Today I subbed in a senior Business Math class. It's in my LA County district. Technically, since it's a math class, I will do "A Day in the Life" today, although as we've seen before, Business Math leans more towards practical skills than actual mathy math.
8:30 -- Second period arrives. As we've seen before, in this district, all fourth quarter classes under the district 4 * 3 plan are even numbered classes. This week is also the first after this district has moved from Level 2 (one in-person day) to Level 3 (two in-person days -- classic hybrid).
The main lesson is on health insurance. The students mostly watch a video on Google Classroom and then answer questions. I'm granted access to neither Classroom nor the video, and so it's mostly just students working independently.
In fact, I'm barely granted access to Zoom. In this district, the office manager is usually the host of Zoom, and I must wait for her to let me in. But when I arrive, the office is crowded, and so I intentionally wait until 8:55 -- the last five minutes of the required half-hour -- so that the office has a chance to clear before I disturb her.
Thus the Zoom students are only online long enough for me to take attendance and state the lesson -- they spend most of their half-hour in the waiting room. In particular, I don't have time to sing a song for them -- today's song is for the in-person students only after I end the Zoom. Since it's Business Math, I perform my default song for this class, which is the Compound Interest Rap.
9:40 -- Second period ends for snack break.
9:55 -- Fourth period arrives.
This time, I call the office early, since I figure that it's less crowded by now. This means that I have time to perform the Compound Interest Rap during the Zoom half-hour.
11:05 -- Fourth period ends for another break.
11:20 -- Sixth period arrives.
One in-person guy has the same name as my uncle -- the one who died exactly six months ago today. In fact, I tell him of the half-anniversary and warn him not to become an alcoholic like his namesake. (I can't help shedding a tear, seeing a student with this particular name on this particular day.)
12:30 -- Sixth period ends for lunch. Like my first Orange County district, there is some sort of academic support for the students after lunch. But it appears that I don't need to stay for it -- typically, when I can't enter Zoom freely and must wait for someone to grant me access, it means that I don't have to stay (since it's possible that the regular teacher will open the Zoom herself and run the support).
Today is Sunday, the third day of the week on the Eleven Calendar:
Resolution #3: We remember math like riding a bicycle.
Returning to the song, I notice that the Compound Interest formula is written in faint marker on the regular teacher's desk -- presumably she teaches the formula at some point in this class. But the students tell me that they don't recognize the formula. My hope is that after hearing the song, the students will learn and remember the formula better, especially if their teacher mentions it in class soon.
Otherwise, there's not much more to say about this. Once again, the actual lesson was on insurance, and I don't watch any part of their video at all.
This is what I wrote last year about today's lesson:
Lesson 15-4 of the U of Chicago text is "Locating the Center of a Circle." According to the text, if we are given a circle, there are two ways to locate its center. The first is the perpendicular bisector method, which first appears in Lesson 3-6. (Recall that the perpendicular bisectors of a triangle are a concurrency required by Common Core.) This section gives the right angle method:
1. Draw a right angle at P (a point on the circle). AB (where angle sides touch circle) is a diameter.
2. Draw a right angle at Q (another point on the circle). CD is a diameter.
3. The diameters AB and CD intersect at the center of the circle.
This method is based on the fact that a chord subtending a right angle is a diameter -- a fact learned in the previous lesson. Indeed, "an angle inscribed in a semicircle is a right angle" is a corollary of the Inscribed Angle Theorem.
Notice that unlike the perpendicular bisector method, this is not a classical construction. That's because the easiest way to construct a right angle is to construct -- a perpendicular bisector, which means that if we have a straightedge and compass, we might as well use the first method. The text writes that drafters might use a T-square or ell to produce the right angles, while students can just use the corner of a sheet of paper.
This lesson was formerly presented as an activity. Activities have already been given in this chapter, and so this should become a regular lesson. It might be a good time to remind the students about points of concurrency -- a Common Core topic (although this particular concurrency point isn't in the Core):
"Each of the three circles below intersects the other two. The three chords common to each pair of circles are drawn. They seem to have a point in common. Experiment to decide whether this is always true."
As it turns out, these three chords are indeed concurrent, except for a few degenerate cases such as if the circles have the same center or if the centers are collinear. (The concurrency of perpendicular bisectors has the same exceptions.) The students are asked to experiment rather than attempt to prove the theorem that these three lines (called radical lines) intersect at a common point (radical center, or power center). The name "power center" refers to "power of a point" -- a dead giveaway that we must wait until Lesson 15-7 before we can attempt to prove the theorem.
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