Wednesday, August 31, 2022

Lesson 1.2.3: Domain and Range (Days 16-18)

Since today is August 31st, let's look at the 31st topic on Shelli's list:

31. Observe yourself!  Record your lesson using your phone in your pocket and use it to reflect

Well, I have only an old flip phone that can't record video or audio. The only "phone pockets" action I did earlier this month was to take two inadvertent photos with my phone -- still in my pocket.

Of course, I can still reflect on today's lesson even though I didn't record it. Today's fourth period Math I lesson involves teaching domain and range, in preparation for the quiz on Friday. But there are a few problems with today's lesson.

First, according to the official pacing guide, this week's quiz really only covers today's lesson -- not the lessons for the entire week. So it puts pressure on me to teach it well to make sure that students get it.

The lesson begins with a Desmos activity -- a puppy is placed on a coordinate plane, and students must find its "domain and range" (taking the puppy to be a relation defined by the set of all its points). Then I give them more examples with functions instead of puppies -- students are asked to find the domain or range, or the domain where the function is increasing or decreasing. I end the day with a VNPS review for the DeltaMath quiz on the next day that this class meets, namely Friday.

But it just seems as if I'm squeezing so much in and rushing the lesson. Potential spots for confusion include mixing up domain and range, including on the increasing /decreasing section where students try to name the maximum/minimum y-value, instead of the domain of x-values where the function is increasing or decreasing.

Keep in mind that I have the right to make changes from the official pacing plan -- and indeed, I've already made some changes, but perhaps not the right ones. Sometimes it just seems better if there's at least one meeting day between the lesson and the quiz on that lesson -- so if the quiz is to be on domain and range, that lesson should have been given yesterday, not today. (Then again, I wonder what made the author of the pacing guide to place this lesson on the last class meeting day before the quiz.)

I also wonder whether it's better to have students enter the range as 1 < y < 7 or [1, 7]. I usually lean towards the former for younger Math I kids and the latter for older Math III students, since DeltaMath accepts either form -- and so I do use the former in today's Math I class. But 1 < y < 7 allows an extra opportunity for the students to make a mistake (that is, entering x instead of y for range) that [1, 7] doesn't allow. So I wonder in reflection whether I should have just used [1, 7].

Interestingly enough, first period Math III also gets a domain and range lesson today. Their Desmos lesson is a card sort on matching functions/relations with their domain/range, but their main lesson consists of similar DeltaMath questions. And I do use the notation [1, 7] with the older students.

This is my final Blaugust post. By the way, if you're wondering where my annual "letter to my first year teacher self is," that's now #34 on Shelli's list, not #31. Then again, I sent several "letters" to my first year self earlier this summer on the other blog, "letters" containing songs I could have performed that year (which were in reality songs I'm hoping to sing this upcoming year).

The song for today is Square One TV's "Wanna Be," performed by Bobby McFerrin, a jazz singer:

Refrain:
Wanna be, wanna be,
Anything you wanna be.
Anything you wanna be,
You've got to know math.
Wanna be, wanna be,
Anything you wanna be.
Anything you wanna be,
You've got to know math.

First Verse:
You wanna be a doctor?
You wanna be a nurse?
You wanna fly a jet plane?
You've got to know math first.
You wanna coach football,
Or run a baseball team?
Operate computers,
Be whatever you dream? (To Refrain)

Second Verse:
You wanna be a stuntman,
A scientist?
A photographer,
An archaeologist?
A firefighter, detective,
Fighting fire and crimes?
You'll have to work with a lot of  numbers,
Using math all the time! (To Refrain)

There's a minimum day coming up on Friday to make up for Back to School Night. This is not a "monthly minimum day," and so it won't be a posting day. Instead, my next post is scheduled for after Labor Day weekend, on Tuesday, September 6th.

And with both Blaugust and the Willis unit over, most of my posts will now contain only the song I perform that day (which will now be on the guitar). The Math I lesson I teach that day can be inferred from the title of the post and the song.

Tuesday, August 30, 2022

Lesson 1.2.2: Defining Functions Graphically (Day 15)

Since today is August 30th, let's look at the thirtieth topic on Shelli's list:

30. How do you support struggling students?  What intervention strategies have you used?

I responded to this same Blaugust prompt three years ago. That year, I mentioned two specific examples of times when I helped struggling students. One was when my eighth graders were having trouble with rotations (isometries), and I helped them by making them more concrete by rotating graph paper. The other involved a seventh grade computer lesson where the students needed to remember mean, median, and mode (measures of center). I jogged their memory with a "Measures of Center" song.

Well, it's still possible for me to use these interventions this year. After all, I do still sing songs in class of course, and rotations will appear later this year in the Integrated Math I curriculum. (Once again, recall that much of Math 8 and Integrated Math I overlap.) But that's not what my  kids need today.

And yes, many of my Math I students are definitely struggling. Chapter 1 of the CPM text is mostly about functions, but all Math I teachers agree that the students need review on solving equations. This is why a week of solving equations was included before we officially started Lesson 1.1.1. But as we can easily see, many students are still having trouble solving the simplest of equations.

Last week at the CPM training, we had discussed turning yesterday's Lesson 1.2.1 into a game of Math Baseball, similar to the old 1980's computer lab game (like Oregon Trail). But Lesson 1.2.1, on the official pacing guide, fell on Monday -- and it's foolish to think we'd have time for Math Baseball on a non-block Monday (or Friday). So I pushed Math Baseball back to today -- and then, instead of functions from Chapter 1, change it to equations instead. (After all, students must solve equations to, for example, derive the input from a given output.)

But still, it didn't help enough students. Too many students go for a single (1B) in Math Baseball and struggle to solve a one-step equation. And of course, many of our previous interventions (the "Don't Call Me After Midnight" mnemonic and the verses of my "Solve 'Em" song) presume that the students are proficient with one-step equations and are having trouble remembering which step in a multi-step equation goes first.

Other Math I teachers are taking even more drastic measures. Some teachers are spending even more time on solving equations and are already behind the pacing guide -- this week is supposed to be the third quiz, but some are giving the second or even the first quiz this week. And one teacher is going yet more slowly -- spending time on PEMDAS and integer operations before even solving equations.

I think back to an old book written by science fiction author Isaac Asimov -- a math book. Here he introduces algebraic concepts. And one line from that book sticks out in my mind -- "there are rules for solving equations." The only reason we solve equations the way we do is because the alternative -- solving them by trial-and-error (plugging in numbers and simplifying) -- takes too long. We are riding our bike instead of walking. But too many of our students (and this applies to many concepts, not just this one) believe that this steps constitute some sort of magic -- that the rules of solving equations are arbitrary, rather than sense-making.

Links to other Blaugust participants: Sue Jones used to be one of my Blaugust go-to sites, and yet I haven't linked to her blog until today. Here's the link to her most recent post:

https://resourceroomblog.wordpress.com/2022/08/28/the-main-point/

Jones writes about the most important things for students to know and use: "Arithmetic, ratio, proportions, expressions and simple equations, people.And that's simple equations, as in the equations that my students are struggling to solve write now.

The song for today is Square One TV's "That's Math," performed by the late Gregory Hines, a world-famous tap dancer:

THAT'S MATH by Gregory Hines

First Verse: 
Hey, thank you,
Hey, come on in here.
Let me tell you something about math,
Let's look at this bill. What have we got here?
I had two plain pies at six bucks apiece,
Add one with extra cheese, that's seven.
Add eight cream sodas, a buck a pop,
Adds up to $27.
We know the tax is five percent,
In this great state we live in.
Multiply by three, 15 percent,
That's the tip that I'll be givin'.

Refrain: That's math! That's math! That's math! That's how you figure it out.
That's math! That's math! That's what it's all about.

Second Verse:
Bottom of the ninth, we're up by three,
Full count, two outs, and three men on.
This guy comes up hitting .405,
Six homers last month alone.
Gotta think, last year he hit my fastball,
Six times out of seven,
He was three for five on my curveball,
But only one for four on my slider.
After going over the numbers,
I wind up and let one fly,
I strike him out with my slider,
And I'm voted Most Valuable Guy.

Refrain: That's math! That's math! That's math! That's what it's all about.
That's math! That's math! That's how you strike 'em out.

Third Verse:
Imagine an island three feet wide,
A thousand feet below,
I gotta drop a survival box,
To save a guy named Joe.
So I calculate my altitude,
Direction and wind speed,
And I factor in the box's weight,
And the angle I will need.
Now I'm not ashamed to say I hit,
A perfect bulls-eye and move on.
Joe can eat until he gets rescued,
I just hope he likes croutons.

Refrain: That's math! That's math! That's math! That's how you figure it out.
That's math! That's math! Bing! Beng!

Fourth Verse:
Now the only thing as great as math I see,
As far as I'm concerned,
Is music I can dance to,
Here's something I recently learned:
Music is a kind of math,
And intervals and beats.
Every time I sing a note,
Every time I move my feet.
And it's not just school,
It begins when you close your book.
Tread any path and you'll find math,
Everywhere you look.

Refrain: That's math! That's math! That's math! Bing! Beng!.
That's math! That's math! That's what you can do with math.


Thursday, August 25, 2022

Back to School Night (Days 12-14)

Since today is August 25th, let's look at the 25th topic on Shelli's list:

25. What’s a practice you keep doing year after year? Either something that works great or something that maybe needs examining. Why do you keep doing it?

Before I answer this question, let me explain why today is doubly special. It is Back to School Night -- and it's also the day of a special all-day training day for math teachers, on the CPM text.

I admit it's a bit odd that the district would choose Back to School Night to hold its training. Then again, if I were to choose any day in August to take off for a PD day, I'd likely choose today. First, it's a Thursday -- the day I have no conference period on the block schedule. Then in addition to having no break, I have to stay late for parent night. That's all the more reason to have a PD day instead.

Let's do "A Day in the Life" for this doubly special day. Along the way, I'll answer Shelli's question too:

8:00 -- The training session begins. We start out with introductions, team-building, and goals. Three participants, including me, are from the high school, with the other three from middle schools.

8:30 -- The presenter discusses understanding balanced instruction, with an example on solving a system of equations to determine how many xylophones and yodelers there are (a clearly contrived example since those words start with x and y).

10:00 -- We take a quick break.

10:15 -- We read an article on proficiency teaching with study teams.

11:30 -- We leave for lunch. Four of us -- the high school trio plus a former high school teacher who's now teaching Math I to honors eighth graders -- go off to eat together.

12:30 -- As we return from lunch, I receive an unsettling email. Apparently, the sub (in reality, another teacher, since most subs in our district cover elementary schools) for second period had to suspend one guy in my class, for playing with a paper gun. Due to Uvalde and other tragedies, it's a serious offense.

The training session now moves on to CPM resources and tips. CPM is a text which is commonly used in integrated math classes. (My last two posts already have CPM lesson numbers in their titles.)

1:15 -- This is lesson planning time. The high school trio come up with a possible functions lesson for next week, including an activity based on Math Baseball (an old 1980's computer game -- one of my favorites, along with Oregon Trail).

2:45 -- The presenter wraps up the lesson and discusses next steps.

3:00 -- The training session ends. We return to school and prepare our rooms for the parent visit. In fact, this is the first in-person Back to School Night since before the pandemic.

5:00 -- Back to School Night begins, and a first period student and his parent arrive. But parents aren't supposed to arrive at classrooms until 6:00 -- the first hour is for other activities in the quad. Still, I host the family and discuss my class with the early birds.

I end their visit with a rendition of the "Let's Get Mathematical" parody. Notice that even though I posted it to the blog yesterday, I don't perform it until today. (This is to avoid controversy with parents. If I sang it in class, students might tell their parents that I was singing the original version with its suggestive lyrics -- so instead, I perform it today directly to parents.)

6:45 -- Seven students and their families arrive from fourth period. This is the largest contingent from any class. (As expected, families are much more likely to attend parent night at elementary schools than high schools.) I heartily sing "Let's Get Mathematical" for the group.

7:30 -- The last sixth period students leave after the "Let's Get Mathematical" finale. Back to School night ends, thus finally ending my super-long day.

Meanwhile, I must think about how the day goes for the subs covering the classes. One teacher took first period, another took second, and one teacher took both Periods 5-6.

There's a lot of shuffling going on in first period Math III. It took a while to figure out which teacher was going to take the class -- and because of this, the Warm-Up and Exit Pass don't occur, and the notebook page that I want to pass out to this class never gets passed out.

And this is on top of changes that I made earlier this week to the Math III pacing guide. After the quiz on Monday, I combined quiz corrections with a tricky lesson on solving systems by substitution in the fifth period class on Tuesday. The students struggled, so for the corresponding first period block yesterday, I did an easier lesson on function definitions along with the quiz corrections instead. This leads into today, where the Math III review lesson on function notation just happens to line up with the Math I new lesson on function notation. So to make it easier for a sub, I intend for the sub to pass out the notebook sheet on function notation to all classes.

Oh, and that notebook sheet contains DIXI-ROYD -- a Sarah Carter-ism that I keep going back to year after year. Earlier during lunch, I mention DIXI-ROYD to my fellow Math I teachers. One of them pointed out that the mnemonic "DIXI" might be considered controversial (for example, consider why The Chicks dropped that word from their name). Then again, there are also Dixie brand cups.

Anyway, all of my classes do get the notebook sheet, except first period (according to the early bird guy at Back to School Night). So now first period is behind fifth -- and I must cover both the missing notebook page and the substitution lesson that they didn't get earlier this week in order to catch up.

The early bird guy also makes a suggestion -- now that we have Google Classroom, I should take matters out of the sub's hands. The Warm-Up, main lesson, and Exit Pass should all be posted directly to Google Classroom, with no notebook or other written pages. Then it won't matter whether my classes are taken by a true sub, or by teachers who take the classes back to their own rooms. The students will have everything they need for that day's lesson.

Links to other Blaugust participants: Stephen Dull also writes about something he uses in his classroom year after year -- a 100 x 100 activity that's apparently ten years old, though I've never heard of it. (By contrast, DIXI-ROYD is only six years old. Its predecessor DIX-ROY might be closer to a decade ago.)

https://tweakingfornoreason.wordpress.com/2022/08/25/something-old-something-borrowed/

Well, that concludes today's post. It's possible that there might be a second CPM training meeting at some point -- though I doubt it, I wonder whether it would land on Parent Conferences night in October.

Wednesday, August 24, 2022

Lesson 1.1.3: Visual Patterns (Day 11)

Since today is August 24th, let's look at the 24th topic on Shelli's list:

24. Time Capsule - revisit an old post and reflect. If you are new to blogging - find a post on this day from the past on someone else's blog-read, share, reflect.

OK, I'll do that. I'll revisit to the last time I posted on August 24th -- two years ago, in 2020. At the time I was writing about the state of the pandemic and the generation gap:

OK, in case you haven't heard it by now, Orange County was indeed taken off of the state coronavirus watch list yesterday. In order for schools to reopen, the county must stay off of the watch list for two full weeks, which takes us to Labor Day weekend.

Then it's up to my new district, and all other districts in the county, to declare a reopening plan. I will continue to monitor my district website and emails for any word on, for example, a board meeting during which such a plan is discussed.

As I mentioned before in my last post, my own opinion on the reopening is mixed, due to my status as a sub. As long as I can get subbing assignments for distance learning, then I'm not in any particular hurry for the schools to reopen. But so far, as you can plainly see, I haven't gotten any calls yet. And I assume, of course, that I'll get calls once the schools reopen. Thus I remain in favor of a reopening.

By the way, as the new school year begins, I've been thinking about the generations again -- in particular, what impact the coronavirus has on each generation. Recall my definition of generations -- the Baby Boom Generation definitely starts in 1946, after World War II. If we then assign eighteen years for each generation, we get the following chart:

Baby Boomers: 1946-1964
Generation X: 1964-1982
Millennials: 1982-2000
Generation Z: 2000-2018

Then each generation graduates high school just as the next one is being born -- for example, the Boomers graduated in 1964-1982, exactly when Gen X was born. The Millennials' name refers to the "millennium" -- they were born in the old millennium and graduated in the new millennium.

There's about two years of leeway in these definitions. Thus even though 1982 is listed as the cusp between Gen X and Millennials, those born in 1980-1984 may be assigned to either generation. This includes yours truly, as I was born in 1980. Thus sometimes we're referred to as the "Xennials," on the cusp between Gen X and Millennials. (Another name for our microgeneration is "Oregon Trail," named after the only game that was available in our school computer labs. And yes, I definitely played "Oregon Trail" as a young elementary student.)

Notice that the generation currently in K-12 is Generation Z, born in the 2000-2018 range. If we cut out two years on either cusp, this leaves 2003-2015 as definitely in Gen Z. Notice that the oldest students in this range are now seniors while the youngest kids are kindergartners. This means that we can equivalently define Gen Z as the generation attending K-12 during the 2020-2021 school year -- a year that's itself defined by the coronavirus. Thus a member of Gen Z is someone whose K-12 education was interrupted by the virus.

Indeed, a new name that's come up for Gen Z is "Zoomers" -- it starts with Z and rhymes with "Boomers," so it sounds like a good name for a generation. And indeed, the name "Zoomers" fits the idea that this is the generation whose education was affected by the virus -- that is, it's the generation that must use websites such as Zoom for its K-12 education.

Current college students are "Zennials," on the cusp between Millennials and Gen Z. Current preschoolers are on the cusp between Gen Z and the next generation.

(Likewise, those in K-12 during the 2002-2003 school year are the Millennials. But there's a tendency to move this up to 2001-2002, as in 9/11 -- the Millennials are those in K-12 during the attacks. The idea is that the tragedies of 9/11 and the virus had a big effect on the education of those generations.)

My eighth graders from the old charter school are now seniors -- in other words, the three cohorts I taught that year are the first three classes that are fully Gen Z.

Apparently, the originators of generation theory are Strauss and Howe. They named generations going all the way back to the fifteenth century, with the Arthurian Generation (1433-1460) and Humanist Generation (1461-1482). Interestingly enough, if we refer to the Arthurians and Humanists as Generation A and B respectively, then X, Y, and Z work out to be the correct generations (although Generation Q according to their list is a short one, 1842-1843).

Returning to the present, let's get ready for music. I will say that I did perform the new version of "Function Rap" in my first and sixth period classes today.

Meanwhile, let's get to the new song for today. Earlier this month a famous singer, Olivia Newton-John, passed away. (She was an older Boomer and considered an icon to Gen X.) In her honor, I want to post a math version of her signature song "(Let's Get) Physical" -- say, why don't I change "physical" to "mathematical" and go from there?

Here is the parody that I come up with:

Verse 1:
I'm sayin' all the things that you like me to know,
Makin' good education.
I gotta answer you just right,
You know what I mean.
I drew a coordinate plane for you,
Then two lines the axes to be.
The y-axis is up and down,
And x goes horizontally.

Chorus:
Let's get mathematical, 'matical,
I want mathematical.
Let's get mathematical.
Let me hear your math mind talk, your math mind talk.
Let me hear your math mind talk.
Let's get mathematical, 'matical,
I want mathematical.
Let's get mathematical.
Let me hear your math mind talk, your math mind talk.
Let me hear your math mind talk.

Verse 2:
I've been working, I've been good,
Tried to graph the points from the table.
It's gettin' hard, this graphin' lines,
You know what I mean.
I'm sure you'll understand my math homework,
Though I did my work mentally.
You gotta know that you're bringin' out,
The math person in me.
(to Chorus)

Since this is a parody of a well-known song, there's no need for me to post the tune here.

By the way, tomorrow is Thursday, which is ordinarily not a posting day. But I will do "A Day in the Life" because it's a doubly special day. You'll find out those two special reasons in tomorrow's post.

Tuesday, August 23, 2022

Lesson 1.1.2 Functions: Word to Table (Day 10)

Since today is August 23rd, let's look at the 23rd topic on Shelli's list:

23. Shoutouts!  Give a shout-out to a former teacher, a colleague, or someone in your school or community who is a difference maker.

Well, I've written about my favorite teachers here on the blog before. So let me give another shout-out to my best teachers:

  • My favorite elementary teacher was my second grade teacher -- who later became my fifth grade teacher as well. She was one of the first to notice that I was good at math, and so she came up with the idea of having a Pre-Algebra teacher from the high school (which went from Grades 7-12 in my district) send me a textbook. As a second-grader I would work on the assignments independently, then my teacher would send my work to the high school before I worked on the next assignment. By the time I reached the fifth grade and was in her class again, she had convinced the high school teacher to send me the textbook for "APA," or Advanced Pre-Algebra.
  • Incidentally, my favorite math teacher was that teacher who sent me the advanced work. I finally met her when I was placed in her Algebra I class in the seventh grade. I was the only seventh grader in a class full of eighth graders, but she made me feel welcome in her class.
  • Just like Fawn Nguyen, I had my favorite history teacher when I was an eighth grader. He was also in charge of the Thespian Club at our school, and so he decided to teach history in a unique way -- he would dress up as a historical figure and lecture as if he were that character. Therefore his lectures were more memorable to the students. About ten years ago, he retired from teaching, and many of my classmates held a big party for him.
  • My favorite science teacher was my junior-year teacher. I was an up-and-down student when it came to science -- the first two years of Integrated Science were more biology-leaning and I struggled a little, but the third year had more emphasis on physical science, which is more closely related to my strongest subject, math (as we spent over a month discussing with Kline's book). And so I did very well in this teacher's class -- indeed, she told me that I would finish the whole test in a few minutes and spend the rest of the time making my writing neat, and of course my answers were correct. She wondered why I wasn't enrolled in the magnet program, and I replied that I had moved to my new district as a freshman, while magnet students are recruited in the eighth grade. And so my science teacher convinced the school to admit me to the magnet program as a junior. Even though I was no longer in her class, she was still my most memorable science teacher for this reason.
  • My favorite English teacher was my senior-year teacher -- or to be precise, one of two English teachers I had that year. You see, the magnet program I'd entered a year earlier was a year ahead in English -- that is, junior-level English for neighborhood students was equivalent to sophomore English within the magnet. This meant that I would have to double up on English my senior year in order to graduate from the magnet -- and I didn't look forward to this, since my strongest subject was math, not English. So even though I was the only senior in a class full of juniors, I enjoyed this English teacher's class the most. This teacher allowed us to be creative in our writing -- I remember that for extra-credit, I wrote parodies of the literature we were reading, except with my friends and me as the characters. There was also an essay contest for seniors in which we were to write about a journey we had taken -- I wasn't going to participate, except that the junior English teacher whose class I had to take decided to assign the same topic for an in-class grade! I was in the unique position of writing an essay for class and submitting the same essay to the contest.  So I wrote about my journey through my education (much of which I just wrote about in this post) -- and won $200.
When I reflect upon my favorite teachers, I notice that they have some traits in common. Two of my teachers taught subjects I didn't enjoy, English and history -- and made them enjoyable by presenting them in a unique way. The other teachers taught my stronger subjects, math and science -- and they recognized that I was talented enough in those subjects to move me up to the next level.

Some traditionalists lament the fact that the Common Core accountability movement encourages teachers to focus on the weaker students at the expense of the stronger students. They say that some strong students want to move ahead in their classes, but the teachers, who claim their hands are tied by Common Core, won't let them.

I owe it to my stronger students to support them and celebrate their talents just as my own teachers celebrated my own talents.

Recall back on Square Root Day the story I told about teaching my second grade friend the square roots of 0, 1, and 144. I admit that this incident, along with my admiration of my second grade teacher, formed the foundation of my desire to become a teacher. At first I didn't know that Grades 7 and higher even existed -- I knew that my elementary school was K-6, and I'd always believed that students went directly from sixth grade to college. I remember that as a kindergartner, to me the sixth graders looked like grown-ups, and so I expected that they were nearly college students.

Naturally, it was the arrival of my Pre-Algebra text that alerted me to existence of 7th grade. I wasn't sure whether I wanted to be a teacher because I wasn't sure I'd be good enough at any subject other than math, but the benefactor who gave me the Pre-Algebra text was a single-subject teacher who taught math and nothing else. And so I knew at that moment that I wanted to become a single-subject math teacher -- which meant that I'd most likely teach in a high school.

And returning to the present, that's exactly where I am now -- teaching high school. But unfortunately, I can't say that I'm as good a teacher as my favorites were. Today in second period, I get into an argument with my class over excessive tardies (some of which were due to the freshmen being confused with our block schedule), while fifth period is as loud as ever (even after I've already switched their seats, and even with the most talkative student being absent today). It shows that I still have a long way to go.

It bears repeating that I owe it to my stronger students to be as good a teacher to them as my teachers were to me.

Today I perform the song "Function Rap." My Math I kids are learning about functions today while my Math III students will review them later this week, so this is a perfect song to rap this week.

I posted the lyrics on the other blog earlier this summer, but I've made changes since then. First of all, the song no longer has a melodic chorus (14EDL) -- it's now a pure rap (still call-and-response). And second, one student today is upset that my rap doesn't rhyme. So let me follow Peterik's rhyming chapter and post an improved version here to this blog:

Verse 1:
When I say 1, you say...5.
When I say 2, you say...7.
When I say 3, you say...9.
When I say 4, you say...11.

Chorus:
Is this relation a function? Yes!
Is this relation a function? Yes!
When I say x, you say...y.
Is this relation a function? Yes!

Verse 2:
When I say 1, you say...5.
When I say 3, you say...-1.
When I say 4, you say...0.
When I say -3, you say...-1.
(to Chorus)

Verse 3:
When I say 1, you say...5.
When I say 4, you say...0.
When I say 2, you say...

Coda:
Is this relation a function? No!

(The last verse corresponds to a relation where 2 is paired with two different values.)

Perhaps I might consider performing this new improved version in first period, which doesn't meet today but will meet tomorrow.

Wednesday, August 17, 2022

Intro to Solving Equations (Days 6-9)

Since today is August 17th, let's look at the seventeenth topic on Shelli's list:

17. How I used something unexpected in my classroom to…

Last year, I wrote that I unexpectedly used some old algebra tiles in my classroom to implement Sarah Carter's "Master Designer" opening activity. But I didn't do that activity this year. Instead I -- well, today, the 17th, is also my new monthly posting day for "A Day in the Life," so let's see how that goes:

8:30 -- First period arrives. This is a Math III class.

After yesterday's disaster, I completely reorder the lessons for today's class. Like yesterday, I started out with the Vanderwerf name tent prompt, "What do you look for in a teacher?" But then I jump directly into the Desmos classwork activity, for two reasons. The first is to reinforce that Desmos is classwork, hence a part of the classwork component of the grade. The second is that many MTBoS members who use Desmos in their classes use it to introduce a new topic, to get their students engaged. Thus it makes sense to have Desmos be as early in the period as possible. Here Desmos introduces students to the Quadratic Formula.

I let the students work on Desmos until music break. Last week, I wrote that most of my songs will be geared towards Math I rather than III, and one exception would be the Quadratic Formula song. What I didn't realize is that the formula would be taught early in the year (as it's technically a Math II topic), and so my very first song of the year in Math III is Quadratic Weasel. (A rendition of the well-known parody also appears in the Desmos lesson as well.) This will be one of the very few times that I will sing a different song in Math III than in I.

After music break, I jump into DeltaMath and start doing some questions from that lesson, which the students then copy into their interactive notebooks. So this is how I'll use INB's in a class where most of the assignments will be on Desmos or DeltaMath.

One thing that's tricky is going over the previous night's homework -- since DeltaMath almost always randomizes the questions, a student can't really ask me to go over the same problem. As it turns out, today I just barely have enough time to do four or five problems from DeltaMath.

As an Exit Pass, I ask the students to find the discriminant of x^2 + 5x + 2. The answer is 5^2 - 4(1)(2) or 17 -- and of course, today's date is the seventeenth.

9:55 -- First period leaves for nutrition, which leads directly into third period conference. Recall that at this school, four classes meet on each block day, tied to the day of the week -- on Wednesdays, periods 1, 3, 4, 6 are the classes that meet. I, along with most of the freshmen, are still getting used to it.

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

As it turns out, Math I has a Desmos lesson as well. But their Desmos is much simpler -- it simply consists of three multi-step linear equations for the students to solve.

So this time, I have the students copy the Desmos equations onto page 5 of their INB's. On the same page, I have them glue in a mnemonic that my next door neighbor teacher uses in her own Math I class -- "Don't Call Me After Midnight" (for Distribute, Combine terms, Move variables, Add/subtract, and Multiply/divide).

For this class, the song for music break is Square One TV's "Count on It." I almost always sing it as the first or second song of the year, to let kids know that they will have a mathematical future. Here are the lyrics and video of the song:

Count On It

Lead vocals by Larry Cedar

Sooner or later, you’re gonna see some math
You can count on it
Sooner or later, those numbers cross your path
You can count on it
You may be hoping it will go away
But let me tell you, math is here to stay
You can count on it, hoo, yeah
You can count on it
Everywhere you look, they’re measuring the action
You can count on it
Everywhere you look, they’re even using fractions
You can count on it
They’re keeping time, and they’re keeping the score
They draw the line, and they’re running the store
You can count on it, hoo
Yeah, you can count on it
Look at the dial; look at how far
Look at how much; look where we are
Look at the gauge; look at the graph
Check out the numbers; you’ve got the last laugh
‘Cause it ain’t mystery; there’s nothing tough about it
You can count on it, that’s right
Soon you’re gonna see that you couldn’t live without it
You can count on it, hoo
Don’t take a genius or a great magician
To make a pretty good mathematician
You can count on it, hoo, yeah
Yeah, you can count on it, whoo
Oh, you can count on it, whoo
Baby, you can count on it
(fade out over Larry singing skat)

After music break, I have the students prepare for their weekly Friday quiz. Like last year, I decided to use the VNPS method -- Vertical Non-Permanent Surfaces. But while last year's desks had whiteboard surfaces, this year's don't. But there is a whiteboard on all four walls, so I divide the class into groups of four and have each group use part of the board as a VNPS.

As an Exit Pass, I ask the students to solve 2(3x - 1)  = 100. The solution is x = 102/6 = 17 -- and of course, today's date is the seventeenth.

1:15 -- Fourth period leaves for lunch.

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

But one thing tricky about the block schedule is that while all classes meet on Mondays and Fridays, yesterday was 2-3-4-5 while today is 1-3-4-6. Thus today is the second block day for fourth period, but only the first block day for sixth period. Thus on Wednesday, I must get used to the fact that today's lesson matches yesterday's fourth period lesson, not today's.

So instead of page 5 of their INB's, these kids are still working on page 4. I have the students copy an equation that requires all five steps, and then I sing yesterday's "Solve 'Em" song. The rest of the time is spent copying equations from DeltaMath into their INB's. There is no Desmos lesson in this class, but I do give them the same Exit Pass (since I want the answer to be 17 today).

3:30 -- Sixth period leaves, thus ending my day of teaching.

Well, I did use something unexpected today -- two things in fact. I used INB's for taking notes even though most assignments are online, and I use VNPS even though my only whiteboards are on walls.

It is still the Willis unit. Classes are still in flux (with three new students in my sixth period), and so I'm still not ready to discuss the demographics of my classes.

By the way, tonight I'm going to watch the newest version of the game show Password. This version is hosted by Keke Palmer -- yes, as a young girl she played the title character in Akeelah and the Bee, one of my favorite movies (as I've mentioned before on the blog). It's nice to see her again -- going from a young girl playing a word whiz to a young woman playing a word game.

My next post will be this upcoming Tuesday.

Tuesday, August 16, 2022

Solving Equations (Day 5)

Since today is August 16th, let's look at the sixteenth topic on Shelli's list:

16. Something I struggle with as a teacher/in the classroom.

Well, I definitely struggle today with technology in the classroom -- including integrating technology throughout my lessons, as well as classroom management while students are using technology.

I did finally hear a reason why there's so much DeltaMath and Desmos on the syllabus for both Math I and III -- last year, online assignments were given for the benefit of students who tested positive for COVID and couldn't access written assignments easily. (Although COVID numbers should be dropping now, I notice that one class has already had two students test positive.)

While the focus of this blog will be Math I, my tech problems are more noticeable in Math III, due mainly to what the department agreed on for the grade percentage breakdown. In Math I there are four categories worth 25% each -- assignments, quizzes, chapter tests, and midterm/final. But in Math III, homework and classwork are separate categories, with each of the five categories worth 20%. So it's more important to distinguish between homework and classwork, even though most assignments are online.

So here's what I do in my fifth period Math III class today -- I start out with a Vanderwerf name tent prompt (which I'm doing for a second week). Then I try to go over last night's HW on exponents -- which is tricky, since everyone gets different questions on DeltaMath. Then I have the students take out their notebooks and write down the Quadratic Formula. I know that they need more practice with the formula -- but the official classwork for today is a Desmos activity on the formula. So I attempt to have them write some info from Desmos into their notebooks -- which only slowed them down, so that they couldn't finish the activity. So now they have both the "classwork" and the homework to do tonight -- and I can't drop either one, since they fit into different 20% categories.

While all of this is going on, a group of talkative guys (including one who is possibly special ed) is loud during the computer lessons. They end of distracting many of the other students.

OK, so those are all my problems -- how about solutions? Well, I'm already considering a seating change the next time this block meets, on Thursday. And as for the lesson, I'm thinking of changing things up when the other Math III block meets for first period tomorrow. I'll save it for tomorrow's post.

Links to other Blaugust participants: Stephen Dull gets ready to start his twentieth year of teaching:

https://tweakingfornoreason.wordpress.com/2022/08/16/year-20/

There are two songs I perform today. In Math III, I sing "Quadratic Weasel" -- that famous "Pop Goes the Weasel" parody for the Quadratic Formula:

Chorus:
x equals negative b,
Plus or minus the square root,
Of b squared minus 4ac,
All over 2a.

Bridge #1:
If a's negative, the curve opens down,
Up for positive a.
Vertex x is negative b,
All over 2a.

Bridge #2:
If c's negative, crosses y below x,
Above for positive c.
Vertex x is negative b,
All over 2a.

The line "All over 2a" counts as a hook, even though it doesn't contain the song title. That's because the corresponding line of song it's parodying is the title line, "Pop Goes the Weasel."

In Math I, the song I sing is "Solve 'Em" -- an original song. I originally titled this song "Solve It" (when I posted earlier on the blog), but I took a suggestion from Jim Peterik's book and included the near rhyme "Solve 'Em" and "problem." It is a cumulative song (a "partridge"):

Chorus:
When you see equations,
In any math problem,
All you have to do,
Is solve 'em!

Verse #6:
Distribute on the left side,
Distribute on the right side.

Verse #5:
Combine like terms on the left side,
Combine like terms on the right side.

Verse #4:
Move the variables to the left side,
Move the numbers to the right side.

Verse #3:
Plus/minus on the left side,
The same done to the right side.

Verse #2:
Times/divide on the left side,
The same done to the right side.

Verse #1:
A letter alone on the left side,
A number alone on the right side.
That's all you have to do,
To solve 'em!

Since this is an original song, I should post its tune in Mocha. I first wrote this song in G major, years before I learned about Mocha or EDL scales.

The following program is written in 15EDL, an approximation of the F major scale (although Degrees 13 and 11 sound out of tune from true F major). Also, instead of READ and DATA, I take advantage of the cumulative nature of the song and use subroutines (GOSUB and RETURN):

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

10 N=8
20 FOR V=1 TO 6
30 GOSUB 200
40 GOSUB 100
50 FOR X=1 TO V
60 GOSUB 200
70 NEXT X
80 GOSUB 100
90 NEXT V: END
100 SOUND 261-N*13,2
110 SOUND 261-N*13,2
120 SOUND 261-N*16,2
130 SOUND 261-N*16,2
140 SOUND 261-N*20,4
150 SOUND 261-N*13,4
160 SOUND 261-N*13,2
170 SOUND 261-N*13,14
180 RETURN
200 SOUND 261-N*12,2
210 SOUND 261-N*12,2
220 SOUND 261-N*15,2
230 SOUND 261-N*15,2
240 SOUND 261-N*20,2
250 SOUND 261-N*15,6
260 SOUND 261-N*12,2
270 SOUND 261-N*12,2
280 SOUND 261-N*11,2
290 SOUND 261-N*11,2
300 SOUND 261-N*15,2
310 SOUND 261-N*15,6
320 RETURN

As usual, click on Sound before you RUN the program.

Wednesday, August 10, 2022

Sara(h) Week Activities (Days 1-4)

Since today is August 10th, let's look at the tenth topic on Shelli's list:

10. Share your #MTBoS Photo Challenge photos (#MathPhoto22)

And you know my problem -- I have an old flip phone rather than a smartphone, and so I can't take photos very easily. Sometimes I would ask my students to take photos and send them to my email address, but I didn't want to do that on the very first day of school, when I know no one and no one knows me.

This isn't to say that my phone lacks a camera. Indeed, my phone does have a camera -- and somehow, my phone took two photos today. Of course, I don't even need to look at them to figure out what they are photos of -- the inside of my pocket, which is where my phone was when I unwittingly took photos.

Then again, even if I had lucked out and taken photos of something other than my pocket, I wouldn't have been able to send them from my phone to the blog for Blaugust. So it appears that I'm unable to complete Shelli's prompt #10.

Instead, I'll begin with a description of today, in "A Day in the Life" format. This is for the special day "my first day of school." (Actually, that's one of Shelli's Blaugust prompts as well -- prompt #33.)

7:17 -- This is the time stamp of my first pocket photo, just as I leave home for work.

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

In all of my classes today, I give opening week activities. This is Sara(h) week, when many teachers give activities promoted by two famous teacher-bloggers -- Sara Vanderwerf and Sarah Carter. But, as I mentioned in my last post, the lead Math III teacher has already created a pacing guide with opening activities, and so I was torn between giving those activities and the ones I already know from Sara(h).

Well, the first activity has students log into a Google Slide and fill it in with personal info. Much of this info is exactly what would be included in a Sara Vanderwerf name tent:

https://www.saravanderwerf.com/week-1-day-1-name-tents-with-feedback/

I know that I'm going to have trouble learning student names this year. Last year, it was easier because I had smaller classes at a smaller school. Now I'm at a full-sized high school with full-sized classes. And I know that it's easier to learn names when I can just look at the name tents and learn to match names with faces, rather than have to check Google Slides to learn names. (And besides, chances are that some students won't bring a charged Chromebook on the first day, no matter how many emails are sent beforehand directing them to bring it.)

And so I decided just to do the Vanderwerf name tents instead of Google Slides. I might pick up some of the opening activities from the pacing guide later on, but I'm starting out with Vanderwerf. The first prompt is "What are you looking forward to this year?" While they fill out their name tents, I fill out a seating chart -- and hand out pencils for the special day "the first day of school."

For the main task of the day, I decided to try Witzzle, from our other Sarah -- Carter this time. This is one of the tasks that I tried out at the end of last year and wanted to introduce this year:

https://mathequalslove.net/witzzle-pro-math-game/

I play the game the way Carter suggests -- use the TI to choose a random number from -12 to 36, then use that as a target number and have the students call out "Witzzle!"

I'm slowly introducing some of my rules each day. Today I introduce Rule #9: "We value instructional time," just as I discuss tough enforcement of the tardy and restroom rules.

Indeed, notice that first period now starts at 8:30, due to the new California law. In theory, a later start time might reduce tardies a little, but not completely -- and I know that because last year, with school starting at 8:00, some students arrived after 8:30 -- the future start time. (And of course, some students would be late even if school didn't start until 8:00 PM -- they'd arrive late because they want to shave off time from an undesirable task such as going to school, not because they can't get there in time.)

So anticipating that there will still be many tardies this year, my new policy is that standards must be written after every fourth tardy. Also, there will be a limit of nine restroom passes in the first semester -- once every two weeks, beyond which there will also be standards. Failure to write the standards will lead to detention, and failure to attend detention will lead to parent contact.

The class ends with an Exit Pass (as the Vanderwerf prompt counts as a Warm-Up). Since the last number for Witzzle is 10, the students write the final equation from Witzzle, 5 + 6 - 1 = 10 -- and of course, today's date is the tenth.

9:25 -- First period leaves for nutrition.

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

Yesterday, there was a CT meeting for Math I (which I attended instead of the Math III meeting). There was a pacing plan for this class as well, but it's a little looser than Math III -- especially when it comes to setting the opening week activities. So I just follow the same Sara(h) activities as in Math III.

In first period, and even more so in second, I spend too much time on the name tents and start Witzzle late, forcing me to rush the description of Rule #9. This also sends the wrong message -- our new math class is more about answering personal questions (the name tents) and basic arithmetic (on Witzzle) than high school math, and they won't even have to worry about following rules -- not the best message to give a class of mostly freshmen.

10:35 -- Second period leaves. Third period will be my conference period this year.

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

This class is a little longer than the others, since this is when announcements are given. The students use this as extra time to work on their name tents. So this provides me with more time at the end to tell them what to expect in a high school math class.

12:40 -- Fourth period leaves for lunch.

1:20 -- This is the time stamp of my second pocket photo, just as lunch ends and fifth period arrives (if only my phone isn't in my pocket). This is the second of two Integrated Math III classes.

This time I finally shave a few minutes from name tents -- but in my zeal to get to Witzzle quickly, I end up not passing out the first day of school pencils.

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

And not until this last period do I finally put it all together and time the class properly. I pass out the pencils and start Witzzle at or just after the 20-minute mark (around 2:50), leaving plenty of time to discuss some rules.

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

All in all, it's a successful first day of school. But one thing I worry about is whether I spend too much time on activity and not enough time on the rules. During my third period conference, I can hear my two neighbor teachers discuss the syllabus with their students. I know -- I've heard that syllabus on the first day isn't the best idea (as students get tired of hearing six syllabi that day). But still, after hearing their classes, it seems as if my first week plans are so light.

And this also might have been a factor in the parent complaint about my songs last year. My first song immediately followed Sara(h) week, so it seemed as if all I did was play games and sing songs. The parent might not have complained about music if I'd started with a syllabus and solid academic content.

Of course, part of the problem is that I haven't completed figured out my policies. I've written so much on the blogs about what I want my classes to look like, but some of that is clashing with what I'm hearing during the CT meetings.

Most, if not all, Math I and III assignments are going to be on DeltaMath or Desmos. Thus neither an interactive notebook nor a weekly Technology 1955 day makes sense. There's no point in forcing students to have notebooks if all the assignments are online.

Then again, I saw some Math III students today taking out phones during Witzzle -- suggesting that they are using calculators to solve one-digit arithmetic problems. This is the main reason that I wanted Tech 55 in the first place -- at least once a week, students need to do simple arithmetic in their heads. So Math III could use a weekly Tech 55 day. But if all assignments are online, they can still use Google calculator on their Chromebooks, even if their phones are put away. So this is what I need to finalize over the weekend, before that first Monday arrives.

As is typical in high schools, my classes are fluctuating, so I don't wish to talk about the demographics of my classes just yet. The size of all classes are in the 30's. There are 35 desks in my classroom. Some of my rosters have more than 35 students, but in no period do more than 35 actually attend (although one class has exactly that number attending today).

As you'd expect, most Math III students are juniors. There are a few seniors in the classes, as well as a total of three sophomores (working at Steve level, headed for Calculus). And of course, most Math I kids are freshmen, but there are some older students, including one junior. The lone Math I junior is one of the first students to ask for a restroom pass today -- and you can probably figure out how this student feels about math and would want to leave class as much as possible.

The rest of this week will be more opening week activities. Some come from the CT pacing guides -- indeed, both of them have an assignment similar to Sarah Carter's Twos through Nines challenge. (For Math III it's For Four 4's, and for Math I it's 5-4-3-2-1.) Also, Math III appears to have a Number Talks activity, similar to one mentioned on Sara Vanderwerf's website. Thus even by following the pacing guides, I'm still having some special activities for Sara(h) Week.

By the way, my blogging schedule will follow the block schedule. As I mentioned last year, the main high school has three block days with four periods each -- Tuesday 2-3-4-5, Wednesday 1-3-4-6, and Thursday 1-2-5-6, with all classes on Mondays and Fridays. The block schedule will begin next week.

I've decided that this blog will follow the fourth period block schedule, and so I'll post on its block days, Tuesday and Wednesday (and not on all classes days). So my next post will be on Tuesday.

Monday, August 8, 2022

The Return of This Blog

This is my first post on my Geometry blog in almost a year. And so this post is another FAQ post where I answer questions about what to expect in the new school year.

Table of Contents

1. Where and what will I be teaching in the new school year?
2. Is Blaugust back?
3. What is my first Blaugust prompt?
4. What will be my cell phone policy?
5. What will be my food policy?
6. What will be my homework/interactive notebook policy?
7. Am I still reading Jim Peterik's Songwriting for Dummies?
8. What is today's Rapoport question?
9. Who are the other Blaugust participants?
10. What will be my new blogging schedule?

1. Where and what will I be teaching in the new school year?

I can now finally say where I'll be working. I will be remaining in my current district, in LA County, and working at the main high school in the district.

This is the school I visited back in November, the school whose AP Calculus teacher I visited in order to gain ideas on how to become a better teacher myself. Now we'll be working at the same school -- and he, a 20+year veteran, is now my department chair.

Coming into today, I still didn't know what levels of math I'm supposed to teach. Our schedules are supposed to be posted on Aeries (the same system where grades are posted), but mine isn't -- likely because I'm new here. I didn't know for sure until the chair posted the schedule for tomorrow's department meetings.

I will be teaching Integrated Math I and III this year.

It is generally known that Math III is essentially equivalent to Algebra II, while Math I and II are an integrated version of Algebra I and Geometry. So this is the closest I've gotten to teaching my favorite math, Geometry, since my teaching career began.

And that's why I'm returning to my original blog -- my Geometry blog -- starting today. My Stats blog will no longer be active. (And on second thought, I admit that I should never have left my old blog, not even when I taught Stats last year.)

The first day of school will be Wednesday, but today is a PD day. Therefore it counts as a Tina Cardone "A Day in the Life" post for the special day "a PD day":

8:00 -- I arrive at my new school. The principal serves the teachers a hearty Welcome Back breakfast.

9:00 -- I visit the first of three PD stations in the gym, where the principal talks to all of us about policies and procedures.

10:00 -- I visit the second of three PD stations in the library, where we hear of emergency procedures and activities.

11:00 -- I visit the third of three PD stations in the cafeteria, where we learn about our academic focus for the 2022-23 school year.

12:00 -- I finally make it to the office, where I receive the key to my new classroom. It's located on the second floor of one of the few two-story buildings on campus, on the southwestern corner -- very similar to the location of my classroom at the old charter school. (All middle school classes that year were upstairs, since we we co-located with a district elementary school on the first floor.)

2. Is Blaugust back?

Well, here's your answer:


And you know what that logo means -- Blaugust is back! Here's a link to the blog of Shelli -- the creator and leader of the annual Blaugust challenge:

https://statteacher.blogspot.com/2022/07/mtbosblaugust-is-back.html

Well... years ago, hubby decided he was going to blog EVERY DAY and has now been blogging every day for like 9 years or something.  He decided to challenge his online community to try it for one month and I decided to give it a shot.  (I should mention here that I've never successfully completed the challenge...)

Obviously, as teachers, time is short in August as we prepare for a new school year and blogging often falls by the wayside.  We would love for you to join in, so feel free figure out the platform that works best for you and try it out!  Maybe it's a traditional blog like this one, maybe it's a micro-blogging platform like Instagram, maybe it's some other platform that I don't even know about.  But ultimately, the Blaugust challenge is about personal reflection and sharing ideas with others in the community, regardless of platform choice! :)

Last year, I was hired at my new school in August and ready to participate in the Blaugust challenge, only to be disappointed that Shelli wasn't doing it last year. This year, I'm ready to be a full participant in the newly restored challenge.

In theory we should be blogging all 31 days this month (even though, as Shelli admits, she's never done so herself). Of course, it's already August 8th, and I won't be making 31 posts this month. I was waiting until I got the full information I needed about my new position -- otherwise I'd have nothing to blog about this month.

So anyway, this is my first Blaugust post.

3. What is my first Blaugust prompt?

Shelli reminds us that we don't need to follow all her prompts. But I always enjoy doing following the prompts as part of the challenge! Since today's the 8th, let's look at the eighth prompt from her list:

8. Write a post related to pandemic teaching.

That's an interesting prompt to start the 2022-23 school year, since it immediately raises the question, is the pandemic over? This sounds like a prompt better suited for the 2019-20, 2020-21, or 2021-22 school years that were more definitely affected by COVID-19.

In fact, let's look back at how I handled the pandemic during those three years:

  • 2019-20: Everything shut down in March. I was a substitute teacher at the time, and so as schools were closed and replaced by distance learning, I found myself with no work at all that spring.
  • 2020-21: Many schools reopened under the hybrid model. I gained a long-term position at a middle school, teaching Grades 7-8 from September through January. I returned to day-to-day subbing the rest of the year as schools gradually added more days of in-person learning.
  • 2021-22: I gained a full-time position at a tiny magnet high school, where I taught Calculus, Statistics, and Trig. Weekly COVID testing and masks were required for part of the year as the number of cases increased and decreased during the year.
That magnet school was closed by the district at the end of the year, which is why I was eventually moved to the flagship high school. I believe that the pandemic was partly to blame for why the magnet was troubled throughout its existence -- it had opened for its initial class of freshmen in Fall 2016, so they had only made it to March of their 12th grade year before switching to distance learning. 

Each year before COVID-19, a new class of freshmen joined the school, but no new students were added since the start of the pandemic. So by the time I got there, only Grades 11-12 were still attending the school. The seniors graduated, and the juniors were transferred to the flagship high school for their final year.

Over the years, I've thought about what I want my own classes to look like, but I wasn't sure whether those ideas would make sense during the pandemic. The next few questions here in this FAQ are all about my plans for the upcoming school year based on those ideas.

By the way, you might be wondering about my COVID What If? stories -- that is, what if the pandemic had occurred back when I was my students' age? Well, most of my kids are freshmen or juniors -- in order to match the + 3 year, I must place the pandemic at COVID-92 for my freshmen, COVID-94 for my juniors. Both of these are tricky -- there's already a COVID-91 What If? that I like, mainly because the dates line up exactly (as it's 4 * 7 years before COVID-19). As for COVID-94, this sort of clashes with my COVID-96 What If? for last year's seniors.

But once again, there will only be a COVID What If? if I'm convinced that the pandemic is ongoing -- for example, if two pandemic-related policies are implemented (say masks and required testing).

4. What will be my cell phone policy?

We all know that cell phones in the classroom were a growing problem even before the pandemic. As I wrote in my March 23rd post, I believe that 2012 was the inflection point, five years after the start of the iPhone, when phones switched from a minor problem to a major problem. So the pandemic only sped up what was inevitable anyway -- during distance learning, students developed the bad habit of spending most, if not all, of class time using their phones, and they brought that bad habit back into the classrooms when they reopened.

And from the perspective of a math teacher, there's another problem with phones besides their existence as a distraction -- the use of calculators to answer basic math problems. Many older people lament how young cashiers can't even calculate their change because ever since their middle school days, they've only ever done arithmetic on a calculator -- more often than not, the calculator on their phones.

One idea that I've posted on the blog is "Technology 1955" -- on certain days, students will not be allowed to use phones, calculators, or anything invented before 1955. The year was chosen because it's the birthyear of three important inventors -- Bill Gates, Steve Jobs, and Tim Berners-Lee.

All three developed the technology that many of today's teens can't live without -- but as young teens themselves, they obviously couldn't use modern technology to do math problems as they hadn't invented it yet! So they had to know how to solve math without a calculator -- and they applied the math they learned to build the technology that made them famous.

My original plan was to have one day, say Monday, be "Tech 1955." The next day would be "Tech 1973" (the year that those born in 1955 graduated), when simple calculators would be allowed, but still no cell phones. This would be followed by "Tech 1991" (the year that those born in 1973 graduated), and so on until full tech, including phones, are allowed on Fridays.

But of course, that will be an uphill battle. Ever since the start of pandemic distance learning, it's unlikely that many of these kids ever went more than one waking hour without using a phone, and now I'm expecting them to do so now in a 90-minute block. Yet Mondays aren't block days -- so no-phone Mondays won't be as painful. Therefore, my plan is to establish "Tech 1955" on Mondays. The rest of the week, phones will be allowed, except perhaps on certain Fridays (the other non-block day) when I give a no-phone quiz.

I believe that I'm not the first teacher to invoke a year as part of a no-phone policy. The year that this other teacher chose was 1995. To me, this is ironic -- 1995 was the summer before my freshman year. I was running near a river for Cross Country practice when I fell in the water. A driver used her car phone to dial 911, and I was rescued and rushed to a hospital. It never occurred to me that we'd go from having a cell phone saving my 14-year-old life, to a time when 14-year-olds feel that we're ruining their lives just for suggesting that maybe they shouldn't spend 100% of their waking hours on a cell phone -- yet that's where we are now.

Again, the idea behind the phone policy is that without the math they're learning in my class now was used to develop the technology that powers the phone. In other words, without math, cell phones wouldn't exist at all.

5. What will be my food policy?

Cell phones in the classroom expose the generational divide -- the young members of Generation Z were taught that they can't go a few minutes without a smartphone, which is difficult for members of generations who grew up before the invention of such phones to comprehend. On the other hand, food has existed longer than humans have on this planet.

When I was a young student, I never ate in the classroom -- unless, of course, it was one of those very rare days when there was a classroom party. I ate breakfast in the morning, then not one bite until it was snack break, then not one bite until lunch break, then not one bite until I got home. Sometimes if I couldn't finish my lunch before the end of the break, I ended up throwing it away -- I'd much rather discard the rest of my lunch than break the "no food" rule. So that's why it annoys me so much when I see students eating in my classroom.

During the pandemic, students had to wear masks in the classroom -- and thus they definitely weren't allowed to eat food during class. And so for much of the year, I hid my "no food" rule behind the general pandemic rules.

But in March, the mask rule was lifted. I was considering implementing a separate "no food" rule at that point -- but it didn't help that the first mask-free day happened to be Pi Day, a day filled with eating pies and other special treats for the day. Since it didn't look good to implement a strict "no food" rule on Pi Day, I ended up not having such a rule at all (except for two weeks in mid-to-late April when there was a slight virus surge).

And indeed, that raises another question -- will there be certain days when I bring treats to school, such as a candy incentive, and how will that affect a possible "no food" rule?

A long time ago, I was considering bringing candy to school. In order to avoid bringing too much or not enough candy, I would assign each period a day of the week to have the candy incentive. For example, first period might be Monday, second period Tuesday, and so on up to sixth period on Friday. By doing it this way, I'd be passing out candy when the students need it the most -- first period on Monday when they are still hung over or influenced by the previous weekend, and sixth period on Friday when they are influenced by the following weekend.

But now I'm starting to wonder whether this is introducing needless complexity. Instead, I should just buy a barrel of Red Vines, and then hand them out to all classes on Monday -- with Red Vines earned based on their performances on the quiz the previous Friday. Then as for the "no food" rule, small snacks will be allowed on Mondays since I'm passing out food anyway, and then it's no food the rest of the week. (This also makes it easier to remember -- food is allowed on "Tech 55" days when phones are not allowed.)

The Red Vine incentive also goes back to how I did it at the old charter middle school six years ago -- except that there will be one additional level:

  • One Red Vine for getting an A on a Hero Quiz
  • Two Red Vines for being the most improved on a chapter/unit test
  • Three Red Vines for earning an A on a regular quiz/test
Yes, Hero Quizzes are back, except that they won't be simple multiplication Mad Minutes, which I believe are insulting to high school students (as much as some of them might need it). Instead, these will contain review problems, from either previous units or previous years.

The Hero Quizzes will also be the quizzes on which calculators are forbidden ("Tech 55"). Phones must be kept away until a grade of A is earned on the quiz, which I grade right away. Those who earn anything less than an A must keep working on it until an A is achieved.

6. What will be my homework/interactive notebook policy?

I've already mentioned interactive notebooks in my previous posts. When I entered my new classroom for the first time this afternoon, I found some old papers from the previous teacher in my desk. It was a scoring guide for a notebook check. So by inspecting this paper, I get to learn more about how to implement interactive notebooks.

Anyway, my predecessor graded a total of 16 assignments in this notebook check -- ten from Chapter 6 on systems of equations, and six from Chapter 7 on basic geometry (Triangle Sum, Pythagorean Theorem, and Congruence). Based on these topics, I assume that he taught Math I last year, perhaps based on CPM, a well-known integrated text (since I see a CPM textbook code still on the board). Each of his assignments took up one or two pages, and each was worth ten points, for a total of 160 points for this notebook check.

OK, so that's Math I -- what about Math III? Well, even though the department meeting isn't tomorrow, the agenda for the meeting is already posted today. Apparently, the math teachers are supposed to divide into CT's ("curricular teams"???) based on our subjects, and I was assigned to the Math III CT. So I'm already getting lots of info about the Math III course:

First of all, the Math III leader has already revealed his grading percentage weights:

20% -- homework (DeltaMath/worksheet)
20% -- classwork (Desmos)
20% -- quizzes (two per chapter)
20% -- chapter exams
20% -- midterm/final

And notice what's missing from that list -- interactive notebooks. The conclusion is inescapable -- there are no notebook checks in Math III.

But didn't I find a notebook check in the teacher's desk? Yes -- but that was Math I, not III. I glean from the info on the board that all five of my predecessor's classes were Math I.

But hey -- didn't my partner teacher (at the old magnet school last year) use interactive notebooks in her own Math III class (from which I got the idea of implementing them myself this year)? Yes -- but she isn't here, so she's not in charge.

I'd already anticipated that once I moved to the flagship high school, I'd be a member of a full math department, and so some decisions (like grading weights) will have already been decided for me. In fact, there's already a complete first semester pacing guide, filled with activities. Even this week's opening activities are already listed on the pacing guide. I was already looking ahead to the Sara(h) activities (from Sarah Carter and Sara Vanderwerf), but I must do the activities listed on that pacing guide instead.

I can start working out how many points each assignment is worth. There are four chapters to be covered in the first semester, namely 1, 2, 3, and 5. (Chapter 4 is a Stats chapter that we're skipping -- all the more reason to post on my Geometry blog rather than my Stats blog this year.) If the total is to be 1000 points, then that works out to be 200 points in each category. This turns out to be 25 points per quiz, 50 points per chapter exam, and 100 points each for the midterm and final.

Then again, the department might tell us how many points each assessment is worth -- and then we must set the weights in Aeries in order for the percentages to add up. I hate doing this because it makes the points seem deceptive -- but once again, when department leaders say "jump," I ask "How high?"

Meanwhile, the assessment retake policy is stricter than my partner teacher's last year. She allows for 75% of the points to be recovered on her retakes, but here we start at 75% for the earliest quizzes and then lower the percentage to 55% as the first semester proceeds, with 65% on the chapter tests. (I assume that there are no retakes on the "midterm" or "final.")

It also means that I can't do the first quiz of the chapter as a "hero quiz," so I've already contradicted what I wrote in this post. Moreover, "Tech 55" might not work on Mondays if the assignments are on either DeltaMath or Desmos, neither of which existed in 1955. (While technically I could still have a "no phones" day on Mondays, students can still do arithmetic on their Chromebooks during those assignments, eliminating one of the reasons of having a "no phones" day.) And I'm wondering whether I can even fit Warm-Ups or Exit Passes in the Math III grades.

So far, I've mentioned the CT meeting for Math III. Apparently, I'm not in a CT for Math I. So it's possible that I have a little more autonomy in running the Math I class. Thus much of what I've mentioned in this post (notebooks, hero quizzes, Tech 55, and so on) might work in Math I -- unless, of course, a leader tells me tomorrow that I can't.

(Note: In order to avoid confusion, if I learn that I can't implement notebooks or anything else that I've listed in this post in Math I, then I'll just edit it out of this post.)

There's one more thing I must say about my Integrated Math classes. Last year, my partner teacher told me that she had to give district Interim Benchmarks in her Math III class. While my predecessor left a mention of Benchmarks on the board for Math I, they don't appear on the Math III pacing guide (unless the "Midterm" mentioned there is really the Benchmark -- and before you ask, even if Benchmarks aren't included in the grade, they should still appear on the schedule). Assuming that there are any Benchmarks this year, they will be in October, February, and May.

7. Am I still reading Jim Peterik's Songwriting for Dummies?

I wasn't going to go far past Chapter 12 anyway. The chapters past 12 are all about how to make money from these songs, while 12 itself is called "Writing for Stage, Screen, and Television" -- which, of course, I won't be doing much of. Instead, I'll be writing math songs for the classroom.

Since Chapter 12 is the last chapter of Part IV of the book, it feels as if I should discuss this chapter briefly, in the name of completion -- and so I will. Here's how it begins:

"When a songwriter dreams, sometimes his flight of fancy takes him to a gilded Broadway theater where his songs are being performed by the cast and orchestra of a long-running, live stage production."

Let's skip up to the section on songwriting for television -- since, after all, the first songs I'll perform aren't my own songs, but are from the 1980's-1990's PBS math show Square One TV:

"Many songs have languished on shelves until some visionary director discovers it while station surfing in his Porsche and decides to feature it in the next episode of his series. Sometimes all it takes for a great song to be recognized is one person in a position of power to hear it at just the right time."

And as I wrote before, some of Square One TV's songs were performed by real music groups (such as the Fat Boys), while other songs were sung by the cast yet fit the genres (such as country). Interestingly enough, "Mathnet" -- a subprogram of Square One TV -- had a few cases that revolved around music and songwriting.

In "The Problem of the Passing Parade," where a famous rock musician is kidnapped so that he'll be forced to perform with a college marching band. "The Case of the Unkidnapping" was about an aging Broadway star who faked her own kidnapping in order to steal money of the production of her show. A memorable scene from the end of this episode is her final capture, where the Mathnet team members run up on stage to perform an impromptu Broadway song about her impending arrest. And in one last ep, "The Case Off the Record," a music producer fakes the sales numbers from his songs in order to make them appear more popular than they really are, so that radio stations will play them more often, which will lead to real sales.

Returning to the Peterik chapter, the author also writes about songwriting for commercials. It's notable that one of the songs that I performed in math class, "Plug It In," was originally based on a commercial jingle, for Glade Plugins air freshener.

The chapter ends with songwriting for musicals. Peterik quotes composer Dennis DeYoung:

"Even when the play finally opens, there is inevitably fine-tuning of songs and scenes. Showboat was written 75 [by now almost 100] years ago and they're still fooling around with the book!"

Now that I know what school I'll be working at. I can now announce my music schedule. I'll perform songs on block days. Since each class meets two block days per week, I'll prepare two songs per week and then sing each song to each class once.

The block schedule doesn't start until next week, so my first songs are next week. My original song "Heroes and Zeroes" will be my first performance, and then this will be followed by songs from Square One TV for the rest of Weeks 2-4, with original tunes returning in Week 5 in September.

Once again, I must be careful to avoid parent complaints about my music. As I wrote before, I won't bring my guitar to school until Week 5, so the Square One TV songs in Weeks 2-4 will be vocal. Then again, I didn't mind not singing last year because it's mainly younger students who enjoy my music -- usually middle school or the younger part of high school. This year, with Math I on my schedule, I really want to make sure that those freshmen will get to hear my songs.

Thus most of my songs this year will be geared towards Math I. Oh, and do you remember those songs I wrote all summer for a Math 8 position that I ended up not taking? Well, I've said before that there's lots of overlap between Common Core Math 8 and Integrated Math I. Therefore I was (unwittingly) writing for my new Math I class all this time! (I'll probably still sing the Math I songs for the Math III juniors anyway -- and from time to time, I might throw them a bone and perform a Math III song -- especially if there's one already written for them, such as "Quadratic Weasel.")

That concludes our reading of Jim Peterik's Songwriting for Dummies. It was an enjoyable read, and I'll continue to use the principles I learned in this chapter as I compose math songs throughout the year.

8. What is today's Rapoport question?

Today on her Daily Epsilon of Math, Rebecca Rapoport writes:

Find R(3, 4) + 1 where R(3, 4) is a Ramsey number.

This is a pure research question. Frank Ramsey was an early 20th century British mathematician who made the following discovery:

In any party of six, there exists at least three mutual friends or three mutual enemies.

Thus R(3, 3) = 6. And R(3, 4) would be the smallest party at which there exists at least four mutual friends or three mutual enemies. It was proven using brute force (that is, on a computer, checking all possibilities) that R(3, 4) = 9.

Therefore the desired answer is 9 + 1 = 10 -- and of course, today's date is the, um, eighth?  Rapoport admits that she made a typo on the calendar. The plus should have been a minus -- and 9 - 1 = 8, which really does match today's date, the eighth.

I'll continue to have Warm-Ups and Exit Passes, with the date as the answer. Of course, I won't give them Ramsey theory problems -- and especially not Ramsey theory problems with errors.

Occasionally, Rapoport will give a problem that matches what I'm teaching in my classes. Otherwise, I won't post any problems from her calendar on the blog during the school year.

9. Who are the other Blaugust participants?

Shelli, the leader of the Blaugust challenge, made a Blaugust post that doubles as part of her "Made 4 Math Monday" series:

https://statteacher.blogspot.com/2022/08/geometry-reference-sheet-mtbosblaugust.html

Here she makes a Geometry reference sheet that students included in their interactive notebooks. Even though I teach Integrated Math, I could do the same when Math I reaches the Geometry units. Based on my predecessor's class, Geometry appears in Chapter 7. According to the board, the Chapter 9 retake was just before the third and final Benchmark. Thus Chapter 7 might be right after the second Benchmark, at the start of March. So I could include something like Shelli's reference sheet then -- assuming, of course, that I do interactive notebooks at all.

And joining me with his first Blaugust post today is Stephen Dull:

https://tweakingfornoreason.wordpress.com/2022/08/08/august/

Dull writes about many things that are on his mind this month. He describes a PD that's in some ways similar to my 11:00 PD today -- both of us are focusing on "linguistically diverse" students (that is, English learners).

And of course, the teachers on his chart correspond to Harry Potter teachers -- "The Warm Demander" is McGonagall, "The Sentimentalist" is Flitwick, and "The Elitist" is Snape. (I'm not quite sure who the "Technocrat" is -- maybe Professor Sprout, who knows her Herbology but isn't quite as caring as McGonagall is shown to be.)

10. What will be my new blogging schedule?

I'm aware that blogging is a dying medium. And so I'm reducing both the length and number of my posts, as follows.

First of all, there will be no more super-long posts (like today's post) during the school year. Most school year posts will contain only the Blaugust topic and the song of the day -- and the song will contain only the lyrics and either a video (if it's from Square One TV) or a link to Mocha EDL code (if it's an original song). The only longer posts will be "A Day in the Life" posts -- there will be both monthly and special posts.

And now I'm usually posting twice per week. The two posting days will be two of Tuesday, Wednesday, Thursday -- the block days, depending on when Math I meets (so I'll decide when I see a schedule).

There are three more "A Day in the Life" days coming up this month -- "first day of school" (which is Wednesday), "Back to School night," and the monthly posting day. I'm still confused regarding whether there will be monthly minimum days this year (they were alluded to in the 11:00 PD). Instead, I'm considering making the 17th my monthly posting day. Like the 18th last year, the 17th this year avoids most weekends -- only September 17th and December 17th are Saturdays, and there are no Sundays.

Like Dull's school, my school is also having a freshman orientation today, but ours is tomorrow. I've decided that I won't post on freshman orientation day (despite my having ninth graders this year), and so my next post will be on Wednesday, the first day of school.