Friday, February 19, 2021

Lesson 11-2: The Distance Formula (Day 112)

Today I subbed in an eighth grade U.S. History class. It's in my new district -- indeed, it's at the same school I mentioned last week in my February 10th post, albeit a different class. (Last week, I subbed in a Grades 6-7 history class.)

Since it's in a middle school and I do have one classroom management crisis today, I will do "A Day in the Life" this time:

8:15 -- First period arrives.

The assignment for today is to look up vocabulary and answer questions for the lesson, which is on westward expansion during the early 19th century. The students cut and paste web images to accompany their vocab terms.

The class begins with a Warm-Up, which is some sort of journal entry. Unfortunately, I'm not able to access it or assign it to the students. One thing that I've found annoying about Chromebooks is that it's impossible to access any email other than district email. Even though the regular teacher sent me a lesson plan last night, he sent it to my personal account, not my district account. Therefore, I'm unable to see or assign any journal entry.

Of course, this problem is completely preventable -- all I had to do last night was forward the teacher's email from my personal to my district account, when I still had the chance. I didn't do it because I thought I didn't need to -- I did print a copy of the plan, but I can't click on a link from a piece of paper. From now on, I should assume that I'll always need a digital copy of the lesson plan -- the next time a regular teacher sends a plan to my personal account.

I will mention what song I choose to sing today. It's Square One TV's "One Billion Is Big" -- and it's easy to explain why I chose it. Last night, Prince Markee Dee of the Fat Boys passed away. It was just shy of his 53rd birthday (which would have been today). Thus I honor him by performing one of his songs today.

9:10 -- First period leaves and second period arrives.

I begin by explaining why there's no journal entry, and then we go directly to the main assignment -- and this I do in all subsequent classes.

10:00 -- Second period leaves for break.

10:20 -- Third period arrives.

I've heard of this happening to teachers in the pandemic era, but it's never happened to me until now. In third period, I was "Zoombombed" -- that is, someone logged into Zoom (actually Google Meet) who isn't actually enrolled in the class.

The Zoombomber posed as a district administrator. Even though Google Meet warns me that this person isn't using a district account, I see the name of our district in the username and so the account looked official. Then the Zoombomber clicks on "raise hand" and starts speaking loudly, saying things that have nothing to do with the class.

I figure out how to kick the Zoombomber out of the meet. Then he attempts to enter the meet again, this time using the principal's name as his username. Once again, Google warns me that it's not a district account -- and of course, the real principal would be using a district account. This time, I refuse to let him in, and I call the office. The (actual) assistant principal enters the meet, and one of the other students and I explain what's going on.

After seeing the Zoombomber today, I can start to appreciate why the district Chromebooks won't let us access personal email -- it's for security reasons, to protect us from people like the Zoombomber. Still, it makes it more difficult to access our account when we have a legitimate reason to.

11:10 -- Third period leaves and fourth period arrives.

Fortunately, the Zoombomber is gone, and there are no major problems in this class.

12:00 -- It is now time for tutorial. The students from fourth period remain in the room.

As I often do during tutorial classes, I sing extra songs. Once again, to celebrate the life of Markie Dee, I perform the other two Square One TV Fat Boys songs -- "Burger Pattern" and "Working Backward." It is the first time I've sung either one in the classroom. Neither song is printed in my songbook -- instead, I get the lyrics to "Working Backward" from this blog, where I posted three years ago. I've never written the "Burger Pattern" lyrics until now -- I simply find the video on YouTube, quietly play and write a small portion of the song, and then perform it. It's the perfect song to sing just before lunch.

I sing one more song that isn't from Fat Boys during tutorial. One girl decides to work on her math assignment in tutorial -- she's in Algebra I, and the assignment is on mean, median, and mode. It goes without saying which song I sing to her -- "Measures of Center Song," a parody of "Row Row Row Your Boat." (I also performed this when I was at this same school last week.)

12:30 -- The students leave for lunch.

1:10 -- Fifth period arrives.

Once again, there are no major problems, and I sing "One Billion Is Big" one last time today.

2:00 -- Fifth period leaves. As is usual for middle schools in this district, sixth period is independent study P.E., and so the students and I leave after fifth period.

Today is Fourday on the Eleven Calendar:

Resolution #4: We need to inflate the wheels of our bike.

Once again, it's not a math class. I do tell them that it's easier to remember math concepts if they're given in a song. The Fat Boys' songs help us remember the difference between a million and a billion, the definition of triangular number, and the working backward strategy.

Of course, I do pay homage to someone today -- Markie Dee. In fact, let me add the "music" label to this post and include lyrics for all the Fat Boys' songs today, including "Burger Pattern."



ONE BILLION IS BIG -- by the Fat Boys

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.

Refrain:
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.
(Repeat Refrain)

3rd Verse:
If we multiply one million by ten,
How close are we to one million 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!
(Repeat Refrain)

You might wish to skip to 3:14 for "Working Backwards":


Notice that the beginning of the video has a scene from "One Billion Is Big" (the headline "Fat Boys Sell One Million Records.") Oh. and by the way, I like the part where the three backup girls start singing the refrain. They come in dancing -- backwards, of course!

As far as I know, neither Barry Carter nor anyone else has recorded the lyrics for this song. So let me write down the lyrics to the best of my ability:

WORKING BACKWARDS -- by the Fat Boys

1st Verse:
Tonight our show begins at ten,
There's a lot we got to do 'til then.
We gotta rehearse, we gotta eat,
Put our makeup on and find time to sleep.
What time do we need to start?
Let's take the backwards day apart.
Working backwards, we'll figure it out,
And show the world what we're all about!

Refrain:
Working backwards is the way,
To solve this problem, working backwards.
Working backwards is the way,
To solve this problem, working backwards!

2nd Verse:
We got part of the day to fix our hair,
We need a half hour in the makeup chair.
They start their job at nine-thirty,
What time do we eat, my friend Markie Dee?
Thirty minutes is all it takes,
To eat a salad, to share a steak.
So tell the chef dinner starts at nine,
Working backwards is working fine!
(Repeat Refrain)

3rd Verse:
We need to nap before we eat,
About forty-five minutes of catching Z's.
We gotta rest, I hear my drum machine,
The lights go out at eight-fifteen.
We can't forget rehearsal time,
An hour and a quarter for beats and rhymes.
So rehearsal starts at seven o'clock,
Beat box, tell me, what time have you got?
Let's see -- my watch says seven o'clock already,
Wow, we better get moving right now!
(Repeat Refrain)


BURGER PATTERN -- bv the Fat Boys

Well I'm going to my favorite burger place,
I'm gonna eat those burgers and stuff my face.
And a shake and fries, I'm gonna munch,
I say, Markee Dee, I love my lunch.
Hey guys, what will it be,
A burger today or two or three?
Monday I had a burger, shake, and fries.
Tuesday three burgers, shake, and fries.
Wednesday six burgers, shake, and fries.
Thursday ten burgers, shake, and fries.
Today I'll have, I'll have, I'll have a...(I'm hungry!)
0 + 1 = 1, 1 + 2 = 3, 3 + 3 = 6, 6 + 4 = 10, 10 + 5 = 15
Fifteen, that's what it'll be,
I bet 15 burgers will fill me.
Fifteen burgers and shake and fries,
I see the pattern before my eyes.
Yeah, you see the pattern before your eyes,
You order 15 burgers and shake and fries.
This pattern didn't get here out of the blue,
It's gotta vibe in the business that we'll tell you.
You see, I start with nothing and then add one,
And add the next highest number to that sum.
I just added one so then I add two,
And then I add three, and you can do this too.
I keep this up and add four more,
You see I have the business I came here for.
So now I have ten and add five to that,
Hey, 15, that's really that.
This can go on forever if you know what I mean,
What's next is added to 15.
Hey, you're really a winner!
So tell me, my man, what time is dinner?

This is what I wrote last year about today's lesson:


Lesson 11-2 of the U of Chicago text is called "The Distance Formula." In the modern Third Edition of the text, the Distance Formula appears in Lesson 11-5.

Let's get to today's lesson. Many students have trouble with graphing throughout Chapter 11, and furthermore, today we learn the Distance Formula, which of course will be difficult for some students.

In the past, I combined Lesson 11-2 with Lesson 8-7, on the Pythagorean Theorem (and indeed, this lesson in the Third Edition is titled "The Pythagorean Distance Formula").

David Joyce has more to say about the Distance Formula:

Also in chapter 1 there is an introduction to plane coordinate geometry. Unfortunately, there is no connection made with plane synthetic geometry. Here in chapter 1, a distance formula is asserted with neither logical nor intuitive justification. Of course, the justification is the Pythagorean theorem, and that's not discussed until chapter 5. In that chapter there is an exercise to prove the distance formula from the Pythagorean theorem. The Pythagorean theorem itself gets proved in yet a later chapter.

Fortunately, the U of Chicago text avoids this problem. Our text makes it clear that the Distance Formula is derived from the Pythagorean Theorem.

Today I post an old worksheet from a few years ago. It introduces the Distance Formula -- but of course, it teaches (or reviews) the Pythagorean Theorem as well  -- including its similarity proof, which is mentioned in the Common Core Standards.

Today is also an activity day, so let's add an activity to this old worksheet. Once again, in order to find a pandemic-friendly activity, I look to the class where I completed my long-term assignment. The Distance Formula is also included in the Common Core Math 8 Standards, and the eighth graders reached it on February 8th. That day, the regular teacher assigned an EdPuzzle on distance, followed by a DeltaMath activity.

I've heard of DeltaMath before, even though this class didn't use it until after I left. Unfortunately, it appears there's no easy way for me to reach the Distance Formula lesson without setting up an account, which I don't have.

Once again, this is what I'll do -- post last year's worksheet, and then declare Deltamath to be the activity for today. It's up to you to access Deltamath.

We still got a way to go, my friend Markie Dee. Rest in peace.

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