Wednesday, February 1, 2023

Lesson 5.2.1: Intro to Geometric Sequences (Days 102-105)

ARITHMETIC AND GEOMETRIC

First Verse:
One, three, five, arithmetic!
Two, four, six, arithmetic!
Three, six, nine, arithmetic!
Four, six, eight, arithmetic!

Chorus:
Two, four, six, eight,
Arithmetic appreciate.
Two, four, eight, sixteen,
Geometric insight is keen.

Second Verse:
One, three, nine, geometric!
Two, four, eight, geometric!
Three, six, twelve, geometric!
Four, six, nine, geometric!
(to Chorus)

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

Today in fourth period Math I, we discuss geometric sequences in earnest. The Desmos lesson for today begins with a classic question -- which would you rather have, a million-dollar lump sum, or one penny on the first of the month and double it for the entire month? The activity actually states that the penny is given on the first of February -- today's exact date. (The creator of this Desmos is another teacher at our school who knows that Chapter 5 is usually taught around now.)

One guy immediately figures out that he'll earn more money if he takes the repeatedly doubled penny -- indeed, he'd earn about $1.3 million on February 28th. (I wonder whether he's heard of this question before, since it is a classic.) Notice that he would have earned even more money if this were still January (or another 31-day month) rather than February -- on the 31st, he'd have over ten million dollars, a rather great sum indeed.

Afterwards, we define and discuss geometric sequences. Keep in mind that this Friday's quiz will be on arithmetic sequences only. While this lesson should be easier than the Stats of Chapter 4, many students are struggling with explicit formulas of arithmetic sequences. It's hard to tell whether they are confused, or simply not paying attention.

Today is Eightday on the Eleven Calendar:

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

Today I don't require the students to show ID's to check out Chromebooks in fourth period. But I catch one student using the wrong Chromebook, and so ID's will be required on Friday, the day of the quiz.

Here is 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 48
40 READ A,T
50 SOUND 261-N*A,T
60 NEXT X
70 RESTORE
80 NEXT V
90 END
100 DATA 13,8,7,4,9,4,12,2,8,2,9,12
110 DATA 13,8,7,4,9,4,12,2,8,2,9,12
120 DATA 13,8,7,4,9,4,12,2,8,2,9,12
130 DATA 13,8,7,4,9,4,12,2,8,2,9,12
140 DATA 13,8,9,8,13,8,9,8
150 DATA 13,6,12,6,7,2,12,2,13,6,12,6,7,2,12,2
160 DATA 13,8,9,8,13,8,9,8
170 DATA 13,6,12,6,7,2,12,2,13,6,12,6,7,2,12,2

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

When I generated this song, Degree 10 was avoided once again -- but so was Degree 11. So while I could have made this into another Phyrgian Dominant song, I didn't want this song to sound too much like yesterday's (especially with my having trouble barring the correct frets).

Instead, the note D at Degree 9 dominates, so I made this a D major song just like "Correlation." As for Degree 13, it's better in this situation to treat it as G# rather than G. That's because 13/9 isn't a true perfect fifth (that would be 3/2), so I'd rather use G#-D (in the Chorus) for 13/9 instead of G-D.

Also, note that in the Chorus, I didn't make Lines 140-170 identical as usual. That's because I couldn't resist including the most well-known arithmetic sequence to appear in a rhyme -- "Two, four, six, eight, whom do we appreciate?" The 13/9 sequence G#-D-G#-D fits the sequence itself, while the more complex line fits the "appreciate" lyrics: G#-A-F#(high)-A.

The riff for the verses now becomes E7-A7-D (just like "Correlation"), while the chorus features E7 during the sequence line and A7 during the "appreciate" line.

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