Test Retake Day (Day 79)

Just like the seventh graders, the eighth graders don't have a Unit 5 Final this week. But the older students already took their Unit 4a Test last week, as originally scheduled. Instead of a final, this week is reserved for Unit 3 and 4a retakes and making up other missing assignments.

With the second quarter coming to an end, grades are becoming prominent again -- and with grades comes the annoying grade weighting in Canvas. Recall that in both Math 8 classes, APEX quizzes are 30%. In first period, APEX tests are 30% and "Assignments" are 40%, while it's vice versa in fourth period. On the other hand, so-called "Imported Assignments" are 0% of the grade/

I mentioned last month that the two Edpuzzles are considered to be Assignments. As it turns out, these are the only two Assignments in fourth period. For some reason, first period has one more Assignment -- the Unit 4 Practice Test in Go Formative. Thus each of these three Assignments is worth 10% of the grade in first period -- that is, one full letter grade. And each of the two Edpuzzles is worth a whopping 20% of the grade in fourth period -- that is, two letter grades.

(You may be wondering, why is this little word "Imported" so important, anyway? "Imported" basically means that they were imported into Canvas from another source, such as the other Math 8 teachers. Still, I'm not sure why the Edpuzzles, which were set up by the lead Math 8 teacher, aren't "Imported," nor why the Unit 4 Practice is "Imported" in one period and a red-blooded "Assignment" in the other.)

What this does mean is that a fourth period student who skipped the Edpuzzles but has a near-perfect 99% in everything else will wind up with a grade of 59%, an F. And a first period student who does the same and omits Go Formative will wind up with a D+. That's why I don't like grade weighting -- assignments that students skip because they think don't matter much suddenly make huge differences in the grade.

The lead Math 8 teacher has set up this week's test retakes so that students should write a paragraph explaining what they did wrong on the test before being granted the retake. They also need to have 100% on the corresponding Go Formative Practice Test. I don't make my students write a paragraph, but I do make them get 100% in Go Formative.

So here's what happened with one particular guy in the Friday cohort of fourth period (that met Monday this week instead): He earned a D on last week's Unit 4 Test. So I told him that he should keep repeating the Go Formative Practice Test, which he eventually does. Then I let him retake the Unit 4 Test -- only to get the very same D the second time around. And all along, this student never did the Edpuzzles -- so in other words, he spent the 100-minute block working on 0% of his grade instead of working on 40%, and so he winds up with an F for the quarter.

After this, for both the Tuesday and Wednesday cohorts, I tell the students that they must complete Edpuzzles as well as Go Formative before granting the retake. And for tomorrow's fourth period cohort (where Go Formative is "Imported"), I'm considering making them do only Edpuzzles to get the retake.

Lesson 4.4.2: Unit 4 Test (Days 74-77)

Today the eighth graders take their Unit 4 Test. But first, there is a Practice Unit 4 Test, which the students take via Go Formative. The questions are "similar" (which really means identical) to the questions that they'll see on the actual test.

Recall that in this class, Unit 4 has been divided into two parts, divided by the semester break. Unit 4a covers Lessons 4.1.1 (solving linear equations) and 4.3.1 (solving square and cube equations), and Unit 4b will cover Lesson 4.2.1 (solving systems of equations). There was some discussion over how we would test the students, and we decided that we will give APEX Test 4.4.2 after all (with the systems questions thrown out). Presumably, a non-APEX test will be given for Unit 4b.

So far, most of the first period students seem to be doing well on the test, with several perfect scores. I wonder whether I helped them out too much by going over the Go Formative questions. Then again, the opposite will probably be true for the fourth period classes tomorrow -- for the special ed students, doing Go Formative won't be enough for some of these students to pass.

After the test, I tell the eighth graders about the Putnam exam. Indeed, today's a good day to do this -- after the students take a test that they think is "hard," I point out that this test is a cinch compared to the Putnam exam. It also fits with the UCLA song I sing for music break, since the Putnam is a test I took when I was a Bruin.

I tell them that after the 2019 Putnam, UCLA placed fourth in the country. Indeed, my own score was 22, which was good enough to place among the top four Bruins -- but this year, our school had five students scoring over 50 points each. The top five students earned $2500 each, while the prizes for the next two levels were $1000 and $500. I also mention Problem 2019 A2 -- while it started out as a problem about triangles, it ended up using slope, which they learned in Unit 3 (and is mentioned in my own parody of the UCLA fight song).

Then I pass out my prizes from the birthday Conjectures game -- some Skittles and Starburst. I know -- my prize is so puny compared to the Putnam prizes.

There is a fire drill today. Unlike the October earthquake drill (drop and cover only), this fire drill obviously requires an evacuation. It occurs during tutorial, which is attached to first period. I never enjoy fire drills as a sub -- and in this case, today's drill involved my largest class, 13 students in the Wednesday cohort under hybrid. A fire drill with fifth period would have been a piece of cake -- only four students are in the Wednesday/Friday cohort (not counting the online students, who can't participate in the drill). The third period class would have in between, with eight in-person students.

I continue to discuss the seventh grade class with the department head. We will try to get through the Inequalities activity tomorrow in second period -- it will have the advantage of being attached to the tutorial session tomorrow, so there's extra time.

I normally don't start thinking about next week's schedule this early, but it's going to affect my blogging schedule, so I'll say it now. Like many districts, my current district has a day off for students between the semesters. My old district in LA County, for example, is closed that Monday after the students return in January (so the first day of school is Tuesday), but my new district closes the Friday that students leave in December -- so the last day of school is Thursday.

This affects the block schedule. Just like Veteran's Day week, the Monday of the short week takes on the identity of the missing day, so Monday's schedule will be like Friday's. And so my blogging schedule should reflect this. I usually don't blog on the days my aide is there, and so there will be no blog entry on Monday. My next blogging day will be Tuesday. (This also means that Thursday of next week becomes a blogging day, for the special day "last day before winter break.")

It also means that tomorrow, Friday, and Monday are all tweeting days. Right now I'm in the middle of a new tweeting challenge, "The 12 Days of Twitter," with different prompts each day.

Lesson 4.3.1: Solving Equations Using Roots (Day 72)

Today is a minimum day, and so this is my monthly MTBoS blogging day for December. I will be describing today in "A Day in the Life" format:

9:00 -- I arrive on campus. On this minimum day, only certain teachers have a meeting before school. There is an all-staff meeting after school, of course.

The big thing that's on my mind right now are the district Benchmark Tests. The students have finished them, but now it's time for us to grade the Performance Tasks. The department head has told me that we should work on them together for the grading to be consistent. But unfortunately, the department heads are the ones in the morning meeting, so I must wait until after school.

9:45 -- First period begins on this online day. This is the first of two eighth grade classes.

All classes today have the same format -- a short lesson followed by an APEX test. For me to have enough time to do both, I decide to do something I haven't done in a while -- play "Who Am I?"/Conjectures Game. As usual, the first question I ask today is "Guess my age."

Yes, I see you running to check the date. Yes, today is December 7th, my birthday -- and I always try to play "Who Am I?" to ask "Guess my age" on my birthday. It's a birthday that everyone dreads -- the Big 4-0. It's also my tenth Julian birthday. As every Julian cycle of four years contains 1461 days, so this is the rare day that I know my exact age in days -- 14610 days.

This is the first time that I've attempted "Who Am I?" since the pandemic, and today is a fully online Monday. So, here's how I do it -- I divide the class into three teams, and I tell them which team they're on. The teams are Team #1 (first names A-Ja), Team #2 (first names Jo-Z), and Team #0 (those who haven't the Benchmark tests yet). Team #0 automatically loses -- they must work on their Benchmarks instead of playing the game.

The second question is usually "Guess my weight," but I haven't stepped on a scale since well before the pandemic. Instead, I change this to "Guess my height" -- since we're online, the students can't just look at me to see what my height is.

Afterwards, the questions are based on the Lesson 4.3.1, on solving equations using roots. This lesson lends itself well to the "Who Am I?" game -- I just ask the students to solve blank times blank equals 25, then segue into x^2 = 25 and explain that +5 and -5 are solutions. I also go over equations with cubes in them as well, not just squares.

Here is the relevant Common Core standard:

CCSS.MATH.CONTENT.8.EE.A.2
Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

The students get 15 minutes for this lesson and then 15 minutes for the APEX quiz. But the APEX quiz is actually based on the previous Lesson 4.1.5, which they haven't taken yet. I've already covered most of this quiz, but I only brushed over linear equations with no/infinitely many solutions (the one topic taught better on APEX than on our worksheets). So I go over this again as the students start the test.

10:20 -- First period ends and second period begins. This is the first of two seventh grade classes and the first class with an aide.

I also play "Who Am I?" with this class. But unfortunately, the lesson doesn't go as well. I attempt to go over the "Working Backwards" problems in APEX 4.3.1, followed by solving some equations of the form p(x + q) = r, as described in the following standard:

CCSS.MATH.CONTENT.7.EE.B.4.A
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Because of this standard, APEX insists on solving p(x + q) = r by first dividing both sides by p, rather than distributing p. The department head and I have already decided that this technique will only confuse the students more, and so we'd like to skip it, if not for the fact that three of the five problems on APEX Quiz 4.3.5 use this technique. So the goal is to use the game to teach both working backwards and p(x + q) = r in the first 15 minutes, then move on to the APEX quiz.

But the lesson doesn't go well. In fact, we'd be hard-pressed to teach all of this in 15 minutes period, with or without the "Who Am I?" game. The students struggle on the APEX quiz.

10:55 -- Second period ends and third period begins. This is the second of two seventh grade classes.

The only difference between this class and second period is that one girl guesses my exact age, while another guy accurately guesses my height. Of course, the game falls apart again as soon as we leave the age and height questions and move on to the math questions.

11:30 -- Third period ends for a short five-minute break.

11:35 -- Fourth period begins. This is the second of two eighth grade classes and the second class with the aide.

During "Who Am I?" one guy -- who just happened to earn a perfect score on the Benchmark multiple choice last week -- decides to guess 0 for my age, and then gives silly answers from then on. Luckily, this might be the rare time when a student goofing off is actually a good thing. If he had taken the game seriously, he might have dominated it, and no other student would bother participating. But since he takes this game off, this gives the others -- both his teammates and his opponents -- a chance to participate in the game.

12:10 -- Fourth period ends and fifth period begins. This is the Math Skills class.

Fortunately, ST Math and Dreambox are now working again. I'd spoken to the regular teacher over the weekend, and so we agreed not to count any grades for last week. This week, of course, the students must get back on track.

12:45 -- Fifth period ends, and so does my teaching day. But my workday is just getting started. This time, we're given a lunch break before the meetings begin (unlike in November).

1:30 -- It's a math department meeting today. We first meet as a department, along with the principal and assistant principal. Then we break off into our usual Math 8, Math 7, etc., groups to discuss the scoring of the Benchmarks, as well as our upcoming week of teaching.

In eighth grade, we decided that the Unit 4 Test will be given this week. This is actually the first part of Unit 4 (that is, Unit 4a) -- the skipped Lesson 4.2.1, on systems of equations, will be taught first thing after winter break.

As for seventh grade, the department head and I realize that today's Quiz 4.3.5 was a disaster. We might throw it out and move on to Lesson 4.4.1 starting tomorrow.

I actually have much more to say about the curriculum, but I don't have time to post much more today because I'm still grading the Benchmark Tasks! I've already completed seventh grade -- I stopped to write this blog post, and then I'll continue with eighth grade after I post. I'll just add a few brief notes about my day today.

Notice that "Who Am I?" is a game that involves competition and speed. Therefore it is what Eugenia Cheng would call "ingressive" -- it might turn off more "congressive" students, including some girls. (I know -- I'm supposed to be done with Cheng for now. But I'll be quick, and I won't include the label "Eugenia Cheng" in this post.) But many students enjoy it -- as long as I don't overdo it and instead play it mainly in situations where speed matters (such as on minimum days wth half-hour periods), then the game is fine.

Four years ago at the old charter school (yes, I'm allowed to mention the old school on monthly blogging days), I also taught on my birthday -- my ninth Julian birthday. It was a Wednesday and hence it was an early day, just as it was today. But I didn't have to spend all night grading Benchmarks, since our school had already completed Benchmarks about a month before my birthday.

Indeed, among the birthdays when I had to work very hard, this one is comparable only to my 21st and 23rd birthdays during my years at UCLA. In both cases, I was studying hard that night for December 8th tests -- one was the GRE to get into grad school, and the other was for a Set Theory final once I was in grad school. This year, I'll have to work hard all week -- coming up on Wednesday is some sort of math department observation, and there are special ed meetings the rest of the week.

Today was the first day of a statewide coronavirus shutdown in California. Just as with the color purple, schools that have already opened may stay open. To me, the only good thing about the shutdown is that there was much less traffic, and so I had a easier commute to and from work today.

Lesson 4.1.3: Solving Linear Equations (Days 69-71)

While eighth grade hasn't been quite as convoluted as seventh grade, this week I still must find a way to balance out this week's Benchmark Performance Task with the regular lesson. Just as with Math 7, I'm taking a 30-40-30 approach -- prepare for Benchmarks the first 30 minutes, take the Benchmarks the next 40, and give the regular lesson the last 30.

There is one question on the eighth grade Benchmarks that I definitely don't like. There is a graph that shows time in seconds on the x-axis and distance in yards on the y-axis, and the question asks to find someone's average speed -- in miles per hour. Even most math teachers probably don't know how many yards there are in a mile -- unlike 12 inches to the foot and three feet to the yard, the number of yards to the mile isn't regularly taught.

(Indeed, the only reason that I know the number of yards to the mile is that as a young student, my PE teacher -- yes, that PE teacher -- would have us run 440's, a lap around a quarter-mile track. There might also have been 880's, a half-mile run. Indeed, my performance in the 440's was the first hint that I was destined to become a Cross Country runner. Double the length of the 880's and we arrive at the length of a mile as 1760 yards -- but then again, we never said we ran "the 1760" -- what we ran was "the mile.")

As for the main lesson, our use of worksheets continues, as there are Kuta (or Kuta-like) worksheets for solving equations with variables on both sides, combining like terms, and distributing. I've decided that I'd much rather do example problems from the worksheets than rely on APEX. For one thing, some topics, such as combining like terms to solve equations, aren't covered well on APEX. So doing problems directly from the worksheet is helpful to them.

On the other hand, equations with no/infinitely many solutions are covered much better on APEX. There is a worksheet with variables on both sides, but the coefficients don't match. Thus the variables never drop out completely, and so each equation on that worksheet has a unique solution. I'll have to go back to more examples of this later on. Notice that neither seventh nor eighth grade has an APEX quiz today. The students work hard to get through their Performance Tasks, so let's not torture them with an APEX quiz on top of that.

This will be my last post for now with the "Eugenia Cheng" label, as I'm getting ready to turn the book back in to the library. I'm mentioning her book again now because today I meet with a parent whose seventh grade daughter is shy and has trouble speaking up in classes. (She's a special ed student, but of course, any further discussion there is inappropriate for blogging.) When I randomly choose her name, she usually does participate -- but I don't choose her name that often. Sometimes I fear that she's slipping through the cracks -- she might not understand the material, but I don't realize this until it's too late. This is what Cheng wants us to watch out for -- girls who struggle to speak up in class.

It's back to my usual blogging and tweeting schedule this week. So you can expect to see some tweets from me on Thursday and Friday.

Benchmark Tests (Day 67)

Today is Cyber Monday. Ordinarily, I would order next year's Rapoport calendar from Amazon on Cyber Monday, but this year I actually found it at a brick-and-mortar Barnes and Noble. I did make an Amazon order today, but no item I ordered is relevant to math or this blog. Also, this is the second straight year that Theoni Pappas doesn't have a math calendar. I suspect that she's now retired from publishing calendars.

Yes, it's the return to school today. On this full-distance Monday, the eighth graders begin the multiple choice portion of their Benchmarks. During today's department meeting, the Math 8 teacher leader suggested reviewing a Unit 1 topic with them -- exponents, since their laws are easy to forget. I spend about 10-15 minutes going over the laws -- only to have her tell me after school that power of a product and power of a quotient weren't covered in Math 8.

If I had been at this school from the start, I could have sung an exponent song in Unit 1 -- and then play that song again today as a quick reminder. Speaking of songs, there are a glut of songs I'd like to do this week based on their current assignments. (As usual, you'll find out tomorrow which songs I choose.)

I suspect that despite my going over exponents, most students fare poorly on the Benchmarks. The first question directs students to "select all that apply," which always seems to trip the students up -- and I think there's at least one more such question on the test. The extra time it takes me to remind the students of exponents is time taken away from finishing the test, and so a few students are unable to finish them.

Today is also November 30th -- the anniversary of the day I hit my eighth grade P.E. teacher and was suspended from school. I continue my tradition today of telling the story to any eighth graders I sub on the last day of November. (I've been doing this the last few years, but I'm surprised that I never mentioned this story on the blog until last week's Thanksgiving post.)

The seventh graders already took their multiple choice Benchmarks before Thanksgiving. And so today's lesson is all about preparing them for the upcoming Performance Task portion, which is about modeling a pattern with a linear expression. The department head has supplied me with a video to show them -- and this time, I don't just play the video the whole period. Instead, I show them a Google Slideshow and then ask a few questions near the end.

This works well in second period, but in third period I had the misfortune of randomly choosing a boy who steps away to the bathroom (at home, since today is online). This slows me down near the end -- I rush through the end of the problem myself, and then I forget to remind the students to go to fifth period for tutorial. Three girls who are in both my 3rd/5th periods neglect to stay for tutorial.

And fifth period itself doesn't go smoothly either. Normally the students log in to Clever and then log in to ST Math or Dreambox to start their weekly 60 minutes, but for some reason, the ST Math and Dreambox icons don't appear on Clever. I inform the district math tech person to investigate the matter.

Lesson 4.1.2: Solving Linear Equations (Days 64-65)

Well, in the eighth grade class, I attempt to go over some more two-step equations after singing the "Solve It" song for music break. But unfortunately, we do only two more equations.

The problem I have today is with the third quaver progress reports. I completed them on Aeries over the weekend, but the actual deadline for submitting them is noon today. And so I tell the students that they should make up any missing work by noon today in order to raise their grade from a D or F in order to avoid getting a progress report.

There are many more students getting progress reports in eighth than in seventh grade -- and this is true for several reasons. Much of it is because of APEX -- in order to advance to the next quiz, APEX is set up to require eighth graders to earn a score of 60%, but seventh graders must earn at least 70%. And since most quizzes have only five questions, "at least 70%" really means 4/5 or 80%. I force the seventh graders to keep retaking the quizzes and tests until they pass them.

Thus it's impossible for seventh graders to earn less than 70% if they pass the test -- and it's impossible for them to earn more than 59% unless they pass it. Therefore there are no seventh graders with D's -- and only two students in each period missed the test and have F's.

On the other hand, more eighth graders get D's on all the quizzes and the test, and so there are eighth graders with D's, in addition to the ones who missed the test and have F's. And the cohort with the most progress reports is today's first period class -- and it also happens to be the last full class meeting before the noon deadline.

And so I spend the entire time after music break checking and resetting APEX tests. This is for students who missed the test as well as those with D's who wish for me to reset the tests in APEX. I'm glad that many of them are able to raise their grades to C's today.

During the snack break, I ask other teachers for advice on changing the progress report grades -- and they tell me that I shouldn't have offered to raise their grades. At some schools, there is no hard "last day of the quaver" (as there would be for a quarter or semester), but just a "window" to enter progress reports. But here, there was a last day of the third quaver -- last Friday. If the students didn't take their test by the due date, then I should have just given the F's on the progress reports. But because I'd already told them that I'd raise the grades, they suggest that I just give them a C- on the progress report, with an N in work habits as a warning.

But notice that what I do today is create a vicious cycle. Instead of going over the two-step equations, I give students time to make up old assignments. Then without the extra guidance on two-step equations, the students struggle and fall behind. They'll fail the APEX quiz on equations and require extra time to make it up -- which then takes time from a future lesson. Instead, at some point I must put my foot down and tell students that they must move on -- this gives them a fighting chance to keep up with the material.

Lesson 4.1.1: Solving Linear Equations (Day 62)

Today is a minimum day, and so this counts as my monthly MTBoS blogging day for November. I will be describing today in "A Day in the Life" format:

9:00 -- I arrive on campus. On this minimum day, only certain teachers have meeting before school. There is an all-staff meeting after school, of course.

The big thing that's on my mind right now are the district Benchmark Tests. Once again, it almost seems as if Math 7 and Math 8 are separate departments. The math department head, who teaches Math 7, has decided that we will at least start the Benchmarks this week. But the eighth grade teachers might come up with a different plan. And so I decide to email the most senior Math 8 teacher (the so-called "head of the Math 8 department) to see what her plans are.

9:25 -- The Math 8 leader responds. She tells me that since there's some Unit 4 material on these tests, we will wait until after Thanksgiving to give them. (Notice that there's also some Unit 4 material on the seventh grade tests, yet the department head still wants to start Benchmarks with them this week.)

9:45 -- First period begins. This is the first of two eighth grade classes on this all-distance learning day.

We begin Lesson 4.1.1 in APEX, which is on solving linear equations. The lesson begins with one-step equations before moving on to two-step equations. Since it's a minimum day, there's not enough time for the entire lesson. So I break the lesson off after one-step equations -- a natural stopping point.

It takes about 20 minutes to reach this point. For the last ten minutes of class, I direct the students to go to Canvas and click on the two Edpuzzle links. One assignment is on one-step equations (which is another reason why I stopped the lesson at this point) and the other is on combining like terms. These assignments are officially due today.

While the students begin their Edpuzzle assignments, I inform them that I worked on their third quaver progress reports over the weekend, and unfortunately, ten students will be receiving them -- just about a third of the class. After last week's Wi-Fi outage, I was afraid that the Tuesday cohort would use it as an excuse to slack off, neglect to work on the test, and then get a progress report. But to my surprise, the majority of the progress reports are earned by the Wednesday cohort (which met Monday last week).

10:20 -- First period ends and second period begins. This is the first of two seventh grade classes, and the first class with the co-teacher.

Today is the special lesson to prepare the students for the Benchmarks. And the topic for today's lesson is two-step equations. That's right -- I teach one-step equations to the eighth graders and then two-step equations to the seventh graders. How does this happen?

Well, let's look at the relevant Common Core standards:

CCSS.MATH.CONTENT.7.EE.B.4.A
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

CCSS.MATH.CONTENT.8.EE.C.7.B
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

From these, we conclude that the most advanced equations that seventh graders are expected to solve are two-step, while eighth graders must solve multi-step equations. But APEX, in Math 8, builds up to multi-step by starting with one- and two-step problems, while the Benchmarks in Math 7 jump directly into two-step problems. Thus the seventh graders get a more difficult lesson only because we've chosen to give them the Benchmarks sooner.

For today, the students watch three Khan Academy videos, which take up most of the period. Since these videos are on YouTube, there's no harm in my posting these videos here:

10:55 -- Second period ends and third period begins. This is the second of two seventh grade classes.

As in all of the other classes, I warn the students who might receive progress reports. There are two such students in each seventh grade class (although one girl in this third period class makes up her missing test later this evening, just before the date/time of this post, to avoid the unsat).

11:30 -- Third period ends for the short five-minute break.

11:35 -- Fourth period begins. This is the second of two eighth grade classes, and the second class with the co-teacher.

In this class, nine students might receive a progress report. While this is fewer than first period, it's a larger part of this later class, with nearly half getting the report. 

12:10 -- Fourth period ends and fifth period begins. This is the Math Skills class.

In this class, three students will receive progress reports -- in a class where the only assignment is to log in 60 minutes on ST Math or Dreambox each week. One guy has a D+ and is just five minutes away from avoiding the progress report (but it's too late now, as ST Math will count any new minutes for this week rather than last week).

Another girl has a D-, but just when I'm about to warn her that she will receive the progress report, she logs out of the Google Meet, having attended only 2-3 minutes of class (even though she attends all of my third period class). At this point, I realize that I need to crack down on slackers in this class -- there's actually no reason why anyone should have a D or F in this class. So in attendance, I mark her as "X" for non-participating -- and I plan on doing the same for those who aren't logging in minutes to ST Math or Dreambox the rest of the week.

12:45 -- Fifth period ends, and the day is over for the students -- but not nearly for us teachers.

1:00 -- The all-staff meeting begins. The first thing the principal mentions is that Orange County has indeed fallen back into the purple coronavirus tier. But as of now, Governor Newsom's rule is that if a county opens schools in the red tier, then those schools can remain open even if the county returns to the purple tier. Thus we will still have hybrid learning tomorrow and the rest of this week. (On the other hand, LA County schools remain distance-only because the county never reached the red tier.)

The main topic for today's meeting is the sharp rise in the number of D and F students since the start of the pandemic. (I assume that this is a problem everywhere, not just at our school.) And so all teachers must work hard to reduce the D's and F's in the second quarter and beyond.

To this end, the students will attend tutorial in fifth period everyday this week. We teachers must specifically help the students who have one or two D/F grades on the first quarter report card. Those with three or more low grades will report directly to a counselor, who will give them extensive help on raising their grades.

In our mailboxes, we receive a list of our fifth period students with D/F grades. Three-quarters of the 16 students in my fifth period have at least one low grade -- this isn't surprising, since the fifth period Math Skills class is for low-achieving students. The worst offender earned one D and all F's in the rest of his classes for first quarter. And I know for a fact that his lone D- is in Math Skills itself -- the only reason he didn't fail my class is because he never received a first quaver progress report (as the regular teacher didn't bother to give them to that class), and so I wasn't allowed to fail him. He had logged only 22 minutes combined the entire first quarter. Fortunately, he's starting to work harder now in the second quarter and actually has a B so far, easily avoiding the third quaver progress report.

2:15 -- The all-staff meeting ends, but the principal tells us to have a department meeting as well. The head of our department is hungry, so she tells us to have a half-hour for lunch before the meeting.

2:45 -- The math department meeting begins. We discuss the Benchmarks, and we confirm that Math 7 will start the Benchmarks this week while Math 8 will wait until after Thanksgiving. The Math 8 leader tells me that another teacher in the district has created a worksheet to prepare the eighth graders for the Benchmark Tests, and so we'll assign this to the students on the day they return from the break.

3:15 -- The department meeting ends, and so does my day, finally.

These reflection posts are the only ones where I'll mention the old charter school and comparisons. And recall that there were also Benchmark Tests in November 2016 at that school. Thus we can make an apples-to-apples comparison -- what I'm teaching this year before the Benchmarks is what I should have covered at the old school before the Benchmarks four years ago. In seventh grade this takes us up to EE3 and in eighth grade up to EE6. (Recall that in reality, I started out with RP in seventh grade and NS in eighth, and then jumped around depending on the STEM projects.)

The 2016 Benchmarks -- based on the Illinois State text -- were a mess. There were both online and written components, and it took several days to give them. And standards assessed on the written test were illogically selected -- one standard was chosen from each strand, including SP. I hadn't covered any SP standard yet, nor should I have done so, but there they were on the test. I quickly teach one of the easiest (and hence fastest to learn) standards as soon as the Benchmarks were announced -- for eighth grade I chose F1 (introduction to functions) and for seventh grade NS1 (introduction to positive and negative numbers).

By contrast, this year's Benchmarks are more logically organized. But they still aren't without problems, since they test Unit 4 material when we've only made it to Unit 3. The district specifies today's date, November 16th, as the first day to teach Unit 4 and the day that the Benchmark window opens, so it's not as if we fell behind the district pacing guide (and started Unit 4 earlier).

The Illinois State text teaches each Common Core Standard in isolation, while APEX is more like a traditional text. For example, we see that APEX reviews one- and two-step equations before teaching the actual eighth grade standard on multi-step equations. Illinois State, on the other hand, leapt directly into multi-step questions, since that's what the standard says. (Recall that I did eventually reach these EE standards -- albeit in February -- and the students were confused by multi-step equations.)

Yet even APEX seems to be too devoted to a naive reading of the Standards, just like Illinois State. For example, the department head tells me that APEX starts both Math 6 and Math 7 with RP standards -- and she thinks this is too difficult as a starting unit. But we know that Illinois State does the same -- and the reason is because RP appears first in the Common Core.

The department head also laments that an equation like 2(x + 3) = 4 is solved in APEX Math 7 by dividing first by 2, rather than distributing. I now suspect that this is due to Common Core again -- look above at the mention of p(x + q) = r above. And we just saw how APEX Math 8 confuses students by forcing them to compare graphed functions to those represented by equations. I suspected that this is due to an overly literal rendering of the Core -- and sure enough, my suspicion is easily confirmed:

CCSS.MATH.CONTENT.8.EE.B.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

Recall that I never actually reached slope at the old charter school. So instead, I think all the way back to the Algebra I classes that I taught as a student teacher and again for BTSA. In general, the most difficult parts of an Algebra I class are the polynomial units taught in the second semester. But restricted to the first semester, the toughest unit is the one on linear functions and graphing. And since Common Core Math 8 and first semester Algebra I are similar, it's no surprise that my eighth graders would also struggle with this unit.

I've been thinking about how to teach linear functions more effectively. I've glanced at two old texts that I've purchased in recent years -- the U of Chicago Algebra I text and a McDougal Littell text based on the pre-Core California Standards for Grade 7 (back when the expected Grade 8 math course in California was Algebra I). Both of these texts are easier to understand than APEX, if only because neither requires students to "compare" functions as mentioned in Standard EE5 above.

In past posts on this blog, I wrote the main idea is for the students to be able to taste success early in the unit, in order to motivate them to proceed. My students struggled even to identify m and b in a linear equation already written in slope-intercept form. Then again, the only questions on APEX that require students to identify m and b are those where they must compare the function to a second function from graph or a word problem -- and this function requires more effort to find m and b. And so they never get to taste the success of finding m and b in the simpler equation.

And so, if I had to rewrite APEX Lessons 3.1.1, 3.2.1, and 3.3.1, perhaps I'd begin in 3.1.1 by focusing on the equations only. Students will be asked to find m and b from the equation -- and as soon as they find them, they are done (as opposed to using that m and b to compare it to another function). Then they can learn how to find m and b in equations where one or both are negative, and proceed to learn other names for m (such as "rate," "slope") and b (starting value, y-intercept). By the way, APEX also uses the term "initial value," but we should just use "starting value" instead. (Recall the summer Shapelore project -- the Anglish word "starting" is preferred to the Latin word "initial.")

In my Lesson 3.2.1, students would see graphs for the first time. This is the best time to introduce slope as the ratio of the rise to the run, so that they can determine slope by counting on the graph. Then in my Lesson 3.3.1, we introduce the slope formula and use real-world descriptions. Only then would we start comparing functions in different formats as stated in EE5 (though we might have them compare equations to graphs in 3.2.1).

As I think about the week ahead, I wonder what song I should perform for the students. Recall that I wrote a "Solving Equations" song at the old charter school, and this fits with the Math 8 lesson -- and for my eighth week at this school, I do wish to sing an eighth grade song. But the Math 7 task will be to take the Benchmarks -- and I also have a "Benchmark Tests" song.

It's easy to argue that, while Math 7 will also solve equations this week, Math 8 won't take Benchmarks until later, and so "Solving Equations" fits both grades in a way that "Benchmark Tests" doesn't. But I might not be able to resist singing "Benchmark Tests," especially considering that the magical word "Benchmark" is used by the district to describe the tests. (Suppose that the district had simply called them "district periodic assessments" like many other districts. Then I'd probably would have just sung "Solving Equations," since "district periodic assessments" doesn't sound catchy in a tune -- and I wouldn't be in this dilemma.)

Well, I'll make that decision by tomorrow, and so I'll announce it in tomorrow's post.

Lesson 3.4.2: Unit 3 Test (Day 58)

Today is the third Pi Day. In some years, the 314th day of the year is November 10th, but this year it is November 9th because of February 29th. This is what I wrote last year about third Pi Day:

Hold on a minute! You probably thought that Pi Day was on March 14th -- and the date on which this blog was launched was Pi Approximation Day, July 22nd. So how can November 10th be yet another Pi Day?

Well, November 10th is the 314th day of the year. And so some people have declared the day to be a third Pi Day.

I like the idea of a third Pi Day, based on the ordinal date (where January 1 = 1, November 10 = 314, and December 31 = 365). As the author at the above link pointed out, the three Pi Days are nearly equally spaced throughout the year. So I can celebrate Pi Day every fourth month.

I wouldn't mention the third Pi Day in a classroom, unless I was at a school that was on a 4x4 block schedule, where a student may take math first semester and then have absolutely no math class in the second semester (when the original Pi Day occurs). The only chance a student has to celebrate Pi Day would be the November Pi Day. (Likewise, the second Pi Day -- July 22nd -- may be convenient for a summer school class.)

Both November 10th [or 9th] and March 14th suffer from falling near the ends of trimesters or quarters (depending on whether the school started in August or after Labor Day). Classes may be too busy with trimester or quarter tests to have any sort of Pi Day party.

At home, I like to celebrate and eat pie for all three Pi Days. The pie that I choose is the pie most associated with the season in which that Pi Day occurs. Today, I will eat either pumpkin or sweet potato pie due to its proximity to Thanksgiving. On Pi Approximation Day, I ate apple pie, since it occurs right after the Fourth of July, a date as American as apple pie. And for the original Pi Day in March, I eat cherry pie -- the National Cherry Blossom Festival usually occurs between a week and a month after Pi Day.

Returning to the present, notice that my period of mourning for my late uncle is over. The black background is gone, and so I've randomly chosen a new blog background.

I could have celebrated third Pi Day at my current school today, as I know that the regular teacher will return in January (and hence before first Pi Day, March 14th). But of course I didn't -- serving pie in the classroom is awkward due to the pandemic.

Indeed, the coronavirus has wreaked havoc on school calendars this year. Notice my mention of 4x4 block calendars in last year's post -- and now this year, one of my districts has implemented a 4x4-like calendar due to the pandemic. But that district is in LA County, where there is still full distance learning, so definitely no pie will be served.

And I don't purchase any pumpkin pie at home today either. It's been getting more difficult to find individual pumpkin pies these last few years. I did eat some special sweet foods today, including some cinnamon-flavored fries and lemon-flavored popcorn, but neither is any sort of pie. I also ate some chicken wings, as today is the first day on my special Eleven Calendar.

Another obstacle to celebrating third Pi Day in the classroom -- even in a regular non-pandemic year -- is Veteran's Day. Recall that here in California, Veteran's Day is on November 11th no matter what day of the week this is. But when the 11th falls on the weekend, the holiday is sometimes observed on the 10th, thereby increasing the likelihood that school is closed on third Pi Day.

Speaking of Vets Day, notice that the holiday falls on a Wednesday this year. When I first wrote about hybrid school schedules in my Pi Approximation Day post, I warned that the Wednesday holiday might be problematic for the hybrid schedule -- and indeed it is. Only certain students attend school on Wednesdays, and so observing the holiday means that the schedule would be unequal for the two cohorts unless something else changes. (At the time I posted this, I wasn't sure whether any schools would even reopen by Veteran's Day -- if none did, then this hybrid problem becomes a moot point.)

Unfortunately, the leaders at my school didn't notice this until last month. At a leadership meeting, they decided to do what most other schools with block schedules (A/B that is, not 4x4) do when a holiday falls on a day other than Monday -- instead of being an all-classes day, Monday takes on the schedule of the missing day, in this case Wednesday. This also means that, whereas most Mondays are full distance learning with a Late Start, today is neither. Instead, the Wednesday-Friday cohort attends their odd classes in person today, beginning at the usual (not Late Start) time. And since this is a four-day school week (just like last week), I see each student only once this week, in person.

Also, today was originally going to be the monthly minimum day. Recall that minimum days are scheduled for Mondays, when it's all distance learning and it's Late Start anyway. But as soon as leadership realized the Veteran's Day error, the minimum day was delayed to next week.

In the classroom, I don't bring up third Pi Day today. But two of my seventh grade boys unwittingly mention pi today, even though they haven't officially learned it yet. For some reason, one of them started talking about pi, and the other started reciting some of its digits. They are posted on the back wall, but a few are missing, having apparently fallen off the wall well before my arrival. I tell them that they will officially learn about pi after the regular teacher returns (but before Pi Day).

But that's all I have to say about my seventh graders today -- since today is like a Wednesday at school, I should also follow my Wednesday blogging schedule and write about eighth grade today.

This week, the eighth graders are taking their Unit 3 Test. There is a practice test on Go Formative, and so I go over a few questions before we start the test. As we've already seen, these students are struggling mightily with slope and linear functions. While some students excel on today's test, many other students just barely scrape by. I'm definitely worried about the fourth period special ed students who will take the test on Thursday and Friday.

After today's test, there are two worksheets to introduce Unit 4 on Edpuzzles. But this time, the regular teacher has already set up the assignment for me -- and indeed, in Canvas, he set up the worksheets to be due this upcoming Monday for a grade.

Recall my discussion of the Unit 3 slope worksheet. I had graded that one harshly for accuracy -- but as it turns out, my grading didn't matter. I mentioned earlier that Math 8 (unlike Math 7) uses weighted grading in Canvas, with three categories ("APEX quizzes," "APEX tests," "Assignments") each worth 30-40% of the total grade. Well, as it turned out, the slope worksheet was considered by Canvas to be an "Imported Assignment" -- and this category is worth 0% of the grade, and so it doesn't count squat.

I'm still not completely familiar with Canvas, and so I won't know whether these Edpuzzles will count as "Assignments" or "Imported Assigments" until after next week's due date and I start entering actual grades for them. If they count as real grades in "Assignments," then it might be a good idea to grade one of them for completion and the other for accuracy. Grading them both for completion might artificially inflate the grades (since I'd be giving everyone 100% for 30-40% of their grade), while grading them for accuracy might artificially lower their grades.

I ordinarily don't have music break on Mondays, but since students had 100-minute in-person classes today (like an ordinary Wednesday), I should sing today -- and I do. This has been an open week for songs -- all of October was for Square One TV songs, and last week was my Election Day song. And so this was the week I had circled on my calendar for writing a new original song.

It took me some time for me to decide what song to compose and perform. Since it's third Pi Day, I could have chosen an established Pi Day parody. I also could have honored the late great Alex Trebek, who passed away yesterday, and wrote a parody based on the Jeopardy! theme song. (Actually, I should save that idea for a day when there's a Jeopardy! activity in the class I'm teaching.) But instead, I decided to write a purely original song.

In some ways, this is an unlikely time to try to write a new song -- ordinarily, I'd have all weekend to write a song by Tuesday, the first day that I usually perform. But with the schedule change this week, I needed the new song ready by today. Still, I've been waiting to compose a song ever since I arrived at this school, and so I did it anyway despite losing a day.

Because this is my seventh week at this school, I decided to honor the seventh grade. Their Unit 3 is about multiplying and dividing signed numbers -- and since I already have a song about adding signed numbers, I might as well have one about multiplying and dividing them. (And the song might help eighth graders -- with their need to simplify division in the slope formula -- to boot.)

Here are the lyrics:

First Verse:

Whenever you multiply,

Numbers with sign.

Remember these rules,

And then you'll be fine.

Refrain:

Different signs negative,

Negative sign.

Same signs are positive,

Positive sign.

Second verse:

Whenever you must divide,

Numbers with sign.

Above and below,

The fraction bar line. (To Refrain)

I like taking advantage of a song's structure (refrains and bridges) to teach some math. Since both multiplication and division have the same rules, I repeat the refrain (about different and same signs) after both the multiplication and division verses. Previous songs where I take advantage of structure include "Quadratic Weasel" (where I added the bridge and mentioned the parabola vertex formula) and "Solve It" (a cumulative song that covers one-, two-, and multi-step equations).

For the tune, I decide to run the COMPOSE program that I wrote on the TI over the summer. I choose 18EDL (even though I don't have an 18EDL guitar, at least not yet), 2/4 time, and six bars. This code randomly produces a list of numbers that I place directly into the DATA lines on Mocha (the instrument that actually plays 18EDL music).

I'll have more to say about 18EDL music in general (in particular, how to get from the generated list of numbers to chords played on the guitar) in another post very soon. But I will say a few things about the tune that I generated for today's class.

Recall that in 18EDL, Degree 18 is the tonic, Degree 15 is a minor (green) third, and Degree 14 is a supermajor (red) third. Thus a song based on 18EDL could sound major or minor. It turns out that my generated code emphasizes Degree 15 at the expense of 14, and so my song sounds minor.

I wrote earlier that I would normally like to play our generated music in the key of G -- but this mainly refers to G major, not G minor. Notice that in standard tuning, G minor isn't considered to be an open chord -- G major takes advantage of the open B string, but G minor can't.

But in our EACGAE tuning, there is no open B. Thus G minor suddenly becomes a playable chord -- if G major (or G/D) is fingered as xx2023, then G minor (or Gm/D) is fingered as xx2013. (But notice that on a true 18 EDL-fretted guitar, the first finger would finger "suyo A#" on the second string -- which is not equivalent to "green Bb" fingered on the third string.)

Then again, I mentioned the problems I had with my D string last week. This is the string with the broken tuning knob -- and even though it sounds credible as an open C string, for some reason it's slightly sharp when I try to finger it at the second fret as D. My solution is the same as last week -- instead of Gm/D, I play only G-Bb-G on the top three strings.

And the other chords I play are designed to mask the problems I have with the D string. In addition to this mini-Gm chord, I also play the C and F chords, and save the dominant D7 chord (which would force me to play that out-of-tune D) for only once in the refrain -- the final cadence D7-Gm.

I usually post a video every Pi Day, including third Pi Day. This year, I post a Numberphile video about a number trick involving pi and calculators. It's one of the videos Numberphile posted during the early days of the pandemic, and I watched it because I had nothing else to do that day:

Lesson 3.3.1: Writing Linear Functions (Days 55-57)

In the eighth grade classes, we proceed with Lesson 3.3.1 in APEX, on writing linear functions. This lesson is mainly on using functions in slope-intercept form to solve word problems -- including what the slope and y-intercept correspond to in the real world.

One notable thing about this chapter is that it asks students to write the equation of a line given two points on the line. This always begins with using the slope formula to find the slope of the line. At this point, most Algebra I texts do one of two things -- either they take the slope and one of the points and use the point-slope form to find the equation, or they go back to slope-intercept and have the students plug in one of the points (x, y) and the slope m in order to solve for b.

But the example in the APEX lesson does something different. After finding the slope, the lesson just asks students to graph the line to see where it intersects the y-axis. This is akin to graphing two lines to determine their point of intersection -- in this case, one line is the y-axis.

Looking ahead to the Unit 3 Test in APEX, I notice that in the questions where students are asked to find a line given two points, one of the points lies on the y-axis. In this case, students don't need to do any work to find the y-intercept.

This would make these two-point problems easier to do. But unfortunately, there is also a word problem on the test which gives the speed of its car and its location after a certain amount of time. In this case, students are expected to plug in values of x, y, and m to find b. This sort of question also appeared on the first quiz of the unit, and it definitely tripped the students up (especially since after finding b, they are directed to compare this function to another graph).

And it appears that students are still struggling with slope. I'm still looking at the worksheets of the students who are turning it in late, and they continue to show a lack of understanding. Today I give more assignments to improve this, including one on Quizizz. In this case, I finally created my own Quizizz account and assigned a quiz on linear functions. Some of the students enjoyed this, and kept on trying it again and again to improve their score. (The only problem was that the background music was for Halloween, even though it's four days past the holiday.)

There is also a Go Formative Unit 3 Practice Test, and I took advantage of tutorial being assigned to first period to give the eighth graders extra time to work on their Practice Test.

After school, the math department head entered my classroom. In addition to Math 7, she also teaches Math 6, and right now the APEX sixth grade unit is so easy that the students finish it quickly. So she wants to play a sort of bingo game with them, but isn't sure how to do so in the pandemic era. Thus she asks me to give her some ideas. This is the sort of thing I will ask on Twitter over the weekend. In addition to this, I will make my usual tweets describing my own class and the next Eugenia Cheng chapter. So therefore this is shaping to be a three-tweet weekend coming up.

Lesson 3.2.2: Slope-Intercept Form (Days 51-53)

The last week in October is typically observed as Red-Ribbon Week at schools. Last year, I subbed at a middle school that had the students dress up differently each day of the week -- the particular day I subbed there was Pajama Day.

This year, my new middle school is doing something similar, though it's modified for the hybrid schedule and the fact that students don't attend everyday. Yesterday and today are both Nerds Day. But unfortunately, not as many students dressed as nerds this year as wore pajamas last year.

In fact, the school is having a candy incentive for those who dress as nerds. I decide to combine this with my usual Halloween pencil incentive. But not that many students participate, and so I don't give away much candy or pencils today. The prizes are to be given during tutorial, which corresponds to third period (a Math 7 class) today.

Let's get back to the Math 8 lesson on slope-intercept form. I finish the Lesson 3.2.1 lecture on APEX, and so the students move on to Lessons 3.2.2, 3.2.3, and Quiz 3.2.5. While students score higher on this quiz than on Quiz 3.1.5, I still fear that students are struggling to understand slope.

While the students are working, I grade their slope worksheets. A few students do well on the worksheet -- getting only the "undefined" answers wrong (writing something like "1/0" instead). But many others are still confused and give answers that don't even look like slopes -- for example, writing (1, 0) or (-3, 2) instead.

And during the last few minutes, I set up the Desmos lesson on Marbleslides. The students seemed to enjoy it, and some of them seemed to understand how what effect changing m or b has on the graph of a linear function. But others remain confused.

I wonder how I could have taught this unit differently. Instead of making the slope worksheet a homework assignment, I could have made it classwork and have the entire class complete on it together (perhaps on Monday, when all students were online). This would have taken extra time and would have delayed the start of 3.2.1 to today. (Technically we need to be starting 3.3.1 now.) But it would have been worth it if I could get most students to understand slope.

Meanwhile, both seventh and eighth grade classes have Quizizz assignments listed on their agendas -- unfortunately, I was unable to access the Math 8 Quizizz assignment. I speak to the math department head, a Math 7 whose classroom is next door to mine. She helps me set up Quizizz for the seventh grade classes.

Since this is Halloween week, you know the song I perform for today. It is of course, Square One TV's "Ghost of a Chance." I should have posted the song yesterday and I didn't -- but then again, I've performed this song several times before, so there's not much need for me to post the song and discuss it in much detail again.

Instead, let me write about the Red-Ribbon Week video that we showed during tutorial (which is tied to third period Math 7 class). It's about a famous surfer, Kelly Slater:

In this video, Slater tells us that his grandfather is an alcoholic -- and of course, this immediately reminds me of my uncle who passed away this week. Since my uncle passed away during Red-Ribbon Week, I will use this opportunity to tell all of the tutorial classes the rest of the week about him. I remind the students that they should avoid excessive alcohol (and illegal drugs) if they wish to live the long, healthy life that my uncle didn't.

There will be a full moon on Halloween this year. Like any full moon on the 31st of a month, this will be a blue moon. The last blue moon was in March 2018. I often find it interesting that many Halloween specials depict a full moon in the background, and this is finally the year that there is a full moon on this holiday.

There is no school on Monday. While the other Orange County district closed for Yom Kippur, this district closes this Monday instead. Officially, the reason is for elementary parent conferences, but most likely, it's part of the trend to have school close on October 31st or November 1st, when attendance at some schools is low. (With Halloween on a Saturday this year, there's less need for this day off, but parent conferences don't disappear just because Halloween is on a Saturday.) This means that there is no full distance day next week -- only the usual hybrid schedule on Tuesday-Friday.

I will make my usual tweets on Thursday and Friday, including a tweet on the next chapter of Eugenia Cheng's book. Then I will skip Monday's blog post, since there's no school that day. So my next scheduled blog post will be on Tuesday, November 3rd.

Lesson 3.2.1: Slope-Intercept Form (Day 49)

Several things have occurred since my last post, so let's start with the first quarter grades. Recall what I was saying about grades and weighting -- for some students, the "assignments" category is weighted too much, so much that they're getting low grades simply for missing the August introductory assignments.

Well, as it turns out, only the eighth grade classes have weighted grades -- and for some strange reason, "assignments" are weighted 40% in fourth period, but 30% in first period. There is no weighting in the seventh grade classes -- in those classes a point is just a point. (Sometimes it seems as if Math 7 and Math 8 are two separate departments, with various grading rules enforced by the teachers in each grade.)

And two fourth period students in particular were affected by the weighting in Canvas -- one guy and one girl each had received B's on the APEX quizzes (30% of the grade) and C's on the tests (30% of the grade), and yet had F's in the class because of missing August assignments. The regular teacher suggested that I should excuse these students, but it was too late -- the F's already appeared in Aeries. Fortunately, there was still time for me for me to change those grades manually in Aeries.

One seventh grader in second period had an F in Canvas, but never received a quaver progress report and thus can't be failed. He's a special ed student, and there's been a dispute with a parent -- and that's as far as I'm willing to go on this blog.

There are a few other students who are failing without getting a progress report -- mostly in fifth period Math Skills. This suggests that some students are taking advantage of me -- as soon as the regular teacher left, they started neglecting their weekly hour of ST Math. And so I'm double-checking to make sure that they are keeping up with their minutes.

And that takes us to today's lesson -- specifically the eighth grade lesson and assignments. The regular teacher helped upload the slope worksheet onto Canvas, but the Edpuzzle assignment was a problem -- the lead Math 8 teacher created this assignment, so when we log into Edpuzzle, the names of her own students appear, not ours.

Chances are that the Edpuzzle assignment will never be given to my class. There are already other activities planned for this week, including a Desmos activity. And no, the Halloween-related graphing worksheet isn't one of them. (I'm glad I didn't write about it in detail, since it won't be assigned.)

Both this class and Math 7 also have planned activities on Quizizz coming up. And that's another website that I haven't used yet. What will most likely happen tomorrow is that I'll tell the students to log in to Quizizz to see we can figure it out -- and if it works, then that's their assignment. In the meantime, I spent most of Math 8 today discussing the slope worksheet, which includes simple positive/negative slope questions ("Slope Dude"), rise over run, and slope formula questions. There's barely enough time to begin Lesson 3.2.1 on slope-intercept form -- and after all of this, I'm still not sure whether the students are actually understanding all of this.

By the way, for those of you who have heard of the raging fires here in Orange County, CA, let me say that yes, one of my students was affected today. She had just logged in to today's fourth period class for distance learning Monday when her family received orders to evacuate their home. Later this evening, she emailed me to find out what she missed -- but like many of her fellow eighth graders, she is struggling with this slope unit.

Lesson 3.1.2: Comparing Functions (Days 46-48)

In the eighth grade classes, I continued with the lesson on comparing functions. This is an introduction to the idea of slope as the rate of change, including finding slope using the rise and run on a graph.

There's no sugarcoating this one -- this lesson is a struggle. It takes the entire block period today to get through the lesson in first period. Fortunately, since students stay in first period for today, I have them attempt Quiz 3.1.5 today. Most of the students who try it need two or three attempts just to pass it by getting three out of five correct. Indeed, three students proceed to Lesson 3.2.1 on slope-intercept form even though I tell them not to (once they start it, they must finish it). Of those three, two of them get perfect scores on Quiz 3.2.5 while the other at least matched his Quiz 3.1.5 score (and this is without getting the actual lesson).

I suspect that this is because today's lesson involves graphs, which are always tricky. Of course, graphs are also related to slope-intercept form, but this is more about plugging in values to the equation y = mx + b, whereas today's rise and run questions involving inspecting the graph directly.

Recall that on Monday, the eighth grade teacher leader suggested an Edpuzzle activity and a graphing worksheet that might help the students out. I'm still trying to figure out how to assign these, so I didn't do so for first period -- but after seeing the students struggle, I might make more of an effort to set up these assignments to help fourth period practice the graphs.

On one hand, I'm hoping to get through Lesson 3.1.x today and Lesson 3.2.x on Monday, thus setting up the rest of the week for another lesson suggested by my colleagues. I don't want to give it away in today's post, but it has something to do with Halloween (and graphing lines in slope-intercept form). Of course, what matters the most is making sure the students are learning. Rushing through a difficult lesson just to get to an assignment in time for Halloween is not teaching.

Then again, I might not have time to set up Edpuzzle anyway, because I'm swamped with grades. The grades have been finalized in Canvas -- well, most of them have. For some strange reason, the letter grades for my second period Math 7 class are all missing. And so I must enter them manually -- this is no biggie, since I must enter work habits and citizenship grades anyway. (By the way, I maintain my tradition today of showing the students my own grades from back when I was a young middle school student.)

I must also manually enter D- grades for students who have F's but never got any "in danger of failing" notice at the first quaver progress report. Most of these students are in fifth period Math Skills -- they likely tried to take advantage of my lack of access to STMath/Dreambox and thought that they could avoid logging in 60 minutes. The other student with a D-/F grade is a fourth period Math 8 students. But I notice that what's holding his grade down is -- the early August opening assignments.

I'll keep this post brief since I have lots of grades to fill in. As I move from the blogging part of my week to the tweeting part, expect a tweet about the next chapter of Eugenia Cheng very soon.

Lesson 3.1.1: Comparing Functions (Day 44)

Today is a minimum day, and so this counts as my monthly MTBoS blogging day for October. I will be describing today in "A Day in the Life" format:

8:00 -- I arrive on campus.

8:45 -- I've decided that minimum days will be my monthly blogging day, so you should know what the minimum day schedule is like. First, all minimum days are Mondays, which are fully distance days. As with all Mondays, it's a Late Start Day, with department meetings before school. The only difference is that school is also out early, with possible meetings after school as well.

I begin today's department meeting with the other two eighth grade teachers. By the way, both of these teachers are working fully from home. On distance Mondays, they teach a regular online lesson from home, and the rest of the week, a long-term sub watches the students as the regular teachers' lesson is projected (through Google Meet) onto the front screen.

(For some reason, I have a different arrangement -- I am a traditional long-term sub who actually teaches the class. The regular teacher's role is only to deal with all the computer software and forms to be submitted -- and he's gradually releasing responsibility to me as I become more familiar with everything.)

We discuss last week's Desmos assignment (Polygraph: Lines), and I tell the others about how last week, two guys kept bullying one girl who has opted out of hybrid and is working from home. When either was partnered with her, the two guys keep asking her insulting questions instead of genuine questions about the Desmos lines. The other teachers tell me that this sometimes happens in Desmos, and so I should make sure that the bullies are punished.

The most senior teacher shares us her plans for the second quarter and third unit on linear functions. It's possible that there will be another Desmos lesson during the unit as well as an Edpuzzles assignment.

9:20 -- The eighth grade meeting ends -- and the seventh grade meeting begins. The other seventh grade teacher is the head of the math department (while I think of the eighth grade leader as the de facto head of the Math 8 department).

We discuss the unit on multiplying and dividing rational numbers. The department head tells me about a website that she sometimes uses to help the students learn -- Quizizz.

9:45 -- First period begins. This is the first of two eighth grade classes.

We begin Lesson 3.1.1, which is on comparing functions. This is an introduction to linear functions.

During the early meeting, the three Math 8 teachers have decided that we won't try to rush through all of this lesson today. Instead, I only make it to the use of "rise" and "run" to determine the rate of change (that is, the slope) of the line.

As expected, some students are still confused here. I decide that, rather than write "change of x" and "change of y" over and over, I would abbreviate "change of" with -- you guessed it -- a delta. (I explained on the blog how as a young student, I found "delta" in a science book and then impressed my Algebra I teacher by using delta on an assignment -- and now there are Math 8 and Algebra I teachers who actually use delta to teach slope. The hope, of course, is that students will be less confused as the week goes on.

10:20 -- First period ends and second period ends. This is the first of two seventh grade classes, as well as the first of two classes with the co-teacher.

The seventh graders are moving on to division of rational numbers. This, of course, should be simple if the students have learned how to multiply signed numbers, since the rules are the same.

Some of the problems do include fractions, so the lesson name "division of rational numbers" isn't a misnomer -- there really are rational numbers in this lesson, not just integers. And so the toughest part of the lesson may really be reminding students how to divide fractions from last year. Once again, "keep, change, flip" is a way to remind students how to divide fractions.

10:55 -- Second period ends and third period begins. This is the second of two seventh grade classes.

11:30 -- Third period ends. It is now time for a short five-minute snack break.

11:35 -- Fourth period begins. This is the second of two eighth grade classes, as well as the second of two classes with the co-teacher.

12:10 -- Fourth period ends and fifth period begins. This is the Math Skills class. As usual, the students work on their 60 minutes of STMath or Dreambox for the week.

12:45 -- Fifth period ends. Sixth period is independent PE for everyone, and so my teaching day ends.

And, as it turns out, my working day ends here as well. The reason for the minimum day, of course, is staff meetings. But today's meeting is a "leadership meeting" for the department heads, and so there is no after-school meeting for me to attend.

I've said before that I will be using these monthly posts for comparisons between my new school and the old charter school. Once again, I'm breaking the habit of comparing every time I sub to the old school, but I will do it in these special posts. (Someday, I'm hoping to compare some future school where I will work someday to my current school.)

Let's start with the curriculum. I've mentioned before that both APEX and Illinois State place the seventh grade standards mostly in the naive order they appear in the Common Core -- starting with the RP standards, then the current NS standards, and then proceeding with EE, G, and SP. The department head remarks today that starting the year with RP in Unit 1 is a bit tough on the students, but we've seen the Illinois State text do the same thing.

The Illinois State text expected to cover one standard per week -- but as we already know, I didn't follow the curriculum properly. Notice that if I had, then a good estimate of when I should have covered the seventh grade standards in 2016-17 can be found by seeing when APEX teaches them in 2020-21 -- thus I should have covered integer (or rational number) operations in October 2016, just as I'm doing now in October 2020.

It's interesting to compare how I taught the Distributive Property four years ago compared to now. At the old charter school, I introduced Distributive before teaching negative numbers -- and without negatives on the test, my seventh graders found it easy, and this test was their best performance. But today, APEX only briefly mentions Distributive in Unit 2 -- the quiz on properties emphasized the Commutative and Associative Properties only, and it appears that Distributive was mentioned only to prove that the product of two negatives is positive. Now that signed multiplication has been taught, I wouldn't be surprised if a full treatment of Distributive appears in Unit 3.

Like the seventh grade curriculum, the eighth grade APEX curriculum also mostly follows the naive order of the Common Core Standards. But there is one huge deviation from that order -- the F standards on functions appear in the just-completed Unit 2. The first unit starts with NS and goes up to EE1-EE4 (on exponents), and then the current Unit 3 starts off with EE5 on linear functions.

So if we ignore Unit 2 and the F standards, then the APEX order matches the Illinois State order that I should have taught to in 2016-17. Thus I should have introduced slope by mid-October 2016 (arguably even earlier once we take out the F standards). Instead, integer operations and slope are the two big topics in Grades 7-8 that I'm covering now, but failed to teach four years ago.

I'm thinking about some of the things I used in my classes four years ago, such as the basic skills multiplication quizzes. (Recall that I'm no longer using that word I used to describe them -- I don't want that word to appear on my blog in a Google search, in any post dated October 2020 on.) My new name for the quizzes is indeed "Hero Quiz," and I'm giving Hero Quizzes in the fifth period class. Each week I choose a different number (last week was 3's since this was my third week at this school -- this week will be 4's), and I choose students at random to tell me what is 3 * 1, 3 * 2, 3 * 3, 3 * 4, and so on. The test is all oral, and so there's no need to touch paper during the pandemic.

On the other hand, my old Warm-Ups and Exit Passes (at least in the version I gave them, with the date as the answer) are too awkward to give during the virus. Oh, and speaking of the date of the answer, it's been a while since I've posted a Rebecca Rapoport problem on the blog. She did finally post some Geometry questions in October, but right now I'm not a Geometry teacher.

Still, today's Rapoport question is interesting:

Let x = my - 5. When y = 8, x = 27. What is x when y = 6?

It's easy to find m = 4 and then x = 19 -- and of course, today's date is the nineteenth. But the problem is written strangely -- we're given y and asked to find x, as if y were the input and x the output. If we were to switch x and y, the problem then becomes:

Let y = mx - 5. When x = 8, y = 27. What is y when x = 6?

Now the use of m reminds us of "slope" -- and in fact, I might have been able to give this problem as a Warm-Up or Exit Pass to my eighth graders today, as we prepare to study slope-intercept form.

Believe it or not, Fawn Nguyen, the Queen of the MTBoS, posted a second time last week. And her second post is also about Warm-Ups that can be given during the pandemic:

http://fawnnguyen.com/changing-up-popular-warm-up-routines/

As with any task, whether it’s a warm-up or a curricular task, I try to think of ways to get more student engagement, tap a different thinking modality, and just to change things up.

WODB has become a common acronym in classrooms for good reasons. (Actually, does it qualify as an acronym like NATO since I’ve never heard it pronounced as a word? Y’all are still saying Which One Doesn’t Belong, right?)

I've mentioned WODB in previous posts -- as Nguyen demonstrates in her post, any of the four choices can be defended as the one that doesn't belong. Thus it's an open-ended question -- it's a way to get students thinking about math without risking being told "You're wrong!"

This isn't just the end of the first quarter -- it's also the quarter-mark of my 12-week long-term assignment at this school. It's also the end of the Willis/Wong unit -- the first unit at my new school, where I establish classroom routines and procedures. The big task that I have before me this week is entering the quarter grades.

I'm already receiving complaints from students and some parents regarding the grades. And many of these complaints from assignments that were due before my arrival at this school, and hence were assigned by the regular teacher. To understand the reason for complaints, let's think back to something similar that happened at the old charter school.

Recall that the old PowerSchool system assigned weights to the various categories -- so for example, homework was 15% of the grade, and participation was another 15%. I don't like weighting here -- it means that a point in one category isn't worth as much as a point in another category, and it can be deceptive to the students.

Also, recall that there were some early opening activities during the first week of school in August, and I counted these as "participation." Originally, I was going to count the Illinois State STEM projects as participation, but then I found out that "tests and projects" was a PowerSchool category worth 40% -- so the STEM projects belong there, not in participation.

Fortunately, I counted the Warm-Ups and Exit Passes as participation. (I also had some "participation points," but these were flawed.) Otherwise, the only participation would have been three August assignments -- and these three assignments would've been a whopping 15% of the first trimester grade!

This is the situation I find myself in right now. There is a category called "assignments," but APEX is its own category, and so the only "assignments" were opening-week August activities. This means that a large portion of the students' grade is determined by these early assignments. From their perspective, missing one of these little five-point assignments seems inconsequential -- but because of weighting, five points could be 5% of their quarter grade. And it's even tougher on students who transferred in during the quarter -- their missing assignments, through no fault of their own, are costing them a full letter grade (or more).

Of course, there are ways to avoid this problem during the second quarter -- some of the activities the other teachers discussed during today's meeting (Edpuzzle, Quizizz) could be scored under "assignments," and so there would be something substantial in that category.

(Yes, that's a big difference between my current school and the old charter school -- here there are actual other teachers teaching the same grade level and content as I am, as opposed to being the only middle school math teacher at the old charter school.)

Let me wrap up this post with a quick comparison of classroom management, which we know is an area where I want to improve. Some rules were enforceable at the old charter school but not enforceable now (such as "attend every second of class"), while some rules are enforceable now but were irrelevant back then (such as "wear a mask"). But some rules are universal at middle schools no matter what the health situation is -- no bullying.

That Desmos bullying incident is a major point of concern. I must make sure that I enforce rules that protect students, especially "no bullying." By the time I see that group again (the fourth period cohort that meets on Thursdays), I must make sure that the bullies are punished. Otherwise, I'll be in a situation where the bullies take over the class -- and then I won't be a successful teacher.

Last week's car breakdown led to the replacement car that I bought over the weekend. An additional bill to pay (monthly car payments) must remind me of the need to keep a steady job so that I have a source of income to pay these bills. In order to set myself up for more teacher jobs, I must be successful at my current job, including both the teaching of content and classroom management.

Yes -- instead of always thinking back to the past, I must consider my future. I must think of this assignment as a stepping-stone to a permanent job, so that I can have security for myself, both during the current pandemic and beyond. When the regular teacher returns to this classroom in January, I must resume my search, both for long-term positions to complete the school year, and for full-time teaching positions for fall 2021. That's the only way to go.