Lesson 1.3.1: Simplifying Exponential Expressions, Continued (Day 34)

MISTAKE, RIGHT WAY

First Verse:

Mistake? h cubed times h fourth.

Mistake? h to the twelfth.

Right way! Add little numbers.

Right way! h to the seventh.

Chorus:

Laws of exponents for you.

Laws of exponents for me.

Laws of exponents stay true.

Laws of exponents, be free!

Second Verse:

Mistake? x squared to the fourth.

Mistake? x to the sixth.

Right way! Times little numbers.

Right way! x to the eighth.

(to Chorus)

This is the sixth song that I'm writing in 10EDL, our main scale for September and October. The next few 10EDL songs will be written in ABAB format, with verses and a chorus.

After the group test last week, we're back on track with the exponents lesson in Math I. The lyrics come directly from the CPM text, an exercise where the students must identify common errors and fix them. Thus the song mentions both the "mistake" and the "right way."

Here's a link to the Mocha code for the song:

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

10 N=8

20 FOR V=1 TO 2

30 FOR X=1 TO 39

40 READ A,T

50 SOUND 261-N*A,T

60 NEXT X

70 RESTORE

80 NEXT V

90 END

100 DATA 10,8,6,8,6,4,9,4,6,4,8,4

110 DATA 10,8,6,8,6,4,9,4,6,4,8,4

120 DATA 10,8,6,8,6,4,9,4,6,4,8,4

130 DATA 10,8,6,8,6,4,9,4,6,4,8,4

140 DATA 5,4,9,4,6,4,6,2,6,2,7,8,9,8

150 DATA 5,4,9,4,6,4,6,2,6,2,7,8,9,8

160 DATA 5,4,9,4,6,4,6,2,6,2,7,8,9,8

170 DATA 5,4,9,4,6,4,6,2,6,2,7,8,9,8

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

This tune contains perhaps our most complex chorus so far, with seven notes that must be repeated, hence it's the most tedious to type. The notes in the chorus are high C-D-A-A-A-F#-D, with the first five notes corresponding to the syllables in "Law of exponents."

The guitar riffs I play with this song are C-Am in the verses and C-D(7) in the chorus. At least one other chording of this song is possible -- perhaps something like Am-Dm in the verse and Am-D7 in the chorus, but then we'd lose the tonic chord C.

Meanwhile, in Math III we return to graphing quadratic formulas. This means that I perform "Quadratic Weasel," with the new bridge on parabola properties. One problem is that my song focuses on the standard form of the quadratic (like the Quadratic Formula itself), while the lesson itself deals more with the vertex form of the quadratic. This reflects a transition that started with the advent of Common Core -- back when I took Algebra I and II as a young student, the vertex form wasn't taught, and we needed x = -b/(2a) to find the x-coordinate of the vertex. But now the focus is more on transformations, including translations, from the parent graph, and so the vertex form y = a(x - h)^2 + k is seen more.

So perhaps I need a new song that focuses on the vertex form of a parabola. But most of my current songs are on Math I material, not Math III, and so I likely won't get around to it.