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/
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:
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.
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