lead into Level 3, or Lesson 6.3.3, as well).

Unfortunately, the Desmos lesson doesn't go well. The first system in this activity is written in an unexpected format, C = By + Ax instead of Ax + By = C. It throws the students -- and me -- off, and it takes some time to figure out where we go wrong. And the other systems include fractions -- one as a coefficient, another in the solution. Indeed, the very first Level 3 system has a fractional solution.

I must admit that today's lesson is influenced by several rigidities -- patterns in how I teach the lessons that I uphold just because they're the way I've always done things. One of those rigidities -- the weekly Friday quiz -- is not in force today. But some others are -- including some influenced by the existence of the weekly Friday quiz.

First is the interactive notebook. In order to avoid having too many notebook pages (which would force the kids to buy three or more notebooks to span the year), I make sure that I assign no more than one page on most days (excluding the Warm-Up page) -- and no pages on Fridays (when, once again, I'd normally just give a quiz anyway).

As I explained in my last post, on the last block day I passed out a guided note worksheet containing the lyrics to the rap (with blanks for the kids to fill in). That worksheet took up the entire page, so there was no room to write anything else (like, say, a few system solutions worked out), since I didn't want to have them write on more than one page. Then today is Friday -- the day that there's no page. Thus during the entirety of Lesson 6.3.2, the students write only rap lyrics, with no Level 2 examples. And of course, I couldn't have saved the rap for today because I only perform on block days, not Fridays.

Yesterday's DeltaMath lesson was far more successful than today's Desmos, so perhaps I should have done more DeltaMath instead. The problem is that I set the DeltaMath assignment at the beginning of each week, to be due the following Friday (again because there's usually a quiz). And we already solved all the planned DeltaMath questions yesterday. Some students regularly finish the work the first day it's assigned, so they wouldn't appreciate suddenly having extra questions, especially on the day it's due.

There's also a problem with avoiding arguments. A few students are eating in class again. I tell them that I'll write the eaters' names down and decide on a punishment later, in order to avoid arguments.

Then I pass out the application forms for students hoping to take Math II this summer so that they can advance to Math III next fall (to reach Steve-level classes -- junior Pre-Calc and senior Calculus). One girl gets upset at this -- she calls herself and others the "D" word, meaning not very smart.

I try to tell her that she has a point -- I could have handed out the applications more discreetly. But then she assumes that I'm trying to argue with her over the food that she's eating. And so, although I'm trying to avoid arguing, an argument ensues anyway. That's the problem with arguing -- the students are so used to my arguing, they interpret anything I say as an argument. And that's why it's important to avoid arguments from the very beginning.

It's tricky to find a good Exit Pass question whose answer involves today's date. A possibility is:

5x - 3y = -1

-3x + 2y = 4

which is a Level 3 system with solution (10, 17). But since I don't reach Level 3 questions, I can't give this Exit Pass (though it's a much better question than the one that appears on Desmos).

10:35 -- Second period leaves. Third period is my conference period -- which means that it's time for my weekly tutoring session with three Math III students and my "prep period buddy" teacher.

Yesterday was Part II of the Chapter 8 Test -- the paper portion. Nevertheless, there's still something for these students to prepare for -- and I don't mean the SBAC. Next week is the Math III midterm exam.

Unfortunately, my prep buddy must cover a class this period -- a Spanish class. She's a native Spanish speaker, so she can handle this class -- after all, that's why we set up tutoring sessions in the first place, namely to help my English learners  (though she tells me that she -- just like me -- took French in high school, not Spanish). We decide to hold the tutoring session anyway -- I help out the math students while the other teacher watches the Spanish class and translates for us from time to time.

We work on a few questions from the last homework assignment, including the end behavior of polynomials -- a simpler topic, but one that I only briefly touched upon in class. I want to make sure that the students understand this ahead of the midterm.

11:40 -- Fourth period arrives. This is the second of three Math I classes.

Fourth period goes much more smoothly than second. I do finish both Level 2 questions, but we still don't reach the Level 3 question. Then again, I'm not quite sure whether Level 3 elimination will even be on the upcoming Chapter 6 Test.

Entering today, I'm slightly ahead of my neighbor teachers. They've just barely begun Level 1 of elimination, with perhaps an intro to Level 2. On the other hand, I'm behind my prep buddy, who's completing substitution today (after teaching elimination first). She could give the chapter test early next week, though she tells me that she'll spend most of the week on review.

I hear one of my neighbor teachers tell his class that Level 3 might not be on the test. The issue hasn't quite been decided yet -- but of course, if it's not on the test, it's not as crucial that I teach it. Instead, I should make sure that they're comfortable with Level 2.

I also attempt to hand out the summer Math II letters more discreetly than in second period, but still, one guy wonders why he doesn't get a letter. (Some teachers might take the time to put letters in envelopes and just hand out sealed letters to the proper students.)

12:40 -- Fourth period leaves for lunch. There is a "pie your teacher in the face" contest during lunch, but I'm not one of the victims. This probably should have occurred on Pi Day, but it takes place outdoors and thus was delayed due to rainy weather.

1:25 -- Fifth period arrives. This is the second of two Math III classes.

Fifth period works on the SBAC Practice Test on Illuminate. This is after I show them end behavior questions on the Warm-Up.

By the way, after mentioning how I overused Desmos in Math I, I underused Desmos in Math III. The teacher who created the Math III Desmos lessons also wrote the Chapter 8 Tests, so if I'd assigned Desmos, my students would have been better prepared for the test.

2:20 -- Fifth period leaves and sixth period arrives. This is the third of three Math I classes.

We do barely make it to the Level 3 question in this class -- but once again, it might not matter if there's no Level 3 on the test. And there's only one student recommended for summer Math II, so I easily give her the letter without others noticing.

3:20 -- Sixth period leaves, thus completing my day.

Last year, this was the last week before spring break. This year, spring break will be the last full week in March, so there's still one week left in the "Big March." Enjoy the rest of your St. Paddy's Day!

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