Today is many things. According to the blog calendar, today is Day 120. Therefore, it is the end of the second trimester -- at least it is in my first OC district. (And as we found out last year, this district has trimester finals for middle school students.) But as we saw in my new district, my new district has quarters in middle school, not trimesters.
Today I subbed in a high school instrumental music class. It is in my first OC district. (Of course, since it's a high school, there are no trimester finals today.)
I won't do "A Day in the Life" today -- but as usual, I will say a little about the classes. It's an even period day -- second period is Band, fourth period is Strings, and sixth period is conference. In each class, most of the students are freshmen.
In Band, the students work independently on their respective instruments. They have three assignments to work on -- two of which involve the Bb major scale. This is a fairly common key for many woodwinds and brass instruments. The students consider practicing outside -- but they don't, due to the weather. Yes, it's a California "snow day" (that is, a rainy day). Instead, they work in the practice room where their instruments are stored.
Unfortunately, things don't go as smoothly in Strings. For some reason, the Zoom link that I've been using suddenly doesn't work. It's almost as if someone flipped a switch -- before school, both the second and fourth period Zoom links work, but after snack break, neither does. It's happened before.
When I complain about it later on, I hear that it has something to do with Chromebooks -- for some reason, many Zoom features don't work on them. This is why it's better for us to create our own Zoom link and then post it in Google Classroom. But that doesn't explain why the links worked before snack on my Chromebook and not after.
Luckily, this class has a few aides (or music "coaches"). One coach is able to get into the Zoom meet, declare himself the host, and then admit me into the meet and declare me a cohost. Then he sets up breakout rooms depending on section (basses, cellos, and so on). This class has three assignments too -- two of which involve the D major scale. Unlike band instruments where flat keys dominate, string instruments are more likely to use sharp scales.
But then the coach host has to leave early for a meeting -- and since no one else is a host (the other coaches and I are merely cohosts), the Zoom meet ends completely. One of the other coaches is able to restart the meet -- but by this point many of the online students leave and don't return.
I always like to sing songs when I'm in music class. The song that I plan for today is "Mousetrap Car Song," since it's an original simple song. And I try singing it in the keys that the students are learning now -- Bb major for Band, D major for Strings.
I originally wrote "Mousetrap Car Song" in the key of E minor, but right at the end I jump to the relative G major, so I can claim the song as a G major song. Then I simply transpose this song from G to either Bb or D major depending on the class. Still, the song spans one full octave of the E minor scale, which in my vocal range takes me from E3 to E4.
For D major, the relative minor is B minor, and I sing the song from B2 to B3. But for Bb major, the relative minor is G major, and both G2-G3 and G3-G4 are difficult for me. I believe that I end up singing G3-F4 (as the highest G isn't emphasized), just as I did for "Whenever You Multiply."
For some reason, there is also a banjo in the main room, and so I decide to try it out. After writing about ukeleles all week, now I find myself playing yet another string instrument.
I know nothing about the banjo, but I notice that it has six strings -- and when I play them, they sound just like the standard tuning of a guitar, EADGBE. This suggests that I can play the same familiar guitar chords on the banjo.
In Band, I play "Mousetrap Car Song" in its original key, G major. But in Strings, I try transposing the song to the key of the week, D major. The guitar and banjo -- themselves string instruments -- share with the violin a preference for sharp scales, and so it's easier to play D major than Bb major. The tricky part is that the relative minor, Bm, is a barre chord on the guitar, as is its dominant F#7. I don't know whether banjo players use barre chords or not. I'd think that since a banjo has the same six strings as the guitar, we'd play the same barre chords as well -- and so I play the barre Bm and F#7 chords today on the banjo. (On the other hand, we saw that barres are unnecessarily on the four-string uke. Also, it appears that there is no preference for sharps or flats on the uke -- the easiest major chord to play is C major, the scale with no sharps or flats.)
Since the students are working independently in Band. there's enough time left for another song. I ask one guy to choose a song, and he chooses "Show Me the Numbers." Since I've found my old songbook, I wrote down part of my original tune from the old charter school and play it. Based on what I wrote, it's ambiguous whether I intended the song to be in the key of C or G major. Today I play it in G major on the banjo (again, I avoid Bb major on the banjo).
But I sing the new lyrics that I posted over the summer for this song. The old lyrics that I wrote at the charter school are obsolete. I also wrote that day that I wanted a new tune for this song using EDL scales -- I suggested using 20EDL. (That was before I found the songbook where I wrote part of the original tune.)
I could continue to write about 20EDL, but I won't. There are other things for me to discuss in today's post, and so I'm done with music for now.
Today is Sunday, the third day of the week on the Eleven Calendar:
Resolution #3: We remember math like riding a bicycle.
I mention this and all the other resolutions as part of the "Show Me the Numbers" song. I also point out that the students should remember how to play their instruments like riding a bicycle.
And finally, today is the day of the Chapter 11 Test. All those other things might be fun, but this is a Geometry blog, so I must post the test -- sorry.
Today is a test day -- hence a "traditionalists" post. Our main traditionalist, Barry Garelick, is still on his victory lap following the publishing of his fourth book. The post in which he announced the publishing has drawn a few more comments, but I won't spend much time on them now.
Instead, I wish to discuss an issue that's been all over the news -- the school reopening debate. I work for two OC districts where schools in all grades K-12 are open under the hybrid model. Some schools are fully open again, while others are still in full distance learning.
I'm surprised that our main traditionalist Garelick hasn't written much on school reopening -- but then again, he was preoccupied with the completion and publication of his fourth book. So instead, the traditionalist who's had the most to say about this is Darren Miller, of Right-(Wing) on the Left Coast.
Miller's high school is currently on full distance learning. But he's made it clear that he would prefer for his school to reopen full-time.
Once again, I'm torn over this issue. On one hand, I'm grateful that at least some schools are open, since teachers who work from home have less need for us subs, even if they get sick (in general, not necessarily sick from the coronavirus). On the other hand, I wonder whether there's any real reason to rush a reopening, especially considering that so many students are opting out of in-person learning at the schools where I sub. (Of course, older students are much more likely to opt out than younger students due to the supervision issue.)
Miller has mentioned mental health to support his side -- he sometimes points out that mental stress has increased in teens lately, and he blames it on the pandemic and school closures. I can't quickly find the specific post in which he makes this claim, but he likely cited reports like the following:
https://www.cidrap.umn.edu/news-perspective/2021/03/teens-mental-health-claims-skyrocket-pandemic
(Before we continue, I point out that I do not wish to offend the family members of anyone who has lost a young loved one due to mental depression. In this post, I refer only to mental stress and not to suicide, which I never want to take lightly.)
The claim here is that teens are stressed out due to the school closures, distance learning, the inability to see friends, and loneliness. The implication here is that teens really, really, want to get back to school, so if we were to open all high schools tomorrow, they'll be very happy and depression will plummet.
But if this were the class, then why do many high school students opt out of in-person learning. Why do I cover so many classes with just one or two students in-person and the rest at home? If distance learning is the source of depression, why are so many students choosing to extend that depression by opting out when they have the chance?
A student who is genuinely depressed due to loneliness might opt in to in-person learning -- only to find out that he or she is the only in-person student because everyone else has opted out (and so that student is still lonely). And even with sports -- where you'd think that students would be enthusiastic to get back to competing -- we see that students are opting out. Recall that at my alma mater, there are only a third as many girls (as I don't have the numbers for the guys) running Cross Country this year as last year.
So let's consider the following wager. For any high school class where in-person learning is allowed:
- I give you $1 for every student who opts into in-person learning.
- You give me $1 for every student who opts out and chooses full distance learning.
Of course, older students are more likely to opt out. In light of this fact, I give you $2 for every junior or senior who opts in to in-person learning, while taking only $1 for each junior/senior who opts out.
If Miller is correct that students really want to come back to school, then you should win easily. So do you take the bet?
I decided to calculate my gain or loss based on the specific classes that I see today. It turns out that today I will break even. In the Strings class, I earn a profit of $2 as slightly more students are opting out than in. In Band, an equal number of freshmen opt in as out -- but I lose money because there happens to be one senior in the class who has opted in. Since he's a senior, I lose $2, so I break even for the day.
Of course, for many high school classes I stand to make a profit. I quickly glance as the roster for an Advanced Strings class that meets on odd period days -- even without counting, I see that I'll make money with this wager, even with the extra $2 premium to you for juniors and seniors.
Yesterday's special ed English class appears profitable for me, as only three students attend each period (but since it's hybrid, I need to know how many students are opting in on the other cohort -- in-person students on either cohort count as wins for you). Monday was special day class, so we expect more students to opt in than usual. There's a slightly majority (five out of nine) students who are opting out, but I don't win the bet since (if you recall) one of the in-person students is a senior. At best I break even, and I might even lose if some of the other in-person students are juniors.
In the case of Miller's specific classes, I'm especially curious about his Financial Math class. I subbed for a similar class yesterday, and there was only one in-person student, a junior. So I assume that I'll win that bet (but once again, there could be ten in-person students on the other cohort as far as I know).
Then again, I suspect that Miller wouldn't take this wager anyway. He knows that he might lose as too many of his students opt out -- not because it's too dangerous to return, but because people act irrationally due to "probability neglect." He mentions "probability neglect" in this post:
https://rightontheleftcoast.blogspot.com/2021/02/he-nailed-it-year-ago.html
Miller is what I once called on the blog a "zero-percenter" -- he believes that the probability of any particular individual (especially one who is sufficiently young without preexisting conditions) dying of the coronavirus, rounded to the nearest percent, is zero. Thus it's rational to do everything that you did before the pandemic (full-time opening, 30-40 students in one classroom, and so on).
Once again, I'm not quite as sure as Miller is. I'm not sure whether my probability of dying is truly that close to zero -- and even if it is, the probability of getting sick from the virus is higher. I don't necessarily want to get sick just because I won't die from it. Then again, I'm still grateful that my OC schools are open -- I wouldn't want there to be a complete shutdown with no schools open in-person anywhere in the state.
And I will continue to keep track of this opt-in/opt-our wager for the high school classes that I cover in the near future. Since this is a music post, I'll repeat SteveH's music comment from Garelick's publishing thread:
Here are the answers to today's test.
1. Using the distance formula, two of the sides have the same length, namely sqrt(170). This is how we write the square root of 170 in ASCII. To the nearest hundredth, it is 13.04.
2. The slopes of the four sides are opposite reciprocals, 2 and -1/2. Yes, I included this question as it is specifically mentioned in the Common Core Standards!
3. Using the distance formula, all four sides have length sqrt(a^2 + b^2).
4. Using the distance formula, two of the medians have length sqrt(9a^2 + b^2).
5. 60.
6. From the Midpoint Connector Theorem, ZV | | YW. The result follows from the Corresponding Angles Parallel Consequence.
7. From the Midpoint Connector Theorem, BD | | EF. The result follows by definition of trapezoid.
8. 4.5.
9. (0.6, -0.6). Notice that four of the coordinates add up to zero, so only (3, -3) matters.
10. At its midpoint.
11. 49.5 cm. The new meter stick goes from 2 to 97 cm and we want the midpoint.
12. Using the distance formula, it is sqrt(4.5), or 2.12 km to the nearest hundredth.
13. sqrt(10), or 3.16 to the nearest hundredth.
14. 1 + sqrt(113) + sqrt (130), or 23.03 to the nearest hundredth.
15. sqrt(3925), or 62.65 to the nearest hundredth. (I said length, not slope!)
16. -1/2. (I said slope, not length!)
17. (2a, 2b), (-2a, 2b), (-2a, -2b), (2a, -2b). Hint: look at Question 5 from U of Chicago!
18. (0, 5).
If you want, you can add the following questions, as the equation of a circle is still missing:
In 19-20, determine a. the center, b. the radius, and c. one point on the circle with the given equation.
19. (x - 6)^2 + (y + 3)^2 = 169
20. x^2 + y^2 = 50
Here are the answers:
19. a. (6, -3) b. 13
Possible answers for c: (19, -3), (18, 2), (11, 9), (6, 10), and so on.
20. a. (0, 0) b. 5sqrt(2)
Possible answers for c: (5, 5), (-5, 5), and so on.
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