Tuesday, March 21, 2023

Lesson 6.3.4: Solving Systems by Elimination, Continued (Day 133)

PALINDROME SONG

Chorus:
Go forward then go backward.
If the number reads the same, then it's a palindrome.
Go backward then go forward.
If the number's still the same, then it's a palindrome.
It's not a palomino on the western plain,
Where cowboys love to roam.
No! The wonder of all wonders, a backward-forward number.
It's called a palindrome!

First Verse:
Let's see! Take a 33! Read it in reverse.
Hey it reads the same, So it's a palindrome.
And 505, or 2002,
So they're both examples of that one I love.
It's a palindrome! It's a palindrome! It's a palindrome!

(to Chorus, except say:)
...then it's a palindrome.
It's not a pachyderm performing in the circus,
At the hippodrome. No! The wonder of all wonders...

Second Verse:
Let's see! Take a 63! Read it in reverse.
Now we're in a fix, 'cause it's a 36.
But don't be sad, all we do is add.
Add the 63 to 36 and see. That's a 99!
Hey we're doing fine! That's a palindrome! Whoa! Whoa!

(to Chorus, except say:)
Go backward and go forward. It's the one that's glad you came,
'Cause it's a palindrome.
If reversing and then adding doesn't work the first time,
Repeat it 'til you're home.
'Cause you'll finally reach that number, that backward-forward number,
You've reached a palindrome!

The fact that I'm posting Square One TV's "The Palindrome Song" means -- you guessed it! -- another Palindrome Week is upon us. The big palindrome day was yesterday, 3-20-2023. Unfortunately, it fell on a Monday, and I don't perform songs on Mondays. But at least Palindrome Week continues with reversible dates from today, 3-21-23, up through 3-29-23.

Since the song is from the Square One TV show, I can post its video here:

Regarding the song itself, it's interesting that not only are the lyrics different each of the three times the chorus is played, so are the rhythm and style. The middle chorus is most striking as its played in 3/4 time while the other two are in 4/4. The rhythms correspond to dances -- the middle 3/4 rhythm is almost certainly a waltz. The first rhythm might be a tango, while the last rhythm could almost be rock and roll (though the dancers also create a conga line).

Today's not supposed to be "A Day in the Life." But a few things out of the ordinary happen today, and so I'll do a quick "A Day in the Life" here:

8:30 -- It's Tuesday, so the block schedule goes 2-3-4-5. Second period arrives -- just as I leave. I have another one of those special ed meetings today, and so a sub comes in to cover this class.

9:55 -- Second period leaves. Third period is my conference period -- except during this time, I have yet another meeting. My prep period buddy asked to have this meeting, and she invited me to join in as well as a "long-term" sub (and by "long-term" I mean "the entire year") who's covering a special ed Math I class. The meeting is led by the TOSA (yes, the same TOSA who saved me from the pink slip last year, but is unable to save me this year), and the topic is SBAC Prep.

Recall that last week, the Math III department already declared an SBAC Prep Boot Camp -- and Math III is expected to have more juniors (read "test takers") than Math I. While I have only a single junior in my Math I classes, my two colleagues have more special ed students, hence more Math I juniors. Still, the state test covers all three years of high school math, and thus it's not too early to get our students thinking about it.

The TOSA shows us how to access the released test questions online, including how to select questions based on topic or question type. One of the questions he shows us is Question 9 from last week (and ultimately from the old SBAC Prep blogposts) -- the one where students must drag two irrational numbers into boxes, one whose square is rational and the other whose square is irrational.

 11:45 -- Fourth period arrives. This is the lone Math I class that I see today.

Today we continue to learn about elimination. Notice that the CPM text doesn't have a Lesson 6.3.4, nor does DeltaMath distinguish a fourth level of elimination. But one of my Math I neighbors -- the one who usually writes the tests -- is teaching Elimination Levels 3-4 this week. If we must discern four levels, we might think of them as follows:

1. Addition Only

2. Subtraction Only

3. Scale One Equation

4. Scale Both Equations

Both CPM and DeltaMath combine some of these so that there are only three levels. This time I follow the strategy I mentioned in my last post -- give advanced elimination problems on DeltaMath and have the students practice them together.

Notice that second period gets the same lesson as fourth period today -- at least in theory. Just as I'd expect, many second period kids are off-task today. Lately, I've been rearranging the quiz and test dates so that they land on sub days -- if I'm going to lose a lesson due to having a sub, I might as well give a test on that day. Indeed, I almost considered giving the Chapter 6 Test today for that very reason, but this is impossible today. The kids won't be ready for the test -- especially now that my neighbor who wrote the test is now billing this as a midterm that includes questions from Chapter 5 as well as 6.

My neighbor also provided a midterm review assignment on DeltaMath today. But here's where another of my rigidities comes in -- I always give my assignments on Mondays, to be due Fridays, but he didn't show us the midterm review assignment until today. Some of my kids started my assignment yesterday, so they wouldn't have appreciated my changing the assignment to the review. But, not knowing whether the test would be a midterm, I didn't include any Chapter 5 questions on my review.

One solution to this dilemma is not to use DeltaMath to review Chapter 5 at all. After all, I just had a meeting about SBAC Prep questions. So I could try to find a question related to Chapter 5 material (namely arithmetic and geometric sequences) and use it to review for Chapter 5, while keeping my DeltaMath assignment as the Chapter 6 review. (After the meeting, my prep period buddy said that she might give an SBAC Prep question "before the midterm" -- neither one of us aware at the time that the midterm would be this week.)

Due to the special ed meeting, my first performance of the "Palindrome Song" isn't until this period.

1:15 -- Fourth period leaves for lunch.

2:05 -- Fifth period arrives. This is the lone Math III class that I see today.

Unlike Math I, Math III really does take their midterm today. Their midterm covers Chapters 7-8 -- recall that Chapter 7 covers the Laws of Logs, Sines, and Cosines, and Chapter 8 is on polynomials.

Today is Tenday on the Eleven Calendar:

Resolution #10: We treat each other the way we want to be treated.

This doesn't really come up today, at least not in the two classes I see today. Fourth period is the best behaved of my Math I classes, while fifth period is usually OK if they have something very specific to work on, such as a midterm.

3:30 -- Fifth period leaves, thus completing my day.

I'm going to look up that SBAC Prep question now and prepare for tomorrow's classes. Enjoy the rest of your Palindrome Week!

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