The Return of This Blog

This is my first post on my Geometry blog in almost a year. And so this post is another FAQ post where I answer questions about what to expect in the new school year.

Table of Contents

1. Where and what will I be teaching in the new school year?

2. Is Blaugust back?

3. What is my first Blaugust prompt?

4. What will be my cell phone policy?

5. What will be my food policy?

6. What will be my homework/interactive notebook policy?

7. Am I still reading Jim Peterik's Songwriting for Dummies?

8. What is today's Rapoport question?

9. Who are the other Blaugust participants?

10. What will be my new blogging schedule?

1. Where and what will I be teaching in the new school year?

I can now finally say where I'll be working. I will be remaining in my current district, in LA County, and working at the main high school in the district.

This is the school I visited back in November, the school whose AP Calculus teacher I visited in order to gain ideas on how to become a better teacher myself. Now we'll be working at the same school -- and he, a 20+year veteran, is now my department chair.

Coming into today, I still didn't know what levels of math I'm supposed to teach. Our schedules are supposed to be posted on Aeries (the same system where grades are posted), but mine isn't -- likely because I'm new here. I didn't know for sure until the chair posted the schedule for tomorrow's department meetings.

I will be teaching Integrated Math I and III this year.

It is generally known that Math III is essentially equivalent to Algebra II, while Math I and II are an integrated version of Algebra I and Geometry. So this is the closest I've gotten to teaching my favorite math, Geometry, since my teaching career began.

And that's why I'm returning to my original blog -- my Geometry blog -- starting today. My Stats blog will no longer be active. (And on second thought, I admit that I should never have left my old blog, not even when I taught Stats last year.)

The first day of school will be Wednesday, but today is a PD day. Therefore it counts as a Tina Cardone "A Day in the Life" post for the special day "a PD day":

8:00 -- I arrive at my new school. The principal serves the teachers a hearty Welcome Back breakfast.

9:00 -- I visit the first of three PD stations in the gym, where the principal talks to all of us about policies and procedures.

10:00 -- I visit the second of three PD stations in the library, where we hear of emergency procedures and activities.

11:00 -- I visit the third of three PD stations in the cafeteria, where we learn about our academic focus for the 2022-23 school year.

12:00 -- I finally make it to the office, where I receive the key to my new classroom. It's located on the second floor of one of the few two-story buildings on campus, on the southwestern corner -- very similar to the location of my classroom at the old charter school. (All middle school classes that year were upstairs, since we we co-located with a district elementary school on the first floor.)

2. Is Blaugust back?

Well, here's your answer:

And you know what that logo means -- Blaugust is back! Here's a link to the blog of Shelli -- the creator and leader of the annual Blaugust challenge:

https://statteacher.blogspot.com/2022/07/mtbosblaugust-is-back.html

Well... years ago, hubby decided he was going to blog EVERY DAY and has now been blogging every day for like 9 years or something.  He decided to challenge his online community to try it for one month and I decided to give it a shot.  (I should mention here that I've never successfully completed the challenge...)

Obviously, as teachers, time is short in August as we prepare for a new school year and blogging often falls by the wayside.  We would love for you to join in, so feel free figure out the platform that works best for you and try it out!  Maybe it's a traditional blog like this one, maybe it's a micro-blogging platform like Instagram, maybe it's some other platform that I don't even know about.  But ultimately, the Blaugust challenge is about personal reflection and sharing ideas with others in the community, regardless of platform choice! :)

Last year, I was hired at my new school in August and ready to participate in the Blaugust challenge, only to be disappointed that Shelli wasn't doing it last year. This year, I'm ready to be a full participant in the newly restored challenge.

In theory we should be blogging all 31 days this month (even though, as Shelli admits, she's never done so herself). Of course, it's already August 8th, and I won't be making 31 posts this month. I was waiting until I got the full information I needed about my new position -- otherwise I'd have nothing to blog about this month.

So anyway, this is my first Blaugust post.

3. What is my first Blaugust prompt?

Shelli reminds us that we don't need to follow all her prompts. But I always enjoy doing following the prompts as part of the challenge! Since today's the 8th, let's look at the eighth prompt from her list:

8. Write a post related to pandemic teaching.

That's an interesting prompt to start the 2022-23 school year, since it immediately raises the question, is the pandemic over? This sounds like a prompt better suited for the 2019-20, 2020-21, or 2021-22 school years that were more definitely affected by COVID-19.

In fact, let's look back at how I handled the pandemic during those three years:

• 2019-20: Everything shut down in March. I was a substitute teacher at the time, and so as schools were closed and replaced by distance learning, I found myself with no work at all that spring.
• 2020-21: Many schools reopened under the hybrid model. I gained a long-term position at a middle school, teaching Grades 7-8 from September through January. I returned to day-to-day subbing the rest of the year as schools gradually added more days of in-person learning.
• 2021-22: I gained a full-time position at a tiny magnet high school, where I taught Calculus, Statistics, and Trig. Weekly COVID testing and masks were required for part of the year as the number of cases increased and decreased during the year.

That magnet school was closed by the district at the end of the year, which is why I was eventually moved to the flagship high school. I believe that the pandemic was partly to blame for why the magnet was troubled throughout its existence -- it had opened for its initial class of freshmen in Fall 2016, so they had only made it to March of their 12th grade year before switching to distance learning. 

Each year before COVID-19, a new class of freshmen joined the school, but no new students were added since the start of the pandemic. So by the time I got there, only Grades 11-12 were still attending the school. The seniors graduated, and the juniors were transferred to the flagship high school for their final year.

Over the years, I've thought about what I want my own classes to look like, but I wasn't sure whether those ideas would make sense during the pandemic. The next few questions here in this FAQ are all about my plans for the upcoming school year based on those ideas.

By the way, you might be wondering about my COVID What If? stories -- that is, what if the pandemic had occurred back when I was my students' age? Well, most of my kids are freshmen or juniors -- in order to match the n + 3 year, I must place the pandemic at COVID-92 for my freshmen, COVID-94 for my juniors. Both of these are tricky -- there's already a COVID-91 What If? that I like, mainly because the dates line up exactly (as it's 4 * 7 years before COVID-19). As for COVID-94, this sort of clashes with my COVID-96 What If? for last year's seniors.

But once again, there will only be a COVID What If? if I'm convinced that the pandemic is ongoing -- for example, if two pandemic-related policies are implemented (say masks and required testing).

4. What will be my cell phone policy?

We all know that cell phones in the classroom were a growing problem even before the pandemic. As I wrote in my March 23rd post, I believe that 2012 was the inflection point, five years after the start of the iPhone, when phones switched from a minor problem to a major problem. So the pandemic only sped up what was inevitable anyway -- during distance learning, students developed the bad habit of spending most, if not all, of class time using their phones, and they brought that bad habit back into the classrooms when they reopened.

And from the perspective of a math teacher, there's another problem with phones besides their existence as a distraction -- the use of calculators to answer basic math problems. Many older people lament how young cashiers can't even calculate their change because ever since their middle school days, they've only ever done arithmetic on a calculator -- more often than not, the calculator on their phones.

One idea that I've posted on the blog is "Technology 1955" -- on certain days, students will not be allowed to use phones, calculators, or anything invented before 1955. The year was chosen because it's the birthyear of three important inventors -- Bill Gates, Steve Jobs, and Tim Berners-Lee.

All three developed the technology that many of today's teens can't live without -- but as young teens themselves, they obviously couldn't use modern technology to do math problems as they hadn't invented it yet! So they had to know how to solve math without a calculator -- and they applied the math they learned to build the technology that made them famous.

My original plan was to have one day, say Monday, be "Tech 1955." The next day would be "Tech 1973" (the year that those born in 1955 graduated), when simple calculators would be allowed, but still no cell phones. This would be followed by "Tech 1991" (the year that those born in 1973 graduated), and so on until full tech, including phones, are allowed on Fridays.

But of course, that will be an uphill battle. Ever since the start of pandemic distance learning, it's unlikely that many of these kids ever went more than one waking hour without using a phone, and now I'm expecting them to do so now in a 90-minute block. Yet Mondays aren't block days -- so no-phone Mondays won't be as painful. Therefore, my plan is to establish "Tech 1955" on Mondays. The rest of the week, phones will be allowed, except perhaps on certain Fridays (the other non-block day) when I give a no-phone quiz.

I believe that I'm not the first teacher to invoke a year as part of a no-phone policy. The year that this other teacher chose was 1995. To me, this is ironic -- 1995 was the summer before my freshman year. I was running near a river for Cross Country practice when I fell in the water. A driver used her car phone to dial 911, and I was rescued and rushed to a hospital. It never occurred to me that we'd go from having a cell phone saving my 14-year-old life, to a time when 14-year-olds feel that we're ruining their lives just for suggesting that maybe they shouldn't spend 100% of their waking hours on a cell phone -- yet that's where we are now.

Again, the idea behind the phone policy is that without the math they're learning in my class now was used to develop the technology that powers the phone. In other words, without math, cell phones wouldn't exist at all.

5. What will be my food policy?

Cell phones in the classroom expose the generational divide -- the young members of Generation Z were taught that they can't go a few minutes without a smartphone, which is difficult for members of generations who grew up before the invention of such phones to comprehend. On the other hand, food has existed longer than humans have on this planet.

When I was a young student, I never ate in the classroom -- unless, of course, it was one of those very rare days when there was a classroom party. I ate breakfast in the morning, then not one bite until it was snack break, then not one bite until lunch break, then not one bite until I got home. Sometimes if I couldn't finish my lunch before the end of the break, I ended up throwing it away -- I'd much rather discard the rest of my lunch than break the "no food" rule. So that's why it annoys me so much when I see students eating in my classroom.

During the pandemic, students had to wear masks in the classroom -- and thus they definitely weren't allowed to eat food during class. And so for much of the year, I hid my "no food" rule behind the general pandemic rules.

But in March, the mask rule was lifted. I was considering implementing a separate "no food" rule at that point -- but it didn't help that the first mask-free day happened to be Pi Day, a day filled with eating pies and other special treats for the day. Since it didn't look good to implement a strict "no food" rule on Pi Day, I ended up not having such a rule at all (except for two weeks in mid-to-late April when there was a slight virus surge).

And indeed, that raises another question -- will there be certain days when I bring treats to school, such as a candy incentive, and how will that affect a possible "no food" rule?

A long time ago, I was considering bringing candy to school. In order to avoid bringing too much or not enough candy, I would assign each period a day of the week to have the candy incentive. For example, first period might be Monday, second period Tuesday, and so on up to sixth period on Friday. By doing it this way, I'd be passing out candy when the students need it the most -- first period on Monday when they are still hung over or influenced by the previous weekend, and sixth period on Friday when they are influenced by the following weekend.

But now I'm starting to wonder whether this is introducing needless complexity. Instead, I should just buy a barrel of Red Vines, and then hand them out to all classes on Monday -- with Red Vines earned based on their performances on the quiz the previous Friday. Then as for the "no food" rule, small snacks will be allowed on Mondays since I'm passing out food anyway, and then it's no food the rest of the week. (This also makes it easier to remember -- food is allowed on "Tech 55" days when phones are not allowed.)

The Red Vine incentive also goes back to how I did it at the old charter middle school six years ago -- except that there will be one additional level:

• One Red Vine for getting an A on a Hero Quiz
• Two Red Vines for being the most improved on a chapter/unit test
• Three Red Vines for earning an A on a regular quiz/test

Yes, Hero Quizzes are back, except that they won't be simple multiplication Mad Minutes, which I believe are insulting to high school students (as much as some of them might need it). Instead, these will contain review problems, from either previous units or previous years.

The Hero Quizzes will also be the quizzes on which calculators are forbidden ("Tech 55"). Phones must be kept away until a grade of A is earned on the quiz, which I grade right away. Those who earn anything less than an A must keep working on it until an A is achieved.

6. What will be my homework/interactive notebook policy?

I've already mentioned interactive notebooks in my previous posts. When I entered my new classroom for the first time this afternoon, I found some old papers from the previous teacher in my desk. It was a scoring guide for a notebook check. So by inspecting this paper, I get to learn more about how to implement interactive notebooks.

Anyway, my predecessor graded a total of 16 assignments in this notebook check -- ten from Chapter 6 on systems of equations, and six from Chapter 7 on basic geometry (Triangle Sum, Pythagorean Theorem, and Congruence). Based on these topics, I assume that he taught Math I last year, perhaps based on CPM, a well-known integrated text (since I see a CPM textbook code still on the board). Each of his assignments took up one or two pages, and each was worth ten points, for a total of 160 points for this notebook check.

OK, so that's Math I -- what about Math III? Well, even though the department meeting isn't tomorrow, the agenda for the meeting is already posted today. Apparently, the math teachers are supposed to divide into CT's ("curricular teams"???) based on our subjects, and I was assigned to the Math III CT. So I'm already getting lots of info about the Math III course:

First of all, the Math III leader has already revealed his grading percentage weights:

20% -- homework (DeltaMath/worksheet)

20% -- classwork (Desmos)

20% -- quizzes (two per chapter)

20% -- chapter exams

20% -- midterm/final

And notice what's missing from that list -- interactive notebooks. The conclusion is inescapable -- there are no notebook checks in Math III.

But didn't I find a notebook check in the teacher's desk? Yes -- but that was Math I, not III. I glean from the info on the board that all five of my predecessor's classes were Math I.

But hey -- didn't my partner teacher (at the old magnet school last year) use interactive notebooks in her own Math III class (from which I got the idea of implementing them myself this year)? Yes -- but she isn't here, so she's not in charge.

I'd already anticipated that once I moved to the flagship high school, I'd be a member of a full math department, and so some decisions (like grading weights) will have already been decided for me. In fact, there's already a complete first semester pacing guide, filled with activities. Even this week's opening activities are already listed on the pacing guide. I was already looking ahead to the Sara(h) activities (from Sarah Carter and Sara Vanderwerf), but I must do the activities listed on that pacing guide instead.

I can start working out how many points each assignment is worth. There are four chapters to be covered in the first semester, namely 1, 2, 3, and 5. (Chapter 4 is a Stats chapter that we're skipping -- all the more reason to post on my Geometry blog rather than my Stats blog this year.) If the total is to be 1000 points, then that works out to be 200 points in each category. This turns out to be 25 points per quiz, 50 points per chapter exam, and 100 points each for the midterm and final.

Then again, the department might tell us how many points each assessment is worth -- and then we must set the weights in Aeries in order for the percentages to add up. I hate doing this because it makes the points seem deceptive -- but once again, when department leaders say "jump," I ask "How high?"

Meanwhile, the assessment retake policy is stricter than my partner teacher's last year. She allows for 75% of the points to be recovered on her retakes, but here we start at 75% for the earliest quizzes and then lower the percentage to 55% as the first semester proceeds, with 65% on the chapter tests. (I assume that there are no retakes on the "midterm" or "final.")

It also means that I can't do the first quiz of the chapter as a "hero quiz," so I've already contradicted what I wrote in this post. Moreover, "Tech 55" might not work on Mondays if the assignments are on either DeltaMath or Desmos, neither of which existed in 1955. (While technically I could still have a "no phones" day on Mondays, students can still do arithmetic on their Chromebooks during those assignments, eliminating one of the reasons of having a "no phones" day.) And I'm wondering whether I can even fit Warm-Ups or Exit Passes in the Math III grades.

So far, I've mentioned the CT meeting for Math III. Apparently, I'm not in a CT for Math I. So it's possible that I have a little more autonomy in running the Math I class. Thus much of what I've mentioned in this post (notebooks, hero quizzes, Tech 55, and so on) might work in Math I -- unless, of course, a leader tells me tomorrow that I can't.

(Note: In order to avoid confusion, if I learn that I can't implement notebooks or anything else that I've listed in this post in Math I, then I'll just edit it out of this post.)

There's one more thing I must say about my Integrated Math classes. Last year, my partner teacher told me that she had to give district Interim Benchmarks in her Math III class. While my predecessor left a mention of Benchmarks on the board for Math I, they don't appear on the Math III pacing guide (unless the "Midterm" mentioned there is really the Benchmark -- and before you ask, even if Benchmarks aren't included in the grade, they should still appear on the schedule). Assuming that there are any Benchmarks this year, they will be in October, February, and May.

7. Am I still reading Jim Peterik's Songwriting for Dummies?

I wasn't going to go far past Chapter 12 anyway. The chapters past 12 are all about how to make money from these songs, while 12 itself is called "Writing for Stage, Screen, and Television" -- which, of course, I won't be doing much of. Instead, I'll be writing math songs for the classroom.

Since Chapter 12 is the last chapter of Part IV of the book, it feels as if I should discuss this chapter briefly, in the name of completion -- and so I will. Here's how it begins:

"When a songwriter dreams, sometimes his flight of fancy takes him to a gilded Broadway theater where his songs are being performed by the cast and orchestra of a long-running, live stage production."

Let's skip up to the section on songwriting for television -- since, after all, the first songs I'll perform aren't my own songs, but are from the 1980's-1990's PBS math show Square One TV:

"Many songs have languished on shelves until some visionary director discovers it while station surfing in his Porsche and decides to feature it in the next episode of his series. Sometimes all it takes for a great song to be recognized is one person in a position of power to hear it at just the right time."

And as I wrote before, some of Square One TV's songs were performed by real music groups (such as the Fat Boys), while other songs were sung by the cast yet fit the genres (such as country). Interestingly enough, "Mathnet" -- a subprogram of Square One TV -- had a few cases that revolved around music and songwriting.

In "The Problem of the Passing Parade," where a famous rock musician is kidnapped so that he'll be forced to perform with a college marching band. "The Case of the Unkidnapping" was about an aging Broadway star who faked her own kidnapping in order to steal money of the production of her show. A memorable scene from the end of this episode is her final capture, where the Mathnet team members run up on stage to perform an impromptu Broadway song about her impending arrest. And in one last ep, "The Case Off the Record," a music producer fakes the sales numbers from his songs in order to make them appear more popular than they really are, so that radio stations will play them more often, which will lead to real sales.

Returning to the Peterik chapter, the author also writes about songwriting for commercials. It's notable that one of the songs that I performed in math class, "Plug It In," was originally based on a commercial jingle, for Glade Plugins air freshener.

The chapter ends with songwriting for musicals. Peterik quotes composer Dennis DeYoung:

"Even when the play finally opens, there is inevitably fine-tuning of songs and scenes. Showboat was written 75 [by now almost 100] years ago and they're still fooling around with the book!"

Now that I know what school I'll be working at. I can now announce my music schedule. I'll perform songs on block days. Since each class meets two block days per week, I'll prepare two songs per week and then sing each song to each class once.

The block schedule doesn't start until next week, so my first songs are next week. My original song "Heroes and Zeroes" will be my first performance, and then this will be followed by songs from Square One TV for the rest of Weeks 2-4, with original tunes returning in Week 5 in September.

Once again, I must be careful to avoid parent complaints about my music. As I wrote before, I won't bring my guitar to school until Week 5, so the Square One TV songs in Weeks 2-4 will be vocal. Then again, I didn't mind not singing last year because it's mainly younger students who enjoy my music -- usually middle school or the younger part of high school. This year, with Math I on my schedule, I really want to make sure that those freshmen will get to hear my songs.

Thus most of my songs this year will be geared towards Math I. Oh, and do you remember those songs I wrote all summer for a Math 8 position that I ended up not taking? Well, I've said before that there's lots of overlap between Common Core Math 8 and Integrated Math I. Therefore I was (unwittingly) writing for my new Math I class all this time! (I'll probably still sing the Math I songs for the Math III juniors anyway -- and from time to time, I might throw them a bone and perform a Math III song -- especially if there's one already written for them, such as "Quadratic Weasel.")

That concludes our reading of Jim Peterik's Songwriting for Dummies. It was an enjoyable read, and I'll continue to use the principles I learned in this chapter as I compose math songs throughout the year.

8. What is today's Rapoport question?

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

Find R(3, 4) + 1 where R(3, 4) is a Ramsey number.

This is a pure research question. Frank Ramsey was an early 20th century British mathematician who made the following discovery:

In any party of six, there exists at least three mutual friends or three mutual enemies.

Thus R(3, 3) = 6. And R(3, 4) would be the smallest party at which there exists at least four mutual friends or three mutual enemies. It was proven using brute force (that is, on a computer, checking all possibilities) that R(3, 4) = 9.

Therefore the desired answer is 9 + 1 = 10 -- and of course, today's date is the, um, eighth?  Rapoport admits that she made a typo on the calendar. The plus should have been a minus -- and 9 - 1 = 8, which really does match today's date, the eighth.

I'll continue to have Warm-Ups and Exit Passes, with the date as the answer. Of course, I won't give them Ramsey theory problems -- and especially not Ramsey theory problems with errors.

Occasionally, Rapoport will give a problem that matches what I'm teaching in my classes. Otherwise, I won't post any problems from her calendar on the blog during the school year.

9. Who are the other Blaugust participants?

Shelli, the leader of the Blaugust challenge, made a Blaugust post that doubles as part of her "Made 4 Math Monday" series:

https://statteacher.blogspot.com/2022/08/geometry-reference-sheet-mtbosblaugust.html

Here she makes a Geometry reference sheet that students included in their interactive notebooks. Even though I teach Integrated Math, I could do the same when Math I reaches the Geometry units. Based on my predecessor's class, Geometry appears in Chapter 7. According to the board, the Chapter 9 retake was just before the third and final Benchmark. Thus Chapter 7 might be right after the second Benchmark, at the start of March. So I could include something like Shelli's reference sheet then -- assuming, of course, that I do interactive notebooks at all.

And joining me with his first Blaugust post today is Stephen Dull:

https://tweakingfornoreason.wordpress.com/2022/08/08/august/

Dull writes about many things that are on his mind this month. He describes a PD that's in some ways similar to my 11:00 PD today -- both of us are focusing on "linguistically diverse" students (that is, English learners).

And of course, the teachers on his chart correspond to Harry Potter teachers -- "The Warm Demander" is McGonagall, "The Sentimentalist" is Flitwick, and "The Elitist" is Snape. (I'm not quite sure who the "Technocrat" is -- maybe Professor Sprout, who knows her Herbology but isn't quite as caring as McGonagall is shown to be.)

10. What will be my new blogging schedule?

I'm aware that blogging is a dying medium. And so I'm reducing both the length and number of my posts, as follows.

First of all, there will be no more super-long posts (like today's post) during the school year. Most school year posts will contain only the Blaugust topic and the song of the day -- and the song will contain only the lyrics and either a video (if it's from Square One TV) or a link to Mocha EDL code (if it's an original song). The only longer posts will be "A Day in the Life" posts -- there will be both monthly and special posts.

And now I'm usually posting twice per week. The two posting days will be two of Tuesday, Wednesday, Thursday -- the block days, depending on when Math I meets (so I'll decide when I see a schedule).

There are three more "A Day in the Life" days coming up this month -- "first day of school" (which is Wednesday), "Back to School night," and the monthly posting day. I'm still confused regarding whether there will be monthly minimum days this year (they were alluded to in the 11:00 PD). Instead, I'm considering making the 17th my monthly posting day. Like the 18th last year, the 17th this year avoids most weekends -- only September 17th and December 17th are Saturdays, and there are no Sundays.

Like Dull's school, my school is also having a freshman orientation today, but ours is tomorrow. I've decided that I won't post on freshman orientation day (despite my having ninth graders this year), and so my next post will be on Wednesday, the first day of school.

The Future of This Blog (Day 2)

OK, my schedule at my new school has finally been revealed:

1. Statistics

2. Statistics

3. AP Calculus AB

4. Statistics

5. Statistics

6. Conference Period

With this schedule, I can no longer justify running a blog with "Geometry" in its name. Just like the only other MTBoS Stats teacher I know -- Shelli -- I need a blog with "Stats" in its name:

https://commoncorestats.blogspot.com/

This doesn't mean that I'm definitely abandoning this blog. Perhaps in some future year, I'll finally be called upon to teach Geometry, and then I can resurrect this blog once again.

I'll see you over at the new blog!

A Major Announcement (Day 1)

In today's post, I have a major announcement to make. I'll add the "FAQ" label and then use the rest of this post to give the announcement.

I am now officially a full-time math teacher. Starting tomorrow and lasting the rest of this year, I will be teaching at a high school in LA County.

Everything has been moving quickly since my August 4th post. I had a Zoom interview with the district last Thursday, filled out paperwork for the position on Monday, and then found out today that I will be reporting to the school tomorrow. I don't know much about the school itself, nor about which levels of math I'll be teaching. I've only been to the district office and have never set foot on the campus itself.

Anyway, here are a few things I know about the district, the school, and my new position:

• It is not in the LA County district where I've been subbing for five years, but it is next door. And because of this, my new LA County district's calendar closely resembles that of the old district.
• Today really is the first day of school in the district, and so I won't see the students until Day 2. The district did try as hard as they could to get me processed, but I still end up missing the first day.
• This is a fairly new magnet school in the district. In fact, its first year of operation was just five years ago (the same year that I taught at the old charter school).
• The school is fairly small -- perhaps around the same size as the old charter school.
• The school has a fairly typical block schedule, with all classes on Mondays, odd periods on Tuesdays and Thursdays, and even periods on Wednesdays and Fridays.
• The district uses integrated math.
• The magnet school is in trouble. In the spring, it was declared that unless a sufficient pool of incoming freshmen applied, the school would admit no freshmen. And indeed, that's exactly what happened -- all students currently at this school are in Grades 10-12.

This is a Geometry blog. But one thing I told myself is that if I ever taught full-time and had a schedule with no Geometry (for example, all Algebra I and II classes), then I would end this blog and start a new blog without Geometry in its name. But as along as I had at least one class with some geometry -- and this includes both middle school classes and integrated classes in high school -- then I would keep this blog with the name Geometry.

But do all integrated classes really have Geometry content? One thing I've noticed is that Integrated Math I tends to include half of Algebra I and half of Geometry, and then Math II includes the remaining half of Algebra I and Geometry. Thus Math III becomes almost identical to Algebra II -- indeed, perhaps calling this class "integrated" is a misnomer.

OK, so that would make it easy -- if I get my schedule tomorrow and I have at least one Math I or II class, then I keep the Geometry name, but if I have only Math III and higher, I start a new blog.

This district does provide a path to AP Calculus -- middle school students who take Honors Math 7 and 8 and excels in both can enter freshman year in Math II. Since this is a magnet school, I wouldn't be surprised if this is a requirement to enter the magnet -- so all freshmen here take Math II. But keep in mind that there are no freshmen this year. The sophomores would all be in Math III this year, thus making Math III the lowest class offered at the magnet this year.

If this is the case, then I'm guaranteed to have no class with any geometry content -- and thus I'd have to start a new blog. I'll find out tomorrow whether I'm correct.

As for how often I'll blog, my blogging schedule needs to be based on the block schedule. If I'm keeping this blog, then it means that I have at least one Math II class -- and then my posting schedule will be based on that Math II class as that one course justifies the Geometry name. So if it's an odd period, then I'll post Mondays, Tuesdays, and Thursdays.

In any case, I wish to tweet on the days I don't blog. At such a small school, there might be only one other math teacher -- and it's likely that I'll have at least one prep that the other teacher doesn't. And so I'll do what I should have done at the old charter school -- post on Twitter, and treat the MTBoS as my math department, at least for the preps where I'm the only teacher.

My mind is at a blur right now. As recently as my August 4th post, I was worried that I might never become a high school math teacher, and now suddenly I have a class to teach tomorrow. I'm still making sure that I have a classroom management plan -- after my experience at the old charter school, I want a much stronger plan for this year. I'm rereading my Harry Wong and Fred Jones books on classroom management to make sure that I'm doing everything right!

The MTBoS also has some ideas on what I should do tomorrow. Over the weekend, one of my favorite MTBoS members, Fawn Nguyen, made a timely post:

https://www.fawnnguyen.com/teach/dear-new-teachers

Congratulations! Whether you’re a brand new teacher or you have a new assignment, whether you’re in a new building or you’re returning to the classroom, I wish you all the best.

Thanks Fawn -- I certainly hope to do my best this year.

Take attendance each day out loud. I wish I could take back the days when I just looked at the empty desks to mark down the absentees. I thought I was being efficient. Greet students each day by saying their names and acknowledging their presence:

Notice that this completely contradicts what Harry Wong and Fred Jones write in their books. To them, taking attendance out loud invites misbehavior and leads to comments such as "He isn't absent -- he's just in the office," as well as arguments.

But since the pandemic, I've read of more teachers leaning towards Nguyen's suggestion here. They believe that after having spent most of last year on Zoom, what students need more than anything else is a sense of belonging. And one way to provide that sense of belonging is to call out their names.

What Nguyen is telling teachers to do is have a conversation with their students. I admit that I often struggle to converse with high school students, and for a simple reason -- when I was a young high school student myself, I had trouble conversing with my classmates! As I've mentioned on the blog, I moved to a different district during my freshman year -- and as so often happens to students in that situation, I struggled to make friends at my new school after leaving my old ones behind. (Once again, to this day I still consider my eighth grade graduation to be my "real" graduation -- one reason is that it's the last graduation where I saw most of my friends.)

One of Nguyen's suggested conversations is:

How was your game yesterday?

My new magnet school apparently has only three sports. One of them is Cross Country -- which, of course, was my sport as well. I can definitely connect to my new students who happen to be distance runners (and once again, as a young XC runner I was at least able to bond with my teammates).

Do math every day, especially on the first day. The kind of math where your students talk in groups for at least 75% of the time. If your principal tells you not to, they are wrong.

Well, I do want to do some math tomorrow, but how can I when I don't even know what grade level of math level my classes are yet?

Oh, that's easy! Instead of Nguyen, I need to look at some other famous bloggers -- the Sara(h)s. The first week projects on the Sarah Carter and Sara Vanderwerf blogs are perfect for any level. I'll certainly do at least one of the Sara(h) activities tomorrow. Afterward, I'll blog and tweet about those activities.

Even though Tina Cardone's challenge is over, I'll continue to post "A Day in the Life" on special days, including tomorrow for the "first" day of school (even though it's really Day 2). I'll also have a monthly posting day for "A Day in the Life." The schedule mentions monthly minimum days similar to the ones I had at my long-term school from last year -- if this is accurate, then I'll continue to use those as monthly posting days.

Oh, and speaking of blogging challenges, now that I'm a real teacher and a full member of the MTBoS, it means that I'm officially a Blaugust participant. Wait -- so Shelli isn't doing Blaugust this year? I'm sorry, but I've been waiting five years to rejoin Blaugust, and no one -- not even Shelli -- can tell me anything else.

In fact, there really is a Blaugust challenge this year, but it has nothing to do with MTBoS or math. But still, I'm taking their logo and declaring this to be a Blaugust post. Here is the source of the logo:

http://www.containsmoderateperil.com/blog/2021/8/10/blaugust-2021-getting-to-know-you

Let's get to today's Blaugust topic. Since today's date is the eleventh, we'll just take the eleventh topic from Shelli's old list from 2019.

• How do you handle homework / daily practice?

This is a tricky one. During my long-term assignment, daily homework was completed on APEX, which included quizzes after each lesson. But now that there's more in-person learning this year, it might be time to return to traditional written homework. Things that I'll take into consideration include what other teachers at my new school are doing (including non-math teachers) and whether there is an online grading system with predetermined weights for homework, such as 10% or 15%. My old charter school weighted homework at 15%.

In fact, I like the topic I found at the above Blaugust link even more -- "getting to know you." This post was all about getting to know me -- I'm a teacher with a brand-new job. And tomorrow's post will be even more "getting to know you," as I get to know what classes -- and what students -- I'm teaching.

What I do know is this -- five years ago, I taught at an old charter middle school. That year didn't go as well as I'd hoped. And so this year, I've been granted a second chance to start a teaching career at a new high school.

And I will do a better job this time around. Notice that I didn't say that I may do a better job, or that I might do a better job. There's no "may" or "might" about it -- I will do a better job this year;. After all, Fawn Nguyen writes:

For the longest time I had only two rules to tell my students on the first day of school: 1) never give up, and 2) never tell an answer.

And that first rule applies to me. When it comes to being a better teacher, I will never give up.

Pi Approximation Day (Cheng Mysteries 3-4: The Garden of Hidden Shapes and the Hall of Endless Doors)

Today is Pi Approximation Day, so-named because July 22nd -- written internationally as 22/7 -- is approximately equal to pi.

It also marks seven full years since my very first post here on the blog. Yes, I've declared Pi Day of the Century -- March 14th, 2015, to be the ceremonial start date of this blog. But the chronological start date was July 22nd, 2014. I like celebrating both Pi Day and Pi Approximation Day -- including eating pie both days -- and so I celebrate both of them as launch dates for the 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. How will the coronavirus affect my current employment?
3. Who is Eugenia Cheng, and what is the Garden of Hidden Shapes?
4. What is the Hall of Endless Doors?
5. What is the actual reopening plan in my OC districts?
6. Who is Laura Lemay, and why am I learning Java?
7. What's "Mocha music"?
8. Who is Rebecca Rapoport?
9. What is Shapelore?
10. What is a COVID What If?
11. How will the coronavirus school plans affect this blog (and Twitter)?

1. Who am I? Am I a math teacher?

I am David Walker. I'm trying to start a career as a math teacher, but I must admit that my career isn't off to as good a start as I'd like.

Five years ago was my first as a teacher at a charter middle school, but I left that classroom. By now, I fear that I won't be hired to teach this year at all. If I'm not hired, then I'll remain a substitute teacher. But this will make the launch of my teaching career that much more difficult.

It's not that I'm having trouble finding work as a sub -- it's that I'm struggling to find work as a regular teacher. As I explained on the blog last month, I didn't always make the best choices inside and outside of the classroom. These decisions have weakened my resume, and so the human resources departments at most schools and districts will reject my application.

So the answer to this question is no, I'm not currently a math teacher, and I'm losing hope that I'll be one again soon.

2. How will the coronavirus affect my current employment?

I currently work as a substitute teacher in two districts here in Southern California. Both of these districts are in Orange County.

At this time last year, I worked in two districts -- one in LA County, the other in Orange. But my LA County district had always called me much less often than my OC district -- and this was even before the pandemic. During the pandemic, my OC district reopened in late September while my LA district remained closed, so at that point all of my subbing calls were from OC.

At that point, a second OC district hired me for a long-term subbing position. I covered both Math 7 and Math 8 from late September to early January. Once that position ended, I was still in the system for both OC districts, and so I continue to work for both of them.

My LA County district finally reopened in early April, and so during April and May I was working in three different districts. But subbing in three districts is awkward, and so I wish to return to two districts in the new year.

And even though I received many calls from LA County after the pandemic, I just can't trust the district to provide me with regular work in the new year -- especially considering how few calls I received the first four years that I worked there.

And so my final decision is for me to keep accepting calls in both of the Orange County districts and forget about LA County entirely.

3. Who is Eugenia Cheng, and what is the Garden of Hidden Shapes?

Eugenia Cheng is a mathematician and author. She has written five books -- the first four are mainly for adults, but her most recent book, Molly and the Mathematical Mysteries, is for children. And her children's book is also our side-along reading book for the second half of summer vacation. So let's go back to where we left off from my last post.

Let's begin Cheng's third adventure, called "The Garden of Hidden Shapes":

"Phew...Molly is glad she found a way out of that Impossible Staircase. Now she's in a huge garden. It's some kind of maze. From her starting point, Molly can see a bright triangular flower bed, a patterned pond of swimming fish, and an odd sculpture. But where is the way out?"

There is another note for Molly on this page:

"This challenge is all about shapes. Can you unfold the hexagon to make a big triangle in two different ways? One of them will make a path to the house."

This is still technically a Geometry blog, and so I definitely enjoy this page. By the way, the "triangular flower bed" is shaped like Sierpinski's triangle, and the "odd sculpture" is an impossible structure, not unlike the Impossible Staircase that Molly just left on the previous page.

But the emphasis here needs to be on solving the maze, which I can't fully describe on the blog. The author tells us more about the hexagon that the reader must unfold to produce a maze solution:

"Sometimes shapes fit together to make other shapes. In this maze, six triangles fit together to make a hexagon. The triangles are special ones where all three sides are the same length: these are called equilateral triangles."

She proceeds to describe tessellations. Tessellations, or "tiling the plane," appear in Lesson 8-2 of the U of Chicago Geometry text.

And there's also a challenge for the reader:

"This hexagon is made up of six tiled triangles. How many other tiling shapes can you find in the garden?"

In fact, the "patterned pond of swimming fish" mentioned earlier is a tessellation of fish.

4. What is the Hall of Endless Doors?

Let's begin Cheng's fourth adventure, called "The Hall of Endless Doors":

"Molly makes her way through the maze and reaches the front door of the house. She steps inside and looks around in awe. In front of her is a grand staircase and a dizzying hallway full of doors. Where could they all lead?"

There is another note for Molly on this page:

"To move forward, choose a door carefully. But watch out -- some doors lead to hallways that go on forever...you don't want to pick one of those!"

The author's math lesson for this page is "self-similarity":

"The doors in this hallway look like they go on forever! Each door pattern has a smaller door inside it, with an even smaller door inside that, and so on...They're a bit like nesting dolls. We could keep zooming in forever...providing the doors keep going on forever."

The name "self-similarity" is weird, but it makes sense. We know that a figure has rotational symmetry if there exists a rotation mapping it to itself. Anyway, a figure has "dilational symmetry" -- more commonly known as self-similarity -- if there exists a dilation mapping it to itself. And just as the trivial rotation of 0 (or 360) degrees doesn't count, neither does the trivial dilation of scale factor 1. The scale factors of all the dilations on this page are slightly less than 1, so that the effect is gradual.

"In math, something that keeps going forever is called infinite. Let's imagine an infinite set of dools. You could keep opening them forever without running out of dolls, but they'd get so tiny iy would be very hard to see them."

Infinity -- or should I say, beyond infinity -- was the theme of Cheng's second book if you recall.

And there's also a challenge for the reader:

"How many nesting dolls can you find hidden in the scene? Can you match up three sets of five dolls?"

One of the three sets is right on the table/dresser, but the other two sets are spread out on the page. I also enjoy looking at the numerous other designs on the screen. One of them is the infinite tree that we programmed Logo to draw back in late March (Lesson 13-8 of the U of Chicago text).

Doors 1, 2, 3 are all infinite dead ends. Door 4 leads to Molly's next adventure -- and my next post.

5. What is the actual reopening plan in my OC districts?

Both districts are hoping to bring all students back for a full five days per week, with the overwhelming majority of these students being in-person. This should end the hybrid plan once and for all. But not everything will be completely back to normal. At the very least, students and teachers must continue to wear masks in the classroom, according to Governor Gavin Newsom.

The reason for the continued masks can be summarized in one word -- Delta. And that's not "delta" as the mathematical symbol for "change," often used in the slope formula. Though it does have something to do with change -- as in the coronavirus changing. The coronavirus numbers had been decreasing until about a month ago, when the Delta variant of the virus fueled a sharp increase in cases.

With the rise of the Delta variant, there's no way that we can remove masks. Indeed, LA County has even declared a return to masks for all indoor public places -- even for vaccinated people.

Governor Newsom has already ended color-coded tiers on June 15th -- just before the Delta surge. But it was pointed out that had the color tiers still existed, LA County -- which had advanced all the way to the yellow tier at the time the tiers ends -- would have regressed all the way back to the red tier. Recall that in the red tier, schools can reopen, but most of them would be open in some sort of hybrid. My LA County district would be in Stage 2, with one day of attendance per week -- and LAUSD itself would have 2-3 days of in-person "Zoom in a room," and so on.

Despite returning to the equivalent of the red tier, most districts in LA and Orange County plan on reopening for in-person attendance five days per week. This could be because of the ineffectiveness overall of the hybrid plans -- the at-home students never succeeded as well as the in-person students.

Last year at this time, I was both overly pessimistic and overly optimistic about the pandemic. While I was hoping to be vaccinated by Tau Day 2021, I was pessimistic that it could take several years for a vaccine to be developed. As it turns out, the vaccines were announced in November, and I received both doses of the Moderna vaccine in May, thus beating my vaccination goal by a few weeks.

But I was optimistic that once the vaccines were developed, we could distribute it widely, and then the pandemic would soon be over afterward. What I didn't imagine was the current situation -- the vaccines are out, and yet the pandemic is still going strong with the Delta variant. It's often stated that we needed to reach a 70% vaccination rate in order to achieve herd immunity. But we're just shy of that level -- because less than 70% are willing to be vaccinated. There are just enough people choosing to remain unvaccinated to allow the Delta variant to spread.

I'm thinking about the Tokyo Olympics -- the opening ceremonies are set for tomorrow. Had the Olympics gone on last summer as scheduled, it would have been a disaster -- a few athletes would have tested positive for the virus each day, and the entire Games would have had to be set in a "bubble" without fans (not unlike the 2020 NBA playoffs that were contested at around the time the Olympics should have been). So instead, we waited until this year to hold the Games -- and now a few athletes are testing positive for the Delta variant each day, and the entire Games are now in a bubble without fans.

When the delay was first announced, there was a possibility that it would have been only about nine or ten months, to spring 2021. Notice that had the Games been contested in May-June, we could have vaccinated the athletes, fill the stadiums with plenty of fans, and returned the athletes safely to their home countries all before Delta had a chance to spread. But by waiting a full 12 months, that gave just enough time for Delta to spread and ruin the Olympics. Indeed, now many people (including the Japanese themselves) are questioning the wisdom of holding the Games at all.

Indeed, this is sort of like what happened with high school sports in California. The state cancelled all sports until December, when schools can start holding practices for January contests. But then there was a November virus surge -- and sports had to wait for February practices and March contests. On the other hand, we were between virus waves in August-October -- so fall sports could have started at their normal time, before the third wave. Most likely, playoffs and state championships (scheduled for November) would still have been cancelled -- but recall that fall playoffs were really cancelled anyway, so it wouldn't have made a difference, except for the regular seasons being played at their proper time.

In last year's annual FAQ, I wrote about how I often divide my life into two- and four-year chunks:

We need to be thinking in terms of periods longer than a year. Earlier on this blog, I mentioned the period of time I call a quaver, or half a quarter (named after a British musical eighth note). I also use musical names for periods longer than a year -- I call two years a breve (a double whole note) and four years a longa (a quadruple whole note).

I first came up with dividing my life into breves and longae when I was in college. I noticed that I had first enrolled in my new high school on November 3rd, 1995, was transferred to a Chemistry class (and ultimately to the magnet program) on November 3rd, 1997 (exactly one breve later), and started my first day of work at the UCLA library on November 3rd, 1999 (exactly one longa later).

Thus I divided my life into breves and longae, beginning with November 1995. Indeed, I've given names to these time periods:

1. Nov. 1995-1999: The High School Longa
    a. Nov. 1995-1997: The Academy Breve
    b. Nov. 1997-1999: The Magnet Breve
2. Nov. 1999-2003: The Bruin Longa
    a. Nov. 1999-2001: The Undeclared Breve
    b. Nov. 2001-2003: The Math Major Breve
3. Nov. 2003-2007: The Between Longa
    a. Nov. 2003-2005: The Gap Breve
    b. Nov. 2005-2007: The Local Library Breve
4. Nov. 2007-2011: The Preliminary Longa
    a. Nov. 2007-2009: The Preliminary Start Breve
    b. Nov. 2009-2011: The Preliminary End Breve
5. Nov. 2011-2015: The Clear Longa
    a. Nov. 2011-2013: The Clear Start Breve
    b. Nov. 2013-2015: The Clear End Breve
6. Nov. 2015-2019: The Teaching Longa
    a. Nov. 2015-2017: The Charter Breve
    b. Nov. 2017-2019: The Two County Breve

I actually announced the end of the fifth longa here on the blog.

Breves and longae have significance outside of my life. Longae are especially important on the Julian and Gregorian Calendars since Leap Days occur approximately once per longa -- about four months after the start of the longa. (Breves occasionally occur on Reform Calendars with 8-10 days per week, since 730 is closer to a multiple of these week lengths than 365 is.)

Presidential elections occur once per longa. Congressional elections occur once per breve, with Election Day about halfway through each breve.

The Summer Olympics usually occur once per longa, while each breve contains either a Summer or Winter Olympics. Even with Tokyo delayed until tomorrow, these Games are still occurring before the end of the current breve.

The longae are named after what diploma I was trying to earn at the time -- high school, college, preliminary credential, or clear credential. Unlike the first breve and longa, my major life events didn't always happen on November 3rd, so the names are approximate. For example, the California BTSA program to clear my credential takes two years -- that is, one breve. But that time doesn't line up with any of the breves listed above -- it does fit fully in the fifth longa. Meanwhile, I was only at the charter school for under a year, but it does fit fully in Breve 6A.

But what shall we call the current seventh longa and breve? 

And that takes us back to 2021. I was going to name it after the pandemic -- the length of the pandemic would determine whether it counts as a breve or a longa. But in that post, I kept equating the arrival of a vaccine with the end of the pandemic. So I wrote things like:

7. Nov. 2019-2023: The ??? Longa
    a. Nov. 2019-2021: The Coronavirus Breve

if a vaccine is developed this breve and:

7. Nov. 2019-2023: The Coronavirus Longa

if there's no vaccine. What I didn't foresee is that we'd have a vaccine here in Breve 7A, and yet the pandemic stretches into 7B due to the Delta variant and many people rejecting the vaccine.

Of course, the breves and longae are supposed to be named after the stages of my own life -- not the pandemic or anything else occurring in the world. Then again, the pandemic has caused me to make some life decisions. The main event of Breve 7A for me is the long-term subbing position -- and the fact that it apparently won't lead to a full-time teaching career will force me to make a huge decision in Breve 7B -- perhaps even a new career:

7. Nov. 2019-2023: The Coronavirus Longa
    a. Nov. 2019-2021: The Long-Term Breve

    b. Nov. 2021-2023: The New Career Breve

I'll make another decision about breve naming this November, as that's when the breve is set to change to a new breve.

As for the pandemic, last year I worried that we might not have a vaccine until Tau Day of the Century in the year 2031. It could be that we have the vaccine now, yet the pandemic still doesn't end until 2031 due to more Greek-letter variants (including the Lambda variant which is just now emerging) -- including several vaccine-resistant strains, and new vaccines to battle those strains resistant to the old strains (also known as "booster" shots).

And of course, if all else fails, it could me that the only way for me to make any money is to leave the field of education altogether.

6. Who is Laura Lemay, and why am I learning Java?

Laura Lemay is the author of an online book about the Java computer language. Here's a link to her online text:

http://101.lv/learn/Java/index.htm

If the schools are shut down for an extended period of time -- and it becomes impossible for subs like me to get work -- then I must seriously consider looking for a job other than teaching.

The cliche response to someone who can't get a job is "learn to code." Well, that's exactly what I'm trying to do here. I chose Java because it's currently the language taught in AP Computer Science -- if AP considers Java to be a language worth learning, then I do as well. I assume this means that there are coding jobs out there where Java is the language of choice.

I've currently involved myself in a number of summer projects that I'm describing on the blog. The most important of these by far is my learning Java project.

So far I've reached Lesson 18 of Lemay. But recently I've been going back a few lessons to redo a few programs that I missed or had trouble figuring out. Today, let's return to Lesson 14:

http://101.lv/learn/Java/ch14.htm

I've tried out most of these programs, but I skipped Listings 14.5 and 14.6 because both of them involve websites that existed back in the 1990's when Lemay first wrote this book -- these websites might not necessarily exist these days. Today I at least wish to do Listing 14.5:

Listing 14.5. Bookmark buttons.

 1: // Buttonlink.java starts here
 2: import java.awt.*;
 3: import java.net.*;
 4:
 5: public class ButtonLink extends java.applet.Applet {
 6:
 7:    Bookmark bmlist[] = new Bookmark[3];
 8:
 9:    public void init() {
10:        bmlist[0] = new Bookmark("Laura's Home Page",
11:             "http://www.lne.com/lemay/");
12:         bmlist[1] = new Bookmark("Gamelan",
13:             "http://www.gamelan.com");
14:         bmlist[2]= new Bookmark("Java Home Page",
15:             "http://java.sun.com");
16:
17:         setLayout(new GridLayout(bmlist.length,1, 10, 10));
18:         for (int i = 0; i < bmlist.length; i++) {
19:             add(new Button(bmlist[i].name));
20:         }
21:     }
22:
23:     public boolean action(Event evt, Object arg) {
24:         if (evt.target instanceof Button) {
25:             linkTo((String)arg);
26:             return true;
27:         }
28:         else return false;
29:     }
30: 
31:     void linkTo(String name) {
32:         URL theURL = null;
33:         for (int i = 0; i < bmlist.length; i++) {
34:             if (name.equals(bmlist[i].name))
35:                 theURL = bmlist[i].url;
36:         }
37:         if (theURL != null)
38:             getAppletContext().showDocument(theURL);
39:     }
40: } //ButtonLink.java ends here
41:
42: //Bookmark.java starts here
43: import java.net.URL;
44: import java.net.MalformedURLException;
45:
46: class Bookmark {
47:     String name;
48:     URL url;
49: 
50:     Bookmark(String name, String theURL) {
51:         this.name = name;
52:         try { this.url = new URL(theURL); }
53:         catch ( MalformedURLException e) {
54:         System.out.println("Bad URL: " + theURL);
55:     }
56: }
57:} //Bookmark.java ends here

But no, it doesn't work. For some reason, line 5 produces a syntax error:

 5: public class ButtonLink extends java.applet.Applet {

There is absolutely nothing wrong with this line -- it comes directly from Lemay, and this is the correct first line for an applet class. Yet there's something about this line that's preventing me from running this applet now.

This is the sort of thing that I need to figure out before I can launch a post-teaching career. I'm not a coder unless I can get the computer to work -- and right now, I can't do that yet.

7. What's "Mocha music"?

In many recent posts, I refer to something called "Mocha music." This is a good time to explain what Mocha music actually means.

When I was a young child in the 1980's, I had a computer that I could program in BASIC. This old computer had a SOUND command that could play 255 different tones. But these 255 tones don't correspond to the 88 keys of a piano. For years, it was a mystery as to how SOUND could be used to make music. Another command, PLAY, is used to make music instead, since PLAY's notes actually do correspond to piano keys.

Last year, I found an emulator for my old BASIC computer, called Mocha:

http://www.haplessgenius.com/mocha/

When we click on the "Sound" box on the left side of the screen, Mocha can play sounds, including those generated by the SOUND command. So finally, I could solve the SOUND mystery and figure out how the Sounds correspond to computer notes.

I discovered that SOUND is based on something called EDL, equal divisions of length. We can imagine that we have strings of different lengths -- as in a string instrument or inside a piano. The ratio of the lengths determine their sound -- for example, if two strings are in a 2/1 ratio, then the longer string sounds an octave lower than the shorter string.

The key number for SOUND is 261, the "Bridge" (or end of the string). Mocha labels the Sounds from 1 (low) to 255, so we subtract these numbers from 261 to get a Degree ranging from 260 (long string) to 6 (short string). The ratios between the Degrees determine the intervals. I found out that the Degrees corresponding to powers of 2 (8, 16, 32, 64, 128, 256) sound as E's on a piano, with Degree 128 being the E just above middle C (that is, E4).

Let's say we were to play the following two notes on Mocha:

10 SOUND 51,8

20 SOUND 86,8

The second number 8 indicates a half note, since 8 is half of 16 (the whole note). But we want to focus on the first numbers here, which indicate the pitches (tones).

We first convert the Sounds to Degrees. Since 261 - 51 = 210, the first note is Degree 210. The Degree of the second note is 261 - 86 = 175. Now the ratio between these two Degrees is 210/175, which reduces to 6/5. This is the interval of a minor third, so the two notes are a minor third apart. As it turns out, the two notes sounds as G and Bb -- "rugu G" and "rugugu Bb."

Let's try another example:

30 SOUND 144,8

40 SOUND 196,8

Warning -- we don't attempt to find the ratio 196/144 (which is 49/36 by the way). We only find the ratios of Degrees, not Sounds. The Degrees are 261 - 144 = 117 and 261 - 196 = 65. Thus the interval between the notes is 117/65 = 9/5, a minor seventh. (Using Degrees instead of sounds makes a big difference, since 49/36 would be an acute fourth or tritone, not a minor seventh.) The names of the two notes played by Mocha are "thu F" and "thugu Eb."

Where do all these strange color names like "gu/green" and "thu" come from? Actually, they refer to Kite's color notation, and the colors tell us which primes appear in the Degree:

• white: primes 2 or 3 only
• green: prime 5
• red: prime 7
• lavender: prime 11
• thu: prime 13
• su: prime 17
• inu: prime 19

Kite's color notation also uses colors such as yellow, blue, and so on. But these are "otonal" colors, while EDL scales/lengths of string are based on "utonal" colors only.

The website where Kite explains his color notation is here:

https://en.xen.wiki/w/Color_notation

Actually, here's another link where Kite's color notation is explained:

http://www.tallkite.com/forum/index.php?topic=86.0

Of course, the whole purpose of this is to compose music. When I was at the old charter school, I used to compose my own math songs for the class, but this was before I discovered that there was a Mocha emulator. Now that I know about Mocha, I can generate random music on Mocha and then make new songs.

By the way, you might notice that I'm not using Java to compose these songs. Deep down, I was hoping that perhaps Lemay wouldd teach us how to do everything above in Java instead of BASIC. But instead, Lemay only tells us how to include sounds from files into our applets -- and just as I don't have access to the CD containing images, I can't access any of these sounds either.

Then again, how would I play any of these songs in an actual classroom (if I ever get back there)? It may be possible to play some Mocha music if the school computers can access Mocha. But in general, I'd like to play some of these songs on my guitar. In fact, in previous posts, I started thinking about how we might refret a guitar so that it plays 18EDL music (that is, by spacing the frets equally apart, 1/18 of the string length, so that it really is an "equal division of length").

Unfortunately, my current guitar is broken. After leaving the old charter school, the tuning knob on one of the strings, the D string, doesn't turn properly. I can tune the string down, but not up.

Thus the note played by the string gradually became flatter. For a while, the note played by the string was at least a third-tone -- nearly a semitone -- too flat. In Kite's color notation, if the correct tuning of the string is white D, it became tuned to red C# instead.

I tried tuning all the other strings so that they were in tune with the flattened D string. But this meant that they were no longer in tune with the outside world. In fact, last Christmas I watched a holiday special, Grandma Got Run Over by a Reindeer. I had the sheet music for the title song, and I tried playing my guitar along with the song during the special. But my guitar wasn't in tune -- the show played the song in the key of E major, while my guitar was more like Eb major.

I was so upset that I tried to tune my D string back to D -- but instead, I made it worse. My D string is now about a whole tone too flat, sounding more like a C.

Afterward, I remembered that there was a guitar shop near one of the schools where I sub. I was thinking about going in to replace the tuning knob one day -- perhaps around the last day of school, and definitely by next Christmas. But you already know what happened -- the coronavirus shut everything down before I had a chance to go in.

It's also possible for me to tune all the strings down a whole tone -- and instead of a tuning knob, I could get a capo and place it at the second fret to recover the original tuning. But I'm tired of having an out-of-tune guitar -- in fact, I used to have perfect pitch, where I could hear a note and identify which note it is. But my out-of-tune guitar corrupted my perfect pitch -- if a note sounded like my D string, I'd want to identify it as D, when in reality it was a C# (or even a C).

Notice that I can kill two birds with one stone here -- I might find a retuning so that my D string can play as the C that it's stuck at, and also anticipate a retuning that fits with Mocha music and a possible 18EDL refretting (that is, whenever I can reach a guitar store again).

In a previous post, I mentioned several possible 18EDL tunings. Unfortunately, all of those tunings involving keeping the D string as D. Here's a possible retuning:

EACGAE

I like to keep as many strings tuned to standard tuning as possible. This tuning keeps four of the six strings -- in addition to the broken D string, the B string is tuned down to A. With four strings tuned correctly, I hope that I'll be able to regain perfect pitch.

In the tunings that I've mentioned earlier, all the open strings are assumed to be white. But for this tuning, the C and G strings are green while the rest are white. (Or if you prefer, keep the C and G white and tune the other strings yellow, which is equivalent.) Using this tuning, the open strings form a just A minor 7th chord (Am7/E).

Here are the notes playable in EACGAE if C and G are green and the rest white:

wa E | su E#, wa F#, gu G, ru G#
wa A | su A#, wa B, gu C, ru C#
gu G | sugu G#, gu A, gugu Bb, rugu B
gu C | sugu C#, gu D, gugu Eb, rugu E
wa A | su A#, wa B, gu C, ru C#
wa E | su E#, wa F#, gu G, ru G#

I'm not quite sure how this tuning will play out in practice, though. For example, it's easy to see how to play a C major chord (xx0030), but A minor chord is tricky. The strings are tuned to Am7 and we'd like to get rid of the G to make it Am. But the A at the second fret on that string is green A, while the open strings are white A. It might sound better just to play Am7 instead of Am. Likewise, an Em chord would need to be played as Em7 (022020).

Meanwhile, G major would be playable except that there aren't quite enough open strings. Instead, we must settle for G/B (x22023) or G/D (xx2023), or perhaps a G6 (322020) or Gadd9 chord (323003, but the add9 here is 20/9 instead of the usual 9/4). While D major isn't playable, there is a playable D7 chord (as xx2232).

(If we prefer all the strings to be white, we might try EABEAE -- one of the tunings I mentioned in a previous post, though it wasn't preferred. But if I tune my D string down to B, then I won't be able to tune it back up to C, since I can only tune it down and not up. I don't wish to commit to this tuning, especially since only three strings would match standard tuning rather than four.)

During my long-term position, I played songs using this tuning, EACGAE (standard fretting, not any EDL fretting.)

So instead, let's just code a pi song based on 16EDL, similar to the song we played for Tau Day:

NEW
10 N=16
20 FOR X=1 TO 32
30 READ A
40 SOUND 261-N*(17-A),4
50 NEXT X
60 DATA 3,1,4,1,5,9,2,6,5,3
70 DATA 5,8,9,7,9,3,2,3,8,4
80 DATA 6,2,6,4,3,3,8,3,2,7
90 DATA 9,5

As is traditional, I stop just before the first zero. Then digits 1-9 map to Degrees 16 down to 8, with the lowest note played on E (line 10, N=16). We can change the value of N to any value from 1 to 16 to change the key.

Here's an actual song converted to 12EDL, a simpler EDL scale, the Sailor Pi theme song:

NEW
10 N=13
20 FOR X=1 TO 26
30 READ D,T
40 SOUND 261-N*D,T
50 NEXT X
60 DATA 8,4,8,2,9,4,9,2,10,4,11,4,9,12
70 DATA 9,4,9,2,10,4,10,2,11,4,12,4,10,12
80 DATA 12,4,12,2,10,4,10,2,8,4,6,4,7,12
90 DATA 8,4,9,4,10,2,11,6,12,16

Only the main verse is coded here. The "bridge" part -- which is instrumental in both the original Sailor Moon and Lizzie's Sailor Pi song -- is too hard for me to code without sheet music.

Here are the lyrics for the first verse -- the part which we coded above:

Fighting fractions by moonlight
Perplexing people by daylight
Reading Shakespeare at midnight
She is the one named Sailor Pi.

Speaking of Bizzie Lizzie, today's a great day to post lyrics after all -- the lyrics to her "Digit Connection," a parody of "Rainbow Connection," which I posted on the blog 2 1/2 years ago:

THE DIGIT CONNECTION
Copyright 1998 by Elizabeth Landau, aka Bizzie Lizzie

1st Verse:
Why are there so many debates about pi?
And what's on the other side?
Pi is a ratio of random proportions.
Its digits have nothing to hide.
So we've been told and some choose to believe it,
But I know they're wrong, wait and see!
Someday we'll find it, the digit connection,
Mathematicians, logicians, and me.

2nd Verse:
Who said that everything has some sort of pattern,
Consisting of nothing but math.
Somebody thought of that, and someone believed it.
Now we're all caught in its wrath....
What's so hypnotic in something chaotic,
And what do we think we might see?
Someday we'll find it, the digit connection,
The optimists, the theorists, and me.

All of us under its spell,
We know it must be math-e-magic...

3rd Verse:
Have you been half asleep? And have you heard voices?
I've heard them calling my name.
Is this the sweet sound that calls the young sailors,
The voice might be one and the same....
I've heard it too many times to ignore it,
Irrational, random, and free.
Someday we'll find it, the digit connection,
The lovers, the dreamers, and me.

3.1415926535 dot, dot, dot!

Bizzie Lizzie also had an "American Pi" song, but there's just one problem. I copied down the lyrics from her old website just before that site disappeared -- into my notebook. That's right -- the notebook that I took out on Pi Day Eve to sing to the class I subbed that day, and just left in the classroom.

Fortunately, I finally found that book, and I posted the lyrics to the song in time for Pi Day.

Bizzie Lizzie's e song was a parody of "Sugar, Sugar," by the Archies. I think I recall the refrain:

e (2.718)
Ah, number number (281828)
You are my natural log,
And you got me calculating.

e (2.718)
Ah, number number (281828)
You are my derivative,
And you got me calculating.

But alas, I can't remember the rest of the song. Well, since it's e Day, let me supply extra lines. Some of these lines are from my faint memories of Landau's original song -- I made up all the lines that I couldn't remember.

1st Verse:
I just can't believe the loveliness of graphing you.
I can't believe you're more than two.
I just can't believe the loveliness of graphing you.
I can't believe you're more than two. (to Refrain)

2nd Verse:
I just can't believe your digits go forever now.
As long as a number can be.
I just can't believe your digits go forever now.
As long as you're the number e. (to Bridge)

Bridge:
Put a little cash in the bank, money.
Put a little cash in the bank, baby.
I'll make more next year, yeah, yeah, yeah!
Put a little cash in the bank.

100% interest on my money.
Compound it continuously, baby.
I'm gonna take the limit now, yeah, yeah, yeah!
My cash is multiplied by you, e. (to Refrain)

The bridge is mostly mine -- Landau didn't mention anything about money in her song. I chose to include money since it rhymes with the original Archies lyrics ("honey") as well as retell the story of Jacob Bernoulli's discovery of this constant.

8. 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 the schools closed, I've been posting non-Geometry as well.

The question for July 22nd this year is:

8!/ sigma(n=1)(60)n (round)

The word "round" suggests that the answer isn't an integer -- and so we should use a calculator, rather than expect all the factors to cancel leaving the answer.

Still, we know that 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 and the summation gives (60 * 61)/2:

(8 * 7 * 6 * 5 * 4 * 3 * 2 * 2)/(60 * 61)

= (8 * 7 * 6 * 4)/61

= 22.03...

The final answer rounds to 22 -- and of course, today's date is the 22nd. (By the way, 7pi = 21.991, which is why today is Pi Approximation Day.)

Let's do one more problem from later this week, since it's an actual Geometry problem:

Segment AB is tangent to circle C with length 24sqrt(3). Find x.

(Here is the given info from the diagram: A is the point of tangency, B is also the center of a circle, and both circles are tangent to each other and have radius x.)

The key is to consider Triangle ABC. There is a right angle at A by the Radius-Tangent Theorem (the radius is perpendicular to the tangent line at the point of tangency). One of the legs, AC, is known to be the radius x, and another, AB, given to be 24sqrt(3)

That leaves us with the hypotenuse BC. The two circles are tangent to each other -- that is, they have a common tangent line and point of tangency. By Radius-Tangent both radii are perpendicular to this tangent line, and so the two radii are collinear since 90 + 90 = 180. Thus two radii add up to the hypotenuse -- that is, the hypotenuse is 2x.

Now we use the Pythagorean Theorem:

x^2 + (24sqrt(3))^2 = (2x)^2

(24sqrt(3))^2 = 4x^2 - x^2 = 3x^2

24^2 = x^2

x = 24

So the desired radius is 24 -- and of course, the date of this problem is the 24th. Notice that the longer leg is exactly sqrt(3) times the shorter leg -- in other words, ABC is a 30-60-90 triangle. The sudden appearance of 60-degree angles explains why exactly six circles surround a seventh circle so that the circles all touch each other and the central circle (that is, why the 2D kissing number is 6.

9. What is Shapelore?

When we teach Geometry, sometimes I fear that students will struggle over the vocabulary. This includes not just longer words/phrases such as "Alternate Interior Angles" and "Reflexive Property," but even the shorter words for the trig functions "sine," "cosine," and "tangent." More often than not, these confusing words come from complex Greek and Latin roots.

And so this project seeks to replace some of these words with roots that come from Old English. It was inspired by the Anglish website, where Anglish is the language we get by removing all Greek and Latin words from our language, leaving behind pure English:

https://anglish.fandom.com/wiki/Main_leaf
https://anglish.fandom.com/wiki/What_is_Anglish%3F

In fact, the name "Shapelore" is itself in Anglish -- here -lore refers to something that is studied, so it's the Anglish equivalent of the Greek suffix "-ology":

https://anglish.fandom.com/wiki/Shapelore

In Shapelore, "Alternate Interior" becomes Otherside Inside and "Reflexive Property" becomes Selfsame Law. I've decided to keep some words as simple even if they are from Latin or Greek -- for example, most people know what a "square" is, so I keep it even though the word is from Latin. I'm also keeping the word "angle," also from Latin. The Anglish website proposes nook for "angle," but I'd rather keep "angle." Thus I refer to this as "Plain English" instead of "Pure English" or Anglish.

The new names for the trigonometric functions are wheelex for "cosine," wheelwhy for "sine," and wheelslope for "tangent." The wheel part indicates that these are the wheel (or circular) functions. So instead of tan(67.5) = 1 + sqrt(2), we'd write ws(67.5) = 1 + sqrt(2). The word "root" is Old English and I already said I'm keeping "square," so sqrt doesn't change, but tan becomes ws, wheelslope.

So far, I've been translating the U of Chicago Geometry text into Plain English. In 1991, the University of Chicago School Mathematics Project published a series of secondary mathematics texts. I was able to purchase both the Algebra I and Geometry texts for two dollars each at a local public library. One thing I discovered was that the U of Chicago Geometry text is based on the same transformations that appear in the Common Core Standards -- even though the U of Chicago published the text nearly two decades before the advent of the Core.

I might return to Shapelore at some point, but I don't know when.

1. Draw Curiosity

Notice that this video, from five years ago, actually acknowledges Pi Approximation Day.

2. Sharon Serano

Well, this gives 20 facts about pi.

3. 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.

4. Coding Challenge #140

Today is Pi Approximation Day, and so this video is all about approximating pi.

5. Ki & Ka

This video came out last year.

6. Sen Zen

This is yet another video that uses the Archimedes method of approximating pi.

7. Stand-Up Math

This video uses the Leibniz series, but all work is done by hand.

8. Think Twice

This video uses a Monte Carlo approximation technique. I attempted to do something similar using Java in an earlier post.

9. NKC Insight

This video came out last year, but I must have missed it.

10. Yearn 2 Learn:

In this new video, here are some classroom activities for either Pi Day or Pi Approximation Day.

11. hurfcharacterlimit:

I had to include this new video since it has the famous Pi Approximation integral from Calculus.

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-97, 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+2, and so n+2 for each of the six What Ifs will resemble the year 2021 under COVID-19.

So far, what we know about Fall 2021 is that masks will be required in schools. This means that my young self is also masked in each Fall n+2. This means that masks extend into my second grade year for COVID-86, my seventh grade year under COVID-91, my freshman year for COVID-93, my first year at UCLA for COVID-97, and my year at the old charter school for COVID-14.

I'll only continue writing the COVID What Ifs if something out of the ordinary (that is, beyond masks) occurs in 2021 or 2022 (mapping back to all the n+2 and n+3 years). Otherwise, I've already completed the main part of the What If stories, focusing on the respective n+1 years.

11. How will the coronavirus school plans affect this blog (and Twitter)?

On this blog, I've always posted one lesson of Geometry per school day -- and these school days follow the calendar in one of my Orange County districts. I still haven't which one, but note that the two calendars are similar.

It's not so much the coronavirus that will affect my blog plans, but my career. If I get a job that's outside of education, then I won't need to have an education blog any longer, and so I'll end the blog.

By the way, last year I started an education Twitter account:

https://twitter.com/DavidWa12688560

But once again, without a teaching job, I won't need an education Twitter account either.

It's just that I don't want to wait years, breves, longae, or decades for my next paycheck. Many people are suffering, not just subs. And it will be difficult for me to find work. (Again, if I do get a job outside of education, I'll no longer post to this blog.) That's the main thing that will be on my mind over the next few months, during these tough times of uncertainty.

And so I wish everyone a happy Pi Approximation Day!