SBAC Prep: Midterm Review and Chapter 7 Preview (Days 134-137)

ABBIE'S CANDLE

First Verse:

She made a movie with a

Romantic candlelight dinner.

Which candle will burn out first?

Which candle will be the winner?

Candle A, twenty

Centimeters at the beginning and,

Candle B is ten

Centimeters at the beginning and,

Candle A, an hour,

Sixteen centimeters later.

Candle B, an hour,

Ten centimeters,

So when Abbie's candle burns first.

So when Abbie's candle burns first.

Second Verse:

I'm in the movie, Julie

Lights our short candle at dinner.

Julie says B burns out first,

Though Candle A is much thinner.

I say Candle A's

Fully burnt out in just five hours, and

I say Candle B's

Isn't burnt out until ten hours, and

Julie, you are wrong,

Julie, B is cursed, because

B burns twice as long,

Julie, you're the worst,

Because Abbie's candle burns first.

Because Abbie's candle burns first.

This is the second song that I'm writing in 15EDL (as opposed to 16EDL) -- the first being "Planting Trees" two weeks ago. The two girls' names in the song refer to a particular SBAC Prep released test question -- one of the two questions mentioned in yesterday's post. By the way, the other question I use today is the Question 20 worksheet previously posted to the blog -- but more on that later.

Today's not supposed to be "A Day in the Life." But a few things out of the ordinary happen today, and so I'll do a quick "A Day in the Life" here. (That's right -- it's three straight "A Day in the Life" posts.)

8:00 -- Today is another one of those half-day meetings called by the Math I TOSA, similar to the February 16th meeting. Last month's meeting was to review Chapter 5 and discuss plans for Chapter 6, and thus this month we review Chapter 6 and prepare for Chapter 7. (By the way, the only class I miss today is first period Math III, but they are taking the same midterm that fifth period took yesterday.)

Today is Elevenday on the Eleven Calendar:

Resolution #11: We follow all protocols for COVID.

But Elevenday is also my day to focus on communication with students and colleagues. Well, at least I communicate a lot with my fellow Math I teachers due to today's meeting.

The TOSA tells us to bring a sample of Chapter 6 student work. One of my neighbor teachers brings a poster from the project (that she herself created -- it's the basis of my "Planting Trees" song) and suggests that the rest of us do likewise. The TOSA is pleased to see all of our students' questions, tables, graphs, and equations.

Then we begin discussing Chapter 7 of the CPM text. This is one of the chapters to which I've been looking forward to the most, because it's a Geometry chapter. For once, I actually get to write about Geometry on this Geometry blog. And perhaps, after finally using some of my old worksheets for SBAC Prep, I'll get to use some of my old Geometry worksheets as well.

Indeed, my preparations to teach our favorite math subject began on the teacher day on March 13th (yes, Pi Day Eve). The TOSA led a math department meeting, except this one isn't just for Math I teachers, or even just high school -- middle school teachers were there as well. The TOSA discussed what the geometry strand looks like across all grade levels, from Grade 5 to Math III.

Since this is a Geometry blog, I really want to discuss both the Pi Day Eve meeting and today's meeting in much greater detail. But I choose not to tie up today's post with such discussion, since the focus should be "A Day in the Life" (that is, today's lessons). Fortunately, spring break is right around the corner, so I'll devote one of my spring break posts to Geometry and Chapter 7.

I will say this now though -- while the previous Geometry chapter (Chapter 3) was on transformations, Chapter 7 is on triangle congruence. Thus it's very much like the same numbered chapter in the U of Chicago text. You can refer back to my old posts from previous Decembers (prior to the pandemic) to get a taste of what I'll be teaching in April.

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

As I mentioned above, in this class we look at Question 20 of the SBAC released questions. That's because this question is on arithmetic sequences -- a Chapter 5 topic that I didn't include on the midterm review assignment. I divide the class into groups and give each group a worksheet. On one side is my Question 20 worksheet (the version I posted in May 2021) and the other is the candle question from today's song, which requires the students to solve an system (equal values method, similar to the ones on the poster project).

While today's worksheet is helpful, one problem is that both SBAC problems include fractions -- the arithmetic sequences have fractional terms and the system has a fractional solution. All of the questions on the DeltaMath exam use integers only, so I risk confusing the students with the fractions. I quickly add more natural numbers sequences to the SBAC worksheet.

Moreover, the worksheet contains no geometric sequences. I incorporate a geometric sequence as the Exit Pass -- find the 22nd (of course, since that's the date) term of the sequence 3, 6, 12, 24, 28, 96, ...

1:15 -- Fourth period leaves for lunch.

2:05 -- Sixth period arrives. This is the second of two Math I classes.

As usual for Wednesday, sixth period is one day behind fourth period. So this class is still answering DeltaMath questions on Elimination Level 3 (and 4), and the song for this class is still "Palindrome Song" from Square One TV.

Unfortunately, there's been a huge problem lately in this class. Some students have started inviting friends from other classes to ditch their classes and attend mine. Today, the three guys who don't belong present me with a pass from a Biology teacher who apparently sent them to my room as a timeout punishment from their class. But I strongly suspect that the pass has been forged -- especially since this isn't the first time this month that students who don't belong in my class have started attending mine (and some of them even have the gall to start working on DeltaMath in an effort to appear legitimate).

I have emailed the teacher whose name is on the pass, but he hasn't responded yet. Unless he confirms that he really did sent the kids to my room for a timeout, I have no choice but to submit a major disciplinary report to the office.

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

Let's get to a discussion of today's new song. It is quite complex -- officially it's an AA song with verses only, but the melody is more complicated. Instead of repeating a single riff four times, I play two lines and then repeat those lines before proceeding to the next section.

Here's a link to today's Mocha code:

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

10 N=8

20 FOR V=1 TO 2

30 FOR X=1 TO 96

40 READ A,T

50 SOUND 261-N*A,T

60 NEXT X

70 RESTORE:FOR M=1 TO 1600:NEXT

80 NEXT V

90 END

100 DATA 10,12,13,2,16,2,16,6,13,6,16,2,12,2

110 DATA 11,4,15,4,10,4,9,4,10,4,12,4,12,4,11,4

120 DATA 10,12,13,2,16,2,16,6,13,6,16,2,12,2

130 DATA 11,4,15,4,10,4,9,4,10,4,12,4,12,4,11,4

140 DATA 16,8,18,8,15,6,11,6,11,4

150 DATA 13,2,11,2,16,4,14,4,13,4,9,4,11,4,16,4,15,4

160 DATA 16,8,18,8,15,6,11,6,11,4

170 DATA 13,2,11,2,16,4,14,4,13,4,9,4,11,4,16,4,15,4

180 DATA 20,8,16,8,16,6,12,6,15,4

190 DATA 11,8,11,2,16,2,16,2,20,2,18,8,16,8

200 DATA 20,8,16,8,16,6,12,6,15,4

210 DATA 11,8,11,2,16,2,16,2,20,2,18,8,16,8

220 DATA 16,8,16,8,16,8,16,4,12,4

230 DATA 15,16,18,8,16,8

240 DATA 16,8,16,8,16,8,16,4,12,4

250 DATA 15,16

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

As I wrote earlier, due to its complex melody, this AA song is written like an ABCD song. It's one of the few songs I've written with a rest between the two verses -- this rest is included in Line 70.

Both this and "Planting Trees" are labeled as 15EDL songs because Degree 15 -- the note F -- serves as the tonic. It includes Degree 12 or A, so it's definitely an F major song as opposed to F minor. And because it's F major, Degrees 13 and 11 must be interpreted as G and Bb.

I used our usual TI randomizer to compose the song. But since I want the song to sound romantic (to fit its candlelight dinner theme), I smoothed out some of the random tune's roughness. In particular, I changed some of the generated tune's octaves so that the song fits between Degrees 20 (the C below the tonic F) and 9 (the D above the tonic). In particular, Degrees 20 and 18 are a low C and D when the TI calculator generated a high C and D. (I could have used Degrees 20-9 as the bounds for the randomizer, but then I might have to deal with Degrees 19 and 17, which would be awkward.)

On the other hand, this tune includes Degree 14, which is an F#. Of course, an F# sounds out of place in an F major song. So I make sure that Degree 14 is always followed by 13, so that 14 serves as a leading tone to 13. The chord riff for the second section includes D7-Gm over these notes. (This is the only section in which 14 appears.)

Here is a possible chord sequence for the entire song: for the first section, go F-C7 (although others, such as C-Bb-F, also sound great here). The second section, as noted above, goes D7-Gm. The third section has a dominant C (or C7) chord. The last section needs an authentic C7-F.

Finally, the lyrics fit the statement of the original SBAC problem, which is a lengthy performance task with six parts. It is about finding the right candle to film a movie with a fancy candlelight dinner scene.

I decide to cast "Julie" from the SBAC problem as the female lead, and I insert the narrator (aka myself) as the male lead of this movie. Julie insists that Candle B will last longer because it's shorter, even though Candle A is thinner (albeit taller). The students are supposed to calculate (in Part 2 of this performance task) that Candle A will last five hours, but Candle B will stay lit twice as long. In other words, they prove that Julie is wrong.

Thus the song implies that Julie and I break up over a silly argument about a candle. It means that this so-called romantic movie is a tragedy, not a comedy. (Fortunately, it is just a movie.)

I must point out that we should have known all along that the taller Candle A would burn out before the shorter Candle B. Had Candle B burnt out first, the candles would never have the same length, and the system (to find the time when the candles are equally long, Part 3 of the performance task) would have no sensible solution. If Julie had known that she was part of a movie about solving systems, she wouldn't have argued for Candle B.

Just as with "Planting Trees," it's possible to add more verses this song to include all six parts of the performance task question. (Poor Julie only appears in Part 2 of the question -- once she's proved wrong about Candle B, she just disappears from the movie.)

This is my last post before spring break. Recall that we're following Tina Cardone's tradition -- the last day before and the first day after spring break aren't "A Day in the Life" special days. Thus I won't post on either day. (The post is labeled Days 134-137, where 137 is the first day after vacation week.)

Once again, I volunteered to write a Math III test for the next chapter. So I won't make my first spring break post until after I write the test (even if it's the last day of break). In that post, I'll discuss the Math III test that I'll have finished by then, and then pivot to Math I Chapter 7 and Geometry.

Lesson 6.3.4: Solving Systems by Elimination, Continued (Day 133)

PALINDROME SONG

Chorus:

Go forward then go backward.

If the number reads the same, then it's a palindrome.

Go backward then go forward.

If the number's still the same, then it's a palindrome.

It's not a palomino on the western plain,

Where cowboys love to roam.

No! The wonder of all wonders, a backward-forward number.

It's called a palindrome!

First Verse:

Let's see! Take a 33! Read it in reverse.

Hey it reads the same, So it's a palindrome.

And 505, or 2002,

So they're both examples of that one I love.

It's a palindrome! It's a palindrome! It's a palindrome!

(to Chorus, except say:)

...then it's a palindrome.

It's not a pachyderm performing in the circus,

At the hippodrome. No! The wonder of all wonders...

Second Verse:

Let's see! Take a 63! Read it in reverse.

Now we're in a fix, 'cause it's a 36.

But don't be sad, all we do is add.

Add the 63 to 36 and see. That's a 99!

Hey we're doing fine! That's a palindrome! Whoa! Whoa!

(to Chorus, except say:)

Go backward and go forward. It's the one that's glad you came,

'Cause it's a palindrome.

If reversing and then adding doesn't work the first time,

Repeat it 'til you're home.

'Cause you'll finally reach that number, that backward-forward number,

You've reached a palindrome!

The fact that I'm posting Square One TV's "The Palindrome Song" means -- you guessed it! -- another Palindrome Week is upon us. The big palindrome day was yesterday, 3-20-2023. Unfortunately, it fell on a Monday, and I don't perform songs on Mondays. But at least Palindrome Week continues with reversible dates from today, 3-21-23, up through 3-29-23.

Since the song is from the Square One TV show, I can post its video here:

Regarding the song itself, it's interesting that not only are the lyrics different each of the three times the chorus is played, so are the rhythm and style. The middle chorus is most striking as its played in 3/4 time while the other two are in 4/4. The rhythms correspond to dances -- the middle 3/4 rhythm is almost certainly a waltz. The first rhythm might be a tango, while the last rhythm could almost be rock and roll (though the dancers also create a conga line).

Today's not supposed to be "A Day in the Life." But a few things out of the ordinary happen today, and so I'll do a quick "A Day in the Life" here:

8:30 -- It's Tuesday, so the block schedule goes 2-3-4-5. Second period arrives -- just as I leave. I have another one of those special ed meetings today, and so a sub comes in to cover this class.

9:55 -- Second period leaves. Third period is my conference period -- except during this time, I have yet another meeting. My prep period buddy asked to have this meeting, and she invited me to join in as well as a "long-term" sub (and by "long-term" I mean "the entire year") who's covering a special ed Math I class. The meeting is led by the TOSA (yes, the same TOSA who saved me from the pink slip last year, but is unable to save me this year), and the topic is SBAC Prep.

Recall that last week, the Math III department already declared an SBAC Prep Boot Camp -- and Math III is expected to have more juniors (read "test takers") than Math I. While I have only a single junior in my Math I classes, my two colleagues have more special ed students, hence more Math I juniors. Still, the state test covers all three years of high school math, and thus it's not too early to get our students thinking about it.

The TOSA shows us how to access the released test questions online, including how to select questions based on topic or question type. One of the questions he shows us is Question 9 from last week (and ultimately from the old SBAC Prep blogposts) -- the one where students must drag two irrational numbers into boxes, one whose square is rational and the other whose square is irrational.

 11:45 -- Fourth period arrives. This is the lone Math I class that I see today.

Today we continue to learn about elimination. Notice that the CPM text doesn't have a Lesson 6.3.4, nor does DeltaMath distinguish a fourth level of elimination. But one of my Math I neighbors -- the one who usually writes the tests -- is teaching Elimination Levels 3-4 this week. If we must discern four levels, we might think of them as follows:

1. Addition Only

2. Subtraction Only

3. Scale One Equation

4. Scale Both Equations

Both CPM and DeltaMath combine some of these so that there are only three levels. This time I follow the strategy I mentioned in my last post -- give advanced elimination problems on DeltaMath and have the students practice them together.

Notice that second period gets the same lesson as fourth period today -- at least in theory. Just as I'd expect, many second period kids are off-task today. Lately, I've been rearranging the quiz and test dates so that they land on sub days -- if I'm going to lose a lesson due to having a sub, I might as well give a test on that day. Indeed, I almost considered giving the Chapter 6 Test today for that very reason, but this is impossible today. The kids won't be ready for the test -- especially now that my neighbor who wrote the test is now billing this as a midterm that includes questions from Chapter 5 as well as 6.

My neighbor also provided a midterm review assignment on DeltaMath today. But here's where another of my rigidities comes in -- I always give my assignments on Mondays, to be due Fridays, but he didn't show us the midterm review assignment until today. Some of my kids started my assignment yesterday, so they wouldn't have appreciated my changing the assignment to the review. But, not knowing whether the test would be a midterm, I didn't include any Chapter 5 questions on my review.

One solution to this dilemma is not to use DeltaMath to review Chapter 5 at all. After all, I just had a meeting about SBAC Prep questions. So I could try to find a question related to Chapter 5 material (namely arithmetic and geometric sequences) and use it to review for Chapter 5, while keeping my DeltaMath assignment as the Chapter 6 review. (After the meeting, my prep period buddy said that she might give an SBAC Prep question "before the midterm" -- neither one of us aware at the time that the midterm would be this week.)

Due to the special ed meeting, my first performance of the "Palindrome Song" isn't until this period.

1:15 -- Fourth period leaves for lunch.

2:05 -- Fifth period arrives. This is the lone Math III class that I see today.

Unlike Math I, Math III really does take their midterm today. Their midterm covers Chapters 7-8 -- recall that Chapter 7 covers the Laws of Logs, Sines, and Cosines, and Chapter 8 is on polynomials.

Today is Tenday on the Eleven Calendar:

Resolution #10: We treat each other the way we want to be treated.

This doesn't really come up today, at least not in the two classes I see today. Fourth period is the best behaved of my Math I classes, while fifth period is usually OK if they have something very specific to work on, such as a midterm.

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

I'm going to look up that SBAC Prep question now and prepare for tomorrow's classes. Enjoy the rest of your Palindrome Week!

Lesson 6.3.2: Solving Systems by Elimination, Continued (Days 129-130)

SYSTEMS RAP by Algo Rhythm

(Verse 1 intentionally omitted)

Verse 2:

y equals mx + b

Ax plus By is C. Different forms you see

Plug in mx and b for y in the Ax plus By is C

Which becomes an equation with just x

You know how it be.

Wait. x we need y, don't

have to hate, straight out

the gate, at this rate,

find the ordered pair

x and y are mates

Substitution.

it's not Subway

But I be keeping math fresh

all day every day

Weird flex but okay

Mr. Walker goin' cray

With my words on play

And all I have to say is

Chorus: (x2)

I'm on a mission

Solving systems

Of equations.

Don't be hatin'.

Intersection

Substitution

Elimination

Combination

Verse 3:

How do we find the answer for

A system of two standard forms

Needa be a bit humble more

Like Harry Potter and Dumbledore

So pay attention on elimination

Today's assessment on Illuminate, son

For variable x or y, first

Create an elimination

Through product combinations

Of system of linear equations

Combine both sides like stereo

To isolate the variable

Jump for joy like Mario

Single step, "let's go."

Then sub for the other one,

And solve the equation,

And now we're done, son

Flow Acapella, no beat, no drum

OK, I admit that I'm not the creator of this rap. Like "Slope Intercept Rap" (mentioned in yesterday's post), it appears on the old Google Classroom shared by Math I teachers. The difference is that "the Slope Intercept Rap" writer posts YouTube videos of his songs. The creator of today's rap appears to be a fellow (or former) teacher at my school.

I don't post complete content created by my colleagues. Thus, like with "Planting Trees" earlier, I post only an edited version of the song. For starters, I omit the first verse (which is on solving systems by graphing) and start with the second verse. Moreover, the creator of this rap posted only a worksheet filled with blanks (like guided notes), with no answer key. Thus I had to guess and fill in some of the blanks myself.

The underlined lyrics are my best guesses at the blanks. Some of them I'm more sure of -- for example, I'm confident that the blank in the first line is y equals mx + b (slope-intercept form), but I had no clue what goes after "which becomes" in the fourth line.

Also, "Algo Rhythm" is clearly a stage name. The creator of the song included his own name in the second verse -- well, at least his last initial (after "Mr.") is there. And so I changed this to my own last name above. (No current math teacher at my school has that last initial, which is why I think it's a former teacher.)

Meanwhile, like many hip-hop songs, this song might have a melodic chorus while the rest of the some is purely rhythmic -- but there's no video or other way for me to know this. And so I decide to create my own melodic chorus using our current EDL scale, namely 16EDL.

Let me make this official. This is the third song that I'm composing in 16EDL, our main scale for March and April. And it's the first 16EDL song in the ABAB format, with verses and a chorus (though only the chorus is melodic).

Before I discuss the chorus, let me discuss the fourth period class itself. Today we return to Lesson 6.3.2 of the CPM text, which is on elimination where one equation must be scaled, or multiplied by a constant in order to eliminate a variable. (The rap above calls this "combination.")

There is a Desmos activity that could go with this lesson, but I think it fits the next lesson better. So instead, I give a few guided elimination questions as part of the DeltaMath assignment. This allows us enough time to glue the rap into notebooks and fill in the blanks.

Meanwhile, in first and sixth periods it's still Pi Day (or at least Belated Pi Day, since those classes didn't meet yesterday). In first period I hand out 7-Eleven pies to the top three scorers on the DeltaMath test in Math III, while in sixth period (right at 1:59, of course) I give away the leftover pies from yesterday's fifth period.

Sixth period Math I finishes their posters today, but some students are once again distracted by the World Cup -- the World Baseball Cup, that is. Many of my Hispanic students are once again supporting Team Mexico, who defeats Canada to advance to the knockout stage. Team USA must beat Colombia to advance as well. (The Americans lead 3-2 at the game's midpoint as of the timestamp of this post.)

I believe that all games in the knockout round will be played in primetime, or at least after school lets out on the West Coast. So today should be the only day with a baseball distraction. (Of course, March Madness starts tomorrow, so that might also cause problems.)

Today is Fourday on the Eleven Calendar:

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

I do attempt to get the kids working more quickly in fourth period, though it's still tricky. Today's Warm-Up is a Level 1 elimination problem, and even though many of them did well on last week's quiz, they still like to waste time during Warm-Ups. (In the other classes, fast Warm-Ups are impossible since I spend much of the first few minutes of class handing out pie.)

Meanwhile, I do wish to get back to pink slip discussion in today's post. Today during third period, I originally plan on meeting up with my prep period buddy (the other Math I teacher with the same conference period) to set up the next tutoring session -- and we'd already been discussing my evaluation and employment situation. But unfortunately, she has to cover another class during third period, and so I don't say much about the pink slip. (Of course, the correct contact person would be a union rep, but they are busy today -- it is still March 15th, after all.)

Just like last year, I won't mention any interviews I have with other schools on the blog, unless they occur on a regularly scheduled posting day and I take the entire day off to interview (thus forcing me to explain why I'm not teaching that day).

Here's a link to today's Mocha code (for the melodic chorus):

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

10 N=8

20 FOR V=1 TO 2

30 FOR X=1 TO 28

40 READ A,T

50 SOUND 261-N*A,T

60 NEXT X

70 RESTORE

80 NEXT V

90 END

100 DATA 12,4,12,4,10,8

110 DATA 12,4,12,4,10,8

120 DATA 12,4,12,4,10,8

130 DATA 12,4,12,4,10,8

140 DATA 11,4,16,4,14,4,10,4

150 DATA 11,4,16,4,14,4,10,4

160 DATA 11,4,16,4,14,4,10,4

170 DATA 11,4,16,4,14,4,10,4

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

I ran my TI randomizer twice, since on the second attempt I found notes that sound good. There are two bars -- one that repeats for the first four lines, and the other that repeats for the last four.

Degree 13 is omitted, and so this is pure 16EDL without worrying about the neutral third problem. The first repeating bar is A-A-C, with Am as the obvious guitar chord. In the second bar, we can interpret Degree 11 as B so that an E power chord can be played -- the melody becomes B-E-F#-C.

This post is labeled as Days 129-130. My next post will be on Friday, Day 131 -- the seventeenth of the month and hence my monthly post.

Pi Day (Day 128)

Today is Pi Day, a key day on the mathematical calendar. I have much to say about how I celebrated it in the classroom this year.

But first things first -- I received the dreaded pink slip today. I've been expecting this ever since I took this job in the first place. Recall that last year I got the pink slip, and I wasn't rehired until July. So I already know that I got the last open position, placing me right at the bottom of the seniority list. And enrollment  is declining everywhere -- there were fewer babies born in the Great Recession, and that's the generation that's now reaching high school age.

Still that doesn't make it any easier once I receive the actual document. It makes it worse that I get in on Pi Day, which ought to be a day of celebration -- but I know it goes back to the California law that pink slips must be sent out by March 15th.

As I wrote above, last year's pink slip was rescinded in July -- and only because the district promoted one of the other math teachers to a TOSA position, thus opening a spot for me. This year, I doubt that there's going to be any TOSA loophole to allow me to stay in the district.

I'm going to save most of this pink slip discussion for tomorrow's post, since once again, the Pi Day post should be all about celebrating pi and math.

Last year, I worked at such a small school that I was able to bring enough pie for every single student who had my class on Pi Day. This year, I work at the main high school, so I can't do that. Instead, I bring pie only for the class that meets at the Pi Minute, 1:59 -- but which class is that?

Well, the block schedule on Tuesdays goes 2-3-4-5. This is my annual Daylight Saving Time post (and yes, Sen. Rubio of Florida reintroduced the Year-Round DST bill after it expired in the House last year). I notice that with school starting at 8:30, some students don't arrive until around 9:30 -- but these are students who arrive very late every Tuesday, not just during DST week.

As for the 1:59 class, in last year's Pi Day post I wondered whether 1:59 would be during a class or a passing period. Since school ends at 3:30 and each block is about an hour and a half, the last block of the day starts around 2:00 -- so 1:59 is during the passing to that block. If high schools were still allowed to start at 8:00, 1:59 would have been near the interior of that period.

Anyway since today is 2-3-4-5, that period that starts after 1:59 is fifth period. So it's this class, a Math III class, that gets most of the Pi Day goodies. I find two pies in the local supermarket (lemon meringue and sweet potato), as well as four individual pies from 7-Eleven for the top scorers on the most recent test (namely the Chapter 8 Test on DeltaMath).

And I even get them some pizza from the local pizzeria. It was one of those giant rectangular pizzas with 32 slices, since that's around how many students I have in that class. Unfortunately, due to its shape, the pizza has nothing to do with the number pi (but at least it's a pizza pie).

And of course, all throughout the period, I sing Pi Day songs. Today I choose "Pi Day Songs (All Day Long" (a "Jingle Bells" parody), "Pi Day Serenade" ("Alphabet Song"), "A Pi Day Carol" ("Row, Row, Row Your Boat"), "I'm a Little Number" ("Teapot"), "12 Decimals of Pi Day" ("Days of Christmas"), "Ludolph the Mathematician" ("Rudolph the Red-Nosed Reindeer"), and of course I had to wrap it up with "American Pi" (Bizzie Lizzie's "American Pie").

By singing "Ludolph" today, that makes this the second "Rudolph" parody I've performed this year, after "Rudolph the Statistician." (I won't post any lyrics in this post, since they're posted either elsewhere on my blog or elsewhere on the web.)

With all of this going on, do we do any actual math in Math III today? Well, today is the first day of "Boot Camp" -- aka SBAC Prep. Most Math III students are juniors who are required to take the state test this year. We're starting it now, even though the SBAC Math Test isn't until May. (The English SBAC is this week, while the California Science Test is next month.)

And, for the first time in this class, I actually use a resource from this blog. I go back to my annual SBAC Prep posts from 2021 and hand out the first eight questions in class, one to each group. The group then works out the problem on the front board (VNPS) and then the class takes a Gallery Walk around the room to get the other answers.

Today is Sunday, the third day of the week on the Eleven Calendar:

Resolution #3: We remember math like riding a bicycle.

On Pi Day, we might try to memorize the first several digits of pi. Unfortunately, there's no math involving pi today. Notice that Question #9 mentions irrational numbers including pi, but there are only eight groups in class today. (And Chapter 9 of the Math III CPM text is on trig, including radians and hence pi. But only Math III Honors classes study that chapter.)

It's my blogging tradition to post some Pi Day videos each year on the holiday.

1. Mathematical Pi:

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

2. "Pi Day video" by musicnotes online

One thing I notice about this song is that the rapper in this video is "Lamar Queen." While I don't perform this song today, I did do one of Lamar's other raps in Math I earlier this year -- namely "Slope Intercept Rap."

3. The Pi Day Song by Michael Bautista

I first posted this one to the blog last year.

4. Vi Hart's Pi Day video 2023

It's Vi Day -- the one day of the year when Vi Hart posts a video. This year, Vi posts a video claiming that the number pi contains only a dozen digits.

Vi would really like one of the songs I perform today in class -- "The 12 Decimals of Pi Day," which also includes only twelve digits of pi. (Notice that Vi already has a "Twelve Days of Christmas" parody -- "12 Days of Christmath.") On the other hand, we shouldn't tell Vi about "Ludolph the Mathematician," which states that Ludolph van Ceulen found 35 digits of the circle constant.

5. Viva la Pi Day by Jon Jacques

This is a parody of Coldplay's "Viva la Vida." Apparently, Jon Jacques is a high school teacher who's had his class perform a Pi Day parody in recent years. Here's his parody from last year:

6. I Learned About the Number Pi by Jon Jacques

The original song here is Marvin Gaye's "I Heard It Through the Grapevine."

7. Dr. Trefor Bazett

This is video from last year is the second video I've seen that demonstrates the Basel formula -- there's another interesting one by 3blue1brown.

By the way, shortly after 1:59, the principal visits my fifth period class to deliver Pi Day pies to all of the teachers. Of course, by this time I've already received his email telling me to visit his office after school to receive a document (which I correct assumed to be the pink slip). Thus the principal gives me a pie and a pink slip in one afternoon.

But once again, that's enough about the pink slip for today. That concludes my annual Pi Day post. I wish everyone a Happy Pi Day -- even if mine isn't exactly a happy one.

Chapter 6 Project (Days 125-127)

PLANTING TREES

First Verse:

Once I planted two trees in my backyard.

Evergreen grew 20 plus 6 per year.

Willow tree grew 40 plus 2 per year.

Which tree's taller? That is so hard.

Second Verse:

Ella decides Netflix or Hulu.

Netflix charges 14 plus 1 per film.

Hulu charges 10 plus 2 per film.

To save money what should she do?

This is the second song that I'm composing in 16EDL, our main scale for March and April. And it's the second 16EDL song in the AAA format, with verses only.

My original plans for today's fourth period Math I class include continuing with the elimination method, perhaps giving systems where one of the equations needs to be scaled (multiplied). But before school, the TOSA appears in my class and asks how we're doing with the Chapter 6 projects. I quickly poll my neighbor teachers and discover that they have already started the projects in their classes.

As it turns out, it all goes back to the WASC visit and coming up with a presentable lesson. One of my neighbor teachers wrote four word problems that could be solved using systems. The idea is to divide the class into groups and assign one problem to each group. Then the group members must create a poster -- the four sections of each poster are for the question, tables, graph, and algebraic solution (which only requires substitution, not elimination).

My neighbors planned on giving the project yesterday (the block day) as opposed to Monday. But as I wrote in yesterday's post, the WASC committee member arrived in my classroom on Monday -- and naturally, if he was in my room that day, then he proceeded to visit my neighbors that day too. Thus the project plans were foiled -- he saw the same thing in their classes that he saw in mine, namely an ordinary traditional lesson (albeit on substitution review, not elimination). They still started the poster project yesterday though.

During third period conference, I visit my "prep period buddy" -- the lone other Math I teacher who shares the same free period. As usual, I tell her that I definitely want to have our usual Math III tutoring session on Friday (especially with the Chapter 8 Test coming up on that same day). But today we discuss our Math I classes as well.

Recall that my prep period buddy taught the lessons in a completely different order. Last week she taught elimination, not substitution like the rest of us. And for WASC, she found some different word problems that are set up to make elimination more suitable than substitution. Her classes still work on them in groups, but on regular paper, not posters. Since poster paper doesn't need to be passed out, she does have them begin their group assignment on Monday. (Her classroom is out in the bungalows -- and WASC did visit her bungalow yesterday.)

I reveal to her how my neighbors taught the lesson, and she asks me to share the poster project document with her as well.

Since we're all eventually going to give this poster project, I do so as well. And so I completely change my own plans -- instead of finishing elimination, I start the poster project today in fourth period.

But notice that this leaves me out of sync with everyone else. My neighbors haven't started elimination yet, while my prep period buddy hasn't begun substitution yet. I've done a little of both, mainly because I was trying to follow the pacing plan, which shows a project as the last week of the chapter (a couple of weeks from now) as opposed to now.

Perhaps I should have known that the others would rearrange their lessons to impress WASC. Then again, perhaps we all should have taken WASC into consideration at the meeting when we first discussed the plan (and thus placed the project during WASC week in the first place). It's also notable that everyone thinks it's better to have a word problem project during WASC, when my original master teacher once told me to avoid word problems on visitation days. (Then again, that was over a decade ago, just before the advent of the Common Core with its added emphasis on problem solving.)

The one thing I said about projects on the blog is that I don't wish to do them on my own, since I'm not necessarily good at implementing them (hence my sixth resolution). Instead, I should follow my neighbors and heed their advice when it comes to projects. That's why I start the project today in fourth period (and tomorrow in my other Math I classes).

How many points should the poster be worth? The pacing plan also shows a Chapter 6 Test, so I don't necessarily want to make this project be worth as much as a test (unless the others change their mind and decide not to give the test). Today is the first day of the project -- I haven't decided yet whether I'll continue this on Friday or give the usual weekly quiz. If I skip the quiz, then I could make this project be worth as much as the quiz it's replacing would have been.

Today is Eightday on the Eleven Calendar:

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

And of course, those materials today include poster paper and markers. (Meanwhile, since Resolution #6 is about projects, note that Sixday was on Monday. None of us started the poster project on Monday, though since it's a multi-day project anyway, we really could have done so.)

Here's a link to today's Mocha code:

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

10 N=8

20 FOR V=1 TO 8

30 FOR X=1 TO 10

40 READ A,T

50 SOUND 261-N*A,T

60 NEXT X

70 RESTORE

80 NEXT V

90 END

100 DATA 16,4,8,4,11,4,10,4

110 DATA 8,4,13,2,10,2,15,4,9,2,9,2

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

This is the first song that I'm interpreting as 15EDL rather than 16EDL. This means that Degree 15 is the tonic -- this note is F, so the song is in F major. For 15EDL songs, Degrees 13 and 11 will always be interpreted as G and Bb respectively, since this fit the F major scale.

The chord riff for this song is a simple C-F (or C7-F). Actually, since Degree 12 (the note A) is avoided, we can get away with interpreting this song as F minor (with C-Fm or C7-Fm as the main riff). Since both Degrees 9 (D) and 8 (E) are including, this would be F melodic minor. Here is the complete melody of the single line: E(low)-E(high)-Bb-C-E(high)-G-C-F-D-D.

This song has just two verses, even though the project has four questions. The reason is that these questions come from one of my neighbor teachers, not the CPM text. I don't like to post anything created by a colleague on my blog, not even a song inspired by their work. Thus I only include two of the questions in the song version that I post here, though I might perform other verses in class. (In addition, one of the questions mentions the name of our school and that of a rival school -- which is also a school where I once subbed during the early days of this blog. But I don't post the names of schools where I work.)

This post is labeled Days 125-127. Monday is a teacher day with no students on campus. (I mentioned this earlier on the blog in explaining why this isn't quite a "Big March" stretch for the students -- but in a way it marks the midpoint of the "Big March" for teachers.) So my next post will be Day 128 on Tuesday -- which also happens to be Pi Day. And don't worry -- this is the last post in which WASC will be mentioned.

Lesson 6.3.1: Solving Systems by Elimination (Day 124)

SYSTEMS

First Verse:

Substitute x,

Then solve for y.

Substitute y,

Then solve for x.

Pre-Chorus:

x, y (four times)

Chorus:

Solve for x.

Solve for y.

Systems x.

Systems y.

Second Verse:

Eliminate x,

Then solve for y.

Eliminate y,

Then solve for x.

(to Pre-Chorus)

This is a repeat of a song I performed a few months ago -- I describe it in my October 19th post. Indeed, I played it in the fall for my Math III class -- and in that post, I even wrote that I'll be playing it again for Math I someday, once that class reaches the chapter on systems. Well, someday is today.

I don't provide a Mocha link or discuss the music theory behind the song, since I already do all of that back in my October 19th post. Keep in mind that the song is written in 10EDL -- the scale I was using for my October songs -- rather than the current 15 or 16EDL.

I think I'll do "A Day in the Life" today -- well, sort of. As I wrote in my last post, by now the observations for the principal and WASC are complete. So I'll write only about the observation periods.

Thursday:

11:45 -- Fifth period arrived. This was a Math III class.

Since I knew that my principal wanted to see real-world applications, I labeled this as Lesson 8.3.3 of the CPM Math III text, which is on applications of polynomials. But I didn't do the actual problem from that lesson of the text.

Instead, I went to the DeltaMath website and find some questions on real-world applications. These were on projectile motion, so they were all quadratic functions with -16 ft./s^2 as the leading term.

Then, since the principal wanted to see student interaction, I set up a DeltaMath assignment with exactly nine questions -- one for each group, with the same questions assigned to the whole class. Then I assigned one question for each group. Some of the questions were on the originally planned topic for the day, difference of squares (with difference of cubes delayed to 8.3.4 the next day), and one question was on projectile motion. (Notice that these are somewhat related -- an object dropped from 64 ft. follows the equation f (t) = -16t^2 + 64, which can be solved using difference of squares.) I had a member of each group describe the problem to the rest of the class so that everyone could complete the assignment on DeltaMath.

1:15 -- Fifth period left for lunch.

Monday:

9:40 -- Second period arrived. This was a Math I class.

The original plan was to teach the elimination method today -- and I stuck to it, despite several other Math I teachers rearranging the lessons to avoid teaching new material during the WASC visit. It was early in the period when the WASC committee arrived. This meant that the committee indeed saw me teach the new material. It was on Desmos, but the committee mostly saw the first example, when meant that they mostly saw me lecture since the kids were seeing elimination for the very first time.

10:35 -- Second period left.

1:25 -- Fifth period arrived. This was a Math III class.

Unlike Math I, in this class I really had completed the Chapter 8 material. So instead, I set up the first review assignment on DeltaMath and had the students work on it. Unlike the day of the principal's visit, today's assignment contained different problems for each student. I invited students to ask questions about the material, and I did some problems on the board. The WASC committee saw me call on random students using the TI, and I'd ask each student how to solve one step of a particular problem.

2:20 -- Fifth period left.

So as you can see, the principal and WASC kept observing the same classes -- second period Math I and fifth period Math III. As you already know, these aren't my best classes. Fortunately, at least second period respected the principal and WASC and grew quiet during the visits. Fifth period was a bit talkative for the principal, but they were quieter for WASC.

Today after school, the principal finally speaks to me about his observation. He said that he appreciated seeing the group interactions in fifth period that day. So even though the class was talkative that day, at least some of them were talking to each other (and me) about math.

As for the WASC observations, perhaps I could have taught elimination last Friday so that today would be guided practice for the students. Then again, many students in this class just sit there and do nothing during practice or groupwork time. Thus I masked the fact that the students don't work independently by teaching a new lesson (when they have a valid reason not to work independently -- they're learning new material) in front of WASC.

And in fifth period, maybe I should have assigned the same problems to all students on Monday, just as I had during the principal observation on Thursday. Indeed, today I do assign the same problems to all students as they continue reviewing for the Chapter 8 Test.

Today is Sevenday on the Eleven Calendar:

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

My students definitely worked hard to earn their grades on the progress report. And we as teachers worked hard during the WASC visit -- thankfully, the observations are finally over.

Lesson 6.2.3: Xylophones and Yodelers (Days 120-123)

YODELING SONG

(Make a long yodel sound at the start of each line.)

First Verse:

Yodelers!

Xylophones!

Gondola!

Let's get on.

Second Verse:

Yodelers!

Two bucks each

Xylophones!

Dollar each.

Third Verse:

Forty bucks.

That's our sum.

How many,

Are welcome?

This is the first song that I'm composing in 16EDL, our main scale for March and April. And it's the first 16EDL song in the AAA format, with verses only.

The song refers to Lesson 6.2.3 of the CPM Math I text, where students are asked to solve a system of equations to determine how many yodelers and xylophones there are on a gondola, based on how much it costs to transport them. It's obvious that the choice of "xylophones" and "yodelers" is a contrivance -- the words start with x and y, which are the natural choices for the variables.

Here's a link to today's Mocha code:

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

10 N=8

20 FOR V=1 TO 12

30 FOR X=1 TO 4

40 READ A,T

50 SOUND 261-N*A,T

60 NEXT X

70 RESTORE

80 NEXT V

90 END

100 DATA 11,16,12,4,16,4,14,8

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

As usual for AAA songs, the riff is captured in a single line repeated over and over. The first note is a long whole note to represent the "yodel," and then the other three notes are the three syllables that appear in each line.

The notes that repeat are Degrees 11, 12, 16, 14. Degree 11, the first note, is either Bb or B. In fact, when I yodeled, I likely trilled between both Bb and B. The other three notes are A-E-F#. As for the chords, I don't play any chords during the yodel. The other notes fit nicely into an F#m chord, a chord shared with the last 14EDL song "Factor Tests" despite this officially being a 16EDL song.

I've pointed out that true 16EDL might be impossible on our standard guitar. The only third available on the tonic in 16EDL is 16/13, which is a neutral third. Degree 16 is E, but neither E major nor E minor quite captures the 16/13 neutral third. It's possible that we might play E power chords, especially in 16EDL songs that lack the Degree 13 third.

Indeed, I suspect that I might end up interpreting Degree 15 as the tonic in some upcoming songs, which is an F. Then 15EDL is the first EDL with a tonic, major third, and perfect fifth (15:12:10), though since it's odd, it lacks an octave above the tonic. I'll probably continue to use Degrees 16-8 as the range for generating the tunes on the TI. A better range for 15EDL might be Degrees 20-9, which takes us from the C below the tonic F to the D above the tonic.

Of course, it really would have interesting if I could have played a xylophone for today's song, since the instrument is mentioned. The following link discusses the relation between bar length and pitch:

https://music.stackexchange.com/questions/16441/how-to-calculate-the-size-of-a-xylophone-bar-according-to-its-pitch

Based on this link, the frequency (in Hertz) of an xylophone bar is inversely proportional to the square of its length, not the length itself as on the guitar. Thus the bar lengths of an EDL xylophone don't form an arithmetic sequence -- instead, it would be a square root sequence.

Today is Day 120 of the school year -- the mathematical two-thirds point of the year. It ought to be the first progress report of the second semester -- and there are indeed progress reports this week. The fact that the second semester is longer than the first almost exactly cancels out the fact that the first progress report is slightly more than a third of the way into the semester.

Thus in first period Math III today, I give the Chapter 8 Quiz, in time to make this progress report. It was delayed in order to put some distance between this quiz and the earlier -- um, test that I'm tired of mentioning. And that takes us to the main topic of today's post -- planning for upcoming observations, with both the principal tomorrow and WASC next week.

As I wrote earlier, I could have had the principal observe sixth period tomorrow. Then he would have seen the xylophones and yodelers problem. While xylophones and yodelers aren't quite a "real-life" problem that's relevant to my students, making decisions based on cost is my underlying theme. So it might be something that's worth showing the principal. But in fourth period today, the activity doesn't quite go well. Too many students keep passively waiting for answers rather than discuss the questions in groups as intended.

And indeed, sixth period today is interesting. Due to the block is a day behind, so today they get the substitution lesson. But an interesting opportunity arises. The cheer coach has decided that, since the season is over, the cheer leaders are assigned to sixth period Math I classes in order to help out. Two of the girls are assigned to my class -- one of them is also a student in my fifth period Math III class.

But at the end of the lesson, very few students answer the Exit Pass -- and that's even with the two cheerleaders plus me to discuss the lesson. It's hard to tell whether it's because they don't understand the lesson, or because many of them are used to the path of least resistance. In any case, I'm glad that this isn't the class the principal will see -- an activity where no one is asking each other questions and hardly anyone is doing the work.

Instead, I choose the principal observation to be fifth period, a Math III class. I'm hoping that at least these older students will be more mature about collaborating with each other, though tomorrow also needs to be corrections for yesterday's quiz (and with progress reports looming, this will definitely be a big distraction). All that remains now is deciding what activity to give them.

As I wrote yesterday, tomorrow's scheduled Lesson 8.3.4 is on the difference of squares and cubes. But Lesson 8.3.3 contains a word problem -- cut four squares from the corners of a sheet and fold the remaining piece to make an open-top box. What square size maximizes the volume of the box?

Then again, today during third period conference, I visit my "prep period buddy" -- the lone other math teacher who shares my free period -- to discuss up this Friday's tutoring session. It appears that the principal will have a follow-up meeting during third period to debrief tomorrow's observation, so I won't be able to tutor our students on Friday.

But she also gives me some helpful tips for the principal's observation. She suggests setting up the Promethean board and having the students come up to solve problems there. If I were to do this, I might set up some polynomial division problems using the box method on DeltaMath. Each individual box needs to be filled in, so this is ideal for group collaboration. (The only other suitable question might be a polynomial graph, but unfortunately graphs don't seem to show up well on my Promethean.) All that's missing is a way to tie polynomial division to the real world (since that's my 1 score on the evaluation), which isn't easy. I'll have to make the final decision later tonight.

Today is New Year's Day and the first day of the week (Friday) on the Eleven Calendar:

Resolution #1: We are prompt and prepared.

And of course, I hope to be prompt and prepared for the observations. I can't waste the entire night typing on a blog, so I must end this post now. By the time I post next week on Tuesday, I will have had both the principal and WASC observations, so I can write about how those go.

Lesson 6.2.2: Solving Systems by Substitution/Day of Observation (Day 119)

RUNNIN'

by Pharrell Williams

First Verse:

Summertime in Virginia was a oven (oven)

All the kids eating ice cream with their cousins (cousins)

I was studyin' while you was playing the dozens (dozens)

Don't act like you was there when you wasn't

Runnin' from the man (man) runnin' from the badge (badge)

Don't act like you was there when you wasn't

Runnin' toward our plans (plans) in the judge's hands (hands)

Don't act like you was there when you wasn't

Pre-Chorus:

I know they say you crawl 'fore you walk

But in my mind I already jog

If I stand still I cannot get far

They want the Moon, I'm on Mars

Chorus:

Sometime my mind dives deep

When I'm runnin'

I don't want no free ride

I'm just sick and tired of runnin'

Some nights I cry

Cause I can see the day comin'

Together we'll fight

Oh, but no more runnin'

Second Verse:

You and I are not different from each other (other)

Shut our eyes, when we slumber I see numbers (numbers)

Black and white, we're computers, I ain't colored (colored)

Don't act like you was there when you wasn't

From runnin' to exams (exams) two jobs for a man (man)

Don't act like you was there when you wasn't

In the law of the land (land) the women were often banned (banned)

Don't act like you was there when you wasn't.

(to Pre-Chorus)

This song, which I've performed several times before, comes from the movie Hidden Figures. Last night was my annual viewing of that film. I usually try to watch it around this time of year -- the end of Black History Month or the start of Women's History Month (since Katherine Johnson was a black woman), or late February (the anniversary of John Glenn's orbital flight, February 20th, 1962). And so it makes sense to declare "Runnin'" to be the song of the day as well.

Here is a link to today's song on YouTube. (I might as well post a lyric video since I sing the original lyrics in class.)

Today is a blank day in the Eleven Calendar to mark New Year's Eve. (Recall that 363 days of the year fit into the weeks, with February 27th, 28th, and possibly the 29th as blank days.) On blank days, I usually default to the eleventh resolution:

Resolution #11: We follow all protocols for COVID.

And perhaps there won't be much use for the eleventh resolution these days. Today is the last day, not only of the Eleven Calendar year, but also of the three-year COVID emergency as declared by California leaders.

Meanwhile, my own personal eleventh resolution is on communication and conversations. And today I have a major conversation -- not with my students, not with my fellow teachers, but with the principal, as I receive my scores from the December 6th observation.

The principal speaks to me during third period conference, but not before he makes a quick informal observation during second period Math I. The lesson is on solving systems by substitution, and the lesson is not that difference from what he saw back in December --  a few examples written in the notebook followed by practice on Desmos.

You might notice that there's a song today despite an observation by the principal (as I worry that he might tell me to stop performing, just as my principal did last year). But I'd already prepared "Runnin'" before learning about the observation -- and as it turns out, he leaves midway during the period, just before my usual performance time. So I end up singing and playing guitar as originally planned.

Then during third period, the principal reveals my observation scores. On a four-point scale, most of my scores are 2's and 3's (where 2's are passing, but 3's are preferred). I do get a score of 1 in one area:

CSTP 1.3: Connecting subject matter to meaningful, real-life contexts. (Here CSTP means "California Standards for the Teaching Profession.)

This is a tricky one. A master teacher (yes, the same one who fell behind during the systems unit in Algebra I and ended up solving only by graphing, not substitution) once warned me not to do word problems -- which is what real-life problems become -- since they confuse and frustrate students. (This applies to observations not just from the principal, but other evaluators like the WASC committee. In fact, a fellow Math III teacher suggests that we finish Chapter 8 this week and spend next week on review, so that WASC doesn't see students frustrated with brand new material.)

On the other hand, recall that the TOSA for Math I gave me an underlying theme for this chapter -- using systems to make financial decisions. During certain lessons, I highlight some of the problems from the CPM text or Desmos that involve making a choice about spending money. But unfortunately, I don't include this in today's lesson.

The Desmos activity does contain one word problem -- if a fast train departs later than a slow train, how long will it take the fast train to catch up? But I skip this question for two reasons. First, it's not directly related to the overall financial theme. And second, I fear that the kids might take up more than half the period just to figure out how to write equations for this situation, and then we'd have to rush the actual solving by substitution -- then no one would learn anything.

At the end of the meeting, the principal tells me that he'll observe my class again on Thursday, to give me a chance to remediate some of my lower scores (especially that dismal 1 score). Forced to make a quick decision as to which class to observe, I end up choosing fifth period Math III. Since Thursday's block schedule goes 1-2-5-6, I know that I want it to be either fifth or sixth period so that I can use the earlier period as a dry run for the observation period. But now that I have time to reflect, I wonder whether fifth period is really a better option than sixth.

Looking ahead to the Math I and III pacing guides, I see that the Math I lesson planned for tomorrow and Thursday is on a certain word problem from the CPM text that we discussed during two previous Math I meetings. The question does mention money, and the entire lesson is devoted to this one problem (so the issue of spending too much time on an "anticipatory set" doesn't arise). Then again, the situation mentioned in the problem is a bit contrived, so it might not be "meaningful" enough for CSTP 1.3 given above. (I'll write more about this problem in tomorrow's post, since I'm teaching it to fourth period tomorrow.)

Meanwhile, the Math III pacing guide shows a difference of squares lesson on Thursday. Not even the CPM text attempts to tie this to any word problem. But there is a word problem in the previous lesson -- so I'm considering doing this on Thursday. (Actually, "considering" needs to be replaced by "planning on," since I already told the principal to observe the fifth period Math III class.)

Well, I know what I'm going to write about in tomorrow's post. Yes, I'll discuss my fourth period class as I usually do on Wednesdays, but I'll also look ahead to Thursday's observation. (Yes, I know -- the past few weeks were about nothing but the district Benchmarks, and now the next two weeks will be about nothing but observations, whether by the principal or the WASC committee.)

District Benchmark Test #2 (Days 115-118)

FACTOR TESTS

First Verse:

Remainder x minus r,

Remainder theorem says,

Remainder that equals,

Remainder f of x.

Pre-Chorus:

Theorems easier,

No need to divide.

Polynomial,

Plug r in to find.

Chorus:

Remainder! Factor! (x2)

Second Verse:

Factor x minus r,

Factor theorem says,

Factor zero is,

Factor f of x.

Bridge:

Testing x minus sign,

That means r's positive.

Testing x plus sign,

That means r's negative.

Today is the second district Benchmark Test in my fourth period Math I class, with the other classes taking their district tests tomorrow. Thus I sing "Benchmark Tests" in fourth period -- but it's also the perfect day for a Math III song.

This is the sixth song that I'm composing in 14EDL, our main scale for January and February. And it's the first 14EDL song in the ABCD format, with verses, a pre-chorus, a chorus, and a bridge.

Here's a link to today's Mocha code:

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

10 N=8

20 FOR V=1 TO 2

30 FOR X=1 TO 24*(V+1)

40 READ A,T

50 SOUND 261-N*A,T

60 NEXT X

70 RESTORE

80 NEXT V

90 FOR W=1 TO 4:SOUND 261-N*7,16:SOUND 261-N*14,16:NEXT

100 DATA 13,12,14,4,7,4,14,4,13,8

110 DATA 13,12,14,4,7,4,14,4,13,8

120 DATA 13,12,14,4,7,4,14,4,13,8

130 DATA 13,12,14,4,7,4,14,4,13,8

140 DATA 14,12,14,4,12,8,9,4,8,4

150 DATA 14,12,14,4,12,8,9,4,8,4

160 DATA 14,12,14,4,12,8,9,4,8,4

170 DATA 14,12,14,4,12,8,9,4,8,4

180 DATA 7,16,14,16

190 DATA 7,16,14,16

200 DATA 7,16,14,16

210 DATA 7,16,14,16

220 DATA 11,12,9,4,9,6,11,6,14,2,10,2

230 DATA 11,12,9,4,9,6,11,6,14,2,10,2

240 DATA 11,12,9,4,9,6,11,6,14,2,10,2

250 DATA 11,12,9,4,9,6,11,6,14,2,10,2

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

While this song includes the entire 14EDL scale, certain notes appear only in certain parts -- indeed, the chorus consists only of two tonic whole notes, a high F# and a low F#. The verse is the only part in which Degree 13 appears, while the bridge is the only part where Degrees 10 and 11 appear.

Thus we might interpret 14EDL as a pure Locrian scale, with Degrees 13 and 11 as G and B -- since these notes don't appear in the same part of the song, there's no need to worry about interpreting 13/11 as a major third. We might instead interpret is as a natural minor scale, since the only appearance of the diminished 7/5 fifth C is as a quick eighth note in the bridge.

Notice that I haven't actually performed this song yet. This tune corresponds to the second block of the week, which is tomorrow for both Math III classes. But the blogging schedule corresponds to the block days of fourth period, which isn't a Math III class (and got "Benchmark Tests" instead).

Thus I have yet to decide which chords to play with this song. I'm actually leaning more towards the minor key interpretation, so F#m will be the chord to play during the chorus.

(By the way, the FOR loops are written oddly. Line 30 is written so that the first verse plays ABC -- 48 notes -- and the second verse plays ABCD -- 72 notes. Line 90 squeezes in one more Chorus to play at the end of the song -- possible only because the Chorus consists of two whole notes repeated.)

The song indicates how the Math III lesson will soon be presented. The Factor and Remainder Theorems each have their own verses, and the bridge reminds us to switch signs (so r = 1 tests the factor x - 1, and r = -1 tests the factor x + 1). Because of syllables, I expect to shorten remainder to 'mainder to fit the tune.

There's not much to say about Math I in this post, since the focus is on the district Benchmarks. I will say that Chapter 6 is briefly covered on today's test just as Chapter 3 was on the first district test. This is why we covered Lesson 6.1.1 before the test. Still, there are a few questions from deeper in Chapter 6, but perhaps some students might remember a little about solving systems from Math 8 (once again, just like transformations in Chapter 3).

Today is Sevenday on the Eleven Calendar:

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

And hopefully my students are working hard to earn their scores on the Benchmarks today.

Lesson 6.1.1: Solving Systems by Graphing (Day 114)

WHEN THE MATH PEOPLE GO MARCHIN' IN

Chorus:

Oh when the math people go marchin' in,

Oh when the math people go marchin' in.

Oh how I want to learn about numbers,

Oh when the math people go marchin' in.

First Verse:

We're gonna learn, learn about systems,

Substitution and elimination,

Equations with x, y, and numbers,

Oh when the math people go marchin' in.

(to Chorus)

Second Verse:

We're gonna learn polynomials,

With degrees and roots and then.

Equations with x, y, and numbers,

Oh when the math people go marchin' in.

(to Chorus)

Well, I've obviously decided not to do a "Big March" song this year. Instead, I brought back another song from my repertoire, namely my "When the Saints Go Marchin' In" parody for Mardi Gras.

Of course, I originally wrote this song six years ago back at the old charter school, where I was asked to teach science in addition to math -- so my parody was "When the Scientists Go Marchin' In." Now that I'm no longer teaching science, there's no need to mention scientists in today's version.

Perhaps I should have replaced "scientists" with "mathematicians" -- referring to professionals who study either math or science. But it was already pushing it to replace the monosyllabic word "saints" in the original version to the three-syllable word "scientists" -- there's no way that the five-syllable word "mathematicians" was going to fit. So instead I choose "math people" (shades of the late John Berray).

The original "Saints" song contains the line "Oh how I want to be in that number." The word "number" fits with a math song, so I decide to retain it here. The other verses refer to the current Math I topic (systems of equations) and the current Math III topic (polynomials). This is something I did in my science parody as well -- include different verses for different classes. But I haven't done that much this year -- write songs with Math I and Math III verses. Today I perform the chorus in the key of D major and the verses in the key of A major.

The fact that today is both Mardi Gras and the first day of the Big March reminds us of the Andrew Usher Calendar. On that calendar, Easter is always between April 5th-11th and Presidents' Day between February 16th-22nd, so in any Gregorian year that matches these dates, Mardi Gras will be the day after Presidents' Day. Easter is on April 9th this year, which is in the Usher range.

Since Mardi Gras is such a big party day, sometimes I wonder whether this should become a four-day weekend on the Usher Calendar, so that the Big March begins on the same day as Lent. But then some might point out that people should spend Ash Wednesday in church, not school. And then it would be a short jump to just taking the entire week off, a Ski Week.

Today in my Math I classes, we begin Chapter 6.1.1 of the CPM text. There is a Desmos activity associated with this lesson -- the students must read a word problem, convert it to equations, graph the equations, and identify the solution. As it turns out, the word problems refer to scenarios mentioned in previous chapters.

For example, the first problem brings back our old typist friends Clara and Tabias. I already wrote a song based on this old problem -- "WPM" (written in 10EDL). So I briefly sing this song -- especially the second verse, starring both Clara and Tabias -- once again today. (So that's all the less reason to sing "The Big March" today, with two tunes already featured.)

The second problem refers to two bicyclists competing in the Big Race. No, I didn't write a "Big Race" song back in that chapter (unless we change "Big March" to "Big Race" -- but unfortunately, the ants weren't racing in the original song of which "Big March" is a parody).

The last problem is about two phone plans -- one costing a flat $25 (per month), the other costing $10 plus five cents per minute of long distance calls. This sort of question ties back to my underlying theme of this chapter -- solving systems to help make financial decisions.

Today is Sixday on the Eleven Calendar:

Resolution #6: We implement all parts of our assignments.

The students work on several different things today -- starting with test corrections from the Chapter 5 Test that the kids took last week. They must work on their Desmos activities for the main lesson, as well as prepare for the Chapter 5 notebook check on Friday (since I neglected to collect the notebooks on the day of the test).

Second period Math I is slightly better behaved today than last Friday. Still, two objects are thrown in the classroom, resulting in a pair of extra questions on the homework. I begin to complain that they shouldn't throw things in class, especially with the WASC visit looming -- the evaluators won't want to see objects being thrown in class. But my complaints contain the seeds of an argument -- and the WASC evaluators won't want to see an argument break out in class either.

So I'm forced to stop myself from arguing. Adding questions to the HW (or sending out individual throwers if they're caught to the office) is the best I can do in this situation without argument.

Fourth period, of course, doesn't have the misbehavior of second period. Still, I mess up when I open the test corrections on DeltaMath but fail to unlock the original test, meaning that two absent students from Wednesday are unable to take the test.

Since I mention the Math III lesson in the song, I might as well bring it up here as well. Today the students are learning polynomial division -- and we've been asked to teach neither the long division nor synthetic division methods. Instead, we teach them the box method, which is often used to multiply polynomials (especially when they're aren't both binomials), but in reverse for division.

Chapter 5 Test (Days 111-112)

SEQUENCE TESTS

First Verse:

Same difference, it's arithmetic.

Find nth term, it's arithmetic.

Distinguish, it's arithmetic.

Find difference, it's arithmetic.

Pre-Chorus:

Don't forget solving,

Two step equations.

Don't forget solving,

Three step equations.

Chorus:

Test out the sequence.

See how it does go.

All common difference,

Or common ratio.

Second Verse:

Same ratio, it's geometric.

Find nth term, it's geometric.

Distinguish, it's geometric.

Find ratio, it's geometric.

(to Pre-Chorus)

This is the fifth song that I'm composing in 14EDL, our main scale for January and February. And it's the first 14EDL song in the ABC format, with verses, a pre-chorus, and a chorus.

As I explained in yesterday's post, today I give the Chapter 5 Test to my fourth period Math I class. It's the rare test that I don't give on a Friday -- indeed the rare test given on a singing day. Therefore the song summarizes the contents of the test. The pre-chorus mentions solving equations because two of the sixteen questions on the test are review from Chapter 1.

Since this is also one of the few tests given on a blogging day, let me discuss how the fourth period kids are doing on the test so far. Naturally, most students are getting the first two questions right -- these questions simply ask for the generator of an arithmetic or geometric sequence and are designated "Level 1" on DeltaMath.

The two most difficult questions both involve geometric sequences with common ratio less than 1 -- for example, a sequence like 32, 16, 8, 4, ... (the bouncing ball sequence from a couple weeks ago). And it's understandable -- students are more likely to think in terms of dividing terms by two than multiplying by one half. They might even have trouble identifying this as a geometric sequence, since the rapid increase associated with geometric sequences isn't visible.

Here's a link to today's Mocha code:

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

10 N=8

20 FOR V=1 TO 2

30 FOR X=1 TO 72

40 READ A,T

50 SOUND 261-N*A,T

60 NEXT X

70 RESTORE

80 NEXT V

90 END

100 DATA 11,6,14,6,9,4,7,2,12,2,10,8,11,2,9,2

110 DATA 11,6,14,6,9,4,7,2,12,2,10,8,11,2,9,2

120 DATA 11,6,14,6,9,4,7,2,12,2,10,8,11,2,9,2

130 DATA 11,6,14,6,9,4,7,2,12,2,10,8,11,2,9,2

140 DATA 12,12,8,2,10,2,10,4,14,12

150 DATA 12,12,8,2,10,2,10,4,14,12

160 DATA 12,12,8,2,10,2,10,4,14,12

170 DATA 12,12,8,2,10,2,10,4,14,12

180 DATA 14,12,8,2,10,2,11,4,7,12

190 DATA 14,12,8,2,10,2,11,4,7,12

200 DATA 14,12,8,2,10,2,11,4,7,12

210 DATA 14,12,8,2,10,2,11,4,7,12

As usual, don't forget to click on Sound before you RUN the program.

This song omits Degree 13. I'm much more likely to interpret Degree 11 as B (as opposed to Bb) in a no-thirteens song like this one, since there's no need to make 13/11 sound as a minor third. (I do the same in most of my 12EDL songs where there is no Degree 13.)

And indeed, in the verse I play the riff Bm-D7, since the first three notes sound like B minor (provided Degree 11 is interpreted as B). For the pre-chorus I play the riff Am-D7, while for the chorus I play a ringing F# major chord. The chorus melody goes (low)F#-E-C-B-F#(high), but only the F# notes stand out in the melody.

There are ways to chord this song if we are more consistent in interpreting 14EDL. Recall some of those chords that I mentioned in previous posts -- F#m7b5 (the half diminished chord F#-A-C-E) and F#7alt (which usually means F#-A#-C-E, provided Degree 11 is Bb or A#). The former chord fits in the pre-chorus and the the latter in the chorus.

In fact, if we consider the half diminished chord to be the "tonic" (or "home") chord of 14EDL, we even might reverse the pre-chorus and chorus melodies so that we can end the song on that chord. The rhythms of the pre-chorus and chorus are identical, so there's no need to change the lyrics here.

Only Math I classes are getting this song. Math III classes will hear a different but familiar song:

Why do we take Benchmark Tests?
The six months are done so let's
See how much we know, know know!
It's some new stuff on Benchmark Tests.
If we don't know it, we take a guess.
'Cause there's still time to grow, grow, grow!
The teacher sees our Benchmark Tests,
Knows what to teach now more or less.
That's the way to go, go, go!

That's right -- the district Benchmark testing window has opened. Only Math III classes are taking their district tests this week -- Math I won't test until next week. (Notice the similarity of the songs -- it's "Benchmark Tests" instead of "Sequence Tests," with both songs describe tests the students are taking.)

Today is Elevenday on the Eleven Calendar:

Resolution #11: We follow all protocols for COVID.

But for me, Elevenday means it's time for me to focus on communication. I wrote a little about my efforts to communicate with my students in yesterday's post.

As for communicating with my fellow teachers -- well, today I was hoping to speak during third period conference to the lone other math teacher with the same prep period. (I've mentioned her a few times on the blog before -- she teaches only Math I.) But unfortunately, she's out today.

There's also an upcoming Math I teacher meeting, led by the TOSA. So perhaps I can communicate with others during that meeting (including perhaps my prep period buddy).

Notice that today's post is labeled "Days 111-112," covering only today and tomorrow. That's because Friday is the seventeenth -- my monthly posting day for "A Day in the Life." Therefore my next post is scheduled for Friday.