Pi Approximation Day: A Major Announcement
Today is Pi Approximation Day, so-named because July 22nd -- written internationally as 22/7 -- is approximately equal to pi. It also marks eight full years since my very first post on my old blog, and almost one year on this blog.
Last year, I used the anniversary to create a FAQ about my blog and myself. I do the same this year -- and this year's FAQ is very different from last year's because I'm focusing on many coronavirus-related questions. As usual, let me include a table of contents for this FAQ:
1. Who am I? Am I a math teacher?
2. What happened at the new charter school?
3. What tough decisions did I make in 2012 and this summer?
4. How should I have handled the job search this summer?
5. What is the new school calendar like?
6. Who is Jim Peterik?
7. What's "Mocha music"?
8. Are there any other 28EDO composers?
9. Who is Rebecca Rapoport?
10. What is a COVID What If?
11. Is there anything else I have to say about my upcoming school year?
1. Who am I? Am I a math teacher?
I am David Walker. And today, I finally have an announcement to make about next school year.
A teaching job has opened up in the district where I worked for the 2021-22 school year. And so, after having received pink slips on March 15th and May 15th, I will be returning for 2022-23. Unfortunately, I don't know much about my new position -- not even whether it is middle or high school. To show you why, let me tell the story of how this position opened up.
Last year, I was one of two math teachers at my high school -- a small magnet school in the district. I taught Calculus, Statistics, and Trigonometry to our juniors and seniors. Last fall, the superintendent announced that due to budget cuts, it was no longer worth the cost of keeping our school open. Those with enough seniority were sent to other district schools, while newer teachers were pink slipped.
The other teacher at my school, my partner teacher, is more experienced than I am -- indeed, she's been there since the school first opened for the 2016-17 school year. For this year, she was assigned a spot at one of the middle schools in the district. But, as she told me just before we left our school, she was also applying to administrative positions in another district. Apparently, she got the job -- and that opened up this position for me in our current district.
But it's not as simple as just plugging me into her spot at the middle school. You see, most of the other math teachers there will be second- and third-year teachers. And so my partner teacher was pegged to be the department chair. I, on the other hand, will be just as inexperienced as my colleagues, and so I can't be the math chair.
I suspect the plan is to move one of the high school teachers down to middle school chair, and then plug me in at the main high school in the district. But until that happens, I don't know where I'll be -- much less what I'll teach.
If it's at the high school, then note that our district uses Integrated Math. So it can't be my favorite class Geometry, but there could be geometry as part of an Integrated Math I or II class. It's also possible that it could be one of the classes I taught last year -- not Calculus (since I already know the Calc teacher at the flagship high school), but perhaps Stats or Trig. Of course, it could still be middle school as well, if there's another way to get an experienced teacher to chair the department. Or it could be at a different middle school.
Believe it or not, I almost got hired at another school -- another charter middle school in LA. Well, technically, I was hired there and and was an employee there for one day. Yes, I know you're confused, so let me tell you the story right now.
2. What happened at the new charter school?
Shortly after my May 15th pink slip, I received an email via my LinkedIn account that a local charter middle school was hiring. Unlike the old charter school where I worked during the 2016-17 year (with just two campuses), this school is part of one of the large charter chains in the LA area.
The application process differed from most other schools. It wasn't enough to submit letters of recommendation -- instead, I had to submit the names of two references, and they'd get emailed questions about my performance. Of course, one of the names I gave was the principal. The other was a parent who told us that she'd write letters on our behalf. Indeed, her son attended the charter chain for middle school -- and now he was graduating from our school as the valedictorian.
Also, as part of the application, I had to submit a video of my teaching. The problem was that this was after the AP exam, and in both Calculus and Stats, I was giving end-of-year projects rather than doing any active teaching at all. As it turned out, one girl from my Calculus class had been absent for several weeks and showed up on the day of senior finals (having already missed the AP exam). And so I taught her some make-up lessons -- which I then recorded and submitted to the charter.
Then I was granted an interview and demo lesson at one school in the chain. This demo lesson was on June 7th -- Day 179 at my current district (which explains why I didn't blog that day). I was asked to teach the Pythagorean Theorem to seventh graders. After the lesson, the charter principal told me that I would be given the position, and that these seventh graders would become my students -- I was to become their Math 8 teacher.
Like all schools, the onboarding process including submitting live scan and TB results. But the school was having trouble receiving my results. The problem was that at many charter schools, all offices are completely closed for one month. At my old 2016-17 charter, the closure was in July, but at this school, the closure started at Juneteenth -- HR offices didn't reopen until this week. Frustrated that my live scan wasn't getting through, I sent an email to the tech department, who reassured me on July 7th that my live scan was received.
And then on July 8th, I got the message from my current district that a position had opened.
The only reason that I'd applied to the charter was that no position was available in my district. And so, with my district poised to retain me, I no longer wanted the charter position.
The next two weeks turned into a big game of phone tag. Because I was already deep in the onboarding process at the charter, it was only right for me to notify the charter HR department. But they were still in the middle of their monthlong closure, so I had to wait until this week -- and so I informed my current district that I'd wait until this week to decide.
At the charter, I was given an appointment date of Tuesday morning to complete the onboarding and sign the papers. When I showed up at the appointment, I told them that I was staying at my current district -- and I was required to submit a resignation letter as I was so deep in the process. Tuesday became my official start date and end date at that charter.
Then I notified my current district that I was ready to accept the new position -- but the person in charge was out for most of the week. Not until yesterday afternoon, at around 2:30, did I finally hear that I have a position in my current district.
And so this was how I spent my summer vacation. It only remains for me to find out what school I'm working at, and what subjects I'll be teaching at my new school.
3. What tough decisions did I make in 2012 and this summer?
Ten years ago, I had to work at an unpaid teaching position. It was the Great Recession and very few teachers were being hired, yet I needed to complete my California BTSA requirements in order to clear my credential. And so a local district had a special program -- we'd teach one period in another teacher's classroom by day, and then fill out the paperwork for BTSA by night. But this position was unpaid -- and so in order to earn money, I applied to several tutoring jobs that fall.
As it turned out, two tutoring companies were considering hiring me. One of them was funded by No Child Left Behind, and I would be tutoring low-income students who struggled on state tests. The other was a small private tutoring company. The NCLB job would pay me an additional $1 per hour.
At the first job, most of my students would be black or Hispanic. Many of them have trouble traveling, so I'd have to visit their houses, at night, in a poor neighborhood. At the second job, all of my students were Korean or Korean-American. Their guardians would drop them off for tutoring and pick them up at the end of their sessions.
I interviewed for both jobs around the same time. But the NCLB job wanted me to come back for a second interview, while the private company notified me by email that I'd been hired -- and even scheduled my for my first student.
I was torn between the two jobs, so I arrived at the private session and informed the supervisor that I was considering a different job. He then agreed to match my hourly pay from NCLB and at least tutor my one guy that night before making a decision. And so I did. I delayed the interview at NCLB until November 1st, right after payday at the private tutoring. On Halloween, I got my first check, verified that I was paid at the higher rate that we'd agreed to -- and then I cancelled the NCLB interview.
But there was one more factor in my decision to work at the private company. I was uncomfortable going into a poor neighborhood at night to help the NCLB students. And so I took the job where I was able to tutor at a single location rather than at students' homes. This is the tutoring company where I worked for three years (overlapping the first year of my old blog, eight years ago).
Nearly a decade later, I found myself teaching not just Stats, but Ethnostats -- a class where we discuss the statistics of race and ethnicity in our society. It's one thing to stand in front of a class of middle-class kids and lecture on how there are gaps between white and minority students, and between poor and higher-income students, and complain about how hardly anyone tries to narrow those gaps. It's another thing to go to the inner city and actually try to narrow those gaps. Yet when I had a chance to do just that ten years ago, I just ran away to the relative safety of the middle class.
Of course, I did work in the inner city for one year -- at the old charter school. But as you already know, that year wasn't successful. Part of the reason I struggled was the lack of a conference period and the unexpected requirement to teach science -- both of which were caused by the science teacher who decided very late to take another position (much as I just did this week).
The charter school where I was slated to work this year has a tough calendar and bell schedule. The reason that onboarding was this week is that next week is training for teachers new to the charter chain (which would have included me), followed by two weeks of training for all teachers. (This, by the way, is standard at most charters.)
This would have been followed by the regular school year, which hasn't been posted yet, but I assume it follows the LAUSD calendar -- which itself was extended an extra week this year. A new holiday, Armenian Genocide Day, was added to the calendar -- but it's impossible to add a new holiday without adding an entire new week to the school year. The other four extra days are billed as optional "student acceleration" days for those who need it. But I have no idea how charters will handle the new days -- I wouldn't be surprised if the optional LAUSD days are required at the charters. Anyway, put it all together and the summer break for teachers is just barely longer than the monthlong summer break for classified workers.
In addition to the extended year, the chain also has an extended day. According to the current schedule, students start class at 7:30 and the day is over eight hours, with the only break a half-hour lunch. Of course, that's before the new California law where middle schools can't start before 8:00 (and high schools before 8:30). So far, I don't know how the charter will respond to the law -- they might push the whole day back and so the school day won't end until well after 4:00. Of course, as a teacher working there, the shorter summer will be long forgotten by the time September is over. But if I'd taken the job, everyday at 4:00 I'll have students still sitting in my class, with the dismissal bell still yet to come -- and knowing that if I'd still been in my old district, I'd already be home by now.
I'd probably get a conference period -- but it appears that different classes meet on different days, and so there will be some days with no prep period. Also, passing periods are short (about 3-4 min.). I understand why inner-city charter schools have schedules like this -- at the surrounding public schools, students misbehave (engaging in illegal activities) in the restrooms during breaks, which is why parents send their kids to the charters. The safest place kids can be is sitting in the classroom in front of a teacher, and so the charter provides as much time for this as possible. The problem is that it means more work and less break time for the teacher.
The charter school will pay me more per year than my current district. But factoring in the extended day and year, I'll be paid more per hour at my current district. And so putting it all together, I decided that I'd rather stay in my current district.
I believe that the charter school was split about equally between black and Hispanic students, while my district is almost all Hispanic. Ironically, on the day I turned down the charter job, I actually helped the lone black student in my class at the district! She wasn't in my Ethnostats class, but in my senior Advisory class, where we worked on a practice resume. She requested edit access to her resume on Google Classroom this week from her personal email account -- it's obvious that, now that she's graduated, she wants her resume so she can use it to apply to jobs. I granted it to her -- and moreover, I suggested corrections she can make in order to impress employers (in particular, she can drop the word "expected" from "diploma expected June 2022).
So I talk about the racial gap in Ethnostats, and help students of all races whenever I can, even after they've graduated. But when it comes to going to where I can really make a difference, I admit that I lack the mental strength to do so. And that's why I'm staying at my current district.
4. How should I have handled the job search this summer?
This year, I just barely got the last open math position in my district. Even though I'm a second-year teacher, no new math teachers will be hired, so I'll still be on the bottom of the seniority list. And, as we all know, enrollment is declining throughout the state.
Thus I should not be surprised if I get a pink slip on March 15th, 2023.
It's likely that I'll have to go through all of this again next year. I'll start applying to jobs again, and maybe a spot will open for me in July -- after I've already applied to another position. I don't want to play phone tag, explain to employers why I'm taking other jobs at the last minute, argue with human resources departments, or submit resignation letters after one day next year.
In the past, I've applied to as many teaching positions as possible. But as I progress in my career, I need to be more selective in my applications. I should apply only to jobs where I'm actually willing to work, as opposed to positions I'm running away from the instant another job opens up.
It's possible to rank and prioritize the schools. Perhaps I should assign a date to every school, and then avoid applying to that school until that date has arrived. My highest priority schools are dated March 15th -- that is, I can apply as soon as I receive the pink slip. The next level is April 15th, and then the third level is May 15th, after the pink slip becomes official.
I won't necessarily avoid charter schools, but instead read up about them before applying, and then assign a date based on what I find out. (Charter petitions are often posted online and contain lots of info there -- I read my school's petition, but not until after I applied.) Indeed, I applied to this charter after May 15th, but perhaps after reading about its shorter breaks and almost 5:00 dismissal, I might have assigned this school a date of June 15th. (Of course, this would have been more like July 15th due to the monthlong closure -- and then it would have been difficult to request reference links or get a teaching video then.)
Then if someone agrees to hire me, then I must commit to that job -- in particular, even if a position opens up in my current district, I must reject them and take the new job. My willingness to take a particular new position should already be baked in to the priority date for application.
5. What is the new school calendar like?
There's not much I know about my new school -- not even the bell schedule. Once again, the 8:00 middle school and 8:30 bell schedules will go into effect this year, and schools are scrambling to come up with new schedules. And I've heard that at the flagship high school, the change might not be as simple as pushing the entire bell schedule back to 8:30.
It appears that our middle schools already start at 8:00, so there might be no changes there. The middle schools currently have a traditional schedule -- albeit with seven periods, not six.
The one thing I do know about is the school calendar. The first day will be Wednesday, August 10th, and there are two changes to the calendar as compared to last year:
- Veteran's Day: Last year Vets Day was on a Thursday, forcing a four-day weekend. This year, the holiday is on a Friday, so only a three-day weekend is required. Due to this change, the last day of school will now be on a Tuesday rather than a Wednesday.
- Spring Break and Chavez Day: In this district, spring break has nothing to do with Easter -- instead, the holiday was the next-to-last week in March. The following week was Cesar Chavez Day, and so there was another day off after spring break. This year, spring break is now a week later so that it includes Chavez Day (much like the Cal States and UC's). The unnecessary extra holiday now appears before the break as an extra PD day. (It's on Pi Day Eve, a Monday, so students return on Pi Day, a Tuesday.)
All middle and high schools should still have a monthly minimum day -- but we'll see what those actually look like next year. My monthly blogging days are, for now, scheduled for those days. But if it appears that schools will start messing around with them, then I'll switch to a fixed blogging date.
And that potential blogging date will be the 17th. I chose it because in only two months will the 17th fall on the weekend -- September and December (both Saturdays). This is similar to the 18th last year -- indeed, I blogged on May 18th after the minimum days fell apart. (I might have chosen April 18th as well, except that was Easter Monday.)
By the way, I've been thinking about the school calendar, and the special names that I've been giving to certain parts of the year ("Willis unit," "Big March," "Horton unit," and so on). I've been reading some other blogs lately, and I believe that I now have enough names to cover the entire school year. Here are the parts of the year, including the sources of their names:
At some high schools, state testing begins during the Big March rather than Spring Fever, especially at schools where spring break is tied to (a late) Easter. Notice that the inventor of the Holiday Stretch has his stretch last through spring break -- his Big March is non-existent, as his school has both an entire week off for Presidents' Day (Ski Week) and an early spring break. Some schools have have spring break as early as Pi Day, so they might likewise have only a Little March.
And I myself began the Horton unit before Memorial Day, especially since I was an AP teacher who gave end-of-year projects after the test. I might not start Horton that early (especially if I end up teaching at a middle school). On the other end of the year, schools that start after Labor Day still have a Willis unit. So DEVOLSON doesn't start until a few weeks later (perhaps late September -- the LS in that acronym).
Depending on your district calendar, most periods outside the Holiday Stretch have no holidays. In my district, there's a four-day Easter weekend near the start of Spring Fever (and so we might not consider Spring Fever to start until after Easter). And both DEVOLSON and the Big March have a PD day where students get the day off, but not teachers. Indeed, I'm still deciding whether I should sing "The Big March" this year -- a later spring break means that there are five weeks after Presidents' Day instead of four, but one of those five weeks now has a day when kids don't attend school.
And LAUSD has several extra holidays -- the Jewish high holidays during DEVOLSON (which again might not start properly until after those holidays), Chavez Day during the Big March, and now Armenian Day during Spring Fever. Again, the optional days aren't optional for teachers, and so they, like the PD days, count as workdays (that is, only days that teachers get off interrupt these periods).
6. Who is Jim Peterik?
Jim Peterik is a songwriter who has penned many songs, such as Survivor's "Eye of the Tiger." He has written a book, Songwriting for Dummies.
In my classes, I like to perform songs to help the students remember math. I didn't sing much in the 2021-22 school year, but music was a staple of my previous math classes. But math songs don't write themselves, so I wish to read Peterik's book in order to become a better songwriter.
So far, we've read and discussed the first eight chapters of Peterik's book. Since today is my special FAQ post, we'll get back to Chapter 9, on melody, in my next post. Still, I will have a little to say about melody in today's post before we study it in earnest in my next post.
7. What's "Mocha music"?
But I think I'll wait until my next post (with Peterik's melody chapter) to write more about EDL. That's because I want to finish the project that I began this summer -- the one where I revisit all my old Math 8 lessons from the old charter school and add songs to them.
OK, I'll admit it now -- I had a devious reason for starting this project. My original plan for this summer would have been a musical revisit of the 2021-22 year (since I didn't perform at all this year), not the 2016-17 year (when I did). But the position at the charter school that I almost got would have been a Math 8 position. I found out that the math curriculum used at this chain is Illustrative Mathematics -- and Unit 1 of that Math 8 text is on geometry, from 8.G1 through G5.
So I was really trying to prepare songs from the upcoming school year, without announcing on the blog that I'd been hired at the charter school. I really wanted to make it to G5 before today, when I'd finally make that big announcement. Of course, now I won't be working there -- and even if my new job turns out to be Math 8 at a middle school, there's no guarantee that it will use Illustrative Mathematics. Still, I might eventually perform the songs that I wrote at some point.
We're going to write one more song in this project -- a song for April. The math standards to be covered are the G standards on geometry.
This takes us to spring break, which at the old charter school was during Holy Week, the week before Easter (on April 16th). And I think I'll end the project there, since in past posts, I've expressed interest in writing an Easter song based on the pattern in the dates for that holiday.
So far, most of the songs that I've written this summer are in the EDL scales that fit Mocha. But the Easter song makes more since in an EDO scale (equal divisions of the octave, like standard 12EDO). In the past, I discovered that 28EDO is the best possible scale for an Easter song.
For Easter 2021, I blogged about a Easter song and how to code it in Mocha. This Mocha coding is only an approximation, since 28EDO doesn't fit Mocha EDL perfectly. I think I'll repost it here in this post:
- Remainder(x|y) = x - y[x/y]
Returning to the present, notice that so far, we know how to play this song in Mocha. For this song, I'm not following many of the Peterik steps of songwriting -- this song so far has no lyrics, and not much rhythm, except for constant quarter notes. (The song sounds good in 3/4 time, but 532 -- the length of the Orthodox version of the song -- is a multiple of 4, not 3. So it might end up being 4/4 after all.) The focus here is only on the melody.
But if I were to play this song in class (say the week before spring break), then we must find a way to approximate this song -- not in Mocha, but on my (12EDO) guitar. Such an approximation requires us to do two steps.
First, we choose one note of our scale to convert to a certain pitch frequency, measured in Hertz. For the standard 12EDO scale, the usual choice is A440 -- that is, 440 Hertz is the note A. This is called concert pitch -- in other words, 440 Hz is Concert A.
As the Hertz increase, the note gets higher -- doubling the Hertz raises the note an octave. This is the exact opposite of the Degrees -- doubling the Degree lowers the note an octave. This tells us that the Degrees and the Hertz are inversely proportional:
Degree * Hertz = constant
So it remains to find the missing constant of proportionality -- since I defined my 28EDO scale above in terms of a certain Mocha note, we must convert from Mocha to Hertz. To do this, I decided to open two tabs -- one to Mocha, and the other to the following free tuning site:
I make sure that both the tuner and Mocha (Sound) are turned on, and then I enter SOUND 1, 100. The tuner reveals that this note is flat of Concert E3 (that is, the E below middle C). Then SOUND 2, 100 is still flat of E3. I keep going until I reach SOUND 7, 100, which is shown as being in tune with E3. We recall that Sound 7 is Degree 254, and the note E3 is about 164.81 Hz. So we multiply to obtain our constant of proportionality as approximately 41862.
By the way, this is also a good time to verify that Sound + Degree really is 261. We go up an octave:
Sound 7 = Degree 254, Degree 127 = Sound 134
and then we see that SOUND 134, 100 is indeed in tune for E4. (In past posts, I referred to 261 as the "Bridge," as Sound 261 would be at the bridge of a guitar -- a string of zero length.)
By the way, this does not mean that E3 or E4 will be our reference note, as neither Degree 254/Sound 7 nor Degree 127/Sound 134 appears in the 28EDO list above. I want our reference note for 28EDO to appear in the scale.
One note in the list that caught my eye is Degree 190/Sound 71. We notice that 41862/190 is a little more than 220 Hz, which is half of 440 (and hence one octave lower). This tells us that this note should be in tune for A3 -- and sure enough, SOUND 71, 100 is in tune. So our reference note is Degree 190 = Sound 71 = 220 Hz, equivalently Degree 95 = Sound 166 = 440 Hz, which will put our note A in line with concert pitch. This note was chosen because all three scales (12EDO, 28EDO, and Mocha Sounds) can be made to agree with it.
Since 12EDO and 28EDO both have 4 as a factor, three other 12EDO notes will have 28EDO equivalents -- C, Eb, and F#. But the 28EDO names for those notes won't be C, Eb, and F#, as we will soon see.
In fact, the usual way to name 28EDO is to letter every fourth note -- A, B, C, D, E, F, G, A (in other words, A-B-C-D-E-F-G-A is a 7EDO subset). Since A is aligned with Concert A and the perfect fifth of 28EDO is flatter than that of 12EDO, it follows that the notes fifthward from A (that is, E and B) will be flatter than the corresponding concert notes, while those fourthward from A (D, G, C, F) will be sharper than the corresponding concert notes.
According to the Xenharmonic website, the in-between notes are named using ups and downs. So the next note higher than C is C^ (C-up), then C^^ = Dvv (C double-up = D double-down), Dv (D down), and then D. If A lines up with Concert A, then 12EDO's C, Eb, F# line up with 28EDO's Cv, Evv, F^.
Of course, not all 28 notes can be played on 12EDO instrument (as 12 is less than half of 28). But there are two ways that a 12EDO major scale can be converted to 28EDO -- the Xenharmonic website calls these methods diatonic major and naive major.
The diatonic major scale is formed by taking the major scale in 12EDO and then rounding each note to the nearest 28EDO note. The C diatonic major scale goes C-D^-E^-F-G-A^-B^^-C. Notice that this method retains all four major sixths in the scale -- F-D (which becomes F-D^), C-A, G-E, and D-B (which becomes D^-B^^).
The naive major scale is formed by maximizing the number of major thirds in the scale, rather than sixths (since 5/4 is so accurate in 28EDO). The C naive major scale goes C-D-E^-F-G-A^-B^-C, which retains the major thirds F-A (which becomes F-A^), C-E, and G-B. The major chords C-E-G (which becomes C-E^-G), F-A-C, and G-B-D all sound fairly accurate in C naive major.
As it turns out, the naive major scale fits the Easter song better than diatonic major. There are many stretches (of at least one bar) where all the notes fit into a particular naive major scale. And so to convert our song to 12EDO, we must identify these naive majors and then convert to the corresponding 12EDO major scale.
OK, so let's look at some actual notes of the Easter song. Here is our conversion chart that maps Easter dates to 28EDO letter note names:
All the other notes are notated using ups and downs.
Now let's look at a table of Easter dates. The Orthodox song is simpler, so we'll look at this table:
http://5ko.free.fr/en/easter.php?y=6
If we continue to 601, the date is March 26th, which is G^. We might play this as G, but notice that G^ also appears in A naive major, so we might play 601 as G# to match A major. Then 602 is April 15th (E^) and 603 is April 7th (C^), which we play as E and C# to match A major. Then 604 is March 22nd, the earliest possible Easter, which is like G triple-down or F^. This is played as F# to fit A major.
Soon double-up and double-down notes will start to appear. A note like C^^ = Dvv should always be played as C# = Db in 12EDO, and the same as other double-ups and double-downs. But E^^ = Fvv is ambiguous in 12EDO, so again it becomes E or F (possibly E = Fb or F = E#) depending on whichever fits the prevailing major scale. The song should eventually rotate through all major scales.
Notice that if I don't give this song any lyrics, then it would have to be played instrumentally -- as in on my guitar. The melody needs to be played -- that is, lead guitar (not rhythm guitar). Barres will likely be required, since the song rotates through all major scales (not just the open-string convenient scales).
8. Are there any other 28EDO composers?
I choose 28EDO because it fits the pattern of the Easter dates closely. Among microtonalists who compose in scales other than 12EDO, I admit that 28EDO is hardly the most popular.
A YouTube search for 28EDO reveals a few other composers in this scale:
1. Claudi Meneghin:
Meneghin celebrated his 28th birthday by writing "Happy Birthday" in 28EDO. The song begins in C diatonic (not naive) major. For him C-D-E-F-G-A-B-C is 7EDO, and so he uses sharps and flats to produce C diatonic major as C-D#-E#-F-G-A#-Bx-C. Here C is aligned with Concert C, and after he jumps up a minor third to Eb in the next part, this Eb is also aligned with Concert Eb.
2. Cinnamon Mavka:
Mavka labels this song as being in "F naive minor." Naive minor scales are like naive majors except that the ups are replaced with downs, so F naive minor is F-G-Av-B-C-Dv-Ev-F. In this song, F is aligned with Concert F (thereby aligning Av with Concert Ab).
By the way, Mavka is from Ukraine -- yes, as I mentioned in a previous post, war is currently being fought in her homeland. (She mentions her experience of the war in another video.)
Mavka has also written in several higher EDO's. Many of these EDO's are related to calendars (which is interesting as my 28EDO is also ultimately based on the Easter calendar). She has a 365EDO song (number of days in a year), a 2022EDO song (the current year), and a 1789EDO song (in memory of the French Revolution). There is also a 1619EDO song, but I don't know why. (The only significance of 1619 I'm aware of is Nikole Hannah-Jones, but this would be irrelevant to a Ukrainian like Mavka.)
Finally, there is a 293EDO song that's apparently based on a leap week calendar! (Arguably, even our standard 12EDO is calendar-based. Let January = F, February = F#, March = G, and so on. Then the long months are white keys and the short months are black keys.)
I might as well include my usual Pi Approximation Day links here as well:
3. Draw Curiosity
Notice that this video, from six years ago, actually acknowledges Pi Approximation Day.
4. Michael Blake
I like the idea of using music to teach math, so here's a favorite, Michael Blake's "What Pi Sounds Like." I tried to find a way to incorporate songs such as this one into the classroom.
5. Ki & Ka
This video came out two years ago. This is yet another video that uses the Archimedes method of approximating pi.
6. Stand-Up Math
This video uses the Leibniz series, but all work is done by hand.
7. NKC Insight
This video came out two years ago.
8. Chota School
This is a new video for this year.
9. The Indianic minds:
This video came out two years ago. It celebrates Casual Pi Day -- a name for Pi Approximation Day that refers to celebrating it "casually" at the beach on a hot summer day in July.
10. hurfcharacterlimit:
I had to include this new video since it has the famous Pi Approximation integral from Calculus.
9. Who is Rebecca Rapoport?
Rebecca Rapoport is the author of Your Daily Epsilon of Math calendar. In most years, she produces a calendar that provides a math problem. The answer to each question is the date. I will post the Rapoport questions for each day that I blog. Traditionally I would post only her Geometry questions, but ever since I started teaching other math, I've been posting non-Geometry as well.
The question for July 22nd this year is:
Find the inflection point of f (y) = ye^(-y/11).
This is a Calculus problem. To find the inflection point, we take the second derivative and set it to zero:
f (y) = ye^(-y/11)
f '(y) = (1 - y/11)e^(-y/11)
f "(y) = (-2/11 + y/121)e^(-y/11) = 0
y/121 = 2/11
y = 22
Therefore the desired inflection point is at y = 22 -- and of course, today's date is July 22nd. My Calculus AB students should have been able to answer this one, but they might have been tripped up by the way this problem was written.
By the way, since it's Pi Approximation Day, this is a great day to me to post the proof, using a certain integral, that 22/7 exceeds pi. This is the proof mentioned in the last video above, and since I just taught a Calculus class, it's worth posting again. The integration goes from 0 to 1:
0 < int(x^4)(1 - x)^4dx/(1 + x^2) (the integral of a nonnegative function is nonnegative)
= int(x^4 - 4x^5 + 6x^6 - 4x^7 + x^8)dx/(1 + x^2) (expand binomial)
= int(x^6 - 4x^5 + 6x^4 - 4x^2 + 4 - 4/(1 + x^2))dx (long division)
= x^7/7 - 2x^6/3 + x^5 - 4x^3/3 + 4x - 4arctan x, from 0 to 1 (integrating polynomials and arctan)
= 1/7 - 2/3 + 1 - 4/3 + 4 - pi (plug in x = 1, since plugging in x = 0 gives 0)
= 22/7 - pi (simplify)
Therefore 0 < 22/7 - pi -- that is, 22/7 > pi. QED (Again, play the video above for more info.)
In theory Calculus AB students can do this (as long division is indeed covered on the exam), but some ideas (like integrating a nonnegative is nonnegative, or anything raised to the second or fourth powers is nonnegative) are likely to confuse them. The polynomial expansion (1 - x)^4 is longer than anything likely to appear on the exam.
10. What is a COVID What If?
This a fictional story that I made up in order to imagine how my life would have been different if the pandemic had occurred earlier than COVID-19, which began in December 2019 and affected most of us by March 2020. It's a way for me to put myself in my students' shoes -- I can't truly understand what it's like to be a young person during the pandemic until I imagine placing the pandemic in my own youth.
I have written six separate versions of the COVID What Ifs. Each one places the pandemic in a different year -- COVID-86, COVID-91, COVID-93, COVID-96, COVID-08, COVID-14. In each case, the numbered year refers to the December when the pandemic ultimately begins -- so just as COVID-19 started in December 2019, COVID-n starts in December n. The schools don't close until March of the year n+1. We are currently in the year n+3, and so n+3 for each of the six What Ifs will resemble the year 2022 under COVID-19.
The COVID stories are supposed to end as soon as the pandemic is "over" -- but that's becoming more difficult to define. It's possible that COVID might become "endemic" like the flu.
What I do know is that cases in Southern California are currently increasing, and so it's likely that masks will again be required by the first day of school. I wrote that if there are masks plus one more COVID-related task (such as having to take home a COVID test), then the What Ifs will continue.
And if the What Ifs continue, then I will focus on placing the pandemic back when I was as young as my students are now. For example, last year I taught mostly seniors (Class of 2022), whose schools first closed in March of their sophomore year. March of my own sophomore year was 1997, and so the pandemic is placed the previous December, making it COVID-96.
Of course, I won't be able to do the same for this year's students until I'm given a class schedule and find out what grade most of my kids will be in. So we'll hold off on the What If? stories until then.
Also, notice that not all What If? stories are COVID-related. Indeed, in this post I've already written a little on "What if I'd taken the charter job instead of staying in my current district another year?"
11. Is there anything else I have to say about my upcoming school year?
One thing I know for sure is that this upcoming year is sure to be more difficult than last year. That's because last year was one of easiest years that a public school math teacher can expect to have.
Our school, which was already very small, had only juniors and seniors. My partner teacher had most of the juniors while I took most of the seniors. Many seniors dropped math during the Willis unit as they realize that they don't need a fourth year of math to graduate, making my classes even smaller. In fact, I ended up with only four math classes instead of five as seniors continued to drop math. My smallest class (Trig) had only three students, while my largest (Advisory and Ethnostats) had 14 each. Most of the students at our magnet school were mature and well-behaved.
This year, I'll be lucky if my smallest class has only 14 students. I'll have five math classes -- probably six if it's middle school, since I see a bell schedule there with seven periods. And at the flagship high school, I must expect bad behavior -- maybe not as bad as those inner-city schools mentioned above, but more than at my magnet school. I just hope that I'll be ready for whatever is thrown at me.
And so I wish everyone a happy Pi Approximation Day!
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