Chapter 14: What Are the Chances? (Day ???)

Today is Pi Day, a key day on the mathematical calendar. It's also the monthly minimum day for March, and hence the lone day that I will post during this current "Little March." As I usually do on monthly blogging days, I will discuss my school day in "A Day in the Life" format.

But first, many things have happened to me during this three-week blogging break, and so there's so much to catch up on here in this post:

• First, those cancelled school days on January 10th-11th are catching up to us. The number of days in the school year needs to be 180, not 178, and so the district must appeal to LA County to avoid having to make up those days in June. In anticipation of a decision later this week, the district cancelled Open House and the associated minimum day last week so that we won't be short on instructional minutes (but monthly minimum days for staff meetings are unaffected). I was going to blog on Open House night as the other special "Little March" post until that was cancelled.
• Governor Newsom has ended the mask mandate for California schools. The official last day of the mandate was last Friday, making today the first day that kids can be in class without masks.
• Two books have arrived from the library. One of them is Eugenia Cheng's sixth book and second children's book -- Bake Infinite Pie with x + y. Yes -- Cheng really did combine the titles of three of her adult books to form the title of her children's book. (And it's only fitting that book about baking pie would arrive in time for Pi Day.) The other is another children's book that I stumbled upon while searching for the Cheng book -- The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger (1998).
• Yesterday was the start of Daylight Saving Time. This is the first post after the time change, which would normally make this my biannual lengthy post on DST (but that has faded recently).
• Oh, and as expected, I received the dreaded pink slip. Tomorrow is March 15th (the official date of such letters), but my principal delivered me the letter last Wednesday.

Let me discuss these in reverse order, since my mind is obviously on the pink slip. I already knew that I was likely to get one -- my school is being shut down, we don't know how many teachers will be needed for the program on the new campus, and I have no seniority. But that doesn't make it any easier when I receive the actual document. (That's one reason I took a blogging break -- I knew that I'd be in no mood to post on Pink Slip Day.)

It's possible that the pink slip may be rescinded by May 15th. The document itself indicates that I'm one of two math teachers in the district who were pink-slipped. Thus I need two current math teachers in the district to choose retirement between now and mid-May. Otherwise the pink slip will become official and I'll really have no job.

(And before you ask, the lone other math teacher, who has been here since we opened six years ago, has already expressed a desire to stay and teach for the new program. She is going nowhere.)

What should I do now? There are two union representatives among our staff, and so I discussed matters with one of them on Friday. He suggested that I not even wait until May 15th to look for other jobs. If I'm called in for an interview on a day I'm scheduled to teach, then I should take a sick day. (So be prepared for more skipped days on the blog if I have an interview on a scheduled posting day.)

Pi Day is supposed to be a happy day, so I don't want these discussions to dominate today's post. But obviously I'll be writing about my job situation a lot on the blog in the next few weeks.

There is one thing I want to say about the time change. Next year, the law will be in effect that no high school will start before 8:30. A later start time goes hand-in-hand with Year-Round Daylight Time (Proposition 7 time), since sunrise will be around 8:30 in the northern part of our state around the winter solstice (and earlier in SoCal). It means that school won't start until after the sun is up.

Indeed, as our school prepares to join the main high school next year, a brand-new schedule will have to be created -- one on which class starts at 8:30. Of course thanks to that pink slip, next year's schedule at the flagship high school might not matter to me.

As I mentioned in previous posts, the reason we don't have Year-Round DST now is that Congress must approve of it. And that's why Scott Yates -- perhaps the biggest advocate of Year-Round DST -- is now running to become a member of that body:

https://www.sco.tt/time/2022/03/high-fives-for-fixing-daylight-saving-time.html

(The title, "High Fives," refers to that fact that Year-Round DST is the only issue for which he gets approval from both Democrats and Republicans.)

OK, so now masks are no longer required in California schools. Choosing today, Pi Day, as the first mask-free day is a bit symbolic, as it's the second anniversary of the original pandemic closures. It's an admission that the pandemic is now becoming endemic -- more like colds or the flu.

Let's briefly look at the two books I'm reading -- normally I'd declare these to be side-along reading books and devote several blogposts to them, but we're in the middle of relative blogging break.

In Enzensberger's The Number Devil, the title character visits twelve-year-old Robert in a dream on a dozen consecutive nights. Each night he teaches the boy a new concept -- on the first night, he introduces perfect squares, which he calls "hopping numbers" (and on subsequent nights, he uses similar "dream names" for other concepts). Robert learns that if he hops numbers like 1, 11, 111, and so on, he gets numbers like 1, 121, 12321, and so on.

I read this book on the first 12 days of March. It was a bit eerie when on March 4th, the fourth chapter ends with "He'd completely forgotten the next day was Saturday, and on Saturday, of course, there's no school" -- and the 4th, the day I read it, really was a Friday.

In the last chapter that I read on the 12th, Robert gets to meet other "Number Devils" -- that is to say, other mathematicians. One of them (which turns out to be Archimedes) introduces him to a number that helps one measure how big our pies are. That number, of course, is what we celebrate today -- pi.

And I read Eugenia Cheng's book today, on Pi Day itself. As the title implies, this story really does combine her adult books with the corresponding titles. As in her first book, the children in this story bake pie and other sweets -- including Cheng's favorite, puff pastry. As in her second book, the children learn about concepts related to infinity, including Zeno's paradox, fractals, and convergence to zero. In particular, X learns that a circular pie can be thought of a polygon with infinitely many angles.

The connection between this book and Cheng's adult book x + y is a bit more subtle. In this book, X and Y are the names of the two children. X wants to bake an infinite row of pies, while Y wants to bake an infinite column of pies. In the glossary, the author tells us that these names correspond to the axes, so X has a horizontal row like the x-axis and Y has a vertical column like the y-axis.

But in the adult book, X and Y correspond to genders (as in X and Y chromosomes). So X in that book means female (congressive) while Y means male (ingressive). And in the children's book, Y "likes diving into difficult things straight away" (ingressive) while on the other hand, X "likes building up to things gradually" (congressive). Indeed, it's ingressive to want to build a tower as high as possible, while congressive people prefer to dish materials out horizontally and share.

Notice that Cheng gives neither X nor Y a gender pronoun in the book. Both children are drawn androgynous -- perhaps X even looks slightly more masculine (despite being more congressive). The only person with a definite gender is Aunt Z, who helps X and Y with the baking. (I see Aunt Z as standing in for Cheng herself.)

We now look at "A Day in the Life." Now that masks are no longer required, students may now eat in the classroom -- and there's a certain food that we might want to eat on this Pi Day. (But no, we don't eat infinitely much of it.)

8:00 -- First period is the first of my two conference periods. I use this time to go out and purchase some Pi Day treats.

8:40 -- Second period arrives. This is the first of two Ethnostats classes.

During the three-week blogging break, we finish Chapters 13 and 14 of the text. Both of these chapters are part of the probability unit. In Chapter 14, the students learn that "or" means to add the probabilities provided the two events are disjoint, and "and" means to multiply the probabilities provided the two events are independent.

For Chapter 13 the students had a quiz. But for Chapter 14, I assigned a project. Since it's now Women's History Month (and the project even began on March 8th, International Women's Day), I decided to focus more on gender than ethnicity. I found a project from last March where the students work in groups to research the inequalities that women face. Then they created a Google Slides document with their findings.

There were three articles in the official syllabus on women and inequality. But I also showed the students Eugenia Cheng's x + y -- both the adult and children's versions. If they wished, they could incorporate her books into their projects (and one pair in this class did).

That takes us to today. The first thing I'm wondering was whether any students would continue to wear masks in class. Of the four guys in this class, two wear a mask and the other pair doesn't. Of course, the masked guys remove them when I pass out the pies. These are individual 7-Eleven pies (since the store tends to have a $1 discount each year around March). I purchase all the pies I see in the store -- 20 pies, which is almost enough for all of my students in all four math classes. Most of the pies I find are flavored strawberry cheesecake, and two of the guys in this class choose chocolate. (I also bring two full pies -- cherry and pumpkin -- to the teachers' lounge.)

In all classes, our students have a survey to fill out from the Mathematical Association of America -- apparently, our school was selected to participate. While I could have assigned the survey at any time in March, I decide to do it today -- it's a minimum day, so there's never going to be any sort of lengthy main lesson today. So it's the perfect day to use for a survey, which I consider to be the Warm-Up.

Then, since I've done it so much this year, I go back to Sarah Carter's blog and find her latest Pi Day worksheet -- "Pi Ku Poetry" consisting of three, one, and four syllables:

https://mathequalslove.net/pi-ku-poetry-pi-day-poems/

The students write their Pi Ku on page 26 of their Stats Scrapbooks. For the exit pass, I just go to the Rebecca Rapoport calendar and have the students copy her joke -- "I 8 sum pi." (Thus the answer isn't the date, 14 -- though it's obviously related to Pi Day today.)

Unfortunately, I'm still not singing songs in class today. Instead, I play an old Pi Day CD that I lost several years ago, but finally find in time for the math holiday this year. It contains (yet another) parody of "American Pie" (which takes place at a Pizza Hut), as well as a parody of "Hey Jude/"

9:20 -- Second period leaves and third period arrives. This is the Calculus class.

While the students take their MAA surveys, I play another Starbird video. This one's perfect for today -- Lecture 15: "Buffon's Needle -- pi from Breadsticks." Of the five students who are present today, two of them choose Boston Cream

After the survey, I have the students log on to DeltaMath and start doing corrections from the Chapter 5 Test last week. That's right -- I finally align test corrections with the minimum day today (after having so much trouble doing so in January and February).

The Exit Pass is also related to pi. There's a certain problem in Chapter 5 of the text that has the students derive the circle area formula using inscribed regular polygons and taking the limit as the number of sides approaches infinity (yes, just like X's pie).

10:00 -- Third period leaves and fourth period arrives. This is the second of two Ethnostats classes.

Unlike second period, this class has everyone still wearing a mask. That's because one student (for unbloggable reasons) not only must continue wearing a mask, but so must all neighbors. Even I keep the mask on in this period, and we remove it only briefly to eat.

The most commonly chosen pies in this class are strawberry cheesecake (of course) and lemon. Of the eleven students in this class, three are absent, thus leaving enough pies for fifth period.

Other than that, we do the same activities as in second period. On Wednesday we will start Chapter 15 of our Stats text.

10:40 -- Fourth period leaves and fifth period arrives. This is the Trig class.

This is the class that I've been thinking about for four months -- Trig class on Pi Day. I'd planned it so that the Chapter 2 Test was taken last Wednesday and Section 3.1 on Friday, thus bringing us to Section 3.2 -- Radian Measure -- just in time for Pi Day.

Since it's a minimum day, I'll properly start Section 3.2 tomorrow -- so today is "Section 3.14." It takes a bit longer than I expected for one student to finish her MAA survey, and so I need something quick to introduce radian measure. Of course, that means quickly returning to the Sarah Carter blog:

https://mathequalslove.net/radian-arts-and-crafts-activity/

My students choose a circular design and then take a string the same length as the design. Then they wrap the string around the circle. By definition, the arc represented by the string measures 1 radian.

For the Exit Pass, I ask the students to convert 180 degrees to radians. Of course, the correct answer is pi radians on this Pi Day. I tell the one guy enrolled in both Ethnostats and Trig that since I gave him pies in each class, I really gave him 360 degrees today (since 360 degrees is 2pi radians).

11:20 -- Fifth period leaves. Sixth period is the second of my two conference periods. But once again, I must cover a class during this period. It's the class I've had to cover the most -- junior English.

These kids are learning about poetry. But whenever I sub in a class on Pi Day, I find some way to tie the holiday to the class, even if it's not a math class. Well, the Ethnostats students just wrote Pi Ku poems -- so I read some of the ones that Carter posted on her blog. My own students' poems are in their Stats notebooks, so I don't read any of those (much to the relief of one girl who's enrolled in both Ethnostats and this English class).

Then while the class works on missing assignments, I start playing some Pi Day songs -- but not the ones from the CD. Instead, I go to YouTube.

It's my blogging tradition to post some Pi Day videos each year on the holiday. Here are links to the five videos that I play in that English class today:

1. Mathematical Pi:

There are so many versions of this song, mainly due to the title of the song it's parodying -- it's just too irresistible to change "American Pie" to "American Pi."

2. "Pi Day video" by musicnotes online

As I wrote, this is one of the few videos that references the Pi Minute -- 3/14 at 1:59. Notice that had today not been a minimum day, 1:59 would have been during sixth period -- and I tell the kids this.

In fact, during the two years that I had a full-time job, both years the students were dismissed well before 1:59 on March 14th. During the year I was at the old K-8 charter school, mid-March (right at the end of the second trimester) was time for parent conferences, and so school for all students (including my middle school kids) was dismissed early all week. And this year, the monthly minimum day (which is usually on a Monday) just so happened to be today.

Recall that the November monthly minimum day was delayed to Friday in order to give the students an early release day leading into Thanksgiving break. I was hoping that our school would do the same thing leading up to spring break. Then today's short day would have been on Friday, and the rest of the week would have been shifted ahead -- making today an odd day and placing Trig at 1:59. Indeed, Trig is the only math class that I can have on any day at 1:59.

The two years that I subbed in Orange County on March 14th, both days were at middle schools -- and both had fifth period dismiss very close to 1:59. Thus so far, I haven't been able to have a Pi Day party actually start at 1:59.

Next year, I might have better luck with the Pi Minute. Pi Day itself will be a Tuesday (hence unlikely to be a minimum day) and with school starting at 8:30, 1:59 is more likely to be during the interior of fifth period (or near the start of a block period) rather than a passing period. Then again, thanks to that pink slip, who knows whether there'll even be a next year.

3. Pi Day -- the song by Gangstagrass

This one first came out last year, but I never noticed it until this year. It's length is 3:15 (and I assume the intent was for it to be 3:14).

4. The Pi Day Song by Michael Bautista

I believe I've heard this one before in the three years since it was first uploaded, but I'm not sure whether I ever posted it to the blog.

5. "Pi Pi Pi" by Everyday Science

As the title suggests, it's a math parody of NSYNC's "Bye Bye Bye," a hit from the year 2000.

By this point, I've already handed out all of my pies to my math classes. Just in case I'd run out of pies, I'd bought some extra cookies and Crunch bars, so I hand these out to the classes.

12:00 -- Sixth period leaves, thus completing my day of teaching. But of course, the minimum day means that there's a teachers' meeting coming up.

During the lunch break, I purchase a Personal Pan Pizza from Pizza Hut -- that's right, just like the CD version of "American Pi." Perhaps I should have also bought some breadsticks, so that it matches the Starbird lecture about pi(e) with breadsticks. (But Buffon was French, so those needed to be French breadsticks, not Italian.)

1:15 -- The teachers' meeting begins.

The principal begins by telling us that there's still too much uncertainty regarding the future of our school or our jobs. So there's not much she can say about the biggest thing on our minds.

But here's something we do know about -- the SBAC (or CAASPP), the upcoming state tests. Here in California, the English and math tests are given only to juniors, but the science test (yes -- the same science test that was the bane of my existence back at the old charter school) is supposed to be given "at least once in high school" -- it's up to each district to decide. And as it turns out, our district has decided to give the science test to seniors. This means that I (whose students are mostly seniors) will be more involved in the state tests than I first thought.

All state tests will be given in April -- the science test in early April, with English/math later on. While the bell schedule won't be changed during state testing, I will be called upon to proctor some of the exams, with another teacher covering my morning classes.

A "State Testing Day (choose one)" was one of the original special days chosen by Tina Cardone for her blogging project so many years ago. So I will do "A Day in the Life" on one of the days I proctor -- especially if it's on a day when I'm already scheduled to blog.

1:59 -- At the famous Pi Minute, the teachers' meeting is still going on. At this particular moment, the principal happens to be discussing an upcoming emergency drill.

The meeting ends shortly after this, so I'll conclude "A Day in the Life" here.

Let me add a few more videos here, including ones that I don't play in any class today:

6. Vi Hart's Pi Day video 2022

It's Vi Day -- the one day of the year when Vi Hart posts a video. This year, Vi posts a new song based on the digits of pi. But unlike previous digit songs, this one is based on the chromatic scale rather than the usual major scale.

Vi explains that the digits 1-9 correspond to the notes Eb-B. The notes (middle) C and D are used to create a "drone" -- with those notes chosen because they remind us of the formula C = pi d. Then Vi represents 0 by using the last remaining note, a high C# (skipping over C).

Notice that it's possible to simulate this song using Mocha scales. (Mocha computer music is something that I described in full detail on the old blog). It turns out that the closest fits in Mocha to Vi's chromatic scale are found by placing digit 1 on Degree 20 or 21 -- then digit 9 falls on Degree 12 or 13, and digit 0 falls on Degree 11 or 12. The fact that Mocha steps grow wider as we ascend the scale works to our advantage since Vi's B-C# is wider than the semitones forming the rest of the scale.

Of course, we can't play accompaniment (including Vi's drones) on Mocha at all. And if we want to include all 314 digits, we'll need lots of DATA lines.

7. "What Pi Sounds Like" by Michael Blake:

8. "Song from Pi" by Song Scout

9. Christopher Bill turns pi into music

In 7-9, I might as well reblog these previous songs based on the digits of pi so that we can compare it to Vi Hart's latest song.

10. Dr. Trefor Bazett

This is a new video for this year. It's the second video I've seen that demonstrates the Basel formula -- there's another interesting one by 3blue1brown.

Let's conclude this post by discussing the first item on the list at the top of this post -- the upcoming schedule, including my blogging schedule. There will be no Open House this week, and the "Little March" concludes this week -- next week is spring break. For some reason, Tina Cardone never include "day before spring break" as a special day, and so my next post should be during spring break itself.

But I wrote in December that I will not blog during spring break until after I write the spring semester final exams for all three of my classes. This is due to some frustration I had with the exams when I'd just barely finished the finals before finals week, only to have the computers break down that week.

The tricky part of this is that I don't know whether Calculus should even have a final exam. The AP exams are about a month before the last day of school, and so not all AP teachers even give finals. I need to consult with other teachers (including the Calculus teacher at the main high school) for more advice on finals.

But that doesn't matter -- I already wrote that I'm writing final exams before blogging. I must write three full exams -- and they must be complete, in that they are all ready to be given on the first day after spring break if desired. And unless I hear before spring break that I don't need to give a Calculus final, I must finish the Calc exam before blogging -- even if it means that I don't blog until Sunday night, March 27th -- the very last day of spring break. Writing the finals comes before blogging.

And so this ends my post, with no idea when I'll be posting again. I wish you a happy Pi Day!