Lesson 5.1.1: Intro to Arithmetic Sequences (Days 97-100)

COMPOUND INTEREST RAP

First Verse:

Nowadays we got money on our minds,

Devisin' ways to pull cash all 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.

Chorus:

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

Yeah, yeah, yeah! (x2)

Second 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 Chorus)

Third 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 Chorus)

This is the second of two songs that I've previously posted to the blog and am now performing for my Math III classes. And -- just like "Whodunnit?" -- I first posted the song in January 2020.

Here is a link to the YouTube video from which I first found the song. Even though I posted the video three years ago, I never posted the lyrics until today. (The lyrics appear as video subtitles, but now we can copy and paste from this post as well.)

Like most hip-hop songs it has a simple riff -- D and A repeating. It was difficult for me to discern from the video whether these are major or minor chords -- I suspect that these could be power chords (which lack the third). When I perform it in class today, I try to use minor chords, Dm and Am. But since I keep jumping my fingers between the strings quickly, the Dm ends up sounding like DmMaj7 (in other words, D minor/major seventh), which sounds quite nice here. (Am-E is the riff produced by moving the fingers the other way, and I use that riff in "Whodunnit?")

I play this song in my fourth period class today, even though it's a Math I class. Due to the block schedule, my first performance of any song will be in Math I, even if it's a Math III song. Today's first period Math III is still doing "Whodunnit?" and fifth period Math III doesn't meet today. Tomorrow is the day when both Math III classes meet -- and that's when I'll give the compound interest lesson.

But believe it or not, this song -- like yesterday's -- has a Math I connection. As you can see by the title of this post, today we are starting Chapter 5 of the CPM text, which is on sequences. While today's lesson is on arithmetic sequences, geometric sequences appear later in Chapter 5. And one application of geometric sequences is -- you guessed it! -- compound interest. (For some reason, simple interest is never presented as an application of arithmetic sequences. Perhaps this is because, as the rap tells us above, the real banks pay interest on interest -- compound interest.)

This goes back to the Common Core standards. Indeed, notice that I first performed this song three years ago in an eighth grade Algebra I class in a district where Algebra I, Geometry, and Algebra II are still taught. In an Integrated Math setting, geometric sequences are perhaps the second Math I topic that's not taught in Math 8 (with the first being a deeper study of slope) -- otherwise Math 8 and Math I cover nearly identical material. (Before the Common Core though, geometric sequences weren't taught until Algebra II.)

Anyway, if we reach a compound interest example in Math I these next few weeks, I might go back and perform this song for the freshmen again. Thus today's song has become my first Chapter 5 song. And since we reach the new chapter today, I'm only half a week behind the official Math I pacing guide.

There's one more connection to songs that I wish to make here. I almost never write about my sixth period Math I class on the blog, since due to the block schedule, this class (like first period) never lines up with the songs I post here, but is always a day behind.

So today, I sing "Whodunnit?" in sixth period. But for the past week or so, one student has thrown glue sticks (intended to be used to glue interactive notebook pages) around the classroom, and I'm been trying to figure out who it is. After threatening to add questions to the homework, one guy finally admits who the culprit is (and it was another guy, the one I've been suspecting all along). Therefore -- on the day that I perform "Whodunnit?" -- I'm able to solve a real "Whodunnit?" mystery in my room.

Today is the first day of the week on the Eleven Calendar. (Sometimes I refer to the first day of the week as "Friday," intending that this would be the new Muslim Sabbath on my calendar.)

Resolution #1: We take pride in our own work & cite our sources.

These days, "cite our sources" isn't as important as it was last year, when I had a monthly current event in my Ethnostats classes. Still, the students should take pride in their own work (especially for deeper assignments such as last week's project).

Notice that Day 100 is right around the corner. (My next post is scheduled for Tuesday, Day 101, and so I acknowledge Day 100 today.) Yes, I'm aware that Day 100 is much more significant in elementary schools than in high schools, but I acknowledge the milestone on my blog anyway.