District Benchmark Test #1 (Days 54-57)

BENCHMARK TESTS

Why do we take Benchmark Tests?

Two or three months are done so let's

See how much we know, know know! (x2)

It's some new stuff on Benchmark Tests.

If we don't know it, we take a guess.

'Cause there's still time to grow, grow, grow! (x2)

The teacher sees our Benchmark Tests,

Knows what to teach now more or less.

That's the way to go, go, go! (x2)

GHOST OF A CHANCE

1. One night on a Pizza Shack delivery

I walked into this spooky house

And just as I was yelling “Two with anchovies!”

The door slammed and the lights went out

Started shouting, “Someone owes me fourteen ten!”

And then I heard a creepy voice

Boy, you’ll never see the Pizza Shack again

Unless you make the proper choice

Chorus:

Probability

Don’t you mess with me

Help me make the most of a chance

Might be win or lose

Still I’ve got to choose

Long as there’s a ghost of a chance

2. There are four dusty bookcases right over there

One of them’s a secret door

Go ahead and try one of them, if you dare

Your chance is only one in four

Did a little eenie, meenie, miney, moe

Pulled the third with all my might

Probability of one-fourth is low

But lucky thing I got it right (to Chorus)

3. Walked in to a hallway full of rattlesnakes

Only five are real ones; forty-five are fakes

Chance is five in fifty that I’m gonna croak

Chances are you thought this was a lark, a joke! (to Chorus)

4. Found myself inside an old Egyptian tomb

Open up the mummy case

Behold the seven keys he clutches in the gloom

Three will let you blow this place

Three in seven chance to pick a key that fits

I picked one of the four that don’t

But now the probability becomes three-sixths;

Three will work and three still won’t

(laughs)

5. Son, you’ve earned your freedom; here are twelve ways out

Eleven lead you to your truck

But what about the one in twelve? My boy, don’t pout;

Good luck; here’s your fourteen bucks

Probability of one-twelfth is slim

The guy was finally being nice

But that’s the one he chose, and I’m so pleased for him

The pizza’s for my poltergeist (to Chorus)

As this school year began and I was planning my songs for the year, there were two established songs that I was sure I'd sing -- "Benchmark Tests" on the day of the first district test and Square One TV's "Ghost of a Chance" on the last block day before Halloween. What I wasn't expecting was for "day of the first district test" and "last block day before Halloween" to be the exact same day.

So what do I sing in Math I classes today? Well, I perform both songs -- "Benchmark Tests" as the students are getting ready to start the district test and "Ghost of a Chance" at the end of the period.

Last year at the old magnet school, the lone other math teacher at my school (my partner teacher) told me about the Benchmark Tests, even though I knew that only Math I, II, and III needed to administer them, as opposed to my own Calculus and Ethnostats classes. The tests are given thrice a year, using the Illuminate platform. (Last year I used Illuminate for some of my own Ethnostats tests, but this year I'm using Illuminate for Benchmarks only and relying on DeltaMath for classroom tests.)

As I explained in yesterday's post, I give Benchmarks in fourth and sixth periods today, while second period will take theirs tomorrow. So far, the average score (as expected) is in fourth period, yet the top two scores are in sixth period. (This doesn't include the two free response questions that I must grade.)

Oh well -- this isn't an official "Day in the Life" post, but it's already turned into one. Here's what the entire day looks like, in a brief "Day in the Life" format:

8:30 -- First period Math III -- I cover the last lesson of Chapter 3, on graphing x-y inequalities (mostly linear, with a few quadratic). This is the first time that I hand out dry erase packets (another Sarah Carter staple) for the students to practice their graphing.

9:55 -- First period leaves for nutrition, which leads into third period conference.

11:45 -- Fourth period Math I arrives to take the Benchmarks.

1:15 -- Fourth period leaves for lunch.

2:05 -- Sixth period Math I arrives to take the Benchmarks.

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

What remains is for me to score the two free response questions -- oh, and decide whether or not to include them in our grade. According to the syllabus, a part of the grade (25% in Math I, 20% in Math III) consists of a midterm and final. Most teachers in both departments want to let the benchmarks count as the midterm, so that there's one fewer test to take, and so that the students take the test seriously (as opposed to the SBAC, which the students know has no affect on their grades).

But my neighbor teachers prefer not to include the Benchmarks in the grades. Their worry is that there are many tricky topics on the test, including a Chapter 3 question that we haven't reached yet, not to mention how we did rush Chapter 2 a little and so I'm not sure how ready they are for a graded test on this material. (It also doesn't help that both neighbor teachers gave their Benchmarks last week, during the first week of the two-week window, so they had even less time to cover Chapter 2 before the test.)

I most likely will follow the majority, and so I'll count my interim as a midterm. In order to prevent the grades from dropping, I'll curve is so that the top score becomes 100%. So far, the top score appears to be 19 out of 27 (though I haven't graded the free response, which could add an extra point or two to the highest score), but I'll wait to see how second period fares tomorrow.

Meanwhile, Math III will take their Benchmarks next week. Last year, the Benchmark window lasted into the first week of November. The Math III leaders convinced the administration to allow us to give their test next week.

A few more things I want to say about today's songs. While "Ghost of the Chance" comes from a TV show, "Benchmark Tests" is my original song. It goes all the way back to when I was at the old charter school, before I learned about Mocha and EDL's, and so it's not in 10EDL or any other EDL. At first, I wrote the song in the key of C major, with the notes C-D-E-F-G-A. But I quickly dropped the F note, which makes the song sound pentatonic -- C-D-E-G-A.

Recall that 10EDL is almost like a pentatonic scale -- C-D-E-F#-A. So I can write the following Mocha code for a 10EDL approximation of the song:

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

10 N=8

20 FOR V=1 TO 3

30 FOR X=1 TO 28

40 READ A,T

50 SOUND 261-N*A,T

60 NEXT V

70 RESTORE

80 NEXT X

90 END

100 DATA 10,4,9,4,10,4,9,4,10,4,10,4,10,8

110 DATA 10,4,9,4,8,4,9,4,10,4,9,4,10,8

120 DATA 9,4,6,4,5,4,6,4,7,4,7,4,7,8

130 DATA 9,4,6,4,5,4,6,4,7,4,7,4,7,8

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

In this code, Degree 7 appears as the last note in lines 3 and 4. It is an F# in the code, but in the original song it sounds as a G. On the guitar, I play a G7 over this note. The full riff is C for the first two lines, and then D7-G7 for the last two lines. If we were to keep the Mocha version as 10EDL, then we might either extend the D7 chord (dropping G7), or else keep G7 and change the last note to D.

Some of the lines contain extra syllables, and so I usually insert sixteenth notes at those extra syllables in order to fit the lyrics.

This is the last music post of October, and so we just completed the 10EDL part of the year. Perhaps it's because we're getting ready to switch to a new EDL, or maybe it's because we've reached Benchmarks, but in either case this is the point where it no longer seems to be "early in the school year."

Anyway, it's a good time to analyze the 10EDL scale -- in particular, the use of a guitar with 10EDL. I have written ten songs in 10EDL -- well, eleven if you count today's version of "Benchmark Tests." I don't think it should count since it was originally written in another scale -- but ironically, today's 10EDL version serves as a microcosm of our entire 10EDL experience.

The 10EDL scale C-D-E-F#-A-C differs from a true pentatonic scale with the G. This is tricky because the most common riff in C major is C-G7-C, but 10EDL takes that G away. So far, my temptation is to use D7 as a secondary chord in 10EDL, especially as all four of its notes D-F#-A-C are part of the new scale in 10EDL.

I'm also still trying to figure out how to play 10EDL on a hypothetical EDL guitar (as described in many previous posts). The pentatonic scale is usually one of the first scales a lead guitarist (as opposed to a rhythm guitarist who focuses on chords) learns, but it's tricky to imagine how a pure EDL guitar can be tuned to play a 10EDL scale. (What makes it tricky is that there are two different minor thirds in 10EDL -- namely 7/6 and 6/5. Our standard fretting makes all minor thirds sound identical.

Well, I look forward to composing in a new EDL scale in November -- happy Halloween!

Lesson 2.3.2: Two Points to Equation (Day 53)

SLOPE INTERCEPT RAP

by Lamar Queen

Chorus (x2)

Let’s talk about slope intercept

I don’t mind if you interject,

just don’t disrespect

You say you got a question for me, yes?

What’s y=mx+b?

Verse 1

This is a line in function form,

it’s also slope intercept for it

Half ya’ll like,

“This is boring”

The other half is like,

“This sounds foreign”

M represents

the slope of a line

If it’s negative

then you know it declines

B is where it crosses the Y axis

If you don’t pay attention then why ask us

To repeat?

Sit down in your seat

Listen to the words

that I say to this beat

Parallel lines have the same rise over run

Even if the y-intercepts are a 9 and a 1

Question:

can you plot three ordered pairs?

Pick the X values and the Y is there, oh my I swear

This math stuff is easy and Imma take you there

Chorus (x2)

Verse 2

Ya’ll sound so typical,

ya’ll like math I’m sick of you

But can you find the reciprocal?

Can you tell me what the power to the tenth will do?

If you can then you can be the principal

Get a loan and don’t think about the principle

Is your variation direct?

Did you know that K = Y/X, yup!

Just food for thought

And please try to remember all the things I taught

And don’t forget where you come from, your origin

And Y = KX always goes through the origin

X = A and Y = B

Vertical and horizontal lines respectively

Doing math is like cooking,

and these notes are the recipe

From Mr. Walker, let’s go [enter district name]!

Chorus (x2)

Bridge (x2)

Do your classwork, do your homework, yes (x4)

Get A’s on the quiz, get A’s on the test (x4)

Notes, notes, notes, notes, notes, notes, put your pens up (x2)

As it turns out, this song and video are posted on our Math I pacing guide for this week. I'm still slightly behind the pace, but doing a lesson with a rap -- and one that I can perform -- is a no-brainer. I point out that the original artist for this rap, Lamar Queen, is a fellow Southern Californian math teacher (or at least he was in 2009, when he produced this video). Today I hand out some guided notes (the lyrics with some keywords missing) for students to glue into their interactive notebooks.

This I combine with the main Desmos lesson for the day, two points to equation -- at least that's what I do in fourth period. Second period is behind due to last week's earthquake drill, and so I only get to do point and slope to equation with them, not two points. (And yes, today's an earthquake in California -- Northern California, that is, so we don't feel it here in Southern California.)

Sixth period, which doesn't meet today, is another story altogether. That special ed meeting that was supposed to happen last Thursday was delayed to this Thursday. On one hand, it allowed me to do the point and slope lesson with sixth period last week. On the other, the meeting is now scheduled for the day I wanted to give the district Benchmarks -- and I don't want to leave something like district tests for a possible sub.

And so I'll give the tests to sixth period tomorrow -- their first block period of the week. It means that sixth period won't get a two points lesson before the tests (but I must admit that there are many low students in this class -- most likely wouldn't understand two points anyway). Then again, this sudden change is affecting my song lineup for the week -- sixth period might not get today's rap. (At least they can still watch the video.)

Notice that tomorrow is also the second block period for fourth period, and so that class is testing as well that day. Only second period will test on Thursday. (Math III, meanwhile, doesn't take Benchmarks until next week.)

By the way, yesterday's Math I lesson was interesting. The TOSA set up a calculator-based laboratory in the library, and invited the Math I classes to go on a "slope walk" -- it was my turn yesterday. The students must walk according to a given linear equation -- so for y = 2x + 1, for example, they must begin a the 1-foot mark and walk 2 feet per second. A motion sensor captures the movement and sends the data to the calculator, and the kids get to evaluate each other on their accuracy.

Lesson 2.3.1: Point & Slope to Equation (Days 49-52)

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.

Bridge:

Excellent linear.

Why do nonlinear?

Extra care 'cause it's new,

While knowing what to do....

(to First Verse)

This is the tenth song that I'm writing in 10EDL, our main scale for September and October. It is the only 10EDL song that I will write in ABCD format -- verses, pre-chorus, chorus, and bridge.

I've had to do some last minute switching around with the lessons, which is thus reflected in the songs. I originally intended to perform a Math III song during first block next week. But with the earthquake drill and a possible special ed meeting in my two Math I classes tomorrow, it's much better for me to do the Math III song for this week's second block song.

Here is the Mocha code for today's song:

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

10 N=8

20 FOR V=1 TO 3

30 FOR X=1 TO 48+(-1)^V

40 READ A,T

50 SOUND 261-N*A,T

60 NEXT V

70 RESTORE

80 NEXT X

90 END

100 DATA 10,2,8,2,5,12,7,16

110 DATA 10,2,8,2,5,12,7,16

120 DATA 10,2,8,2,5,12,7,16

130 DATA 10,2,8,2,5,12,7,16

140 DATA 9,16,6,16

150 DATA 9,16,6,16

160 DATA 9,16,6,16

170 DATA 9,16,6,16

180 DATA 9,8,7,8,10,16

190 DATA 9,8,7,8,10,16

200 DATA 9,8,7,8,10,16

210 DATA 9,8,7,8,10,16

220 DATA 8,16,9,4,10,4,7,2,10,2,9,4

230 DATA 8,16,9,4,10,4,7,2,10,2,9,4

240 DATA 8,16,9,4,10,4,7,2,10,2,9,4

250 DATA 8,16,9,4,10,4,7,2,10,2,9,4

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

As an ABCD format song, line 30 contains a strange formula, but it works to be 36 notes when the verse is 1 or 3 and 60 notes when the verse is 2. That way, the extra 24 notes in the bridge only play after the second verse.

Just as with ABC songs, there are so many notes to type in the DATA lines. But as my TI generator included many whole notes, there are actually fewer notes here than in last week's "Slope Dude," so this shouldn't be that much more tedious to type into Mocha. These whole notes are sung over the lyrics x or y (including "Ex-cellent" and "Why?" in the bridge).

The verses describe substitution and elimination methods for solving systems, which is what the Math III classes will be learning tomorrow. But they will be solving nonlinear systems, for which only the substitution method works. That's why the bridge leads directly into a repeat of the first verse.

(Hmm, the students will also learn about solving three variable linear systems, for which elimination is generally used. Perhaps I should add a second bridge to the song, with z mentioned over one of the whole notes, and then leading directly into a repeat of the second verse.)

The chord riffs are C-D7 in the verses, G7-Am in the pre-chorus, D7-C in the chorus, and C-G7 in the bridge -- at least, they would have been if I'd played the guitar today in fourth period. That's because yet another curveball was thrown at me today.

In Monday's post, I mentioned that district Benchmarks are coming soon. Well, the window for the district exam is this week and next week. And, much to my surprise, some Math I teachers -- including both of my next-door neighbors -- give the Benchmarks today. During my third period conference, I can hear both teachers directly their students to place their backpacks against the wall.

So now suddenly my mind is racing, as I'm afraid that I'm supposed to give the test today as well but somehow missed it. I visit another math teacher's classroom -- the only other one who also has third period prep. She reassures me that we still have until next week to give the Benchmarks -- indeed, she herself won't administer them until next week either.

My colleague also tells me that she's wants to give two more lessons before the district test -- deriving an equation from a point and a slope, and deriving it from two points. So I switch out today's lesson on the Big Race and replace it with a Desmos on point-slope, although I only use y = mx + b (where the students plug in values for x, y, m and solve for b, not the Point-Slope Formula). I'll do two points next week, as the last lesson before the Benchmarks.

Indeed, I must work hard to keep my freshmen quiet while my neighbors are taking the test. So instead of taking out my guitar, I give a pure vocal performance. And I only sing part of the song -- it is, after all, a Math III song (though due to the block schedule, a Math I class is always the first to hear any song that I perform). I inform them that this Math III song can also double as a Math I song, as students will solve systems later in Math I as well. (For Math I, I'll likely leave out the bridge, as this class doesn't learn about those more complex systems.)

I don't mind a stripped-down version of the song in fourth period Math I as Math III is the intended audience of the song. But one of my neighbors teaches nothing but Math I, and so he'll be giving the Benchmarks in all his classes tomorrow. So now I must wonder whether I'll play the full version of the song for my Math III tomorrow.

Math III will take Benchmarks as well. Earlier, the Math III teachers were trying to petition the district to extend the testing window by a week, but I don't know whether they were successful or not. I'll likely find out during Friday's Math III meeting. At any rate, the next few weeks in my math classes will definitely be shaped by the impending district tests.

(Enjoy watching sports tomorrow -- another sports equinox is upon us!)

Lesson 2.2.2: The Big Race (Day 48)

X'S AND Y'S

First Verse:
I walked into math class, the math teacher said,
"We're gonna graph our x's and y's."
Today, I just wanna say.
Took out my calculator to add,
Wrote the numbers on the graph.
You know my x's and y's.

Pre-Chorus:
One, two, three, they gonna run back to me,
'Cause I'm the math genius that they never have seen.
One, two, three, they gonna run back to me,
I always want an A but I keep getting a B.

Chorus:
x's and y's, I solve them,
And graph my x's and y's.
I just might try,
x's and y's.

Second Verse:
Where y = 0, that's the x-intercept,
Where x = 0, that's the y-intercept.
My my, how the lines go by.
Plus-y gets high, minus-y gets low,
Plus-x goes right, minus-x goes left.
You know, that's how the graphing goes.
(To Pre-Chorus)

Originally, these last two weeks of October would be for the last 10EDL songs -- and the most complex structures of all, the ABCD format, where D stands for the "bridge." But as it turns out, I have several previously written songs from earlier on the blog that happen to fit this part of the chapter.

Three years ago, I had a multi-day subbing assignment in an Algebra I class, and I decided that I wanted to perform a new song based on the upcoming lesson, graphing using intercepts. On YouTube, I found a parody of Elle King's "Ex's and Oh's," called "x's and y's." I changed a few lines to graphing using intercepts and performed it in the class I was covering that day.

This year, we reached the lesson on standard form yesterday, but Mondays aren't singing days. So I had to wait until today to perform this song in my second and fourth period Math I songs. It's the first time that I sang "x's and y's" since before the pandemic. (While I taught linear equations to Math 8 during my long-term assignment two years ago, eighth graders generally don't study standard form.)

Today's performance is a rousing success. Parodies are usually the easiest songs to write and perform -- the tunes are already written, so all I need are the new lyrics. And if I already know how to play the original tune (by ear), then all I need to make sure of during performance is singing the right words.

Since this is a parody, there's no need for Mocha code -- the original parodists are two former high school students who wrote it during their actual math class, Brianna and Chase. So let me use the rest of this post to mention a few other things happening in my Math I classes.

First of all, the lesson title "The Big Race" refers to a particular activity in the CPM text. Several young children are participating in a tricycle race. Each rider is moving at a constant rate, but slower riders are given a head start in order to make the race more suspenseful (and to show both slope and y-intercept).

The Big Race has already been converted to Desmos. But I fear that, while the Big Race uses linear equations to model a real-world situation, it doesn't give the students much practice (again, a common complaint of Desmos lessons). So I take one page from the packet that one of my neighbor teachers gave me during last week's Wi-Fi blackout, copy it, and have students glue them into their notebooks.

This page has two types of questions -- one where they must find the slope of a line given its graph, and the other where they are given a starting point and a slope and must draw the graph. My original plan is to have the students complete the worksheet, sing "x's and y's" midway through the period, and then transition to Desmos and the Big Race. But, as usual, it's a struggle to get the freshmen to work, and so we only complete the finding slope questions before it's time for the song and the Big Race.

Meanwhile, as I mentioned in my last post, I'm still exploring my Promethean board. I notice that it has a Whiteboard app -- and this whiteboard has a grid background, perfect for graphing. The tech guy is supposed to visit my room tomorrow morning. So if all goes well, I'll be able to use the Promethean in my fourth period class tomorrow. I hope to be able to use technology to engage my young freshmen and get them to work harder in my math classes.

Lesson 2.2.1: Standard to Slope Intercept Form (Day 47)

This is my monthly "Day in the Life" post for October, since today is the seventeenth. It falls on Monday, which is an all-classes day at this school. On some Mondays and Fridays, there are teacher meetings before school, but today isn't one of them. (There will be a Math III meeting on Friday morning.)

And it is definitely still DEVOLSON ("the Vortex"). After today, there are still eighteen days of school left until Veteran's Day. Let's now start "A Day in the Life":

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

I usually give one quiz per chapter in Math III on DeltaMath, about midway through the chapter. And so today is the Chapter 3 Quiz. It covers equations involving absolute value, radicals, and powers.

One problem that I've had lately with Math III quizzes is that, since the entire department has agreed to give common quizzes, various curveball questions written by other teachers appear on a quiz. Often the curveball question involves something that I taught differently from the other teachers. And more often than not, it's the last lesson before the quiz or test on which the curveball question is based. So it means that instead of a review day, the day before the quiz turns into "let me reteach the previous day a new way, and rush through it, so that the students have at least a chance of getting this particular question."

Of course, this is not ideal. So I was really hoping just to get through the lessons before the quiz without any problems, especially the final lesson on power equations last Thursday. Then there would be no issues coming into today's quiz.

Last Thursday was also Parent Conferences Day. I wrote that I wouldn't do "A Day in the Life" that day, but I admit that I was tempted to post anyway because of something unusual that happened then. There was a Wi-Fi outage that day, and Internet wasn't restored until -- you guessed it! -- just minutes before the end of sixth period.

Normally I'd look at the DeltaMath or Desmos lesson before first period in order to prepare. But with no Internet, I couldn't see the lesson at all. So I had to go into that day's lesson blind -- I knew only that lesson was on power equations, but not how complicated the power equations on the quiz would be. Of course I had the students take notes in their notebooks, as there was no DeltaMath or Desmos. Most of the examples I gave were equations of the form a(x - h)^n + k = c, so that students would have to isolate the power and take the nth root of both sides (noting that if n is even then there are two real roots, whereas there's only one real root if n is odd).

The next day was Friday, and so by then I could access the lesson and quiz. I found out that while my examples were good, I needed to show the students the cases where n is a fractional exponent. And so I was forced to spend that day -- the minimum day after Parent Conferences -- rushing through yet another lesson, this time on fractional exponents, to make sure that the students get it correct. In other words, here we go again.

After looking at the stats for today's quiz on DeltaMath, I can see that the question the students struggle with the most is, just as you'd expect, the power equations. Once again, the students get a curveball question on the quiz just because last week's Wi-Fi outage ruined that day's lesson.

9:25 -- First period leaves for nutrition.

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

Today we proceed with the next lesson in the CPM text, on the standard form of a linear equation. A Desmos lesson has already been set up for today. It mentions a real life example -- the ways dimes and nickels add up to a dollar, which leads directly to a linear equation in standard form.

Last Friday was the Hero Quiz, given as Tech 55 with no computers allowed. (In hindsight, I almost wish that Thursday was the Hero Quiz, as there was no Internet anyway. But I wouldn't have wanted to devote a full block day to a Hero Quiz.) One good thing about a Friday Hero Quiz is that Monday isn't spent doing quiz corrections (since on Hero Quizzes, everyone should already have an A), and so more time can be devoted to the main lesson.

Even so, I have trouble getting through the entire lesson. Another time suck on Mondays, besides quiz corrections, is passing out the new Warm-Up/Exit Pass sheets and getting them glued into notebooks. I don't have enough glue sticks for everyone, so they must be passed around. It often takes up to a third of the period just dealing with Warm-Up sheets and notebooks.

And so I only reach the Desmos slide where the students are asked to graph .10x + .05y = 1.00 using intercepts, and not reach the slide where they convert it to slope-intercept form (hence the title of the lesson and this post). This isn't terrible, since the upcoming quiz this week focuses more on graphing lines that are already in slope-intercept form.

(You might recall from the blog that I already have a song about graphing using intercepts. That song would have fit today's lesson, but unfortunately Mondays are not singing days. So the best I can do is sing it tomorrow.)

One thing about Desmos lessons is that they're excellent at introducing a topic -- showing connections to the real world or how some equations are derived. But they take time away from actual practice. I've already dropped Desmos from Math III lessons on Mondays (that is, saving Desmos for block days only) because they forced me to rush the main lessons (thus leading to the aforementioned student angst with the Math III quizzes), and perhaps I should do the same with Math I as well. Yes, today's Desmos demonstrates why graphing with intercepts works, but the kids have really seen just that one example with the dimes and nickels -- I can't hand them an arbitrary example and count on them being able to graph it using intercepts.

10:35 -- Second period leaves. Third period is my conference.

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

Fourth period has always been slightly better behaved than second period, although there are still a few corners of the room where the students regularly talk through the lesson. Therefore I'm sure that more students have taken notes from the Desmos in fourth period than in second -- but still, I don't think that these kids are more capable of graphing a line using intercepts, again based on how little they've seen of the topic in today's Desmos introduction.

I'm worried about one special ed student in particular, only because he's often pulled out of class. On Friday, he was all set to take his Hero Quiz, but then he was summoned to leave. And since he's absent today, he still can't take the quiz. A few weeks ago, he started a DeltaMath quiz and then is summoned to be pulled out. Once a quiz begins, DeltaMath counts the time and then locks the student out of the system once time has run out. That day, I ended up granting him an extra point on his quiz corrections due to this unlucky timing.

12:40 -- Fourth period leaves for lunch.

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

A few students are concerned when they make errors that causes DeltaMath to mark them wrong. One girl is marked wrong on a power equation question with a fractional exponent when she lists both the positive and negative solutions when DeltaMath asks only for the positive solution. If I recall correctly, the exponent in question is 4/5. Technically speaking, an equation like x^(4/5) = 16 does have two real solutions, x = 32 and x = -32 -- if the numerator of the original exponent is even and the denominator is odd, then the equation may have two real solutions. But this is usually considered confusing to students, so most textbooks (and DeltaMath) only ask for the positive solution when dealing with fractional exponents -- only for n = 2 does it expect students to list both solutions.

Another student is confused because during the Warm-Up, I remind the students to check for extraneous roots for absolute value and radical equations. I point out that it's possible for both solutions to be extraneous, and so the solution set would be the empty set, which I write as an O-slash. This student asks whether this symbol means that zero is a solution to the equation, so I explained that no, it means that there is no solution at all, so they shouldn't type {0} as the solution set. Then she begins her quiz and -- you guessed it! -- she gets an equation with the unique real solution x = 0. And since I'd told her not to type {0} as the solution set, she inputs the empty set and is marked wrong. The moral of the story is that I shouldn't have used O-slash for the empty set -- instead, I should have followed DeltaMath and used empty braces, {}.

2:25 -- Fifth period leaves and sixth period arrives. This is the third of three Math I classes.

Unfortunately, many students in this class were absent on Friday -- hence they missed the Hero Quiz. I spend lots of time today handing out Hero Quizzes and checking them (as I'm supposed to grade them right away and let them know whether they got an A or less than an A). All of this took time away from the main lesson -- in other words, it was just like a quiz correction day where more time is spent redoing quizzes than learning the new material.

Of course, this wouldn't have mattered if I could have assigned the Desmos lesson to the students who weren't absent last Friday and expected them to work. But that's too much to ask of a (typically) immature class of freshmen. Many of them talk or otherwise do no work while the absent students are making up their Hero Quizzes. And so I end up rushing the Desmos lesson even more than in my second and fourth period classes.

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

In my last monthly post, I mentioned how I wish to make connections with my students -- especially in my freshman classes. As of now, I'm still worried that I'm not making strong enough connections. The classes are often loud and disengaged, and I often have trouble communicating with them in such a way to motivate them to learn. Once again, I hate arguing with my students, but sometimes that's the only way I can get their attention.

Once again, I want to find better ways to communicate with my freshmen -- and get them to work well with each other as well. I'm still trying to find a way to incorporate the Promethean board into my lessons, in particular the group assignments. The board seems to work well -- the problem is that I'm not skilled enough to use it with group lessons on a regular basis.

Coming up on the horizon are the district tests. Between now and my November monthly post, I'll have given district Benchmarks in both Math I and III. Both departments (actually curriculum teams) are scrambling to cover all the necessary material before the district tests.

This concludes my monthly "Day in the Life" post for October.

Lesson 2.1.4: Graphing Linear Equations (Days 44-46)

NINE NINE NINE

Chorus: 

Nine nine nine

Fantastic number nine

It’s perfectly consistent

It works out every time

Nine nine nine

That crazy number nine

Times any number you can find

It all comes back to nine

First Verse:

Two times nine is eighteen, Eight and one is nine

Three times nine is twenty-seven, Seven and two is nine

Four times nine is thirty-six, Six and three is nine

Five times nine is forty-five, Five and four is nine

Six times nine is fifty-four, Five and four is nine

Seven times nine is sixty-three, Six and three is nine

Eight times nine is seventy-two, Seven and two is nine

Nine times nine is eighty-one, Eight and one is nine (to Chorus)

Second Verse:

Nine times ten is ninety, Just drop the zero sign

Nine times eleven is ninety-nine, Makes me rhyme with another line

Then nine and nine is eighteen, And eight and one is nine

Times any number you can find

It all comes back to nine

This work for bigger numbers, too? Yup.

Let’s try this’un: three thousand four hundred’n eighty seven

Hmm … nine times three thousand four hundred eighty seven is

Thirty-one thousand three hundred eighty-three

Three plus one plus three plus eight plus three is eighteen;

One plus eight is nine.

It always works! (to Chorus)

It's been some time since I performed a Square One TV song in class. There are several reasons why I choose this week for "Nine Nine Nine":

• First, I already have performed several slope songs during this chapter.
• It is Week 9 of the school year -- well, it is if Sara(h) Week counts as Week 0. The other Math I teachers have posted a pacing plan where the school year starts with Week 0. And since there was no homework during Week 0, Assignment #1 was due Week 1 and Assignment #9 is due this week, so this week is already associated with nine. (I also sang "Nine Nine Nine" two years ago, during the ninth week of my long-term assignment.)
• Tomorrow is Parent Conferences Day. While there likely won't be much time to perform for parents who are concerned with grades, I might be able to squeeze at least part of the song (maybe the chorus) in between conferences. (I also sang "Nine Nine Nine" for parents six years ago, during Back to School Night at the old charter school.)
• Two years ago, I sang "Nine Nine Nine" just ahead of the 9's Hero Quiz. Well, as it turns out, I'm bringing back Hero Quizzes for my Math I students.

Yes, I mentioned earlier on the blog that I was considering Hero Quizzes, and Friday, the minimum day associated with Parent Conferences Night, is the perfect day to do one. However, this quiz will be different from the ones I implemented at middle schools.

I believe that at high schools, students will consider pure multiplication quizzes to be "beneath them" (no matter how much these students really need practice multiplying one-digit numbers). So instead, they will be consist of two review questions from a previous chapter. This week's Hero Quiz will contain two equations (one two-step, one with distributive).

The quiz will be Tech 55, with no calculators, computers, phones, or earbuds allowed. I will tell them that their notes likely won't help them. One of the coefficients in the equations will be nine, so that the "Nine Nine Nine" song is useful. (And the lyrics will still be posted on the wall for them, where I usually post song lyrics.) We'll see how it turns out.

Last year, I counted Parent Conferences Day as a special post for "A Day in the Life" -- though it helped that it fell on a regularly scheduled posting day. This year, I've decided not to post on either Parent Conferences Day or the following minimum day (which is not a monthly minimum day, as these no longer exist).

Instead, my next posting day will be on my new monthly posting day -- the 17th, which is Monday. I'll do "A Day in the Life" in that next post.

Lesson 2.1.3 Continued: Two Points Slope (Day 43)

SLOPE DUDE

First Verse:

Slope, puff puff positive.

Slope, nice and negative.

Slope, boring zero.

Slope, danger undefined.

Pre-Chorus:

Slope Dude! Positive.

Slope Dude! Negative.

Slope Dude! Zero.

Slope Dude! Undefined.

Chorus:

Slope Dude! Up he goes.

Slope Dude! Down he goes.

Slope Dude! Stay the course.

Slope Dude! Aaaaaaahhhhhhh!

Second Verse:

Slope, uphill positive.

Slope, downhill negative.

Slope, flatland zero.

Slope, cliffside undefined.

(to Pre-Chorus)

This is the ninth song that I'm writing in 10EDL, our main scale for September and October. The next few 10EDL songs will be written in ABC format, with verses, a pre-chorus, and a chorus.

Today's Math I lesson centers around a Desmos lesson that starts out with the Slope Formula. This is combined with a Desmos staple -- Marbleslides. Since the first few slides introduce positive, negative, zero, and undefined slope, this is a great time to write an original song incorporating Sarah Carter's "Slope Dude."

Here's a link to the Mocha code for the song:

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

10 N=8

20 FOR V=1 TO 2

30 FOR X=1 TO 64

40 READ A,T

50 SOUND 261-N*A,T

60 NEXT V

70 RESTORE

80 NEXT X

90 END

100 DATA 9,6,10,6,7,4,6,2,5,2,10,12

110 DATA 9,6,10,6,7,4,6,2,5,2,10,12

120 DATA 9,6,10,6,7,4,6,2,5,2,10,12

130 DATA 9,6,10,6,7,4,6,2,5,2,10,12

140 DATA 5,8,8,8,10,6,7,6,5,4

150 DATA 5,8,8,8,10,6,7,6,5,4

160 DATA 5,8,8,8,10,6,7,6,5,4

170 DATA 5,8,8,8,10,6,7,6,5,4

180 DATA 5,8,8,8,5,12,6,2,8,2

190 DATA 5,8,8,8,5,12,6,2,8,2

200 DATA 5,8,8,8,5,12,6,2,8,2

210 DATA 5,8,8,8,5,12,6,2,8,2

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

Interestingly enough, my TI music generator program had the Pre-Chorus and Chorus lines start with the same two notes -- (high)C-E, both half notes. I decided to put the title of the song, "Slope Dude," as the lyrics over both sets of half notes.

The chord riffs are D7-Am for the verse, C-D7 for the pre-chorus, and C-Am for the chorus. Even with the same notes leading both the B and C sections, the chords make these parts sound distinct. The chorus melody goes (high)C-E-(high)C-A-E, so the Am chord fits these notes.

In the pre-chorus, the chords repeat, but we might consider adjusting the melody to fit the words. The notes (low)C-F#-(high)C sound good with "Positive," but for "Negative" we might reverse these notes so that the melody is descending, (high)C-F#-(high)C. For "Zero" we can play F#-F#, but suitable notes for "Undefined" are tricky. We might even move "Aaaaaaahhhhhhh!" (a non-melodic scream) up to the channel, or even whisper or rap "Undefined." The new notes for "Negative" and "Zero" can be reflected in the Mocha program, but the code for "Undefined" would be, uh, ill-defined.

The final "Aaaaaaahhhhhhh!" as Slope Dude falls down the cliff can be played without a chord, thus allowing the tonic chord C to be the final chord of the song. Naturally the students in my classes enjoy this part of the song -- and Desmos Marbleslides are always fun.

Lesson 2.1.3: Slope (Days 39-42)

GROWTH SLOPE

First Verse:

Nine minus three is six. Growth!

Three minus zero's three. Growth!

Six over three is two. Growth!

That's how you find the growth!

Pre-Chorus:

Find the change in y. Slope!

Find the change in x. Slope!

y change o'er x change. Slope!

That's how you find the slope!

Chorus:

Almost all lines have growth,

Almost all lines have slope.

Once you have found the growth,

Then you have found the slope.

Second Verse:

Three minus zero's three. Growth!

Six minus zero's six. Growth!

Three over six, one half. Growth!

That's how you find the growth!

(to Pre-Chorus)

This is the eighth song that I'm writing in 10EDL, our main scale for September and October. The next few 10EDL songs will be written in ABC format, with verses, a pre-chorus, and a chorus.

This song is influenced by another Desmos lesson, where students are asked to find the "growth" of a linear graph, just as they can from a tile pattern or table. Of course, "growth" in this lesson is just a euphemism for "slope." Interestingly enough, the students find this growth using "slope triangles," as opposed to "growth triangles." (Oh, and I also used "delta" for change -- the Greek letter appears in this CPM lesson, but not in this Desmos lesson.)

Here's a link to the Mocha code for the song:

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

10 N=8

20 FOR V=1 TO 76

30 FOR X=1 TO 2

40 READ A,T

50 SOUND 261-N*A,T

60 NEXT V

70 RESTORE

80 NEXT X

90 END

100 DATA 7,2,9,2,9,2,7,2,7,4,10,4,9,16

110 DATA 7,2,9,2,9,2,7,2,7,4,10,4,9,16

120 DATA 7,2,9,2,9,2,7,2,7,4,10,4,9,16

130 DATA 7,2,9,2,9,2,7,2,7,4,10,4,9,16

140 DATA 5,4,5,2,7,2,6,4,5,4,7,16

150 DATA 5,4,5,2,7,2,6,4,5,4,7,16

160 DATA 5,4,5,2,7,2,6,4,5,4,7,16

170 DATA 5,4,5,2,7,2,6,4,5,4,7,16

180 DATA 9,6,10,6,10,4,7,2,9,2,9,12

190 DATA 9,6,10,6,10,4,7,2,9,2,9,12

200 DATA 9,6,10,6,10,4,7,2,9,2,9,12

210 DATA 9,6,10,6,10,4,7,2,9,2,9,12

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

This is the most complex 10EDL song yet, with no short lines in the chorus or any other part. At this point, I start to wonder whether there's an easy way to make Mocha repeat each line four times without having to type in the corresponding DATA line that many times. (Perhaps we might dispense with DATA and use GOSUB subroutines, but each subroutine would still be long.)

As for the guitar riffs, I use D7-G7 in the verse, C-D7 in the pre-chorus, and C-G7 in the chorus. Since there is no G in 10EDL, I've been avoiding the G7 chord (even though the tonic is C). The only 10EDL note that fits in the G7 chord is D, so I play it over the long D notes, including the dotted half note at the end of the chorus melody, D-(low)C-C-F#-D-D.

This is the second of two Chapter 2 lessons to be given before the Chapter 1 DeltaMath Test.

Lesson 2.1.2: Constant Rate of Change (Day 38)

WORDS PER MINUTE

First Verse:

Thirty words per minute,

That's how fast Clara can type.

How many words in eighty?

How long will she type 75?

Pre-Chorus:

Let x be minutes in equation,

Let y be typed words in equation.

Then you must write down the equation,

Then you must now solve the equation.

Chorus:

WPM (4 times)

Second Verse:

Thirty words per minute,

That's how fast Clara can type.

She has written 75,

Tobias's rate is 45.

(to Pre-Chorus)

This is the seventh song that I'm writing in 10EDL, our main scale for September and October. The next few 10EDL songs will be written in ABC format, with verses, a pre-chorus, and a chorus.

As you can see, I've decided to start Chapter 2 this week after all. This chapter is on linear functions, including slope. But we will still take the Chapter 1 Test, created and posted by one of the other Math I teachers, at the end of this week. (Clara and Tobias are two names mentioned in today's Desmos lesson, which was on words per minute as an introduction to rates.)

Here's a link to the Mocha code for the song:

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

10 N=8

20 FOR V=1 TO 68

30 FOR X=1 TO 2

40 READ A,T

50 SOUND 261-N*A,T

60 NEXT V

70 RESTORE

80 NEXT X

90 END

100 DATA 6,4,5,4,5,4,6,4,7,8,10,8

110 DATA 6,4,5,4,5,4,6,4,7,8,10,8

120 DATA 6,4,5,4,5,4,6,4,7,8,10,8

130 DATA 6,4,5,4,5,4,6,4,7,8,10,8

140 DATA 8,4,9,4,5,2,9,2,5,2,6,2,10,6,6,6,6,4

150 DATA 8,4,9,4,5,2,9,2,5,2,6,2,10,6,6,6,6,4

160 DATA 8,4,9,4,5,2,9,2,5,2,6,2,10,6,6,6,6,4

170 DATA 8,4,9,4,5,2,9,2,5,2,6,2,10,6,6,6,6,4

180 DATA 8,16,7,16

190 DATA 8,16,7,16

200 DATA 8,16,7,16

210 DATA 8,16,7,16

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

Since we moved up a level from having just verses and chorus to adding a pre-chorus as well, this time I fell back to having a simple chorus with just two whole notes (E-F#). I sing the initials WPM during this part -- W during the long E note and PM during the F#. Again, a simple chorus makes it easier to type in the Mocha code (so we worry less about whether we have enough WPM speed to type it fast).

The chord riffs for this song are Am-D7 for the verses, E7-Am for the pre-chorus and C-D(7) during the chorus section. I avoid the tonic chord C during the pre-chorus -- this section is supposed to lead into the chorus, and E7-Am sounds better here than a C chord.