SBAC Prep: Midterm Review and Chapter 7 Preview (Days 134-137)

ABBIE'S CANDLE

First Verse:

She made a movie with a

Romantic candlelight dinner.

Which candle will burn out first?

Which candle will be the winner?

Candle A, twenty

Centimeters at the beginning and,

Candle B is ten

Centimeters at the beginning and,

Candle A, an hour,

Sixteen centimeters later.

Candle B, an hour,

Ten centimeters,

So when Abbie's candle burns first.

So when Abbie's candle burns first.

Second Verse:

I'm in the movie, Julie

Lights our short candle at dinner.

Julie says B burns out first,

Though Candle A is much thinner.

I say Candle A's

Fully burnt out in just five hours, and

I say Candle B's

Isn't burnt out until ten hours, and

Julie, you are wrong,

Julie, B is cursed, because

B burns twice as long,

Julie, you're the worst,

Because Abbie's candle burns first.

Because Abbie's candle burns first.

This is the second song that I'm writing in 15EDL (as opposed to 16EDL) -- the first being "Planting Trees" two weeks ago. The two girls' names in the song refer to a particular SBAC Prep released test question -- one of the two questions mentioned in yesterday's post. By the way, the other question I use today is the Question 20 worksheet previously posted to the blog -- but more on that later.

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. (That's right -- it's three straight "A Day in the Life" posts.)

8:00 -- Today is another one of those half-day meetings called by the Math I TOSA, similar to the February 16th meeting. Last month's meeting was to review Chapter 5 and discuss plans for Chapter 6, and thus this month we review Chapter 6 and prepare for Chapter 7. (By the way, the only class I miss today is first period Math III, but they are taking the same midterm that fifth period took yesterday.)

Today is Elevenday on the Eleven Calendar:

Resolution #11: We follow all protocols for COVID.

But Elevenday is also my day to focus on communication with students and colleagues. Well, at least I communicate a lot with my fellow Math I teachers due to today's meeting.

The TOSA tells us to bring a sample of Chapter 6 student work. One of my neighbor teachers brings a poster from the project (that she herself created -- it's the basis of my "Planting Trees" song) and suggests that the rest of us do likewise. The TOSA is pleased to see all of our students' questions, tables, graphs, and equations.

Then we begin discussing Chapter 7 of the CPM text. This is one of the chapters to which I've been looking forward to the most, because it's a Geometry chapter. For once, I actually get to write about Geometry on this Geometry blog. And perhaps, after finally using some of my old worksheets for SBAC Prep, I'll get to use some of my old Geometry worksheets as well.

Indeed, my preparations to teach our favorite math subject began on the teacher day on March 13th (yes, Pi Day Eve). The TOSA led a math department meeting, except this one isn't just for Math I teachers, or even just high school -- middle school teachers were there as well. The TOSA discussed what the geometry strand looks like across all grade levels, from Grade 5 to Math III.

Since this is a Geometry blog, I really want to discuss both the Pi Day Eve meeting and today's meeting in much greater detail. But I choose not to tie up today's post with such discussion, since the focus should be "A Day in the Life" (that is, today's lessons). Fortunately, spring break is right around the corner, so I'll devote one of my spring break posts to Geometry and Chapter 7.

I will say this now though -- while the previous Geometry chapter (Chapter 3) was on transformations, Chapter 7 is on triangle congruence. Thus it's very much like the same numbered chapter in the U of Chicago text. You can refer back to my old posts from previous Decembers (prior to the pandemic) to get a taste of what I'll be teaching in April.

11:45 -- Fourth period arrives. This is the first of two Math I classes.

As I mentioned above, in this class we look at Question 20 of the SBAC released questions. That's because this question is on arithmetic sequences -- a Chapter 5 topic that I didn't include on the midterm review assignment. I divide the class into groups and give each group a worksheet. On one side is my Question 20 worksheet (the version I posted in May 2021) and the other is the candle question from today's song, which requires the students to solve an system (equal values method, similar to the ones on the poster project).

While today's worksheet is helpful, one problem is that both SBAC problems include fractions -- the arithmetic sequences have fractional terms and the system has a fractional solution. All of the questions on the DeltaMath exam use integers only, so I risk confusing the students with the fractions. I quickly add more natural numbers sequences to the SBAC worksheet.

Moreover, the worksheet contains no geometric sequences. I incorporate a geometric sequence as the Exit Pass -- find the 22nd (of course, since that's the date) term of the sequence 3, 6, 12, 24, 28, 96, ...

1:15 -- Fourth period leaves for lunch.

2:05 -- Sixth period arrives. This is the second of two Math I classes.

As usual for Wednesday, sixth period is one day behind fourth period. So this class is still answering DeltaMath questions on Elimination Level 3 (and 4), and the song for this class is still "Palindrome Song" from Square One TV.

Unfortunately, there's been a huge problem lately in this class. Some students have started inviting friends from other classes to ditch their classes and attend mine. Today, the three guys who don't belong present me with a pass from a Biology teacher who apparently sent them to my room as a timeout punishment from their class. But I strongly suspect that the pass has been forged -- especially since this isn't the first time this month that students who don't belong in my class have started attending mine (and some of them even have the gall to start working on DeltaMath in an effort to appear legitimate).

I have emailed the teacher whose name is on the pass, but he hasn't responded yet. Unless he confirms that he really did sent the kids to my room for a timeout, I have no choice but to submit a major disciplinary report to the office.

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

Let's get to a discussion of today's new song. It is quite complex -- officially it's an AA song with verses only, but the melody is more complicated. Instead of repeating a single riff four times, I play two lines and then repeat those lines before proceeding to the next section.

Here's a link to today's Mocha code:

https://www.haplessgenius.com/mocha/

10 N=8

20 FOR V=1 TO 2

30 FOR X=1 TO 96

40 READ A,T

50 SOUND 261-N*A,T

60 NEXT X

70 RESTORE:FOR M=1 TO 1600:NEXT

80 NEXT V

90 END

100 DATA 10,12,13,2,16,2,16,6,13,6,16,2,12,2

110 DATA 11,4,15,4,10,4,9,4,10,4,12,4,12,4,11,4

120 DATA 10,12,13,2,16,2,16,6,13,6,16,2,12,2

130 DATA 11,4,15,4,10,4,9,4,10,4,12,4,12,4,11,4

140 DATA 16,8,18,8,15,6,11,6,11,4

150 DATA 13,2,11,2,16,4,14,4,13,4,9,4,11,4,16,4,15,4

160 DATA 16,8,18,8,15,6,11,6,11,4

170 DATA 13,2,11,2,16,4,14,4,13,4,9,4,11,4,16,4,15,4

180 DATA 20,8,16,8,16,6,12,6,15,4

190 DATA 11,8,11,2,16,2,16,2,20,2,18,8,16,8

200 DATA 20,8,16,8,16,6,12,6,15,4

210 DATA 11,8,11,2,16,2,16,2,20,2,18,8,16,8

220 DATA 16,8,16,8,16,8,16,4,12,4

230 DATA 15,16,18,8,16,8

240 DATA 16,8,16,8,16,8,16,4,12,4

250 DATA 15,16

Don't forget to click on SOUND before you RUN the program.

As I wrote earlier, due to its complex melody, this AA song is written like an ABCD song. It's one of the few songs I've written with a rest between the two verses -- this rest is included in Line 70.

Both this and "Planting Trees" are labeled as 15EDL songs because Degree 15 -- the note F -- serves as the tonic. It includes Degree 12 or A, so it's definitely an F major song as opposed to F minor. And because it's F major, Degrees 13 and 11 must be interpreted as G and Bb.

I used our usual TI randomizer to compose the song. But since I want the song to sound romantic (to fit its candlelight dinner theme), I smoothed out some of the random tune's roughness. In particular, I changed some of the generated tune's octaves so that the song fits between Degrees 20 (the C below the tonic F) and 9 (the D above the tonic). In particular, Degrees 20 and 18 are a low C and D when the TI calculator generated a high C and D. (I could have used Degrees 20-9 as the bounds for the randomizer, but then I might have to deal with Degrees 19 and 17, which would be awkward.)

On the other hand, this tune includes Degree 14, which is an F#. Of course, an F# sounds out of place in an F major song. So I make sure that Degree 14 is always followed by 13, so that 14 serves as a leading tone to 13. The chord riff for the second section includes D7-Gm over these notes. (This is the only section in which 14 appears.)

Here is a possible chord sequence for the entire song: for the first section, go F-C7 (although others, such as C-Bb-F, also sound great here). The second section, as noted above, goes D7-Gm. The third section has a dominant C (or C7) chord. The last section needs an authentic C7-F.

Finally, the lyrics fit the statement of the original SBAC problem, which is a lengthy performance task with six parts. It is about finding the right candle to film a movie with a fancy candlelight dinner scene.

I decide to cast "Julie" from the SBAC problem as the female lead, and I insert the narrator (aka myself) as the male lead of this movie. Julie insists that Candle B will last longer because it's shorter, even though Candle A is thinner (albeit taller). The students are supposed to calculate (in Part 2 of this performance task) that Candle A will last five hours, but Candle B will stay lit twice as long. In other words, they prove that Julie is wrong.

Thus the song implies that Julie and I break up over a silly argument about a candle. It means that this so-called romantic movie is a tragedy, not a comedy. (Fortunately, it is just a movie.)

I must point out that we should have known all along that the taller Candle A would burn out before the shorter Candle B. Had Candle B burnt out first, the candles would never have the same length, and the system (to find the time when the candles are equally long, Part 3 of the performance task) would have no sensible solution. If Julie had known that she was part of a movie about solving systems, she wouldn't have argued for Candle B.

Just as with "Planting Trees," it's possible to add more verses this song to include all six parts of the performance task question. (Poor Julie only appears in Part 2 of the question -- once she's proved wrong about Candle B, she just disappears from the movie.)

This is my last post before spring break. Recall that we're following Tina Cardone's tradition -- the last day before and the first day after spring break aren't "A Day in the Life" special days. Thus I won't post on either day. (The post is labeled Days 134-137, where 137 is the first day after vacation week.)

Once again, I volunteered to write a Math III test for the next chapter. So I won't make my first spring break post until after I write the test (even if it's the last day of break). In that post, I'll discuss the Math III test that I'll have finished by then, and then pivot to Math I Chapter 7 and Geometry.

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!

Lesson 6.3.3: Solving Systems by Elimination, Continued (Days 131-132)

Today is the seventeenth, and so this is my monthly "A Day in the Life" post for March. It is Friday, often a day for department or other meetings. But there is no such meeting today.

Of course, today is also St. Patrick's Day. I used to have a St. Paddy's Day pencil giveaway, but no such pencils are sold in stores these days. Thus I no longer have one.

8:30 -- First period arrives. This is the first of two Math III classes.

This is the second day of SBAC Prep Boot Camp. According to the pacing guide, today's task is to answer fifteen practice test questions on Illuminate. This platform is mentioned in the song I perform yesterday -- it's always used for district Benchmarks, but non-Benchmark tests can be taken there as well. Indeed, last year I used it for some Calculus and Trig tests, and this year another teacher has set up a practice SBAC there on Illuminate.

The pacing guide also states that the Chapter 8 DeltaMath test corrections are assigned as homework, which is atypical for me. But the other teachers want to make sure that the corrections don't take an extra day away from the SBAC Prep Boot Camp.

The Exit Pass question comes from a SBAC question. Eva wants to buy a bike for $240, but she only has $42 in the bank. If Eva is paid $12 per hour as a babysitter, then how many hours must she work in order to afford the bike? The correct answer is 16.5 hours -- but for the Exit Pass, I have the students round off the answer to 17 hours, because today's date is the seventeenth. After the Exit Pass, the students turn in their notebooks, since Chapter 8 is essentially over.

9:25 -- First period leaves for nutrition.

9:40 -- Second period arrives. This is the first of three Math I classes.

Normally, I give some sort of quiz or assessment every Friday in Math I. But this week, I'm leaning towards counting the poster project as this week's quiz. So instead I try to give a lesson -- unfortunately, there are several problems with today's lesson.

I'm labeling today's post as Lesson 6.3.3, but I'm torn between an extra of 6.3.2 and starting 6.3.3. Here the CPM lesson numbers refers to the three levels of the elimination method as defined by DeltaMath -- Level 1 is for pure addition or subtraction, Level 2 is where one of the equations must be scaled, and Level 3 means that both equations are scaled.

Today is Sixday on the Eleven Calendar:

Resolution #6: We implement all parts of our projects.

Yesterday was the first day of Lesson 6.3.2. As I explained in my last post, I decided to go over the DeltaMath questions on guided elimination last time and save Desmos for today (especially since the Desmos questions lead into Level 3, or Lesson 6.3.3, as well).

Unfortunately, the Desmos lesson doesn't go well. The first system in this activity is written in an unexpected format, C = By + Ax instead of Ax + By = C. It throws the students -- and me -- off, and it takes some time to figure out where we go wrong. And the other systems include fractions -- one as a coefficient, another in the solution. Indeed, the very first Level 3 system has a fractional solution.

I must admit that today's lesson is influenced by several rigidities -- patterns in how I teach the lessons that I uphold just because they're the way I've always done things. One of those rigidities -- the weekly Friday quiz -- is not in force today. But some others are -- including some influenced by the existence of the weekly Friday quiz.

First is the interactive notebook. In order to avoid having too many notebook pages (which would force the kids to buy three or more notebooks to span the year), I make sure that I assign no more than one page on most days (excluding the Warm-Up page) -- and no pages on Fridays (when, once again, I'd normally just give a quiz anyway).

As I explained in my last post, on the last block day I passed out a guided note worksheet containing the lyrics to the rap (with blanks for the kids to fill in). That worksheet took up the entire page, so there was no room to write anything else (like, say, a few system solutions worked out), since I didn't want to have them write on more than one page. Then today is Friday -- the day that there's no page. Thus during the entirety of Lesson 6.3.2, the students write only rap lyrics, with no Level 2 examples. And of course, I couldn't have saved the rap for today because I only perform on block days, not Fridays.

Yesterday's DeltaMath lesson was far more successful than today's Desmos, so perhaps I should have done more DeltaMath instead. The problem is that I set the DeltaMath assignment at the beginning of each week, to be due the following Friday (again because there's usually a quiz). And we already solved all the planned DeltaMath questions yesterday. Some students regularly finish the work the first day it's assigned, so they wouldn't appreciate suddenly having extra questions, especially on the day it's due.

There's also a problem with avoiding arguments. A few students are eating in class again. I tell them that I'll write the eaters' names down and decide on a punishment later, in order to avoid arguments.

Then I pass out the application forms for students hoping to take Math II this summer so that they can advance to Math III next fall (to reach Steve-level classes -- junior Pre-Calc and senior Calculus). One girl gets upset at this -- she calls herself and others the "D" word, meaning not very smart.

I try to tell her that she has a point -- I could have handed out the applications more discreetly. But then she assumes that I'm trying to argue with her over the food that she's eating. And so, although I'm trying to avoid arguing, an argument ensues anyway. That's the problem with arguing -- the students are so used to my arguing, they interpret anything I say as an argument. And that's why it's important to avoid arguments from the very beginning.

It's tricky to find a good Exit Pass question whose answer involves today's date. A possibility is:

5x - 3y = -1

-3x + 2y = 4

which is a Level 3 system with solution (10, 17). But since I don't reach Level 3 questions, I can't give this Exit Pass (though it's a much better question than the one that appears on Desmos).

10:35 -- Second period leaves. Third period is my conference period -- which means that it's time for my weekly tutoring session with three Math III students and my "prep period buddy" teacher.

Yesterday was Part II of the Chapter 8 Test -- the paper portion. Nevertheless, there's still something for these students to prepare for -- and I don't mean the SBAC. Next week is the Math III midterm exam.

Unfortunately, my prep buddy must cover a class this period -- a Spanish class. She's a native Spanish speaker, so she can handle this class -- after all, that's why we set up tutoring sessions in the first place, namely to help my English learners  (though she tells me that she -- just like me -- took French in high school, not Spanish). We decide to hold the tutoring session anyway -- I help out the math students while the other teacher watches the Spanish class and translates for us from time to time.

We work on a few questions from the last homework assignment, including the end behavior of polynomials -- a simpler topic, but one that I only briefly touched upon in class. I want to make sure that the students understand this ahead of the midterm.

11:40 -- Fourth period arrives. This is the second of three Math I classes.

Fourth period goes much more smoothly than second. I do finish both Level 2 questions, but we still don't reach the Level 3 question. Then again, I'm not quite sure whether Level 3 elimination will even be on the upcoming Chapter 6 Test.

Entering today, I'm slightly ahead of my neighbor teachers. They've just barely begun Level 1 of elimination, with perhaps an intro to Level 2. On the other hand, I'm behind my prep buddy, who's completing substitution today (after teaching elimination first). She could give the chapter test early next week, though she tells me that she'll spend most of the week on review.

I hear one of my neighbor teachers tell his class that Level 3 might not be on the test. The issue hasn't quite been decided yet -- but of course, if it's not on the test, it's not as crucial that I teach it. Instead, I should make sure that they're comfortable with Level 2.

I also attempt to hand out the summer Math II letters more discreetly than in second period, but still, one guy wonders why he doesn't get a letter. (Some teachers might take the time to put letters in envelopes and just hand out sealed letters to the proper students.)

12:40 -- Fourth period leaves for lunch. There is a "pie your teacher in the face" contest during lunch, but I'm not one of the victims. This probably should have occurred on Pi Day, but it takes place outdoors and thus was delayed due to rainy weather.

1:25 -- Fifth period arrives. This is the second of two Math III classes.

Fifth period works on the SBAC Practice Test on Illuminate. This is after I show them end behavior questions on the Warm-Up.

By the way, after mentioning how I overused Desmos in Math I, I underused Desmos in Math III. The teacher who created the Math III Desmos lessons also wrote the Chapter 8 Tests, so if I'd assigned Desmos, my students would have been better prepared for the test.

2:20 -- Fifth period leaves and sixth period arrives. This is the third of three Math I classes.

We do barely make it to the Level 3 question in this class -- but once again, it might not matter if there's no Level 3 on the test. And there's only one student recommended for summer Math II, so I easily give her the letter without others noticing.

3:20 -- Sixth period leaves, thus completing my day.

Last year, this was the last week before spring break. This year, spring break will be the last full week in March, so there's still one week left in the "Big March." Enjoy the rest of your St. Paddy's Day!

Lesson 6.3.2: Solving Systems by Elimination, Continued (Days 129-130)

SYSTEMS RAP by Algo Rhythm

(Verse 1 intentionally omitted)

Verse 2:

y equals mx + b

Ax plus By is C. Different forms you see

Plug in mx and b for y in the Ax plus By is C

Which becomes an equation with just x

You know how it be.

Wait. x we need y, don't

have to hate, straight out

the gate, at this rate,

find the ordered pair

x and y are mates

Substitution.

it's not Subway

But I be keeping math fresh

all day every day

Weird flex but okay

Mr. Walker goin' cray

With my words on play

And all I have to say is

Chorus: (x2)

I'm on a mission

Solving systems

Of equations.

Don't be hatin'.

Intersection

Substitution

Elimination

Combination

Verse 3:

How do we find the answer for

A system of two standard forms

Needa be a bit humble more

Like Harry Potter and Dumbledore

So pay attention on elimination

Today's assessment on Illuminate, son

For variable x or y, first

Create an elimination

Through product combinations

Of system of linear equations

Combine both sides like stereo

To isolate the variable

Jump for joy like Mario

Single step, "let's go."

Then sub for the other one,

And solve the equation,

And now we're done, son

Flow Acapella, no beat, no drum

OK, I admit that I'm not the creator of this rap. Like "Slope Intercept Rap" (mentioned in yesterday's post), it appears on the old Google Classroom shared by Math I teachers. The difference is that "the Slope Intercept Rap" writer posts YouTube videos of his songs. The creator of today's rap appears to be a fellow (or former) teacher at my school.

I don't post complete content created by my colleagues. Thus, like with "Planting Trees" earlier, I post only an edited version of the song. For starters, I omit the first verse (which is on solving systems by graphing) and start with the second verse. Moreover, the creator of this rap posted only a worksheet filled with blanks (like guided notes), with no answer key. Thus I had to guess and fill in some of the blanks myself.

The underlined lyrics are my best guesses at the blanks. Some of them I'm more sure of -- for example, I'm confident that the blank in the first line is y equals mx + b (slope-intercept form), but I had no clue what goes after "which becomes" in the fourth line.

Also, "Algo Rhythm" is clearly a stage name. The creator of the song included his own name in the second verse -- well, at least his last initial (after "Mr.") is there. And so I changed this to my own last name above. (No current math teacher at my school has that last initial, which is why I think it's a former teacher.)

Meanwhile, like many hip-hop songs, this song might have a melodic chorus while the rest of the some is purely rhythmic -- but there's no video or other way for me to know this. And so I decide to create my own melodic chorus using our current EDL scale, namely 16EDL.

Let me make this official. This is the third song that I'm composing in 16EDL, our main scale for March and April. And it's the first 16EDL song in the ABAB format, with verses and a chorus (though only the chorus is melodic).

Before I discuss the chorus, let me discuss the fourth period class itself. Today we return to Lesson 6.3.2 of the CPM text, which is on elimination where one equation must be scaled, or multiplied by a constant in order to eliminate a variable. (The rap above calls this "combination.")

There is a Desmos activity that could go with this lesson, but I think it fits the next lesson better. So instead, I give a few guided elimination questions as part of the DeltaMath assignment. This allows us enough time to glue the rap into notebooks and fill in the blanks.

Meanwhile, in first and sixth periods it's still Pi Day (or at least Belated Pi Day, since those classes didn't meet yesterday). In first period I hand out 7-Eleven pies to the top three scorers on the DeltaMath test in Math III, while in sixth period (right at 1:59, of course) I give away the leftover pies from yesterday's fifth period.

Sixth period Math I finishes their posters today, but some students are once again distracted by the World Cup -- the World Baseball Cup, that is. Many of my Hispanic students are once again supporting Team Mexico, who defeats Canada to advance to the knockout stage. Team USA must beat Colombia to advance as well. (The Americans lead 3-2 at the game's midpoint as of the timestamp of this post.)

I believe that all games in the knockout round will be played in primetime, or at least after school lets out on the West Coast. So today should be the only day with a baseball distraction. (Of course, March Madness starts tomorrow, so that might also cause problems.)

Today is Fourday on the Eleven Calendar:

Resolution #4: We start our Warm-Ups and the main lesson promptly.

I do attempt to get the kids working more quickly in fourth period, though it's still tricky. Today's Warm-Up is a Level 1 elimination problem, and even though many of them did well on last week's quiz, they still like to waste time during Warm-Ups. (In the other classes, fast Warm-Ups are impossible since I spend much of the first few minutes of class handing out pie.)

Meanwhile, I do wish to get back to pink slip discussion in today's post. Today during third period, I originally plan on meeting up with my prep period buddy (the other Math I teacher with the same conference period) to set up the next tutoring session -- and we'd already been discussing my evaluation and employment situation. But unfortunately, she has to cover another class during third period, and so I don't say much about the pink slip. (Of course, the correct contact person would be a union rep, but they are busy today -- it is still March 15th, after all.)

Just like last year, I won't mention any interviews I have with other schools on the blog, unless they occur on a regularly scheduled posting day and I take the entire day off to interview (thus forcing me to explain why I'm not teaching that day).

Here's a link to today's Mocha code (for the melodic chorus):

https://www.haplessgenius.com/mocha/

10 N=8

20 FOR V=1 TO 2

30 FOR X=1 TO 28

40 READ A,T

50 SOUND 261-N*A,T

60 NEXT X

70 RESTORE

80 NEXT V

90 END

100 DATA 12,4,12,4,10,8

110 DATA 12,4,12,4,10,8

120 DATA 12,4,12,4,10,8

130 DATA 12,4,12,4,10,8

140 DATA 11,4,16,4,14,4,10,4

150 DATA 11,4,16,4,14,4,10,4

160 DATA 11,4,16,4,14,4,10,4

170 DATA 11,4,16,4,14,4,10,4

Don't forget to click on Sound before you RUN the program.

I ran my TI randomizer twice, since on the second attempt I found notes that sound good. There are two bars -- one that repeats for the first four lines, and the other that repeats for the last four.

Degree 13 is omitted, and so this is pure 16EDL without worrying about the neutral third problem. The first repeating bar is A-A-C, with Am as the obvious guitar chord. In the second bar, we can interpret Degree 11 as B so that an E power chord can be played -- the melody becomes B-E-F#-C.

This post is labeled as Days 129-130. My next post will be on Friday, Day 131 -- the seventeenth of the month and hence my monthly post.

Pi Day (Day 128)

Today is Pi Day, a key day on the mathematical calendar. I have much to say about how I celebrated it in the classroom this year.

But first things first -- I received the dreaded pink slip today. I've been expecting this ever since I took this job in the first place. Recall that last year I got the pink slip, and I wasn't rehired until July. So I already know that I got the last open position, placing me right at the bottom of the seniority list. And enrollment  is declining everywhere -- there were fewer babies born in the Great Recession, and that's the generation that's now reaching high school age.

Still that doesn't make it any easier once I receive the actual document. It makes it worse that I get in on Pi Day, which ought to be a day of celebration -- but I know it goes back to the California law that pink slips must be sent out by March 15th.

As I wrote above, last year's pink slip was rescinded in July -- and only because the district promoted one of the other math teachers to a TOSA position, thus opening a spot for me. This year, I doubt that there's going to be any TOSA loophole to allow me to stay in the district.

I'm going to save most of this pink slip discussion for tomorrow's post, since once again, the Pi Day post should be all about celebrating pi and math.

Last year, I worked at such a small school that I was able to bring enough pie for every single student who had my class on Pi Day. This year, I work at the main high school, so I can't do that. Instead, I bring pie only for the class that meets at the Pi Minute, 1:59 -- but which class is that?

Well, the block schedule on Tuesdays goes 2-3-4-5. This is my annual Daylight Saving Time post (and yes, Sen. Rubio of Florida reintroduced the Year-Round DST bill after it expired in the House last year). I notice that with school starting at 8:30, some students don't arrive until around 9:30 -- but these are students who arrive very late every Tuesday, not just during DST week.

As for the 1:59 class, in last year's Pi Day post I wondered whether 1:59 would be during a class or a passing period. Since school ends at 3:30 and each block is about an hour and a half, the last block of the day starts around 2:00 -- so 1:59 is during the passing to that block. If high schools were still allowed to start at 8:00, 1:59 would have been near the interior of that period.

Anyway since today is 2-3-4-5, that period that starts after 1:59 is fifth period. So it's this class, a Math III class, that gets most of the Pi Day goodies. I find two pies in the local supermarket (lemon meringue and sweet potato), as well as four individual pies from 7-Eleven for the top scorers on the most recent test (namely the Chapter 8 Test on DeltaMath).

And I even get them some pizza from the local pizzeria. It was one of those giant rectangular pizzas with 32 slices, since that's around how many students I have in that class. Unfortunately, due to its shape, the pizza has nothing to do with the number pi (but at least it's a pizza pie).

And of course, all throughout the period, I sing Pi Day songs. Today I choose "Pi Day Songs (All Day Long" (a "Jingle Bells" parody), "Pi Day Serenade" ("Alphabet Song"), "A Pi Day Carol" ("Row, Row, Row Your Boat"), "I'm a Little Number" ("Teapot"), "12 Decimals of Pi Day" ("Days of Christmas"), "Ludolph the Mathematician" ("Rudolph the Red-Nosed Reindeer"), and of course I had to wrap it up with "American Pi" (Bizzie Lizzie's "American Pie").

By singing "Ludolph" today, that makes this the second "Rudolph" parody I've performed this year, after "Rudolph the Statistician." (I won't post any lyrics in this post, since they're posted either elsewhere on my blog or elsewhere on the web.)

With all of this going on, do we do any actual math in Math III today? Well, today is the first day of "Boot Camp" -- aka SBAC Prep. Most Math III students are juniors who are required to take the state test this year. We're starting it now, even though the SBAC Math Test isn't until May. (The English SBAC is this week, while the California Science Test is next month.)

And, for the first time in this class, I actually use a resource from this blog. I go back to my annual SBAC Prep posts from 2021 and hand out the first eight questions in class, one to each group. The group then works out the problem on the front board (VNPS) and then the class takes a Gallery Walk around the room to get the other answers.

Today is Sunday, the third day of the week on the Eleven Calendar:

Resolution #3: We remember math like riding a bicycle.

On Pi Day, we might try to memorize the first several digits of pi. Unfortunately, there's no math involving pi today. Notice that Question #9 mentions irrational numbers including pi, but there are only eight groups in class today. (And Chapter 9 of the Math III CPM text is on trig, including radians and hence pi. But only Math III Honors classes study that chapter.)

It's my blogging tradition to post some Pi Day videos each year on the holiday.

1. Mathematical Pi:

There are so many versions of this song, mainly due to the title of the song it's parodying -- it's just too irresistible to change "American Pie" to "American Pi."

2. "Pi Day video" by musicnotes online

One thing I notice about this song is that the rapper in this video is "Lamar Queen." While I don't perform this song today, I did do one of Lamar's other raps in Math I earlier this year -- namely "Slope Intercept Rap."

3. The Pi Day Song by Michael Bautista

I first posted this one to the blog last year.

4. Vi Hart's Pi Day video 2023

It's Vi Day -- the one day of the year when Vi Hart posts a video. This year, Vi posts a video claiming that the number pi contains only a dozen digits.

Vi would really like one of the songs I perform today in class -- "The 12 Decimals of Pi Day," which also includes only twelve digits of pi. (Notice that Vi already has a "Twelve Days of Christmas" parody -- "12 Days of Christmath.") On the other hand, we shouldn't tell Vi about "Ludolph the Mathematician," which states that Ludolph van Ceulen found 35 digits of the circle constant.

5. Viva la Pi Day by Jon Jacques

This is a parody of Coldplay's "Viva la Vida." Apparently, Jon Jacques is a high school teacher who's had his class perform a Pi Day parody in recent years. Here's his parody from last year:

6. I Learned About the Number Pi by Jon Jacques

The original song here is Marvin Gaye's "I Heard It Through the Grapevine."

7. Dr. Trefor Bazett

This is video from last year is the second video I've seen that demonstrates the Basel formula -- there's another interesting one by 3blue1brown.

By the way, shortly after 1:59, the principal visits my fifth period class to deliver Pi Day pies to all of the teachers. Of course, by this time I've already received his email telling me to visit his office after school to receive a document (which I correct assumed to be the pink slip). Thus the principal gives me a pie and a pink slip in one afternoon.

But once again, that's enough about the pink slip for today. That concludes my annual Pi Day post. I wish everyone a Happy Pi Day -- even if mine isn't exactly a happy one.

Chapter 6 Project (Days 125-127)

PLANTING TREES

First Verse:

Once I planted two trees in my backyard.

Evergreen grew 20 plus 6 per year.

Willow tree grew 40 plus 2 per year.

Which tree's taller? That is so hard.

Second Verse:

Ella decides Netflix or Hulu.

Netflix charges 14 plus 1 per film.

Hulu charges 10 plus 2 per film.

To save money what should she do?

This is the second song that I'm composing in 16EDL, our main scale for March and April. And it's the second 16EDL song in the AAA format, with verses only.

My original plans for today's fourth period Math I class include continuing with the elimination method, perhaps giving systems where one of the equations needs to be scaled (multiplied). But before school, the TOSA appears in my class and asks how we're doing with the Chapter 6 projects. I quickly poll my neighbor teachers and discover that they have already started the projects in their classes.

As it turns out, it all goes back to the WASC visit and coming up with a presentable lesson. One of my neighbor teachers wrote four word problems that could be solved using systems. The idea is to divide the class into groups and assign one problem to each group. Then the group members must create a poster -- the four sections of each poster are for the question, tables, graph, and algebraic solution (which only requires substitution, not elimination).

My neighbors planned on giving the project yesterday (the block day) as opposed to Monday. But as I wrote in yesterday's post, the WASC committee member arrived in my classroom on Monday -- and naturally, if he was in my room that day, then he proceeded to visit my neighbors that day too. Thus the project plans were foiled -- he saw the same thing in their classes that he saw in mine, namely an ordinary traditional lesson (albeit on substitution review, not elimination). They still started the poster project yesterday though.

During third period conference, I visit my "prep period buddy" -- the lone other Math I teacher who shares the same free period. As usual, I tell her that I definitely want to have our usual Math III tutoring session on Friday (especially with the Chapter 8 Test coming up on that same day). But today we discuss our Math I classes as well.

Recall that my prep period buddy taught the lessons in a completely different order. Last week she taught elimination, not substitution like the rest of us. And for WASC, she found some different word problems that are set up to make elimination more suitable than substitution. Her classes still work on them in groups, but on regular paper, not posters. Since poster paper doesn't need to be passed out, she does have them begin their group assignment on Monday. (Her classroom is out in the bungalows -- and WASC did visit her bungalow yesterday.)

I reveal to her how my neighbors taught the lesson, and she asks me to share the poster project document with her as well.

Since we're all eventually going to give this poster project, I do so as well. And so I completely change my own plans -- instead of finishing elimination, I start the poster project today in fourth period.

But notice that this leaves me out of sync with everyone else. My neighbors haven't started elimination yet, while my prep period buddy hasn't begun substitution yet. I've done a little of both, mainly because I was trying to follow the pacing plan, which shows a project as the last week of the chapter (a couple of weeks from now) as opposed to now.

Perhaps I should have known that the others would rearrange their lessons to impress WASC. Then again, perhaps we all should have taken WASC into consideration at the meeting when we first discussed the plan (and thus placed the project during WASC week in the first place). It's also notable that everyone thinks it's better to have a word problem project during WASC, when my original master teacher once told me to avoid word problems on visitation days. (Then again, that was over a decade ago, just before the advent of the Common Core with its added emphasis on problem solving.)

The one thing I said about projects on the blog is that I don't wish to do them on my own, since I'm not necessarily good at implementing them (hence my sixth resolution). Instead, I should follow my neighbors and heed their advice when it comes to projects. That's why I start the project today in fourth period (and tomorrow in my other Math I classes).

How many points should the poster be worth? The pacing plan also shows a Chapter 6 Test, so I don't necessarily want to make this project be worth as much as a test (unless the others change their mind and decide not to give the test). Today is the first day of the project -- I haven't decided yet whether I'll continue this on Friday or give the usual weekly quiz. If I skip the quiz, then I could make this project be worth as much as the quiz it's replacing would have been.

Today is Eightday on the Eleven Calendar:

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

And of course, those materials today include poster paper and markers. (Meanwhile, since Resolution #6 is about projects, note that Sixday was on Monday. None of us started the poster project on Monday, though since it's a multi-day project anyway, we really could have done so.)

Here's a link to today's Mocha code:

https://www.haplessgenius.com/mocha/

10 N=8

20 FOR V=1 TO 8

30 FOR X=1 TO 10

40 READ A,T

50 SOUND 261-N*A,T

60 NEXT X

70 RESTORE

80 NEXT V

90 END

100 DATA 16,4,8,4,11,4,10,4

110 DATA 8,4,13,2,10,2,15,4,9,2,9,2

Don't forget to click on Sound before you RUN the program.

This is the first song that I'm interpreting as 15EDL rather than 16EDL. This means that Degree 15 is the tonic -- this note is F, so the song is in F major. For 15EDL songs, Degrees 13 and 11 will always be interpreted as G and Bb respectively, since this fit the F major scale.

The chord riff for this song is a simple C-F (or C7-F). Actually, since Degree 12 (the note A) is avoided, we can get away with interpreting this song as F minor (with C-Fm or C7-Fm as the main riff). Since both Degrees 9 (D) and 8 (E) are including, this would be F melodic minor. Here is the complete melody of the single line: E(low)-E(high)-Bb-C-E(high)-G-C-F-D-D.

This song has just two verses, even though the project has four questions. The reason is that these questions come from one of my neighbor teachers, not the CPM text. I don't like to post anything created by a colleague on my blog, not even a song inspired by their work. Thus I only include two of the questions in the song version that I post here, though I might perform other verses in class. (In addition, one of the questions mentions the name of our school and that of a rival school -- which is also a school where I once subbed during the early days of this blog. But I don't post the names of schools where I work.)

This post is labeled Days 125-127. Monday is a teacher day with no students on campus. (I mentioned this earlier on the blog in explaining why this isn't quite a "Big March" stretch for the students -- but in a way it marks the midpoint of the "Big March" for teachers.) So my next post will be Day 128 on Tuesday -- which also happens to be Pi Day. And don't worry -- this is the last post in which WASC will be mentioned.

Lesson 6.3.1: Solving Systems by Elimination (Day 124)

SYSTEMS

First Verse:

Substitute x,

Then solve for y.

Substitute y,

Then solve for x.

Pre-Chorus:

x, y (four times)

Chorus:

Solve for x.

Solve for y.

Systems x.

Systems y.

Second Verse:

Eliminate x,

Then solve for y.

Eliminate y,

Then solve for x.

(to Pre-Chorus)

This is a repeat of a song I performed a few months ago -- I describe it in my October 19th post. Indeed, I played it in the fall for my Math III class -- and in that post, I even wrote that I'll be playing it again for Math I someday, once that class reaches the chapter on systems. Well, someday is today.

I don't provide a Mocha link or discuss the music theory behind the song, since I already do all of that back in my October 19th post. Keep in mind that the song is written in 10EDL -- the scale I was using for my October songs -- rather than the current 15 or 16EDL.

I think I'll do "A Day in the Life" today -- well, sort of. As I wrote in my last post, by now the observations for the principal and WASC are complete. So I'll write only about the observation periods.

Thursday:

11:45 -- Fifth period arrived. This was a Math III class.

Since I knew that my principal wanted to see real-world applications, I labeled this as Lesson 8.3.3 of the CPM Math III text, which is on applications of polynomials. But I didn't do the actual problem from that lesson of the text.

Instead, I went to the DeltaMath website and find some questions on real-world applications. These were on projectile motion, so they were all quadratic functions with -16 ft./s^2 as the leading term.

Then, since the principal wanted to see student interaction, I set up a DeltaMath assignment with exactly nine questions -- one for each group, with the same questions assigned to the whole class. Then I assigned one question for each group. Some of the questions were on the originally planned topic for the day, difference of squares (with difference of cubes delayed to 8.3.4 the next day), and one question was on projectile motion. (Notice that these are somewhat related -- an object dropped from 64 ft. follows the equation f (t) = -16t^2 + 64, which can be solved using difference of squares.) I had a member of each group describe the problem to the rest of the class so that everyone could complete the assignment on DeltaMath.

1:15 -- Fifth period left for lunch.

Monday:

9:40 -- Second period arrived. This was a Math I class.

The original plan was to teach the elimination method today -- and I stuck to it, despite several other Math I teachers rearranging the lessons to avoid teaching new material during the WASC visit. It was early in the period when the WASC committee arrived. This meant that the committee indeed saw me teach the new material. It was on Desmos, but the committee mostly saw the first example, when meant that they mostly saw me lecture since the kids were seeing elimination for the very first time.

10:35 -- Second period left.

1:25 -- Fifth period arrived. This was a Math III class.

Unlike Math I, in this class I really had completed the Chapter 8 material. So instead, I set up the first review assignment on DeltaMath and had the students work on it. Unlike the day of the principal's visit, today's assignment contained different problems for each student. I invited students to ask questions about the material, and I did some problems on the board. The WASC committee saw me call on random students using the TI, and I'd ask each student how to solve one step of a particular problem.

2:20 -- Fifth period left.

So as you can see, the principal and WASC kept observing the same classes -- second period Math I and fifth period Math III. As you already know, these aren't my best classes. Fortunately, at least second period respected the principal and WASC and grew quiet during the visits. Fifth period was a bit talkative for the principal, but they were quieter for WASC.

Today after school, the principal finally speaks to me about his observation. He said that he appreciated seeing the group interactions in fifth period that day. So even though the class was talkative that day, at least some of them were talking to each other (and me) about math.

As for the WASC observations, perhaps I could have taught elimination last Friday so that today would be guided practice for the students. Then again, many students in this class just sit there and do nothing during practice or groupwork time. Thus I masked the fact that the students don't work independently by teaching a new lesson (when they have a valid reason not to work independently -- they're learning new material) in front of WASC.

And in fifth period, maybe I should have assigned the same problems to all students on Monday, just as I had during the principal observation on Thursday. Indeed, today I do assign the same problems to all students as they continue reviewing for the Chapter 8 Test.

Today is Sevenday on the Eleven Calendar:

Resolution #7: We earn our grades through hard work and dedication.

My students definitely worked hard to earn their grades on the progress report. And we as teachers worked hard during the WASC visit -- thankfully, the observations are finally over.