Wednesday, March 24, 2021

Lesson 13-5: Tangents to Circles and Spheres (Day 135)

Today is the second day of the two-day assignment in the high school Physics class. This time, I will "A Day in the Life," because there's something different about the schedule today:

8:00 -- The students begin taking the ELPAC exam for English learners -- the first state standardized test to be given this year.

There's been much discussion about whether state tests such as the SBAC should be given this year -- a year that has been disrupted so much by the pandemic. Last year, this very school had already started giving some of the state tests, including the SBAC, just before the shutdown -- and then in the end, all the tests were cancelled. This year, the ELPAC and SBAC will still be given -- although the SBAC won't be until after spring break this year.

Of course, some people might point out that the ELPAC has much more value to students -- since it really does matter whether they are learning the English language effectively -- than the SBAC does. So at least today's test is definitely worth giving.

Last year on testing day, all of us subs were told to report to the staff lounge and stay there just in case we're needed to fill in for one of the proctors. This year, our services aren't needed -- at least not for today's ELPAC exam. It remains to be seen whether we must proctor the SBAC or not.

Oh, and since today (like all Tuesdays and Wednesdays at this school) is a Cohort A day, it means that Cohort B (along with those opting out of hybrid) take the ELPAC at home.

Since today is an even period day, the ELPAC is followed by second period -- which just happens to be this teacher's conference period.

11:00 -- Fourth period arrives.

You might recall how on testing days the last two years, there were several tardy students, even though school started much later. Whether this will be the third straight year of post-exam tardiness remains to be seen, only because the class students would arrive late to is my conference period. There are two students tardy to fourth period -- the typical kids who walk leisurely from second to fourth period.

I cover the same assignment as yesterday -- and I might as well sing and play "Count on It" again on the music lab/piano website.

11:40 -- Fourth period leaves for snack break.

11:55 -- Sixth period arrives.

This class has one tardy student -- to be more precise, she's not "tardy" so much as to be yet another student who asks for a restroom pass right after break.

12:35 -- Sixth period leaves. Due to the ELPAC, there is no academic support today, and so my day ends here.

Today is Saturday, the second day of the week on the Eleven Calendar:

Resolution #2: We make sacrifices in order to be successful at math.

This doesn't really fit -- not even with the "Count on It" song, which discusses the importance of learning math and science but not the need to make sacrifices. The only sacrifice I ask a student to make is of the girl who leaves for the restroom -- I remind her that she should have already gone before getting to my class.

Here are the stats for the Miller wager for the even periods today:

4th period: 11 in-person, 24 opt out, I win $2.
6th period: 15 in-person, 20 opt out, I lose $10.

Of the in-person students, 15 have opted into the four-day schedule (six in fourth period, nine in sixth).

At first, I thought I'd lose money in fourth period, since there are so many kids in the room. It turns out that there are many Cohort A (and four-day) students and only a single Cohort B student, so I just barely scrape by. Miller makes most of his money in sixth period -- even more if I pay double for the four-day students.

A much more reasonable wager, now that there are four-day students, is for me to pay $1 for two-day students (regardless of grade level) and $2 for four-day students. While I still make a profit of $7 for fourth period, I give $4 of it back for sixth period.

Since I keep discussing the Darren Miller wager over and over again, I really need to look at what's going on with the actual Darren Miller. His worst nightmare -- the hybrid schedule -- is beginning at his school this week:

https://rightontheleftcoast.blogspot.com/2021/03/stranger-than-you-can-even-imagine.html

He mentions that some students are opting out, but I don't know whether it's enough for me to win the Miller wager for Miller's actual classes:

Now, however, students are opting out of in-person school, which starts at 8:05 and gets out around 11 am, so that they can take online class, which doesn't start until well after noon.

Ah, so this is a huge difference between Miller's hybrid and the hybrid plan in my two districts. Instead of teaching to in-person and online students at the same time, his day is split AM/PM, with in-person in the morning and online in the afternoon.

It appears that at Miller's school, Cohort A is Monday/Tuesday while Cohort B is Thursday/Friday. As for Wednesday, today the students take the SAT -- all in person, of course. You'd think that Miller's Wednesdays would be like my Mondays -- every period meets online. I won't know until next week when there's no SAT -- provided, of course, that Miller blogs about it next Wednesday.

And speaking of next Wednesday, that's my next scheduled traditionalists' post. The frustration that Miller is having with the hybrid schedule really does merit its own post, so I'll save it for next week. (I remind you that you can click on the link if you want to read about his problems now.)

Today on her Daily Epsilon on Math 2021, Rebecca Rapoport writes:

How many vertices does a truncated cube have?

An ordinary cube has eight vertices. Truncation of the cube replaces each of these with a small triangle with three new vertices. Therefore a truncated cube has 8 * 3 = 24 vertices -- and of course, today's date is the 24th.

https://mathworld.wolfram.com/TruncatedCube.html

Yes, a truncated cube is an Archimedean solid, with eight octagons and six triangles as faces.

Lesson 13-5 of the U of Chicago text is called "Tangents to Circles and Spheres." I never wrote much about this lesson -- neither last year nor the year before last.

I believe that tangents to circles appear in Chapter 10 of the Glencoe text -- most likely it's just around the corner in Lesson 10.5 or 10.6, so the kids at my school will see them soon. This also reflects the placement of this lesson in the modern Third Edition of the text, where it appears as Lesson 14-5, in the circle chapter. (Recall that our current Chapter 13 doesn't appear in the new edition, and so Chapter 14, not 15, is the circle chapter.)

So I'll post the worksheet from two years ago.


No comments:

Post a Comment