Tuesday, March 3, 2020

Lesson 12-3: Properties of Size Changes (Day 123)

Today I subbed in a high school special ed English class. Since it's not math and some of the classes have an aide, there is no "A Day in the Life" today.

This is my third visit to this classroom and second this school year. I wrote about my most recent visit in my October 22nd post.

Both senior and juniors have stories to read plus questions to answer. (The seniors are reading about 1990's Alaska, while the juniors are reading about 1960's Vietnam.) Unlike my October 22nd visit --when there weren't enough copies of the novel and the students refused to go to the library to check them out -- today the stories have been uploaded onto Chromebooks.

The regular teacher, who has on-campus meetings all day, warns me about the sixth period juniors. In October, some of these students were throwing objects. Today, many of these students play the "loud music on Chromebooks" prank -- effective because it's impossible to know who's doing it. Students also play another common game -- if I call them out on their bad behavior, then they claim that I am the one stopping them from doing the reading by interrupting them.

On my calendar, today is Sunday, the third day of the week:

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

Once again, there's not much math today, so it's hard to tie this resolution in. So many other rules end up being more relevant today, including the sixth (on heroes) and ninth (on time management). In particular, the senior classes had both length restroom breaks and two students leaving early, and so I attempt to block sixth period from doing the same. But it doesn't work -- one junior still spends 15 minutes at the restroom, and when I tried to block students gathering at the door from leading early, they respond by hitting/pushing each other.

I end up with four names on the bad list -- three for pushing each other in line (including the guy who was gone for 15 minutes) and one for writing his name on the good list (which gives him grade points for reading that he doesn't do) while I'm distracted with all the shoving.

But also relevant are the seventh and eighth rules on singing for math and procedures. Today I sing my default song for this time of year, "The Big March." During tutorial, I add in "Angle Dance" and "All About That Base and Height" by request.

Oh, and I play these songs on the guitars and ukeleles that this teacher keeps in his classroom. I wrote about these instruments some in my October 22nd post as well.

This is a good time to add "music" to this post and write more about the ukelele. As a guitar player who's never played a uke outside of this classroom, it's interesting to compare the string instruments.

(That's right, I'm posting music twice in a row -- turning Super Tuesday into a music/color post, and now the ukelele.)

I've discussed on the blog that the standard guitar tuning for the six strings is EADGBE -- that is, the lowest string is E, the next (fifth) string is A, the fourth is D, and so on up to the high E string. Well, the ukes in this classroom have four strings, GCEA. The top three uke strings play a perfect fourth higher than the top three guitar strings, but the fourth string (G) is actually more than an octave above the fourth guitar string (D). Indeed, the G is musically higher than the C and E strings, so that the strings don't go low to high as we move left to right.

Despite this, the fact that the four uke strings are each a fourth higher (on the scale at least, if not in the octave) than the top four guitar strings helps us when making chords. For example, the D major chord on the guitar is fingered on the top four strings as DADF#. If we finger the four uke strings the same way, then the resulting chord sounds as a G major chord, GDGB. Likewise, the D minor and D7 guitar chords sound as G minor and G7 chords on the uke.

As for guitar chords of five and six strings, these convert to the uke simply by dropping the fifth and sixth strings. Thus the A, B, and C guitar chords become D, E, and F uke chords. And E and G guitar chords become A and C uke chords. In converting Em and G guitar chords, the resulting Am and C uke chords require only one finger on the fretting hand (G at the second fret for Am, and A at the third fret for C). This makes playing "The Big March" on the uke convenient -- I play it today in the key of E minor (including a G chord) on the guitar, and the key of A minor (including a C chord) on the guitar.

Notice that since the uke has only four strings, the barre is never needed. Thus the B major guitar chord, ordinarily played with a barre at the second fret (xBF#BD#F#), converts to an E major uke chord as (BEG#B) with the index finger on the top string only, second fret and the other three fingers on the other three strings, fourth fret. The Em uke chord (BEGB) is slightly easier to play.

By the way, I'm also wondering whether my 18EDL fretting system that I've referred to in previous posts might work better with four uke strings rather than six strings. I'm still working on whether this will work out.

Lesson 12-3 of the U of Chicago text is called "Properties of Size Changes." In the modern Third Edition of the text, properties of size changes appear in Lesson 12-1.

This is what I wrote last year about today's lesson. Admittedly it isn't much.

Finally, here are the Geometry worksheets for today. They are based on Lesson 12-3, with an extra page for the proof of the Dilation Distance Theorem -- this proof comes directly from PARCC.

Meanwhile, the old first page makes an reference to FTS (an old Hung-Hsi Wu proof). Even though I no longer include Wu's FTS as part of the lesson, it's actually too much work to redo the entire page just to get rid of two little FTS mentions (especially when I'm already posting this late). So you'll just have to ignore FTS.


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