Chapter 11 Review (Day 119)

Today I subbed in a high school special ed class. It's in my first OC district -- and yes, it's in the room I covered in my February 11th post, and the teacher for whom I subbed several times last year, including the last three days before the pandemic.

Unlike February 11th, which was an even period today, today is an odd period day. This teacher has two English periods each on odd and even days. Sixth period is his conference period, and so he has one more class on odd days -- and that class just so happens to be Business Math. (No, he didn't teach a Business Math class last year.)

Since there's a math class today, that means I will do "A Day in the Life" today, even though there are aides covering the classes.

9:00 -- This is the district where "first period" really means zero period, and so odd days begin for most students (including most special ed students) with third period. It is a senior English class.

The students are still reading the same novel from my February 11th post -- The Great Gatsby. They have now reached Chapter 6. We already know that this teacher has very small in-person classes, due to the combination of it being a senior class (higher grades tend to opt out of hybrid) and a special ed class (which was smaller even before the pandemic).

I haven't performed "Big March Song" for this class yet, and so I sing it today. Once again, some of the seniors do remember me from last year.

9:55 -- Third period leaves for snack break.

10:10 -- Fifth period arrives. This is the Business Math class.

The students learn about stocks and bonds today. There actually isn't much calculation today -- instead, they learn the difference between them and why anyone would want to invest in them. The assignment is some sort of Google Slides assignment where they answer questions. This class has only one student who attends in the classroom -- a junior guy.

I tell the students about how I, as a young sixth grader, participated in a stock market project where we "purchased" stocks and followed their progress in the newspaper. It appears that one of the slides requires these students to do something similar, but the aides tell them to wait for their regular teacher to explain this project in more detail.

10:20 -- Suddenly, the regular teacher appears in the Zoom meeting. He needs to meet with one of the students to prepare for a special ed meeting.

I ask him about his guitar and ukeleles, and he tells me that they're still in his old classroom -- the same room where I lost and found my old songbook. (I'll consider looking for them the next time I sub in the self-contained class that's there now.)

Then I try setting up a breakout room on Zoom for the regular teacher and student -- but I end up pushing all the other students into another room as well. The aide must go to the other room in order to send them back to the main room.

Last year, I once subbed in another Business Math class (not this one), and there was a special song that I sang that day -- "Compound Interest Rap." Thus I perform this rap again today.

11:05 -- Fifth period leaves and seventh period arrives. This is a junior English class.

As we saw on February 11th, the juniors are also reading The Great Gatsby. There are three in-person students, including the same guy from Business Math.

I sing "Big March Song" again, especially since one in-person guy (and some of the online students) already heard "Compound Interest Rap" earlier.

12:05 -- Seventh period leaves for lunch.

Normally, after lunch is academic support. The aides inform me that the regular teacher usually cancels academic support on sub days, and so I don't need to stay. (Notice that February 11th was a minimum day with no academic support for anyone, so I didn't know that this is his policy.)

Today is Saturday, the second day of the week on the Eleven Calendar:

Resolution #2: We make sacrifices in order to be successful at math.

I tell the students this in the Business Math class. I also tell them that they must make sacrifices and work hard in order to be successful in English -- especially during the Big March when many of us are always tired. (I say this just before I sing "Big March Song.")

Yes, I include the "music" label today on a day when I sub for the guitar/uke teacher. It's not for any guitar song though, but so I can post "Compound Interest Rap." As it turns out, I've never posted the lyrics to the blog (and thus had I not found my old songbook in this teacher's old room, I wouldn't have had the words for today's performance).

"Compound Interest Rap" by Scalar Learning:

COMPOUND INTEREST RAP

1st Verse:

Nowadays we got money on our minds,

Devisin' ways to pull cash on the time.

It's a common situation in the western world,

Building dreams with steam and then we make it work.

A lot of folks pullin' all the right strings,

Make a dime on a feelin', pull a dollar on the whim.

But once we get that bank roll flowin',

The interest rate is how we keep it growin'.

I know a lot of you wanna keep it simple,

Percentage and time is all you tryin' to get through.

Well that's simple interest and it's pivotal,

Rate times the number of years and the principal.

That's the way we calculate our funds,

While the money stays in, the beat goes in.

But next verse we take a real look into this,

A lesson on finding the simple interest.

Refrain:

A equals P times 1 plus r over n, to the nt, yeah, yeah, yeah, yeah!

2nd Verse:

Step back to the terms of the simple,

To comprehend this piece is critical.

Principal, it's not about a head of school,

Instead it represent the initial cash pool.

It's like if we deposit a quick grand,

With a rate of interest set to 10 percent.

We leave it be for 5 years and it grows,

But just how much? I'll tell you how we know.

We take 1000 times point 10,

Which is the decimal equivalent of 10 percent.

And multiply again 5 to unlid,

The interest earned, which is 500.

It's pretty simple to follow these steps,

But the real banks pay interest on interest.

To make true life calculation,

Compound interest is what you makin'. (To Refrain)

3rd Verse:

The time has come, and we can move another level,

To answer the question that we came to settle.

Compound interest, how does it work?

As the money grows we recognize the new net worth.

So let's push back to the hook,

And jot down what we just got to make it work.

A is the final amount of cash,

And once again big P is the principal stash.

We got t for years and r for interest rate,

Small n is the number of compounds that we take.

Let's plug it all in, same example as before,

We got a G in the bank, 10 percent on a roll.

We keep it in for 5 years and we compound twice,

We get 16 hundred 28 89.

With the simple rate we had 15 bills, right?

But this way it's another 1 28 89. (To Refrain)

Today is the review for the Chapter 11 Test. This is what I wrote last year about today's lesson:

In particular, this test is based on the SPUR objectives for Chapter 11. As usual, I will discuss which items that I have decided to include and exclude, and the rationale for each:

One major topic that I had to include is coordinate proof, as this appears in Common Core. I did squeeze in some coordinate proofs involving the Distance or Midpoint Formulas, but not slope. So therefore, the coordinate proofs included on this review worksheet all involve either distance or midpoint, not slope. The only proofs involving parallel lines had these lines either both vertical or both horizontal. Once again, a good coordinate proof would often set it up so that the parallel lines that matter are either horizontal or vertical.

What good are coordinate proofs, anyway? Well, a coordinate proof transforms a geometry problem into an algebra problem. Sometimes I can't see how to begin a synthetic geometry proof, so instead I just start labeling the points with coordinates and see what develops.

So coordinate geometry reduces an unknown problem (in geometry) to one whose answer is solved (in algebra, in this case). Mathematicians reduce problems to previously-solved ones all the time -- enough that some people make jokes about it:

http://jokes.siliconindia.com/recent-jokes/Reducing-the-problem-nid-62964158.html

I ended up including six straight problems -- Questions 8 through 13 from U of Chicago. Most of these questions are from Objective C -- the Midpoint Connector Theorem. The text covers this here in Chapter 11, but we actually covered it early, in our Similarity Unit, because we actually used the Midpoint Connector Theorem to start the proof of the basic properties of similarity. Still, this was recent enough to justify including it on the test.

Next are a few center of gravity problems. This is straightforward, since all we have to do is average the coordinates. Afterwards are a few midpoint problems, including two-step questions where one must calculate the distance or slope from one point to the midpoint of another segment.

Then there are a few more coordinate proofs where one has to set up the vertices -- notice that some hints are given in earlier questions.