Introduction
Today is Baptism Sunday on the Christian Calendar. It is defined as the Sunday after Epiphany, and is based on an interpretation of the Bible that Christ was baptized around his 30th birthday. Thus Baptism Sunday is the last holiday of the "Christmas season."
Orthodox Christians celebrated Christmas yesterday, and their Epiphany (or Theophany), will be twelve days later, on January 19th. This is also their day to celebrate Baptism -- indeed, it's the Baptism, not the Three Kings, that is more significant in Eastern Churches.
What are my Hispanic students celebrating today? After doing some research, I did read about how some Spanish-speakers observe Octavitas, an eight-day celebration for Epiphany and Baptism. But this is mainly observed in the Caribbean, not Mexico. Thus, unless I find out that one of my students is of Caribbean descent, I shouldn't assume that my mostly Mexican-American students are celebrating any holiday today. In Mexico, the Three Kings are more significant than the Baptism.
Baptism Sunday is the end of the Christmas season, and sometimes (though not always) it marks the end of winter break, including this year. I often post my twelfth Yule Blog post on Baptism Sunday as well.
Yule Blog Challenge #18: My Goals/One Word Challenge for 2023
Last year, Shelli -- the leader of the Yule Blog Challenge -- came up with a "one word challenge" for the new year. In other words, we should select one word to describe the entire year. Last year, she chose "journey" as her one word. But there's no evidence that she's doing a One Word Challenge this year.
Last year, I selected "travail" as my one word. I got the idea from 365 New Words-a-Year Calendar, where "travail" was the word for January 2nd. And last year, making our way through this stage of the pandemic depended on the travails of all of us -- that is, our hard work.
This year, I turn to that same calendar to choose a word for 2023. But some of the words on that calendar aren't appropriate. The January 1st word was "ab initio," Latin for "from the beginning," as in from the beginning of the year -- good for New Year's Day, but inappropriate for One Word. And the January 2nd word was "shard," as in "shards of glass." I might choose "shard" if I were planning a trip to England in 2023 to visit that country's tallest building, The Shard (which really is shaped like a shard of glass), but I'm not.
Fortunately, there's one more "hidden" New Year's Day word on the calendar. One thing about the calendar is that it often combines weekends, with Saturday and Sunday sharing a page, even though each day has its own word. The weekend of December 31st-January 1st was tricky because it was split between years. Although the 2023 calendar printed "ab initio" on its own page, the 2022 calendar had words for both the 31st and the 1st. And so New Year's Day had an extra word this year -- and this word is more appropriate.
And so my one word for 2023 is (drumbeat) --
blithesome
The calendar defines "blithesome" as "joyfully exuberant" or "merry." And with all the arguments I've been having with my students lately, I definitely need to be more blithesome in the classroom this year, and so this is a great word to choose for the One Word Challenge in 2023.
Shelli once chose "joy" as her One Word. "Blithesome" means "joyful" -- indeed, "joy" itself can be said as "blithe." But "blithesome" comes from Old English (unlike "joy" with is French). It's been some time since I blogged about Shapelore and Anglish (the thought that Old English words are better than French or Latin words like ab initio). So for those folk who like Anglish words more, let's keep this year's One Word as "blithesome" instead of "joy." ("Shard," by the way, also comes from Old English.)
Last year, I mentioned a Desmos activity that's related to the One Word Challenge:
And I wrote the following:
I haven't decided whether I'll assign One Word to my students this year or not. In my last post, I wrote that I might have more Desmos lessons in my classes, and so I could give this activity. But the one above is all about equations of lines, which is not what any of my students are learning.
Well, this year, equations of lines fit the Math I curriculum, so I could give it this year. After glancing at this Desmos though, I notice that the students are to choose their One Word, and then try graphing an image of the word on Desmos.
In other words, it's just like the infamous Linear Art Project in Math I -- and we know that my students didn't find that project very joyful -- uh, blithesome -- at all. The last thing I want to do is give another version of that project, especially when it will take time away from the Stats project. But hey -- at least you blog readers get to see what such a project actually looks like.
(It's too bad that I couldn't have delayed the Linear Art Project to January. Perhaps this version might have gone more smoothly than the November version, especially if I kept the Desmos lesson open during the entire project. But the Linear Art Project goes with Chapter 2 -- and there's no way that we should still be doing Chapter 2 stuff in second semester.)
Well, I've already written about Math I in my last post, so that's enough about Math I prokects. In today's post, I'll preview for the upcoming chapter for Math III instead.
We just finished Chapter 5 on inverses and logarithms. Chapter 6 of the Math III CPM text is a bit like Chapter 4 of the Math I text -- it focuses on Stats. But unlike Math I, the Math III department has decided to skip over the Stats chapters and proceed directly to Chapter 7.
Previewing Math III Chapter 7
Chapter 7 of the Math III CPM text is called "Logarithms and Triangles." Section 7.1 deals with logs and is a continuation of the content taught in Chapter 5.
We know that Math III follows the pacing guide much more strictly than Math I. So let me write out the plan for this chapter with the exact dates:
January 9th: Desmos Reflection
Like Math I, the first day back is a sort of "ease back into math class" day. The Desmos Reflection asks students to give a New Year's Resolution -- I could have them write One Word about their goals (but they won't have to graph it, like the Desmos link above). And since this should be completed quickly, there should still be time for Sarah Carter's 2023 Challenge as well.
January 10th-12th: Lesson 7.1.1, Using Logarithms to Solve Exponential Equations.
Two block periods are used to introduce exponential equations and the idea of taking logs of both sides to solve them.
January 13th-18th: Lesson 7.1.2, Investigating the Properties of Logarithms.
One Friday and one block period (after MLK Day) are devoted to the properties of logs, including the product, quotient, and power rules. There are worksheets associated with this lesson, but nothing to do with Desmos.
January 19th-20th: Lesson 7.1.3, Writing Equations of Exponential Functions
One block period and one Friday are devoted to exponential functions and their equations. There is a Desmos activity associated with this lesson.
January 23rd-25th: Lesson 7.1.4, Applications of Logarithms
One Monday and one block period are devoted to word problems involving logs. One day is for compound interest and the other day is for a murder mystery (where Newton's Law of Cooling is used to determine when the murder took place).
January 26th-27th: Lesson 7.2.2, Law of Sines
One block period and one Friday are devoted to the "Triangles" mentioned in the chapter title. And this leads me to wonder, how exactly is Trigonometry taught in Integrated Math classes?
Back when it was Algebra I/Geometry/Algebra II, right triangle Trig began in Geometry classes (and indeed, it appears in Chapter 14 of the U of Chicago Geometry text). The fact that the first appearance of Trig in the Math III text is on the Law of Sines suggests that right triangle Trig is taught in Math II (as it's definitely not in our Math I text).
On the other hand, when I taught that one semester of Trig last year, I moved through the text slowly and didn't quite make it to the Law of Sines. (Of course, my students should have at least seen it in their Math III classes the previous year -- but that was the pandemic year, so who knows?)
January 30th-February 1st: Lesson 7.2.3, Law of Cosines
Naturally, if there's a Law of Sines, there needs to be a Law of Cosines. One Monday and one block period are devoted to this lesson. One day should be solving for missing sides and the other day for missing angles.
February 2nd: Lesson 7.2.4: The Ambiguous Case
One block period is devoted to the ambiguous case of the Law of Sines -- that is, SSA. But according to the pacing guide, we won't actually have the students solve for two triangles. Instead, we will give a Desmos lesson and then direct DeltaMath to give SSA questions with only one possible triangle on the chapter test. (This is what the U of Chicago text calls the SsA case -- when the side opposite the given angle is longer than the adjacent side, then there is only one possible triangle.)
February 3rd-6th: Chapter 7 Test
As usual, there is a written part and a DeltaMath part. In the first semester, I've been giving the written part first. But one of my fellow Math III teachers usually gives the DeltaMath part first -- and the Math III leader apparently agrees with her, since the pacing guide now directs us to give the DeltaMath part on Friday and the written part the following Monday.
There are a few things worth mentioning about Chapter 7. We are directed to have DeltaMath give only questions with one possible triangle, not two. But as we've seen before, we can tell DeltaMath to give only certain types of questions on the test, but not the homework. I wish to avoid the situation where students can't do their homework because DeltaMath keeps asking them for two triangles.
Fortunately, there's a way to avoid this. Since the Ambiguous Case is the last lesson before the test, the homework that night should be test review. So the only practice in class will be the Desmos lesson, and then the night's HW is on reviewing everything except SSA for the test.
But before the test, there should be a quiz. As usual, we're directed to give the students a quiz, but there's no day on the pacing guide devoted to a quiz. In the first semester, I usually give quizzes on the second Monday after the chapter begins -- this works out to be January 23rd. The pacing plan mentions a quiz on Illuminate (not the usual DeltaMath) after Lesson 7.1.3, so this fits the 23rd nicely.
On the other hand, a more natural dividing point is between 7.1.4 and 7.2.2, in order to separate the logs from the Trig. This suggests a quiz day on one of the block days that week.
In the end, I'll watch to see whether the quiz is on Illuminate or DeltaMath, and whether or not it contains 7.1.4 material. If the quiz contains 7.1.4, a possible plan is to give it on that Thursday, and then start the Law of Cosines (not Sines) on Friday. The plan devotes one day for missing sides and the other day for missing angles for both Laws. But the only time one ever needs to use the Law of Sines to find a missing angle is the SSA case -- which is already taught as the Ambiguous Case. So we can afford to have one fewer day for the Law of Sines and replace it with the quiz day.
By the way, if February 3rd-6th are the test days, then Chapter 8 should begin the following block day, February 7th or 8th. But we know that in reality, an extra day is needed for test corrections (especially due to the Math III department's "70% rule" where students must first do corrections to raise their grade to 70%, and then they can do the test retake). Now I don't mind using February 7th for test corrections, because that's a special day anyway -- 2/7 is "e Day." (Yes, we just finished celebrating Phi Day, and now I'm already looking ahead to e Day.)
But here's the thing -- recall that e didn't appear in Chapter 5 (which led to a problem with the test as DeltaMath kept asking questions with e and ln). So surely e and ln appear in Chapter 7, where logs are studied in more detail, right?
Wrong -- in the CPM text, e doesn't appear until Chapter 10, on series! In fact, we must also tell DeltaMath not to include continuous compound interest questions (A = Pe^rt), since there's no e yet.
So that means we really shouldn't celebrate e Day. But then again, since a day will be wasted for test corrections anyway, we might as well have an "e Day/Chapter 7 Test make-up/corrections" party. Those who need to work on the test can do so, and those who don't can celebrate instead.
February 7th falls on a Tuesday, when fifth period Math III meets, but not first period. The morning class can celebrate the next day, "e Day Observed/Chapter 7 Test make-up/corrections." After all, remember that e starts out 2.71.828, so both 2/7 and 2/8 are e Days (as is 1/8 -- hey, that's today).
Looking ahead to Pi Day, we notice that Chapter 9 is on trig functions, including radians and pi. But it appears that Chapter 9 is for Honors Math III only -- my class will skip directly to Chapter 10. (In other words, my class will finally learn about e on or just after Pi Day.) After all, recall that in the old days, radians were taught only in Honors Algebra II/Trig, or else not until Pre-Calculus (or a separate Trig class like the one I taught last year.)
So there goes my Pi Day party. Then again, the schedule shows us finishing the Chapter 8 Test (or some sort of midterm) just before Pi Day. So March 14th is the "Pi Day/Chapter 8 Test make-up/correction" party, it appears.
Music in the 14EDL Scale
Now is a good time to start thinking about songs that I might perform in the upcoming weeks. Indeed, whenever I look ahead to the next chapter, I always think about the songs.
There are two songs previously posted to the blog that fit Math III Chapter 7. One is "The Compound Interest Rap," and the other is "Whodunnit" (about a murder mystery). Unfortunately, both of those songs go with Lesson 7.1.4 -- and one of those lessons might land on a Monday (that is, a non-singing day) and the other on a quiz day. I'll be playing close attention the week of January 23rd to see which of these songs might go with these lessons.
The Mega Millions jackpot for Tuesday will be over one billion dollars. Even though I've already performed "One Billion Is Big" when the Powerball jackpot was that high, it might be fun to let this rap be the first performance of the new year.
All remaining songs will most likely be for Math I. I've already done the first Stats song, "Rudolph the Statistician," before winter break. The only other Stats song I have is "Measures of Center," but this one about mean, median, and mode was intended for middle school students. These aren't included in Chapter 4 because they're to be considered below high school level. (It's too bad that I couldn't have performed for Ethnostats classes last year, as some of those songs might have fit this class.)
So that means I'll need some brand new songs for Math I. And there will be a new scale to compose them in -- our main scale for January and February will be 14EDL.
As a reminder, here is the 14EDL scale:
This scale has seven notes, just like the usual major and minor scales. But while its length is familiar, its actual notes aren't. It's the first EDL scale to include Degree 13, which is about halfway between G and G#, just as Degree 11 is about halfway between Bb and B.
Our familiar seven-note scales are called "modes." If we play all the white notes starting from C, this is the major mode. If we start at D, it's the Dorian mode (which I used as part of my UCLA fight song parody in order to honor quarterback Dorian Thompson-Robinson). If we start at E, it's the Phyrgian mode, and so on.
If we interpret Degrees 13 and 11 as G and B, then we obtain a mode -- the Locrian mode. If we play all the white notes starting from B, we obtain B Locrian. Starting from F# and then playing white notes from G to E is called F# Locrian (related to the G major scale).
But interpreting 13 and 11 as G and B is awkward, since 13/11 sounds more like a minor third. So we might use the 13=G# or 11=Bb interpretations. Here 13=G# produces the Locrian sharp-2 (or #2) scale, since its second note is sharpened. If we use 11=Bb instead, the resulting scale is called Superlocrian.
F# Locrian: F#-G-A-B-C-D-E-F#
F# Locrian #2: F#-G#-A-B-C-D-E-F#
F# Superlocrian: F#-G-A-Bb-C-D-E-F#
Knowledge of the three Locrian scales can help us come up with chords for our 14EDL songs. For example, here's a link to Levi Clay, a guitarist who composes in the Superlocrian scale:
https://www.premierguitar.com/lessons/beyond-blues-how-to-use-the-super-locrian-scale
Clay's examples use B Superlocrian, but we can change it to F# by starting at the fret 2 instead of 7. To Clay, the tonic chord for his B Superlocrian scale is something called "B7alt," which is a B7 chord with the fifth and ninth degrees altered. Converting this to F# Superlocrian, we get these F#7alt chords:
b5b9: F#-Bb-C-E-G (14-11-10-8-13)
#5b9: F#-Bb-D-E-G (14-11-9-8-13)
b5#9: F#-Bb-C-E-A (14-11-10-8-6)
#5#9: F#-Bb-D-E-A (14-11-9-8-6)
Notice that all of these interpret 14/11 as a major third. Indeed, 14EDL is the first EDL scale to have two plausible thirds -- major (14/11) and minor (14/12 = 7/6).
Of course, at first I'll want to figure the new scale out. I'll save these altered 7th chords for later on. And as usual, we'll start out with simple AAA songs (that is, with a verse only) in the new scale before attempting more complex tunes.
Let me run the random song generator on my TI to see what 14EDL tunes look like. My first attempt produces the following melody:
9-7-8-7-11-10-9-9-9 (or D-F#-E-F#-Bb-C-D-D-D)
This is a lousy excuse for a 14EDL song. Degrees 12, 13, 14 are all left out, so this is really just a glorified 12EDL song. If we needed to play one of the F#7alt chords it would likely be F#7#5, but I'm likely just to play a D chord with so many D's in the song.
A second run of the generator produces the following melody:
11-9-13-8-8-9-8-10-9 (or Bb-D-G-E-E-D-E-C-D)
In many ways this is worse -- while Degree 13 is included, there is no tonic (Degree 14 or 7). We might play this melody over a b9 altered chords, probably F#7#5b9, but again it doesn't sound right. The way this is going, I'd do best to start with "One Billion Is Big" until I get 14EDL figured out.
Problems in Fifth Period Math III
I've been having problems avoiding arguments and staying blithesome in some of my Math I classes, but this is to expected since the students are freshmen. But in some ways, the most problematic class of all isn't any of the freshman classes, but the fifth period Math III class.
In this class, a group of students talks through almost every lesson. And this talking didn't stop on the day of the final exam. I'm still doing some last minute sorting out regarding which students deserve zeroes before the first semester grades are due.
(By the way, I normally watch The Simpsons, but tonight there's an episode of Bob's Burgers on instead of The Simpsons. And of course, the whole episode is about a girl who's accused of cheating on a test.)
Anyway, this week I checked the rosters -- every year, students transfer in and out of classes and make schedule changes at the semester. Every class is losing students, and every class except sixth period is gaining students as well.
The class that's losing the most students by far is fifth period -- a whopping six are transferring out. (All other classes are losing just two.) And while there could be many reasons for them to be moving (such as making the number of students in each class equal), one obvious possible reason is that they find my class too noisy -- in other words, because I'm a bad teacher. After all, several of the moving students did sit near the loudest corner of the room.
And even if just these six are transferring out, more likely think the class is too loud. Several of them requested to take the final exam in another classroom. That should never happen. Indeed, this is what prompted me to start handing out zeroes in the first place -- if the class is too noisy during the test, someone needs to get a zero.
I also can't help but notice that of the six leaving students, five are girls. With many of the loud students being guys, I'm wondering whether these girls accuse me of being sexist. The loud guys are trying to take over the class, and these girls can't learn -- and I, a male teacher, have an environment in which the guys are preventing the girls from learning. My biggest fear is that as a male teacher, I could be making subconscious decisions that favor the guys -- and this is one reason why many girls don't do well in math or seek out STEM careers.
Earlier, I wrote that I want to make more connections with my freshmen and avoid being the teacher than none of them want to have the next three years. While this is more important than with the older Math III students, I see right here that being an adequate teacher matters for these students as well. On Aeries, I can see the destinations of the six leaving students. If these girls requested a schedule change, then I can figure out which teachers they are flocking to -- and then that's the sign for me to be more like those popular teachers.
Of the six transferring students, one is going to the continuation school. (This is a bit surprising for a Math III junior who seems to be on grade level in math, but she must have failed some of her other classes that aren't math.) Two of them are seniors -- both are going to the department chair's class.
The three remaining juniors are all moving to the same teacher's class -- as it happens, her open math class is first period, not fifth. This might mean that I'm such a bad teacher that these students are willing to rearrange their schedule just to get rid of me (and the fact that they choose the lone female Math III teacher could be because they think I'm sexist).
By the way, she's also the teacher who gives her students the DeltaMath test before the written test. So that already gives me an easy way to emulate her -- give my students the DeltaMath test first. But there are other habits I need to get from her, or any other veteran popular teacher -- how to keep a group of loud students quiet, and how to be fair to all students regardless of gender.
Because so many students are leaving fifth period, it's also the class gaining the most students. Of the three new students, one is moving from my first period. And I feel sorry for her -- she's leaving my very quiet first period for the very loud fifth period. (But she's a special ed student who regularly takes tests in another room, so at least my noisy guys won't affect her during tests.)
The other two have been demoted from the Math III Honors class due to a low first semester grade -- along with a third girl who is moving into my first period. Of the three demoted students, one got an F, but the other two have D+'s -- that is, they just barely missed staying in Honors (since I assume that C- is the grade they need to stay).
The Honors classes have moved at a slightly faster pace. They finished Chapter 7 at the end of the semester in order to have more time for extra chapters (like Chapter 9, the Trig chapter). I hope that the three demoted girls remember something from Chapter 7 in December, so they can get off to a good start by passing the Chapter 7 Test now.
At any rate, I must make sure that the new girls don't have a sexist teacher this semester. I must treat all students equally without regard to gender.
Rapoport Question of the Day
Today on her Mathematics Calendar 2023, Rebecca Rapoport writes:
cot^2(pi/6) + csc(5pi/6) + 3tan^2(pi/6) + sec(11pi/6)cot(7pi/6)
This is the sort of question that Honors Math III will see in Chapter 9, but my regular Math III students won't see at all. (Indeed, the only trig they'll see this year are sine and cosine -- and these are only the two functions that don't appear in this function.)
The reference angle for all of the angles in this problem is pi/6, so that makes it easy:
= sqrt(3)^2 + 2 + 3/sqrt(3)^2 + 2sqrt(3)/sqrt(3)
= 3 + 2 + 1 +2
= 8
So the desired answer is eight -- and of course, today's date is the eighth.
Conclusion
And so I officially make it to twelve Yule Blog posts for the second straight year. I'm still not the champion, though, since Shelli had thirteen posts (and with a shorter winter break to boot).
Several more posts are coming in the next several days. Tomorrow is my "first day after winter break" post, which is a special "Day in the Life" post. Then Tuesday and Wednesday are my regular block day posts as we continue to focus on my Math I classes and the songs I sing in them.
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