Friday, November 20, 2020

Lesson 4.1.2: Simplifying and Rewriting Algebraic Expressions (Day 66)

I normally don't post to the blog on Fridays during my current long-term assignment. But today is the last day of school before Thanksgiving break -- and so following Tina Cardone's old rules, the last day of school before a break counts as a special day. So it's time for "A Day in the Life" for this special day:

8:00 -- I arrive on campus.

8:45 -- Even periods meet on Fridays, so this is second period. This is a seventh grade class, and the first of two classes with a co-teacher/aide. In fact, that's one reason why I'd chosen Friday as a non-blogging day -- the aide helps with classroom management, and there are special ed students whose specific situations aren't appropriate for discussion on a blog. Still, I want the readers to know a little bit about the cohorts I see on Fridays -- and I get to do "A Day in the Life" on a hybrid day, not distance.

The seventh grade cohort I see on Fridays is one of the smallest classes I have. There are only eight students, including one guy who opted out of hybrid and is thus is an online-only student. But with one girl absent, and another boy who goes back and forth between hybrid and distance and chooses to go distance today, there are only five students in the classroom.

As I wrote on Tuesday, Math 7 has been problematic all week, as I try to balance the Benchmark Tests with today's APEX lesson. Since I already have two posts this week labeled "Math 8," I'll count this as a Math 7 post, and so I'll focus on this class in more detail.

Here's how I decided to time the 100 minutes of this class, based on how long it took me to do things earlier this week. We begin with 20 minutes of going over two-step equations. To introduce this, I sing the "Solve It" song.

9:05 -- We start the Benchmark Tests. For most students, this takes anywhere from 20 minutes to just over 30, and so I allot a half-hour to this district assessment.

9:35 -- I sing my second song -- the "Benchmark Tests" song, which explains to the students the reasons for taking this test. I use this as a transition to the APEX portion of the day, and so I begin teaching the lesson on simplifying and rewriting algebraic expressions, including like terms. Students also must add, subtract, multiply, and factor (with constant GCF) linear expressions. We begin with Example #6 on the study guide and work our way to #11.

10:05 -- This leaves 20 minutes for the students to take APEX Quiz 4.1.5. Some of the students are able to pass it, but others struggle. The aide and I try to help these students, but they still end up leaving the classroom without passing the quiz.

10:25 -- Second period ends. This is followed by tutorial. Like everyday this week, students report to their fifth period class for tutorial, and we discuss ways to improve their grades after the alarming number of D's and F's the students earned during the first quarter.

Like second period, fifth period has only eight students in this cohort. Of these eight students, four of them have opted out of hybrid. And another girl is also attending online, thus leaving only three students in the classroom.

Since the class is so small, I discuss goals with each student individually. Each one tells me what he or she has done to improve the grades, including keeping up with when assignments are due on Canvas and asking teachers for help when they need it.

Students with at least three D's or F's are supposed to meet with a counselor during tutorial. But two such students haven't done so -- one is the girl who chooses to attend class online today, and the other is a guy who is always online. It's easy to see why these online students are the ones who are having trouble meeting with a counselor.

11:10 -- Tutorial ends, and it's time for snack break.

11:25 -- Fourth period begins. This is an eighth grade class, and the second of two classes with the aide/co-teacher.

There are a dozen students in this class, including four students who having opted out of hybrid at the start of the year. But there is one guy who officially switched to online this week, along with two more students who unofficially attend online today. Thus this is the second straight class where online students are in the majority.

On the other hand, one girl announces today that she plans on doing the opposite -- she now has permission to attend both last name cohorts in-person, not just her own. Thus she'll be on campus four days a week, and she'll be in my fourth period both Thursday and Friday, presumably starting after Thanksgiving break.Since eighth graders aren't taking Benchmarks this week, I begin lesson on APEX right away. Then I set them loose to work on the Kuta equations worksheets that are posted online.

My intent is to call on some students to solve some one- and two-step equations with me as I sing the "Solve It" song with them. My most successful day doing so was yesterday, butoing this today is trickier for two reasons. First, so many students are online today, and so I must keep going back and forth between calling on in-person and online students. Second, the students are doing so many different things at this time -- some are doing the worksheets, while others are waiting until they can print them up at home, so they do something else instead, such as making up Edpuzzles from Monday.

Still others are making up the Unit 3 Test from last week. This has nothing to do with the third quaver progress reports (by now it's way too late to change them), but just to make up the material in order to be successful for the whole quarter. Two of the students who struggle to make them up are special ed students who keep retaking the test, but to no avail. One is a girl who's online for family reasons (and that's all I'm saying about that on the blog) -- the aide tells me that before the pandemic, she was able to help this girl one-on-one, but with online learning it's so much harder. The other is a guy who may need accommodations, but I missed the meeting last week when those accommodations were discussed.

Two other students who need to make up the test are gen ed. Both of them moved online today (one officially, the other unofficially). They both need to make up several quizzes before they can even reach the Unit 3 Test. The aide suggests that I send parent emails to the students who need to finish the test.

There are also some seventh graders who email me during class to ask me to reset APEX for second chances on their own Quiz 4.1.5. These students are in the Tuesday cohort -- the group to which I rushed the lesson the most, and so are struggling with it now. Thus they are working today (on their asynchronous day) to make up the work.

1:05 -- Fourth period ends for lunch.

1:45 -- Fifth period (which meets everyday) returns. This is the Math Skills class.

The girl from this class who unofficially attends tutorial online is absent for fifth period proper. It's possible that she's just confused about the schedule and erroneously believed that attending tutorial counts as attending fifth period proper. So there are three in-person and four online students today.

The students finish their 60 weekly minutes of ST Math or Dreambox today. I inform the students that they must have completed at least 42 minutes (since this is 70% or a C) by the end of the period, or I'll count them as non-participating. One guy (the same online student who hasn't seen his counselor yet) wonders why his Dreambox minutes don't seem to be counting. Another online guy helps him out by showing him how to log out properly -- I allowed them to share their screens so they can see each other's Dreambox sessions -- so that his minutes can count. In the end, all students at least make it to the 42-minute mark.

I end the class with the weekly "Hero Quiz." Since today is my eighth week at this school, I decide to do the 8's Hero Quiz (orally) today. One online guy isn't paying attention when I ask him what 8 times 2 is -- he probably just logged into Google Meet and then walked away from his computer. Fortunately, he already has well over 60 minutes completed on Dreambox.

2:35 -- Fifth period ends, thus completing my day of teaching.

Just before the final bell, I receive an email from a special ed teacher. Apparently, there will be a meeting soon on behalf of the fourth period girl who is having trouble with her Unit 3 Test. Perhaps some accommodations will be discussed there that will help her out. I spend the rest of my day sending out emails to the parents of the other fourth period students who haven't finished the Unit 3 Test. Then I finally go home.

The principal sends us teachers an email telling us that we've worked so hard during hybrid, and now we've finally reached a well-deserved week off. We shouldn't do anything related to work during our Thanksgiving break.

This turned out to be a strange week for me on the blog. I've used the label "MTBoS" three times. Two of these are to indicate the "A Day in the Life" format. The other was to discuss the writings of Fawn Nguyen and Eugenia Cheng on Tuesday -- but I wrote about that day extensively as well, and so it might as well have been "A Day in the Life" too.

And today in the classroom is also weird. With so many students choosing to go online today, no more than five students are in my room during any period. Even stranger is the fact that the maximum number of male students in my room during any period is one (which is also the minimum).

There is a Google Doodle today celebrating a famous mathematician -- Benoit B Mandelbrot, who was born this day in 1924. I was considering briefly mentioning him in class today, but I didn't. (I'm rushed for time with everything going on in Math 7, and then I forget in every class thereafter.)

But I will reblog something I wrote five years ago on the blog. This was when I was reading a Mandelbrot book on -- what else? -- fractals. Since eight is the number of the week -- this being my eighth week of the long-term assignment (out of twelve -- I'm two-thirds of the way home) and the week of the 8's Hero Quiz -- let me reblog Part 8 of Mandelbrot's book. (I'm also adding my old "Benoit B Mandelbrot" label for this reason.)

Part VIII of Benoit B. Mandelbrot's The Fractal Geometry of Nature is called "Stratified Random Fractals" and consists of Chapters 23 through 26 of the book. As I mentioned in yesterday's post, the fractals in this section are randomly generated.

And so Mandelbrot devotes a chapter to each of the types of fractals discussed earlier in the book, but this time giving a randomized example. For example, in Chapter 23, he describes random "curdling" similar to the formation of the Cantor set -- instead of always choosing the middle thirds interval, one chooses a random interval, then a random subinterval after each step. If one begins with a cube of three dimensions, the resulting fractal has approximately 1 dimension, and this is a more accurate model of the universe than can be given using nonrandom curdling, as the locations of the galaxies appear more or less at random.

In Chapter 24, Mandelbrot moves on to randomized fractals that are analogous to the Koch coastlines and snowflakes. Afterward, he moves on to Brownian motion, which describes how subatomic particles move. Recall that these fractals are random, and so they aren't self-similar -- no dilation maps the fractal to any part of the fractal.

And this completes today's post. As usual, I'll be blogging twice over the Thanksgiving holiday, so watch for those posts next week.

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