Lesson 5.1.3: Bouncing Balls (Day 101)

EDIT: At first I had an original 14EDL song here, but I don't like how it turned out. But six years ago at the old charter school, I played Weird Al's "Polka Patterns." It was right around this same time of year, and it was also on the day of a Bouncing Balls activity in Math 8.

I didn't want to play this because I felt guilty for going so long without a true 14EDL song. But if this song sounds better and fits the lesson, then I should have played it.

So I'm EDITing this in as a reminder to perform it the next time I teach a Math I class -- and to remind me to purchase some bouncier balls in order to make this a better activity as well.

Chorus:

Everywhere, I see them there
I stop and stare at patterns
I don't care, I must declare
I've got a flair for patterns
On my hair, the clothes I wear
My savoir faire is patterns
All I see is patterns
The patterns that repeat

First Verse:

I know we're in a room where you would not expect much math
Usually you're in here for a shower or a bath
But if you gaze upon the floor, and if you're kinda smart
You'll see the repetition is like geometric art (to Chorus)

Second Verse:
A polkameister like myself never has to be bored
I just grab my ax and play some patterns on my keyboard
Now's the time for earplugs if you care about your health
So stand back, everybody, I'm gonna express myself
Look at this, patterns
I've got blisters on my fingers
Woo, hey, aw, get down
Yeah, help me, somebody, woo

Third Verse:

Next time you find yourself at an exciting polka party
You can make some patterns with your feet and with your body
If you don't know the steps yet, here's the gang with all the answers
Ladies and gentlemen, introducing, the "Weird Al" Polka Dancers (to Chorus)

Outro:
Wallpaper, skyscrapers, funny papers, patterns
Evergreens, nouvelle cuisine, human beings, patterns
Garden rakes, wedding cakes, rattlesnakes, patterns
Golden wheat, little feet, my heartbeat -- Patterns!

And here's a link to the relevant Square One TV video:

Chapter 5 of the CPM Math I text continues with arithmetic sequences. But the last lesson of Section 5.1 is called "Bouncing Balls," and it serves as a transition to non-arithmetic sequences, in preparation for geometric sequences in the next section.

The song indicates how I teach the lesson today. I take a real ball and bounce it near a yardstick to measure how high they bounce. When I start from a height of six inches, my ball bounces -- well, it's not exactly three inches, but I obviously want the numbers here to be simple. I demonstrate how bouncing the ball from taller heights results in higher bounces. Then I ask a student or two to bounce a ball starting from their desk or the side of the whiteboard -- a height of 32 inches (close enough). Some are able to figure out if the first bounce is sixteen inches, then the next bounce will be eight inches, and so on.

You might recall that back at the old charter school, there was a "Bouncing Balls" project in the eighth grade Illinois State STEM text (and it was even right around this same time of year -- late January or early February). This project is not quite the same -- that one was about bouncing a ball once from different heights, while this is about bouncing it several times from a single height. (Recall that geometric sequences is one of the few topics that's part of Math I but not Math 8, so multiple bounces was not part of the old lesson.)

Since the Math 8 "Bouncing Balls" activity fell on a non-blogging day, I don't have much record of how that project went, but I believe that my eighth graders enjoyed it. Perhaps I could have made today's activity more extensive like that old one -- say by having a ball for each group and having the students compare their bounce heights.

But today I decide to do the quiz corrections instead -- especially since so many students had trouble with the last Chapter 4 Quiz last Friday. In second period, students talk throughout the entire lesson -- even as I try to explain how to correct their answers. I end up contacting a whopping five parents to notify them of their students' talking during the lesson, quiz, and corrections. Fourth period, as usual, is much better behaved, so perhaps a deeper Bouncing Balls activity might have worked here.

Today is Sevenday on the Eleven Calendar:

Resolution #7: We earn our grades through hard work and dedication.

And that's exactly what the student do during their quiz corrections. I do wish to improve my lessons in second period. Yesterday students received their honor roll certificates in second period -- thirteen of my kids got them (about 40% of the class). I definitely want to get this class quieted down, since I know that at least thirteen students in there are interested in learning.

Today's not supposed to be "A Day in the Life," but I wish to do an extra one today -- not for today, but for last Saturday. That was the day of the Academic Decathlon, and my school participated in it. It's the first in-person Acadeca competition since before the pandemic.

I've always wanted to watch the Super Quiz, ever since I almost made my own school's team as a rare young freshman (before I moved and switched to a school that didn't have an Acadeca team), and so I decided to watch it in person last weekend.

So here's a quick summary of the afternoon's events, written in "A Day in the Life" format, and taken directly from the program that was handed to us spectators:

3:15 -- Opening Procession & Ceremony. The defending champions, Mark Keppel High School, led the procession, followed by the other schools in alphabetical order. The pledge of allegiance followed.

I point out that Keppel High is located in Alhambra, which is not far from the Monterey Park shooting that had occurred a week earlier. There was a moment of silence to honor the victims.

3:35 -- Welcome. Several leaders from the community introduced us to the competition.

3:45 -- Start of Super Quiz Relay. The theme this year was the American Revolution. But, as I found out, all subjects were covered during the Super Quiz, including math. The final two questions in each round were math questions. If I recall correctly, here are the math topics covered:

Round 1: Simplifying expression with powers of i, solving an absolute value inequality

Round 2: Identifying solutions of a trig equation, solving a quadratic equation

Round 3: Solving a triangle, identifying equations of perpendicular lines in standard form

I tried to solve some of the math problems myself, but with only twenty sections per question, it was very difficult -- especially since it's hard for me to read the questions from my seat. I got one wrong for misreading the sign, and other because I couldn't distinguish the "less than" and "greater than" symbols.

5:15 -- End of Super Quiz Relay. As expected, Mark Keppel won the Super Quiz again. But the written parts of the competition continue this week. We'll know in about three weeks whether our school will advance to the state-level competition.

None of my current students are decathletes. (After all, freshmen at Acadeca are rare, so that rules out my Math I classes. While many decathletes might be in Math III, they're more likely to be in the honors classes that I don't teach.) 

I can't help but think about the COVID What Ifs, and whether it's possible for me to have participated in the Academic Decathlon in one of those alternate universes. But that's a topic that we should save for a vacation post to discuss on the blog.

Instead, I think back to my Math III class. And yes -- I cover part 2 of the last Chapter 7 topic before the test, namely the Law of Cosines (which might have come in handy at Acadeca this year).

But what worries me is that another student has dropped my fifth period Math III class and switched to another teacher. And I think I know exactly what incident drove her away from my class.

Last week we took the Chapter 7 Quiz, and my fifth period class was quiet (for once). But the next day was the quiz corrections, and several students were talking and whispering that day. I mentioned this on the blog last week -- recall that I ultimately decided not to give credit for any corrections.

At no point did I ever name this particular girl as one of the talkers. And her grade even without the corrections was a B- (which is higher than her grade at any point in the first semester). Still, she felt that she was being treated unfairly -- her corrections didn't count even though she wasn't talking. Apparently this was enough for her to ask her counselor to switch out of my class.

As I wrote last week, anything I could have done would be deemed unfair by at least one student. I wonder what would have happened if I had made a positive list of those students who weren't talking and declared that only their corrections would count -- would this student still be in my class today?

Lesson 5.1.1: Intro to Arithmetic Sequences (Days 97-100)

COMPOUND INTEREST RAP

First Verse:

Nowadays we got money on our minds,

Devisin' ways to pull cash all the time.

It's a common situation in the western world,

Building dreams with steam and then we make it work.

A lot of folks pullin' all the right strings,

Make a dime on a feelin', pull a dollar on the whim.

But once we get that bank roll flowin',

The interest rate is how we keep it growin'.

I know a lot of you wanna keep it simple,

Percentage and time is all you tryin' to get through.

Well that's simple interest and it's pivotal,

Rate times the number of years and the principal.

That's the way we calculate our funds,

While the money stays in, the beat goes in.

But next verse we take a real look into this,

A lesson on finding the simple interest.

Chorus:

A equals P times 1 plus r over n, to the nt,

Yeah, yeah, yeah! (x2)

Second Verse:

Step back to the terms of the simple,

To comprehend this piece is critical.

Principal, it's not about a head of school,

Instead it represent the initial cash pool.

It's like if we deposit a quick grand,

With a rate of interest set to 10 percent.

We leave it be for 5 years and it grows,

But just how much? I'll tell you how we know.

We take 1000 times point 10,

Which is the decimal equivalent of 10 percent.

And multiply again 5 to unlid,

The interest earned, which is 500.

It's pretty simple to follow these steps,

But the real banks pay interest on interest.

To make true life calculation,

Compound interest is what you makin'. (To Chorus)

Third Verse:

The time has come, and we can move another level,

To answer the question that we came to settle.

Compound interest, how does it work?

As the money grows we recognize the new net worth.

So let's push back to the hook,

And jot down what we just got to make it work.

A is the final amount of cash,

And once again big P is the principal stash.

We got t for years and r for interest rate,

Small n is the number of compounds that we take.

Let's plug it all in, same example as before,

We got a G in the bank, 10 percent on a roll.

We keep it in for 5 years and we compound twice,

We get 16 hundred 28 89.

With the simple rate we had 15 bills, right?

But this way it's another 1 28 89. (To Chorus)

This is the second of two songs that I've previously posted to the blog and am now performing for my Math III classes. And -- just like "Whodunnit?" -- I first posted the song in January 2020.

Here is a link to the YouTube video from which I first found the song. Even though I posted the video three years ago, I never posted the lyrics until today. (The lyrics appear as video subtitles, but now we can copy and paste from this post as well.)

Like most hip-hop songs it has a simple riff -- D and A repeating. It was difficult for me to discern from the video whether these are major or minor chords -- I suspect that these could be power chords (which lack the third). When I perform it in class today, I try to use minor chords, Dm and Am. But since I keep jumping my fingers between the strings quickly, the Dm ends up sounding like DmMaj7 (in other words, D minor/major seventh), which sounds quite nice here. (Am-E is the riff produced by moving the fingers the other way, and I use that riff in "Whodunnit?")

I play this song in my fourth period class today, even though it's a Math I class. Due to the block schedule, my first performance of any song will be in Math I, even if it's a Math III song. Today's first period Math III is still doing "Whodunnit?" and fifth period Math III doesn't meet today. Tomorrow is the day when both Math III classes meet -- and that's when I'll give the compound interest lesson.

But believe it or not, this song -- like yesterday's -- has a Math I connection. As you can see by the title of this post, today we are starting Chapter 5 of the CPM text, which is on sequences. While today's lesson is on arithmetic sequences, geometric sequences appear later in Chapter 5. And one application of geometric sequences is -- you guessed it! -- compound interest. (For some reason, simple interest is never presented as an application of arithmetic sequences. Perhaps this is because, as the rap tells us above, the real banks pay interest on interest -- compound interest.)

This goes back to the Common Core standards. Indeed, notice that I first performed this song three years ago in an eighth grade Algebra I class in a district where Algebra I, Geometry, and Algebra II are still taught. In an Integrated Math setting, geometric sequences are perhaps the second Math I topic that's not taught in Math 8 (with the first being a deeper study of slope) -- otherwise Math 8 and Math I cover nearly identical material. (Before the Common Core though, geometric sequences weren't taught until Algebra II.)

Anyway, if we reach a compound interest example in Math I these next few weeks, I might go back and perform this song for the freshmen again. Thus today's song has become my first Chapter 5 song. And since we reach the new chapter today, I'm only half a week behind the official Math I pacing guide.

There's one more connection to songs that I wish to make here. I almost never write about my sixth period Math I class on the blog, since due to the block schedule, this class (like first period) never lines up with the songs I post here, but is always a day behind.

So today, I sing "Whodunnit?" in sixth period. But for the past week or so, one student has thrown glue sticks (intended to be used to glue interactive notebook pages) around the classroom, and I'm been trying to figure out who it is. After threatening to add questions to the homework, one guy finally admits who the culprit is (and it was another guy, the one I've been suspecting all along). Therefore -- on the day that I perform "Whodunnit?" -- I'm able to solve a real "Whodunnit?" mystery in my room.

Today is the first day of the week on the Eleven Calendar. (Sometimes I refer to the first day of the week as "Friday," intending that this would be the new Muslim Sabbath on my calendar.)

Resolution #1: We take pride in our own work & cite our sources.

These days, "cite our sources" isn't as important as it was last year, when I had a monthly current event in my Ethnostats classes. Still, the students should take pride in their own work (especially for deeper assignments such as last week's project).

Notice that Day 100 is right around the corner. (My next post is scheduled for Tuesday, Day 101, and so I acknowledge Day 100 today.) Yes, I'm aware that Day 100 is much more significant in elementary schools than in high schools, but I acknowledge the milestone on my blog anyway.

Lesson 4.1.4: Residuals and LSRL (Day 96)

WHODUNNIT?

First Verse:
Was Mrs. fixing snacks in kitchen?
Was Dr. hearing songs in atrium?
Professor's iPad by the pool now?
Did Miss kill the victim?

Second Verse:
A cougar's mauling was the method?
Or had a green snake's bit begun it?
Or object's falling was the weapon?
Just tell me whodunnit!

As I mentioned in one of my winter break posts, this week I'm bringing back two of my previously performed songs since they fit this week's Math III lessons. So I guess this means that I'll be blogging more about Math III than Math I this week.

For starters, yesterday was the Chapter 7 Quiz. And now I'm rearranging the later Chapter 7 lessons to make the order a bit more logical. Today I do the murder mystery based on Newton's Law of Cooling -- which explains today's "Whodunnit?" song. There are no examples of this in DeltaMath -- there's just a single question in Lesson 7.1.4 of the CPM text. Thus it fits on a day like today -- the quiz corrections take over most of the block, and then there should be time left for the murder mystery.

Tomorrow will be the other main topic of Lesson 7.1.4 -- compound interest. Originally I was going to do compound interest yesterday, but since I gave the quiz yesterday, I'll teach it tomorrow instead. (And before you ask, the rearrangement wasn't done just to make the lessons fit the songs.) On Friday we'll begin the two main laws of Trig -- and I have decided to do the Law of Cosines before Sines, even though Sines come first in the CPM text.

As for the "Whodunnit?" song, I first performed it in December 2019 (even though I didn't blog abut it until January 2020, during winter break), and so I wrote it my usual EDL for December, 12EDL. In order to make it a 14EDL song for January, let's change the last note to Degree 7, which is F#. As I explained on the blog three years ago, the tune originally ended on F# before I changed it, and now I change it back. It contains only verses, so it's another AA song. So it marks our third AA song since we switched to 14EDL.

Here's what it looks like in Mocha. It's exactly like the version from three years ago except it now contains F# as the last note (Line 160):

https://www.haplessgenius.com/mocha/

10 N=16
20 FOR V=1 TO 2
30 FOR X=1 TO 3
40 IF X=3 THEN Y=14 ELSE Y=9
50 FOR Z=1 TO Y
60 READ A,T
70 SOUND 261-N*A,T
80 NEXT Z
90 FOR R=1 TO 1400
100 NEXT R
110 RESTORE
120 NEXT X,V
130 DATA 8,2,10,6,8,2,11,6,8,2

140 DATA 8,6,7,2,11,6,12,2

150 DATA 9,6,8,2,6,6,9,2

160 DATA 7,32

As usual, don't forget to click on the Sound box before RUN-ning the program. If you wish to restore the original version, change Degree 7 in Line 160 to Degree 6.

It's written differently from our previous AA songs because it contains rests (Lines 90-100), which make the song sound more mysterious. The first three lines of each verse are identical, while the last line is different, as it now goes D-E-A-D-F#. (What word do those first four notes spell again?)

As the original was in 12EDL (which is like A minor), the riff for the first three lines is Am-E-Am. But with F# in the last line, I need a new chord. We might simply play Am over F# -- Am/F#, which is also an F# half-diminished chord (F#m7b5). In ordinary songs, we don't expect a half-dim chord to be a resolution, but in 14EDL, this is a 7:6:5:4 subharmonic chord, which might be more stable. Playing this chord in class today serves to make the song sound even more mysterious.

Today is Elevenday on the Eleven Calendar:

Resolution #11: We follow all protocols for COVID.

By now we've all completed our second post-winter break COVID tests, so now it's all about staying safe and being careful. Then this is my eleventh resolution in the classroom. On the blog a few years ago, I've declared that my own Elevenday resolution is to focus on my communication skills with my students and fellow teachers -- and that resolution is still in force.

In fifth period Math III today, I begin the quiz corrections, intending to play "Whodunnit?" halfway through the class and then starting the murder mystery in CPM. Unfortunately, there is way too much talking during the corrections.

On one hand, this is a carryover from the final exam, when I had to give out several zeroes. On the other, talking during the actual quiz was a non-issue yesterday. Going into today, I'm hoping that today would be more like yesterday and less like finals day last month, but my hopes are quickly dashed.

I don't know the exact number of talkers, but it's somewhere between six and ten. And this sets up a situation that almost always lead to arguments. No matter what I do, someone will say that it's unfair:

• If I punish only one student, then I'm singling out a student, which is unfair.
• If I punish several students, I'm unlikely to figure out the exact set of talkers. I'm likely either to punish an innocent student or fail to punish a guilty student, which is unfair.
• If I punish everyone, that will contain innocent students, which it's unfair.
• If I punish no one, everyone will talk through the quiz and the lessons. Then when it's time for the common department Chapter 7 Test, students will complain that they never learned the material, so their grades will drop, which is unfair.

After going back and forth among these options, I end up choosing the third -- today's quiz corrections no longer count, and so their original quiz scores remain.

The scenario where a significant number of students are talking is a fairly common one -- it happened all the time at the old charter school. It usually means that I allowed the students to get away with something early in the year (the Willis period), and so they figure that they can break rules all year.

In this case, back during the Chapter 1 Quiz corrections in August, one student probably asked me, "Is it OK for me to talk during corrections, since I'm already done (or already had 100%)?" I didn't want to say "no," because the student would think I was mean for not allowing finished students to talk. But as I now see, silence is the only way to go. By letting my students talk during quiz corrections, I convince them that it's OK to talk during the actual quiz, lessons, and ultimately the final.

And unfortunately, the talkers include two girls who were demoted from honors. They already learned Chapter 7 in their honors class, and both students scored 100% yesterday -- so naturally the others want to talk to them in order to get help on their own quizzes.

There's not much I can do once the class has reached this point. A significant number of students will talk during the upcoming Chapter 7 Test, and it will be difficult to punish them.

Keeping my eleventh resolution in mind there, perhaps communication is the key here. Before the test, I can inform the students that they are not to talk during the test. If a few students are talking, then those students will get zeroes. But if, say, five or more of them are talking, then rather than attempting to figure out who's in violation, I will immediately assign standards to the entire class. (In other words, they must close their Chromebooks and start writing standards.)

Yes, this is unfair -- but anything I can do at this point is unfair. It's not the same as giving the entire class a zero, although grades might drop because the standards would take time away from the test.

(By the way, the answer to the murder mystery in the CPM text is that the murder must have occurred around 3:15 PM -- and it was around 3:15 in class when we arrived at this conclusion.)

Just as it's important for me to communicate with students, I must also do so with other teachers. I admit that I don't really communicate with my fellow teachers today -- yes, it's Elevenday, but it's also Tuesday, and getting together is tough on Tuesdays. Yesterday was Monday -- a common day for department meetings. And so I talked with the other Math I teachers yesterday.

As it turned out, some teachers waited until this week to give the Math I Stats Project. Since I'm already finished with the project, I move on to Lesson 4.1.4, on residuals and LSRL (least squares regression lines -- in other words, lines of best fit). Technically, there is a Desmos activity for this lesson -- but the Desmos directs students to go to DeltaMath instead, and DeltaMath takes the entire period.

The built-in Stats calculator easily handles linear regressions. And some of the DeltaMath examples involve crime rates in a New York county -- crimes, as in murders, as in "Whodunnit?" Thus my song for today, originally intended for Math III, unwittingly fits the Math I lesson as well.

I'm also starting to have more problems with my freshmen not putting their Chromebooks away properly -- they leave them either on their own desks, or on an empty desk (so they all point to each other and say "That's not mine! You put it away!), or in the wrong slot in the cart.

So I talked to my neighbor teachers yesterday. Both of them are implementing a checkout system where students must surrender either an ID or something else of value (such as a phone), and the collateral isn't returned until the Chromebook is returned properly. I'm strongly considering doing the same in my own Math I classes, perhaps as early as Friday (the day of the quiz, so the Chromebooks are needed).

This is another example where a classroom structure can replace arguing. I care deeply about putting the Chromebooks in their proper slot, but our students obviously don't care. I could try to convince them that taking care of Chromebooks matters -- and since they won't easily be convinced, it would turn into an argument. Instead, the trick is to convert this into something the students do care about, like an ID (or a phone). Arguments are eliminated -- students who don't surrender the collateral will just fail the quiz, and those who don't put the Chromebooks back will lose the collateral.

This is my first post since the celebration of Chinese New Year -- the Year of the Rabbit. Sadly, there was a shooting in Monterey Park, a town here in Southern California with majority Chinese population, over the weekend.

But as usual, I like to discuss the calendrical significance. January 22nd seems a bit early for the big holiday -- and indeed, it's the earliest that it's occurred so far in my lifetime. It's possible for Chinese New Year to fall on January 21st. The last time it did so was 1966, and the next time will be 2061 (so it's possible that I can make it to that date -- I'd be eighty years old).

According to this link to the Archetypes Calendar (a calendar similar to the Chinese Calendar), it's possible for Chinese New Year to be as early as January 20th:

https://www.hermetic.ch/cal_stud/arch_cal/arch_cal.htm

But it hasn't happened in over a thousand years, since the year 497. Note the significance of that year -- it's just before the Gregorian exceptional year (no Leap Day) of 500, and nearly two centuries after the last exceptional year of 300. Thus the equinoxes and solstices occurred earlier in 496 than in almost any other year -- and so Chinese New Year 497 was about a month after that early winter solstice.

Anyway, I wish many condolences for the families of those whose lives were in Monterey Park.

Statistics Project, Continued (Days 92-95)

NO ZEROES

First Verse:

A ZERO for a guy that thinks he's fly

And is also known as a buster

Always talkin' about what he wants

And CAN'T EVEN DO BASIC MATH

So (no) 

Pre-Chorus:

I don't want your number (no)

I don't want to INTERVIEW you and (no)

I don't want YOUR RESUME (no)

I don't want none of your time and (no)

Chorus:

I don't want no ZERO

A ZERO is a GRADE that can't get no JOB from me

Hanging out the passenger side

Of his best friend's ride

Trying to GET HIRED BY me

I don't want no ZERO

A ZERO is a GRADE that can't get no JOB from me

Hanging out the passenger side

Of his best friend's ride

Trying to GET HIRED BY me

Second Verse:

But a ZERO is HIS GRADE

'CAUSE his MATH is kinda weak

And I know that he cannot approach me

'Cause I'm lookin' like class and he's lookin' like trash

WHEN HE DOESN'T KNOW BASIC MATH

So (no) (to Pre-Chorus)

This is a parody of TLC's "No Scrubs." I've performed versions of this song many times before, going all the way back to the old charter school. Of course, the original version contained a certain word that I no longer say or sing. This new version emphasizes "zeroes" as the grade that young people should avoid if they want to pursue several high-paying professions. Thus even though the title has changed, it still retains its message.

There are several reasons why I choose this song for today. First, the current Stats project in Math I directs us to play a video for the students:

The video title "The NBA Data Scientist" refers to Ivana Seric. She helps the Philadelphia 76ers by analyzing basketball data (just as the students are doing with this project) -- and based on the way the Sixers (and their star big man Joel Embiid) dominated our local SoCal teams this week, I think that Seric's work has been successful thus far. But of course, if someone who gets zeroes in math tries to apply to a similar job position, they'll be told "No!" just like the song.

Another reason I perform this song today is that, ever since the old charter school, it's been a tradition to sing it at the first Hero Quiz (or its former name) after winter break. I was originally planning to give the Hero Quiz last week, but it makes more sense to give it during project week -- an easy way to end the week after working hard on the project all week. The words "heroes" and "zeroes" rhyme, and I want to contrast math heroes (including Seric and hopefully most of my kids) with math zeroes.

Today is Fiveday on the Eleven Calendar. But as I promised earlier, once the project begins, we skip directly to the new sixth resolution:

Resolution #6: We implement all parts of our projects in class.

Today in fourth period Math I, we finish the last four slides of the ten-slide Desmos component. And this time I figure out how to copy the English and Spanish instructions for the students. Another teacher helps me figure out how to print in the copy room -- ironically, it's a Spanish teacher. She points out that Google Translate has improved over the years, though no computer translation is perfect. And I attempt to pronounce the Spanish instructions in class. The plans are for the students to work on the group assignment on Friday, followed by the Hero Quiz.

I'm still communicating with the other teachers to see how they are implementing the project. The official Math I leader visits my classroom this morning. Naturally, he started the project last week, and so his students have reached the part where they get to research one of their own favorite players (who may play a sport other than basketball). Since I started later, my classes likely won't get to this part of the project at all.

Meanwhile, I'm going at the same pace as one of my neighbor teachers. He suggests coming up with some sort of quiz to wrap up the week as well. I don't know what sort of quiz it will be -- it might be a full regular quiz (since I don't believe he gave his class a quiz last week), and I don't know whether it will be on paper or DeltaMath. If it's on paper, I might use part of it as a Hero Quiz. The plans are to include a Chapter 3 review equation (such as a fraction buster) and a Chapter 4 scatterplot question, but this may change.

Since today's song is a parody, I won't post any Mocha code here. But there are a few more things I wish to say about "No Zeroes" and what it inherits from its original song "No Scrubs."

The riff is relatively simple -- iv-i-V-i, as its key is minor. But here's the thing -- the girl group TLC originally sings "No Scrubs" in the key of G# minor, and that's a rather strange key indeed. G# minor contains five sharps, just like its relative B major.

Two types of minor keys are used in the song. The melody is in G# natural minor (pure Aeolian mode):

G#-A#-B-C#-D#-E-F#-G#

Indeed, the first note of the melody is F#. But as for the chords, the existence of the dominant seventh chord D#7 suggests that the song is in G# harmonic minor, with a raised seventh:

G#-A#-B-C#-D#-E-Fx-G#

And there you have it -- the raised seventh becomes Fx, or F double-sharp. (Some scores avoid the double-sharp by writing the chord as Gdim7, with its enharmonic equivalent G. But a true dominant chord includes Fx here.)

Notice that no song is ever written in G# major -- instead, we'd write it as Ab major (four flats). But the key G# minor exists -- while Ab minor (seven flats) is possible, it's usually not written that way. Once again, the double-sharp appears only in G# harmonic (or melodic) minor, not natural minor.

Some scores avoid the double-sharp altogether by raising the song a semitone to A minor. And indeed, I actually play it on my guitar today as A minor. The chords used are Am, Dm7, E7.

(By the way, all of what I write about G# minor applies to the standard 12EDO scale only. In other equal temperaments such as 19EDO, Fx is distinct from G, and G# minor is distinct from Ab minor.)

As for the vocals, the girls sing the song in the range F#3-C#5. They are strong altos (or mezzosoprani), so I must lower it an octave to reach my range, F#2-C#4 (or G2-D4 in A minor). This is quite a wide range, a twelfth (or tritave), the same as "The Star Spangled Banner," and thus it tests the limits of my own range. (By contrast, of the two 14EDL tunes I sang recently, one of them is near the upper part of my range and the other near the lower part -- I'd have to sing one right after the other to stretch my range as much as this one song does.)

Oh, and there's one more thing to say about this song. The late Lisa Left Eye Lopes (who died tragically in a car crash a few years after performing this song) added her own verse to this song -- a rap verse. I had no idea that this verse even existed -- the non-rap version has been playing on my radio ever since my senior year of high school, but never the rap version.

The rap verse contains some interesting lines here, such as "See, if you can't spatially expand my horizons" and "Inundate your mind with intentions to turn you out." So perhaps I can add a rap verse to my "No Zeroes" parody as well -- after all as teachers, we want to "inundate your mind" with math. I might add this rap verse in time for a future performance of this song.

Statistics Project (Day 91)

Today is the seventeenth of the month, and so this is my monthly "A Day in the Life" post for January.

8:30 -- On block Tuesdays, periods 2, 3, 4, and 5 meet. So today begins with second period. It's the first of two Math I classes meeting today.

I begin with a Warm-Up -- the students copy the statement. "This week our project will contain both individual and group components." Then they are to work on corrections for the first true quiz of the semester that they took last Friday.

Before I describe how my students do on this project, let me explain what the project is and how I ended up getting there. And that takes us back to last Friday morning's math department meeting.

At that meeting, the Math I TOSA (the de facto head of the curriculum team) was present, and he met with each of the Math I teachers during our respective conference periods. At that time, he described how we should run the projects.

First, there is a Desmos component. We have a choice of two Desmos activities -- one is on the correlation between income and SAT score, and the other is on NBA superstar Steph Curry, who plays for the Golden State Warriors (where the "Golden State" is right here in California). I choose the latter, figuring that my kids will find this more interesting. (The SAT one might have been a good choice for my Ethnostats class last year, since demographics were a major theme of that class.)

For the Steph Curry project, the students are asked "What do you notice?" and "What do you wonder?" as they look at the superstar's field goals made and attempted over his entire 15-year career. (These are common questions to ask during projects popular on the MTBoS.) His current season is incomplete, and so only his stats for the season so far (at the time this Desmos was created -- he was 230 for 450, with just over a quarter of the season completed so far).

As the Desmos proceeds, students create a line of best fit for the relationship between shots attempted (x) and shots made (y), based on Curry's career. Then they use this line to extrapolate how well he'll shoot this season, based on this line and how well he's shot in its first few months.

After the Desmos component, the kids move on to group portion. They will answer a question from the CPM text and analyze the correlation between amount of medicine taken and length of a cold. The idea for this question came from one of my neighbor teachers -- he suggested it after school last Friday.  I'm taking my neighbors' input into consideration, rather than just the department chair or the TOSA.

And indeed, because I had so many tough decisions to make (Curry vs. SAT, neighbors vs. TOSA), I arrive at school this morning still undecided about what exactly the project will look like. What ends up making the decision for me was my inability to print files from my computer on campus. Originally I considered starting the Desmos today, and having them glue a helper page into their notebooks (with instructions on how to complete the Desmos in English and Spanish). But once that page doesn't print, I instead photocopy the medicine problem directly from a print copy of the CPM text, and then have the students glue it into their notebooks (even though we won't get to it until later this week).

He also suggests that I leave out the part where the groups do their own research based on an NBA player of their choice. As we've seen with "Linear Art," if we give the students a choice in their project (draw a picture, choose an NBA player), many will instead choose to do nothing.

9:10 -- About halfway through the period, it's time for music break. Today is another short 14EDL song in AA format (verses only), and it describes this project:

HOW MANY MORE?

First Verse:

What do you now notice?

Three-point shots, Steph Curry.

Three-points shots, Steph GOAT is.

Making shots. Don't worry!

Second Verse:

What do you now wonder?

Three-points shots, Steph Curry.

Now he's made five hundred,

How many more? Hurry!

I'll write more about this song after finishing "A Day in the Life."

9:15 -- I begin the project now, after allowing the students time to work on quiz corrections. But as is usual for this period, the project doesn't run smoothly.

First of all, only about half the students who scored below 100% on Friday even bother working on the quiz corrections -- instead, they spend the whole time either on phones or taking about non-math. And then this continues into the main Desmos lesson.

The Desmos lesson contains ten slides. After the experience of the fateful Linear Art project, I know better than to have the kids just work on Desmos on their own -- many of them won't. Instead, we go over the first six slides together, and I choose names at random to answer the questions (such as "What do you notice?") from the slides.

On the fifth slide that we reached, we must "predict" the number of shots Curry made in the 2015-16 season, based on his actual number of shots attempted, 1598. I use the line of best fit that I'd eyeballed earlier in the activity, y = (1/2)x - 17, but the students can use their own equation as well.

By the way, adjustments are still being made to the schedule. One new freshman guy joins the class -- at first he wasn't on my roster, and then he was placed in a different period. But now his schedule has settled with him in my second period class. I send him to the office to get Google Classroom access. He returns, and he's the first to figure out that to extrapolate Curry's first 1/4-season stats to the entire season, we should multiply by four.

9:55 -- Second period leaves for nutrition, but not without incident. One guy tries to leave early, or at least line up at the door during the last few minutes of class. When I tell him that he must return to his seat, he claims that he's about to "throw up," which is why he must be at the door. (Of course, he only seems to have that urge during the last few minutes of class each day.) So I assign him a one-minute detention, which he then tries to avoid serving. I must block the door to prevent him escaping, which then causes a huge traffic jam at the door.

After nutrition is my third period conference. During this time, I remember that today is Fourday on the Eleven Calendar:

Resolution #4: We start our Warm-Ups and the main lesson promptly.

I keep this mind as I prepare for the next class, since this resolution shows me how I can run the project more smoothly.

11:45 -- Fourth period arrives. This is the second of two Math I classes today.

First of all, in order to honor the fourth resolution, I change the Warm-Up. Now I ask the students, "What grade did you earn on last Friday's quiz?" And then I tell them that I won't stamp their Warm-Up sheets unless they either earned 100% on the quiz, or else completed the quiz corrections.

This goes much better. Only two students fail to finish their corrections. Then we move on to starting the project -- even starting it a little before music break. We reach my goal of matching the six slides that second period completed.

Of course, the fourth resolution isn't the only one on my mind. All three new resolutions come into play today -- most obviously the sixth resolution on implementing all components of projects.

The fourth period class also has a new student, a girl. Technically she's not new -- she missed class all of last week for unbloggable reasons. She quickly makes up her missing quiz and assignment and prepares to work on the project.

1:10 -- With only a few minutes left in class, I put up the same Exit Pass as second period: "Using my line of best fit y = (1/2)x - 17, how many shots do you expect Curry to have made in 1598 attempts?"

The answer isn't the date, although the date (17) does appear in the question. (OK, I admit it -- when I eyeball my equation earlier, I intentionally include the date.) While I sometimes find other ways to incorporate the date besides the answer, perhaps in hindsight, today isn't the best day to do so. After all, there are new kids in both second and fourth period, and I want to introduce them to the idea that the answer is usually the date. Also, this Exit Pass might lead the students to believe that they should all just use my equation in their project rather than attempt to find an equation themselves.

Instead, I should have just asked them to write "Mr. Walker's line of best fit is y = (1/2)x - _____," and had them fill in the blank.

1:15 -- Fourth period leaves for lunch.

2:05 -- Fifth period arrives. This is a Math III class.

We begin the Warm-Up question -- condense the expression log a + 3 log c into a single log. Then we move on to the main lesson -- the second part of Lesson 7.1.2, on properties of logs. Today, instead of condensing, the students must now expand log expressions.

After music break, we move on to a short activity -- Concentration. The students are supposed to divide into pairs, cut out the game pieces, and then flip them over. If the two expressions are equal (one condensed, the other expanded), then it counts as a match. Then they must write them as an equation in their notebooks.

I want the students to work with their neighbor as a partner -- indeed, I pass out the gameboards to cut to every other row, so that each pair has exactly one gameboard. But then some students try to partner up with those other than the ones I choose for them, which leads to an argument.

And then that invokes the second resolution, on avoiding arguments. In fact, as soon as I realize that I'm arguing, I lose the will to talk about the activity -- I'm afraid I might start arguing again. A few pairs do successfully complete the activity after all. I don't even put up a valid Exit Pass question and end up just stamping papers for merely writing the date.

By the way, there are certain things I say during today's argument that I only say because it makes me feel better -- not because it's worth saying. It's like a back scratch when your back is itchy. It's hard to scratch my own back physically, but when I need a mental back scratch, I should do so -- scratch my own back in my mind, and don't say anything out loud at all.

And in order to get myself to argue less, I actually give school PBIS tickets to the two students I argue with the most. I'm trying to force myself to stop arguing so much -- and this goal is so important that I will reward students who catch me arguing (but only if I start arguing, not if they argue with me).

How could I have avoided this argument altogether? One way is to tell the students in advance that they must work with their assigned partner sitting next to them, or otherwise it's a detention.

Another, more interesting way is to pass out index cards with matching numbers, and then tell the students that they must work with their match. This way actually fits Concentration, which is after all a game about making matches. I could even put log expressions on the cards, but I must be careful -- if students get confused, they might match up with the wrong people. I should use only trivial expressions such as log(x^1) = 1 log x, log(x^2) = 2 log x, log(x^3) = 3 log x, ..., log(x^n) = n log x with a different n for each card.

This also goes with another MTBoS strategy for pairing and grouping -- VRG, which stands for "visibly random grouping." This idea means that students are more willing to work with others who aren't their friends if it is obvious ("visible") that the choice is random (such as a name generator, or random index cards as in this example). If the pairing instead appears forced, then they will argue (even if it's just the same pairing that we could have obtained randomly).

Unlike second and fourth periods, there are no new students in this class. But one student, a senior girl who had apparently passed the first semester as a junior but needs to repeat the second semester, started to enroll in my class last week -- and she promptly transferred out the next day. When I started teaching that complicated lesson on solving exponential equations, she felt as if she didn't belong here and asked her counselor to move to another class.

Today's lesson is much easier. I suspect she wouldn't have been scared away if last Tuesday had been more like today. Just change "Part 2" of today's log properties lesson to "Part 1," and keep the Concentration game (with VRG to avoid arguments), and I think she'd still be in my class.

So for tomorrow's first period Math III class, I think I'll set up the index cards. Of course, this means that I won't pass out gameboards until after the students have paired.

3:30 -- Fifth period leaves, thus completing my day.

The "holiday stretch" continues. Yesterday was the MLK holiday, and of course we have the usual Presidents' holidays coming up in February.

And my goal to reduce and eliminate arguments continues. Once again, the idea is to say the right things and put enough structures (such as index cards for choosing partners, a la VRG) so that most arguments are avoided.

One fifth period guy is on the baseball team, so he enjoys using sports analogies. It's important to avoid arguments, whether in the classroom or on the baseball field. Of course, arguing with an umpire will get a player ejected. In the classroom though, I am the umpire -- and it does no good for the umpire to start arguing on the field. So neither should I argue in the classroom.

Let's get to the Mocha code for today's song:

https://www.haplessgenius.com/mocha/

10 N=8

20 FOR V=1 TO 8

30 FOR X=1 TO 6

40 READ A,T

50 SOUND 261-N*A,T

60 NEXT X

70 RESTORE

80 NEXT V

90 END

100 DATA 14,6,14,6,11,4,13,12,9,2,12,2

Don't forget to click on Sound before you RUN the program.

Once again, as an AA song, it consists of a single riff. Unlike the last tune, this is a true 14EDL song where the tonic F# really does appear.

Since Degrees 14 and 11 appear in the first bar, it's best to treat 14/11 as a major third, and so we should write Degree 11 as Bb rather than B. So Degree 13 becomes G in order to make 13/11 a minor third. We can now write the repeated line of melody as F#-F#-Bb-G-D-A.

This ought to be written as song in the Superlocrian scale. But with Degree 10 missing, our ear naturally wants to fill in the perfect fifth (C#), making the song sound more like Phyrgian (or Phyrgian Dominant, like a Middle Eastern scale). The resulting riff then becomes F#-G (both chords major).

Also, originally I wanted to sing our 14EDL songs in the F#2-F#3 range (as my main vocal range is Octave 3, the octave below middle C). But with the high tonic at Degree 7 missing, this song was easier for me to sing with Degree 14 as F#3 instead of F#2. The range of the song becomes F#3-D4, which aligns better with my vocal range.

Soon we will reach more complex 14EDL songs, with a verse and chorus (AB). These generated songs are more likely to include the entire 14EDL scale rather than skip some tones.

Lesson 4.2.2: Correlation and Association (Days 88-90)

CORRELATION

First Verse:

Positive correlation, increase, increase.

Negative correlation, increase, decrease.

No correlation, no connection.

One correlation, one perfection.

Second Verse:

Strong correlation, points are so close.

Moderate correlation, points almost close.

Weak correlation, points far from it.

For correlation, lines of best fit.

This is the first song that I'm composing (at least nominally) in 14EDL. It's also one of our simplest songs as it's in AA format, with verses only.

But this is one of the tunes that I composed in Sunday's intro to 14EDL post -- it doesn't even include Degrees 14 or 7 (the tonic). I use it anyway since I want a simple song to get back in the hang of playing music on the guitar.

And yes -- I know that the Mega Millions jackpot is still over a billion dollars. But there's no need for me to sing "One Billion Is Big" a second time this week.

Today in fourth period Math I, the students have a Desmos activity on correlation and association. It was created by the Math III colleague who's known for writing lengthy Desmos assignments for that class, so it's no surprise that this one is also long, with 28 total slides.

The first few slides contain notes on the definitions of various types of correlations -- the namely the ones listed in the song (positive, negative, strong, weak). Therefore I decide to have the kids copy these definitions into their notebooks (including outlier, which appears in the DeltaMath assignment).

Then Desmos asks the students to identify the different types of correlations, and then guess their own lines of best fit for various scatterplots. Sliders are used so that they can adjust the slopes and intercepts of their lines, and then on the next slide they can compare them to the true trendlines found by Desmos.

Notice that there's no real mention of "association," despite it being mentioned in the lesson title. Last year in Ethnostats, I taught the difference -- "association" is for qualitative data, while "correlation" is for quantitative data. But we don't even talk about qualitative data today.

Today is Nineday on the Eleven Calendar:

Resolution #9: We value instructional time.

I often use Ninedays to focus on students being out of class -- excessive tardies and restroom passes. Both first and sixth period had more tardy students then there ought to be, while fourth period had one student ask for two passes in the period. I charge him for two passes (towards the 19 that he's allowed).

Here is the Mocha code for today's song:

https://www.haplessgenius.com/mocha/

10 N=8

20 FOR V=1 TO 8

30 FOR X=1 TO 9

40 READ A,T

50 SOUND 261-N*A,T

60 NEXT X

70 RESTORE

80 NEXT V

90 END

100 DATA 11,4,9,4,13,4,8,2,8,2,9,8,8,4,10,2,9,2

Don't forget to click on Sound before you RUN the program.

It's an AA song with verses only, so I can repeat a single line the entire song. I already wrote out the Degrees for this tune in Sunday's post -- 11-9-13-8-8-9-8-10-9.

To convert this to notes, we must make a decision on Degrees 13 and 11 -- we can choose G and Bb, or G# and B, in order to make 13/11 a minor third. I end up choosing the latter:

B-D-G#-E-E-D-E-C-D

The first few notes spell out E7, and with D in the second bar, I use E7-D as the main riff. This is like the double dominant riff E7-A7-D.

If we were to use the flat versions of 13 and 11 instead, we would have Bb-D-G-E, which is considered to be an E half-diminished chord. It would suggest the common riff Eo7-A7-Dm. While this is playable as there's no F# to suggest D major instead of minor, this would make an even bigger mockery of this so-called 14EDL song (with supposed tonic F#).

Martin Luther King Jr. Day is on Monday, and so my next post will be the regular Tuesday post. At least I'm done with my four straight days of posting.

Lesson 4.1.0: Fit Fights (Day 87)

ONE BILLION IS BIG

1st Verse:

Have you seen the headline? We did OK,

We sold a million records in just one day.

That's a thousand times a thousand sold,

That's plenty of vinyl, a million whole.

A million dollar bills reach for the sky,

Stack 'em about three hundred feet high.

A billion dollars is a thousand times more,

A lot more money than we bargained for.

Chorus:

One million is big,

One billion is bigger.

One thousand times one million,

That's one billion.

2nd Verse:

We're getting kinda hungry for our favorite food,

Hey, what do ya say? Are you in the mood?

Let's satisfy our special taste,

And get some lunch at the burger place.

See that sign? "One billion served!"

Beat box, that's a lot of hamburgers.

One thousand times, when ya order fries,

A million times one thousand apple pies.

(to Chorus)

3rd Verse:

If we multiply one million by ten, How close are we to one billion then?

If we take a look, we will see, We got a way to go, my friend Markie Dee.

If we multiply by one hundred this time, Let's take a look, and we will find,

That we're not even halfway there, We need a lot more to be a billionaire.

If we order one billion cheeseburgers, And eat one million cheeseburgers,

It would be enough to knock us off our feet,

'Cause we'd still have almost one billion burgers to eat.

One million's not even one percent of one billion. Wow!

(to Chorus)

Yes, I do perform "One Billion Is Big" a second time in honor of the Mega Millions jackpot. It's really only the first time I've performed it in Math I classes -- in November when the Powerball jackpot was that high, I rapped it only in Math III.

Even though "One Billion Is Big" is a rap with its chorus as the only melodic section, it's a great song to play on the guitar as my first post-vacation song. During those idle weeks, the guitar fell out of tune -- so by playing today's song, I get to retune my guitar ahead of attempting any 14EDL songs.

In second period, I open up the Desmos lesson. It is labeled as "Lesson 4.1.0" of the CPM text -- that is, it's an introduction to Section 4.1. But as I try to present the Desmos, it becomes painfully clear that many kids are confused by the whole idea of line of best fit. Yes, the red line is close to the the blue dots, but what do red lines and blue dots have to do with anything?

So I pause the Desmos activity and switch to the notebooks instead. With first semester grades still fresh on our students' minds, my example is a scatterplot of days absent vs. test scores. I draw the same scatterplot twice and drew a different line on each one, then asked, "Which is the better fit? Suppose I were to pay a billion dollars for the line of better fit, then which line would I pay for?"

Of course, mentioning a billion dollars is an excuse to tie this to the "One Billion Is Big" song (and thus justify singing it in class today). But in reality, grants are paid to researchers who can find lines of best fit between related sets of data (maybe not a billion dollars, but sometimes in the millions). So the idea of paying for a line of best fit isn't as far-fetched as it might seem at first.

One girl figures out that the line of better fit is the one that's closer to the dots. So this leads to a discussion of what exactly that means.

As usual, I make adjustments to this lesson in time for fourth period. In the later class, I start with the notebooks, not Desmos. Then after discussing what lines of best fit are, the kids are ready to attempt to find such lines in Desmos. The "fight" mentioned in the lesson title refers to a competition set up in Desmos where the students compete to find the line of best fit for a particular set of points.

 A good teacher makes adjustments when it's clear that the students aren't getting it. But a great teacher doesn't need to make adjustments, because the original lessons are already understandable. Especially when it's time for the Stats project, I want that project to go well from the start, in all classes. I don't want to begin the project, run into trouble, and say "Oh well, at least I'll get it right by sixth period."

Indeed, I don't like the way the fifth period Math III lesson goes today either. The official lesson is on solving equations with logs, with the properties of logs to be taught on Friday. But here's the rub -- many equations require the properties of logs in order to solve them! The logarithmic equations on DeltaMath require the product, quotient, and power laws of logs. And the exponential equations often involve bases other than 10 -- the change of base law is necessary since since calculators can only do logs in base 10 (or e, but recall that e doesn't appear until Chapter 10).

The reason that equations are taught before properties is that equations appear in Lesson 7.1.1 of the CPM text, while properties are in Lesson 7.1.2. But the equations in 7.1.1 appear to be either simple equations that can be solved without a calculator, or else involve bases slightly greater than 1 that can be solved to the nearest integer by trial-and-error. Yet the pacing plan has the students solving more complex equations under the 7.1.1 umbrella than what CPM presents there.

This is a tricky one. During the lesson, I wonder whether I could have switched 7.1.1 and 7.1.2, and make sure that the students know the properties they need to solve equations. I'm not one for making excessive arbitrary rearrangements of the lessons, but perhaps this one was warranted.

Since I'd already assigned the homework (and some of my faster fifth period students like to do the HW right away), I don't want to make any changes to the lesson order now (and penalize them). Still, I can at least present the lesson differently in first period tomorrow -- for example, start with log equations before moving on to exponential equations (with bases other than 10).

Today is Eightday on the Eleven Calendar:

Resolution #8: We are mindful of books and other materials.

I enforce this resolution during the Exit Pass in my freshman classes. After they use glue and scissors to paste the Chapter 4 title page into their interactive notebooks, I have the students pass these items to the side of the room where they are kept. Then they only need to write the date as the Exit Pass.

Unfortunately, being mindful of where the glue and scissors belong makes one guy in fourth period be less mindful of his borrowed Chromebook. Instead of putting it where it belongs, he leaves the room with the Chromebook. At least fourth period meets tomorrow, so I'll ask him to return it then.

2023 Challenge (Day 86)

This counts as my "A Day in the Life" post for the special day "first day after winter break."

8:30 -- First period arrives. This is the first of two Math III classes.

I begin this period with a Warm-Up of reflection -- "What was your first semester grade? Are you satisfied with your grade? What will you do second semester to maintain your grade?"

Then it's time for the main task -- Sarah Carter's 2023 Challenge. I won't link to it here, but I assume that you readers are already familiar with Carter's blog. I print out the 100 version, and the top students in this class are able to figure about twenty or so in the allotted time.

As an Exit Pass, this is the rare time that I can use a problem directly from the Rapoport Calendar. On her Mathematics Calendar 2023, Rebecca Rapoport writes:

4! / 4 + (4 - 4 / 4)

This works out to be 4! / 4 + 3 = 24 / 4 + 3 = 9. Therefore the desired answer is nine -- and of course, today's date is the ninth. This question looks just like the classic "For Four 4's" puzzle -- plus a 4 -- that I gave this class during the first week of school (from which the 2023 Challenge is derived.) It uses add, subtract, divide, parentheses, and factorial -- all of which are used in the 2023 Challenge today.

9:25 -- First period leaves for nutrition.

9:40 -- Second period arrives. This is the first of three Math I classes.

This class is noisy, as usual. Only nine students are actually working on the 2023 Challenge. At the end of class, I threaten to assign standards to the kids who aren't doing the assignment.

10:35 -- Second period leaves. Third period is my conference period.

11:40 -- Fourth period arrives. This is the second of three Math I classes.

While fourth period is quieter than second period (as usual), even fewer students are working on the 2023 Challenge -- just five. During the conference period, I'd decided to set up some standards for those students who aren't working. After all, there will be a Chapter 4 Project starting soon -- we can't have another project where hardly anyone's doing the work. We're past the time for threats -- now I have to assign the standards for real.

12:40 -- Fourth period leaves for lunch.

1:25 -- Fifth period arrives. This is the second of two Math III classes.

Today most of fifth period is on task (admittedly a rarity). Only a few students end up having to write down standards.

2:20 -- Sixth period arrives. This is the third of three Math I classes.

Sixth period ends up being just like fourth period -- only five kids are on task. But problems occur when it's time for me to assign standards.

Here's what happens -- first of all, this class often has too many students ask for restroom passes, some almost every day that the class meets. So I've purchased a clipboard to use as a pass, but with a limit -- once a student asks for the twentieth time in the semester (starting today) for a restroom pass, I won't give it to them -- if they leave, they do so at their own risk (of being stopped by security).

Sometimes students ask for passes to the drinking fountain, not the restroom. This is a gray area. My decision is that if they're willing to go without a pass, then they can do so at their own risk. But if they want to go with a pass, then they must wait for someone to bring back the pass. Today a few thirsty kids choose to wait for the pass to return.

But then, near the end of class, the group waiting to go to the fountain decide to leave all at once without a pass -- not coincidentally, it's right when I announce that they must write standards. (In other words, they were really just trying to avoid writing standards.) My policy is that students who are assigned standards must stay for detention or else I must contact the parent (for avoiding the work, the standards, and the detention). Only one student stays, thus forcing me to contact four parents today.

Of these four, at least two are intentional non-learners -- they almost never do any work whatsoever. If I'm going to have this standards policy, then I might end up contacting their parents all the time (which is counterproductive).

This is a tricky one. Today is an all-classes day, so it's understandable that many students are thirsty (as opposed to a block day when sixth is just after lunch, so they could have had water then). I could allow more kids to leave the room for water earlier in the class, so that they can't use it as an excuse to leave at standards time. But those intentional non-learners may just leave to get water a second time anyway.

My other two classes have students who do very little work, but all are special ed students. Sixth is the only class with students who don't leave for special ed pull-outs, instead putting their heads on their desk when it's time to work.

So how to deal with these students is something I must figure out as we approach the Stats project.

3:20 -- Sixth period leaves, thus completing my day.

Even though the holidays are over, the "holiday stretch" continues. For teachers, the holiday stretch runs from Veterans Day to Presidents' Day -- the time of year when most school off-days occur.

Let's get back to the habit of posting how I'm keeping up with my New Year's Resolutions. Today is Sevenday on the Eleven Calendar:

Resolution #7: We earn our grades through hard work and dedication.

Well, as I mentioned above, the Warm-Up was a reflection of the students' first semester grades, so we all think about today's resolution. Hopefully, they will take this rule to heart and plan to maintain or improve their grades in the new semester.

My next post will be tomorrow -- the regular Tuesday post.

Baptism Sunday (Yule Blog Challenge #12)

Table of Contents

1. Introduction

2. Yule Blog Challenge #18: My Goals/One Word Challenge for 2023

3. Previewing Math III Chapter 7

4. Music in the 14EDL Scale

5. Problems in Fifth Period Math III 

6. Rapoport Question of the Day

7. Conclusion

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:

https://teacher.desmos.com/activitybuilder/custom/5ff4fde1dad0813c40aee6f4?collections=5efb5e06d6b26b71b2e1090d

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:

Degree     Note

14             ru F#

13             thu G/G#

12             wa A

11             lu Bb/B

10             gu C

9               wa D

8               wa E

7               ru F#

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.