Lesson 4.1.0: Fit Fights (Day 87)

ONE BILLION IS BIG

1st Verse:

Have you seen the headline? We did OK,

We sold a million records in just one day.

That's a thousand times a thousand sold,

That's plenty of vinyl, a million whole.

A million dollar bills reach for the sky,

Stack 'em about three hundred feet high.

A billion dollars is a thousand times more,

A lot more money than we bargained for.

Chorus:

One million is big,

One billion is bigger.

One thousand times one million,

That's one billion.

2nd Verse:

We're getting kinda hungry for our favorite food,

Hey, what do ya say? Are you in the mood?

Let's satisfy our special taste,

And get some lunch at the burger place.

See that sign? "One billion served!"

Beat box, that's a lot of hamburgers.

One thousand times, when ya order fries,

A million times one thousand apple pies.

(to Chorus)

3rd Verse:

If we multiply one million by ten, How close are we to one billion then?

If we take a look, we will see, We got a way to go, my friend Markie Dee.

If we multiply by one hundred this time, Let's take a look, and we will find,

That we're not even halfway there, We need a lot more to be a billionaire.

If we order one billion cheeseburgers, And eat one million cheeseburgers,

It would be enough to knock us off our feet,

'Cause we'd still have almost one billion burgers to eat.

One million's not even one percent of one billion. Wow!

(to Chorus)

Yes, I do perform "One Billion Is Big" a second time in honor of the Mega Millions jackpot. It's really only the first time I've performed it in Math I classes -- in November when the Powerball jackpot was that high, I rapped it only in Math III.

Even though "One Billion Is Big" is a rap with its chorus as the only melodic section, it's a great song to play on the guitar as my first post-vacation song. During those idle weeks, the guitar fell out of tune -- so by playing today's song, I get to retune my guitar ahead of attempting any 14EDL songs.

In second period, I open up the Desmos lesson. It is labeled as "Lesson 4.1.0" of the CPM text -- that is, it's an introduction to Section 4.1. But as I try to present the Desmos, it becomes painfully clear that many kids are confused by the whole idea of line of best fit. Yes, the red line is close to the the blue dots, but what do red lines and blue dots have to do with anything?

So I pause the Desmos activity and switch to the notebooks instead. With first semester grades still fresh on our students' minds, my example is a scatterplot of days absent vs. test scores. I draw the same scatterplot twice and drew a different line on each one, then asked, "Which is the better fit? Suppose I were to pay a billion dollars for the line of better fit, then which line would I pay for?"

Of course, mentioning a billion dollars is an excuse to tie this to the "One Billion Is Big" song (and thus justify singing it in class today). But in reality, grants are paid to researchers who can find lines of best fit between related sets of data (maybe not a billion dollars, but sometimes in the millions). So the idea of paying for a line of best fit isn't as far-fetched as it might seem at first.

One girl figures out that the line of better fit is the one that's closer to the dots. So this leads to a discussion of what exactly that means.

As usual, I make adjustments to this lesson in time for fourth period. In the later class, I start with the notebooks, not Desmos. Then after discussing what lines of best fit are, the kids are ready to attempt to find such lines in Desmos. The "fight" mentioned in the lesson title refers to a competition set up in Desmos where the students compete to find the line of best fit for a particular set of points.

 A good teacher makes adjustments when it's clear that the students aren't getting it. But a great teacher doesn't need to make adjustments, because the original lessons are already understandable. Especially when it's time for the Stats project, I want that project to go well from the start, in all classes. I don't want to begin the project, run into trouble, and say "Oh well, at least I'll get it right by sixth period."

Indeed, I don't like the way the fifth period Math III lesson goes today either. The official lesson is on solving equations with logs, with the properties of logs to be taught on Friday. But here's the rub -- many equations require the properties of logs in order to solve them! The logarithmic equations on DeltaMath require the product, quotient, and power laws of logs. And the exponential equations often involve bases other than 10 -- the change of base law is necessary since since calculators can only do logs in base 10 (or e, but recall that e doesn't appear until Chapter 10).

The reason that equations are taught before properties is that equations appear in Lesson 7.1.1 of the CPM text, while properties are in Lesson 7.1.2. But the equations in 7.1.1 appear to be either simple equations that can be solved without a calculator, or else involve bases slightly greater than 1 that can be solved to the nearest integer by trial-and-error. Yet the pacing plan has the students solving more complex equations under the 7.1.1 umbrella than what CPM presents there.

This is a tricky one. During the lesson, I wonder whether I could have switched 7.1.1 and 7.1.2, and make sure that the students know the properties they need to solve equations. I'm not one for making excessive arbitrary rearrangements of the lessons, but perhaps this one was warranted.

Since I'd already assigned the homework (and some of my faster fifth period students like to do the HW right away), I don't want to make any changes to the lesson order now (and penalize them). Still, I can at least present the lesson differently in first period tomorrow -- for example, start with log equations before moving on to exponential equations (with bases other than 10).

Today is Eightday on the Eleven Calendar:

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

I enforce this resolution during the Exit Pass in my freshman classes. After they use glue and scissors to paste the Chapter 4 title page into their interactive notebooks, I have the students pass these items to the side of the room where they are kept. Then they only need to write the date as the Exit Pass.

Unfortunately, being mindful of where the glue and scissors belong makes one guy in fourth period be less mindful of his borrowed Chromebook. Instead of putting it where it belongs, he leaves the room with the Chromebook. At least fourth period meets tomorrow, so I'll ask him to return it then.