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/
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.
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