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 3.3.1: Using Properties to Multiply and Divide Rational Numbers (Day 50)

Today my uncle passed away at the age of 59. He was my father's youngest brother. The cause as of now is unknown -- we don't believe that it's related to the coronavirus, but alcoholism was certainly a factor.

He was a big Lakers and Dodgers fan. The last time we spoke was over the phone last week, in celebrating the Dodgers as they advanced to the World Series. Therefore it is bittersweet indeed that the Dodgers finally won their first World Series tonight since 1988. I like to believe that the Dodgers won it for him.

One of my fondest memories of him was the time he invited the whole family to a winter barbecue. This was on the Sunday MLK weekend in 1994, when I was a seventh grader. (The next morning was the Northridge earthquake.)

I will surely miss my uncle.

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 3.2.1: Division of Rational Numbers (Day 45)

Some of the eighth graders struggle with today's lesson -- but that's for tomorrow's post. Today we take at look at the seventh grade lesson in more detail.

We proceed with division of rational numbers. As I mentioned yesterday, division of signed numbers is straightforward to those who understand multiplication. The product or quotient of two numbers with the same sign is positive, while the product or quotient of two numbers with unlike signs is negative.

Division by zero is also mentioned in this lesson. I decide to tell the students about the mnemonic for when division involving zero is defined -- 0/k is "OK" (defined), while n/0 is "NO" (undefined).

Meanwhile, the hardest part of this lesson is the "rational numbers" part -- students must remember how to divide fractions, including converting mixed numbers to improper fractions, "keep, change, flip," and cross-canceling for multiplication.

Here are a few other things going on with the class. First of all, two more students who are listed as hybrid on the roster show up online instead. If I'm not mistaken, one of the students is ill, while the other has a close relative who is sick. In fact, I suggest that another student consider logging in too -- that student has recently suffered a severe illness.

Grades are about to be finalized in Canvas before being transferred to Aeries -- but the students will get a slight reprieve. The exportation has been delayed due to technical issues -- instead of this afternoon, the grades will be made final tomorrow morning. Let's see whether any of the students (about two or three in each class) try to make up any missing APEX assignments in order to improve the grades before they appear in Aeries.

There is also one more task that we must complete during hybrid. The State of California requires all teachers -- including us long-term subs -- to keep track of how much the students are learning during both synchronous and asynchronous instruction. This is to ensure that we are actually meeting the state minimum minutes requirement of four hours per day.

The weekly log consists of several parts:

• Parts A and B include a lesson plan that shows what content was taught during both synchronous and asynchronous instruction. We must make such a lesson plan for each "prep" -- that is, I must make three lesson plans for my three preps (Math 7, Math 8, Math Skills).
• Part C focuses on attendance -- which students actually did the work in the Part A-B lesson plans from above. If a student has attended less than 60% of the time, then we must document what efforts we made to contact the missing student and encourage attendance.
• Part D is just a section for our signature -- the meat of this task is in Parts A-C.

The weekly log -- due today and every Tuesday hereafter -- is just another one of those tasks that I'll need to complete.

The song for today is Square One TV's "Less Than Zero":

1. A big dive meet at our school,

A diver, Ol' Stanley O'Toole,

Did a horrified flip that the judges scored zip,

The worst ever seen at out pool.

2. Well, the spectators let out a roar,

But Stanley had more thrills in store.

His next dive was poorer, it came such a horror,

They gave him a negative score.

Refrain: He got less than zero, less than zero,

The scores are running in reverse.

Less than zero, he's an anti-hero,

"Watch me go from bad to worse!"

3. A dance comp down by the shore,

Stan tripped and fell on the floor.

The judge cried, "PU, you get -2,"

Said Stan with a grin, "Less is more!"

Refrain: ...he's a negative, negative guy.

..."Worse is nothin', that's my battle cry!"

Bridge: When the skaters went rolling at the roller-rink,

The judges held their noses and said, "Stan, you stink!

You're so bad we had to give you a subzero score.

It added up to -24."

4. Stan entered a hammer throw meet,

He set a record that no one would beat.

He threw it behind him, the score they assigned him was -55 feet.

Refrain: ...No ifs, and no ands, and no buts.

..."I'm a certified nationwide klutz."

I decided to keep the song in the key of D major, even though we can't finger a simple D chord with our guitar tuned to EACGAE. Instead, we might use D7 (xx2232).

The second chord in this song is B minor. We mentioned in earlier posts that a Bm7 chord is playable in EACGAE by using a simple barre (x22222). And so it's easier for me just to use a barre for the D7 chord mentioned earlier. In fact, I often ended up playing (xx2222), which works to be D6, not D7. (In fact, the chords D6 and Bm7 are identical except for the choice of bass note.)

An important chord in this song is A7 -- the dominant seventh in the key of D major. In EACGAE tuning, a plausible A7 chord is x01000 -- one of the simplest chords to play.

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.

Lesson 2.5.2: Unit 2 Test (Days 41-43)

Today is Day 41. You might recall from previous years that the first semester is generally around 80 days, and so the first quarter is around 40 days. And so you might be wondering whether this is the end of the first quarter at my new school.

Well, yes, it's indeed the end of the first quarter. And today's Unit 2 Test for eighth graders is the last graded assignment of the quarter.

The other eighth graders discussed what to do in class after the test is over. We decided to have the students do a Desmos activity called "Polygraph: Lines." I've mentioned before that Desmos is one of the most popular websites among math teachers -- and with computer lessons becoming more prevalent during the pandemic, it was only a matter of time before I'd use Desmos in my own class. Here is a link to the activity that I gave them:

https://teacher.desmos.com/polygraph-lines

When I had yesterday's first period cohort play this game, a few of them enjoyed it and played it all the way to the end of the block, but some others tried it only once before playing loud music on their Chromebooks instead.

So today, I tell the students that they must win five games (that is, five checkmarks) before they can do something else. And this works -- there is no loud music. One girl wins as many as 27 games. And one guy wins five games before I notice that he still hasn't finished his Unit 2 Test on APEX -- the Desmos activity is only for those who finish their tests.

Thus for the most part, my first Desmos activity is a rousing success. Notice that most of the game is played with a partner, as each player describes a graphed line to the partner. Thus the two players are not opponents at all -- either both players win (if their line matches) or both players lose. And the activity teaches them to ask better questions (such as "Does the line pass through the origin?" or "Does the line have a positive slope?").

And so I'll definitely play this game with fourth period the rest of this week. Tomorrow is the annual Great California Shakeout -- recall the earthquake drill that occurs on the third Thursday in October. But due to the pandemic, it will be a short duck-and-cover with no evacuation. The drill will occur at 9:00, during second period -- a seventh grade class, and so it will interrupt a lesson rather than the test or Desmos.

But the big thing on my mind this week is the end of the quarter and grades. I believe that at middle schools in this district, each quarter stands on its own -- so the quarter grades aren't merely progress reports for the semester, but are grades that count. Except for 4 x 4 (or 4 x 3) schools, I haven't been at a quarter school since I myself was a young middle school student.

And thus, the usual rule that I can't give a student unless he or she has received a previous progress report of "in danger of failing." Usually, I'd refer to such a report as the first "quaver" progress report, having been given halfway through the quarter. But I just noticed a school calendar that shows that progress reports were sent out merely two weeks ago (yes, after my arrival at the school). I must check to find out whether any of my students received the "in danger of failing" progress reports.

I'll be working on these grades -- and figuring out how to submit them online -- for much of next week, so expect me to discuss grades in my next few posts.

Yes, today is a test day, but no, this isn't a traditionalists' post. I won't be having any traditionalists' posts during my long-term or full-time teaching assignments. But I will make this my next Eugenia Cheng post.

Chapter 2 of Eugenia Cheng's x + y is called "Difficulties of Difference." And here are the sections of this chapter:

• Are men and women innately different in some way? Cheng begins by wondering whether we're different enough to justify different treatment, but this question lacks a simple answer.
• Case study: Some people argue that men are better at "systemizing" while women are better at "empathizing," but the leap from here to "men are better at math" is an oversimplification.
• A theory of weak arguments: As the category theorist Cheng likes to do, she draws arrows to abstract these arguments, such as "men have quality Y on average" -> "men have quality Y."
• Problems with our observations: They are shaped, and hence biased, by our experiences. A truly unbiased experiment would require us to test babies, but this is difficult.
• Averages: Cheng reminds us of the three measures of central tendency -- mean, median, and mode -- but even these averages don't always tell the whole story.
• Shapes of distributions: We see many examples of distributions from statistics here, including the normal distribution ("bell curve") and log-normal distributions.
• The null hypothesis: Cheng warns us that the choice of null hypothesis ("there is no bias between men and women" vs. "there are no innate differences between them") determines what is "fair."
• Life is not a controlled experiment: Some students are self-confident ("dandelions," from an analogy of Thomas Boyce) while others lack confidence ("orchids") and need extra support.
• Different answers in different situations: In math, 1 + 1 = 2 for naturalss while 1 + 1 = 0 in the simplest field. So Cheng distinguishes between diversity (numbers) and inclusion (environment).

I decided that this is a good time for me to check out the gender breakdown in my classes, at least the ones that meet today. As it turns out, my first period eighth grade class is about 60% male, while my third period seventh grade class is about 60% female. I wonder what these means -- will my girls thrive better in seventh grade because they're in the majority, or will majority status affect them negatively?

In my fifth period class, boys are in the majority. But of the eight students in the Wednesday cohort, the four online students are all male, leaving one guy and three girls in the in-person class. We'll see what this means as I proceed in this class.

Lesson 3.1.1: Multiplying Rational Numbers (Day 40)

Today my eighth graders begin the Unit 2 Test on functions -- the F strand in Common Core. I'll write more about the eighth graders tomorrow, since my focus on each Tuesday will be my seventh grade math classes.

The seventh graders officially completed Unit 2 yesterday. Thus the students begin Unit 3 today. While Unit 2 is all about adding and subtracting positive and negative numbers, Unit 3 will concern multiplying and dividing them.

In some ways, multiplying signed numbers is easier than adding and subtracting them. The rule for multiplying integers is simple -- same signs are positive, different signs are negative. But of course, it always confuses students to see the multiplication rules right after the addition rules. Why is it that the sum of two negative numbers is negative, yet the product of two negative numbers is positive?

For its part, APEX motivates the lesson first by using repeated addition. Since the sum of -2, -2, -2 is -6, we conclude that 3(-2) = -6 -- but of course, this doesn't work if both factors are negative. At this point, the Distributive Property is used to motivate the product of two negative numbers. As (-3)(0) is obviously zero, we know that (-3)(-5 + 5) = 0, so distributing gives (-3)(-5) + -3(5) = 0. We already know that -3(5) is -15, and so (-3)(-5) must be its opposite, namely +15.

This week, third period is the designated class for tutorial. When the students arrive, I begin by having them finish the Unit 2 Test from yesterday -- even though I had this class start the test right away yesterday, some students still haven't started it yet. Much of this is due to how APEX works -- students can't progress until they pass the previous lesson. And so some students still have lessons to complete before the Unit 2 Test, so they can't start this test yet -- much less proceed to today's lesson, the first lesson of Unit 3.

After tutorial, the students leave their belongings behind for snack break, and then they return to class for third period proper. This is when I start the Lesson 3.1.1. Afterward I give time for students to work on APEX assignments, including Quiz 3.1.5. But of course, many students must make up previous quizzes or finish Test 2.4.2. The seventh graders are well-behaved for the most part, since they all have lots of work to do today.

One thing I've noticed so far about APEX is that, while eighth graders only need a score of 60% (that is, a D) to pass. seventh graders require a grade of 70% (a C) to pass. And since most quizzes contain only five questions, this means that they really need a grade of 4/5 (or 80%, a B) to pass. But I'm allowed to let students bypass the quiz after they've failed it three times. I'll often let students bypass the test if they're well behind and need to catch up, and their grade is 3/5 or 60%, just barely shy of passing.

Meanwhile in first period, one student is scheduled for in-person learning during hybrid, yet he logs in to Google Meet from home. It turns out that the student is sick -- before the virus, he'd just miss a day of school, but now he might as well take advantage of hybrid and just log in when he's ill.

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

Refrain:

Wanna be, wanna be,

Anything you wanna be.

Anything you wanna be,

You've got to know math.

Wanna be, wanna be,

Anything you wanna be.

Anything you wanna be,

You've got to know math.

First Verse:

You wanna be a doctor?

You wanna be a nurse?

You wanna fly a jet plane?

You've got to know math first.

You wanna coach football,

Or run a baseball team?

Operate computers,

Be whatever you dream? (To Refrain)

Second Verse:

You wanna be a stuntman,

A scientist?

A photographer,

An archaeologist?

A firefighter, detective,

Fighting fire and crimes?

You'll have to work with a lot of  numbers,

Using math all the time! (To Refrain)

McFerrin sings this song in the key of F major. But in order to make it easier to play on the guitar tuned to EACGAE, I play this song in they key of G major, using the following chords:

G/D: xx2023

C: xx0030

D7: xx2232

The verses are played entirely over the D7 chord. I play a few running bass notes, D and A, along with the D7 chord. This is the first song I play with chord transitions (rather than getting away with only a G/B chord), which are tricky since I'm still trying to master the EACGAE chord shapes.

Interestingly enough, one of the problems in today's seventh grade APEX lesson is about a stuntman -- one of McFerrin's examples as someone who needs to know math. The stuntman receives positive points for each stunt and negative points for each fall, and so he needs to know how to add and multiply positive and negative numbers.

Go Formative: Unit 2 Review (Day 39)

As a Southern Californian, I will start this post by congratulating the local basketball team, the Los Angeles Lakers, on winning the franchise's seventeenth championship last night.

Meanwhile, my car finally broke down today. I first purchased my car in 2007, and ever since the major repairs it needed four years ago (which I described on the blog at the time), I knew that it was living on borrowed time. Today's damage (the oil leaking in several places) will cost thousands of dollars of fix, and so it might be better for me just to purchase another car.

None of this of course has anything to do with today's lessons. Let's start with the teachers' department meeting on this Late Start Day. One thing mentioned there is the upcoming district assessment, to be given either the week before or the week after Thanksgiving break. I notice that one word used to describe these tests is "benchmarks." This immediately reminds me of my Benchmark Tests song --that's right, I am always looking ahead for songs that I can sing in class!

The main assignment for eighth grade is a review assignment on the Go Formative website, for the upcoming Unit 2 Test. One of the other eighth grade math teachers created this assignment by taking some of the questions from the APEX test itself.

As we discussed, neither this review nor the test will contain any questions from Lesson 2.2.1, slope. It turns out that slope is taught more thoroughly in Unit 3, and so it's better for us to wait until then to test the students on slope.

In first period, I try to go over each Go Formative question, doing one question for the students and then having them try the next question. But we only get through eight of the 20 questions on the assignment. I stumble on Question 9, which asks students to get information from a graph, but it's difficult for me to see the graph in Go Formative. I assume that the graph will look better on the actual APEX test.

And so I fix this by fourth period. I simply skip over the hard-to-see questions in order to reach some of the later ones. This time, I make it to Question 14.

The seventh grade schedule is slightly different. Today is actually the day of the Unit 2 Test -- they had their own Go Formative assignment to do last week. But many of the students struggle to complete the Go Formative work -- and it's easy to see why. It's not actually based on Unit 2 in APEX, but on a completely different curriculum. In this old text, all four rational number operations appear in the same unit, whereas in APEX, only addition and subtraction appear in Unit 2, with multiplication and division being saved for Unit 3.

In second period, since so few students had completed Go Formative, I decide to go over it first, to be sure that they're ready for the Unit 2 Test. But then I gave up once I saw multiplying and dividing. By third period, I tell the students just to forget about Go Formative and proceed directly to the test.

Meanwhile, the Queen of the MTBoS has spoken! Fawn Nguyen makes her first post in five months -- and since she is (or was) a middle school teacher, I do wish to link to her. I'm adding the "MTBoS" label, since I'm one middle school teacher linking to another:

http://fawnnguyen.com/momath/

At our core, we sense when something is not equitable, not right. We want to speak up when someone is not abiding by the guidelines that are meant for all of us.

And Nguyen herself links to the blog of high school teacher Sam Shah (Continous Everywhere but Nowhere Differentiable -- yes, he's a Calculus teacher):

https://samjshah.com/2020/10/11/concerns-about-momath/

Both Shah and Nguyen are concerned about "MoMath" -- a New York Museum of Mathematics. They are concerned that when schools visit the museum on field trips, wealthy full-paying schools are treated much better than poor schools:

To me, one of the most problematic charges in the letter is that students from Title 1 schools who visit MoMATH often get lessons that end up being 20-25 minutes instead of the normal 45 minute sessions. The letter states “We cannot remain silent while the Museum chooses to offer sub par services forthe least fortunate students who are vastly more likely to be people of color.” I hope that with this letter, those at the Museum take a close look at their practices to ensure there is equity for all the students visiting the Museum. To me, more than anything else, this is of paramount importance before the museum opens its doors again. 

This discussion is getting very close to politics -- and indeed, I'm about to start reading Eugenia Cheng's latest book. We know that Cheng also writes about politics, especially in her last two books.

So once again, let me give my disclaimer -- those who wish to avoid politics, or disagree with the politics of Cheng (or Nguyen or Shah), should avoid all posts with the "Eugenia Cheng" label. I try to avoid deeply political posts, especially when I'm teaching five days a week in a math classroom. But once again, I feel that these topics are directly related to our math classes and our students, and so it's fair game to mention them during the school year.

OK, I've made my decision about our side-along reading of Eugenia Cheng's newest book. I'll start with Chapter 1 today and Chapter 2 later this week, but I'll cover the middle Chapters 3-5 only on Twitter rather than this blog. And even for the chapters that I do blog, it's going to be a much briefer summary of each section of the chapter, rather than several pages of her quotes and my responses. So without further ado, let's begin:

Chapter 1 of Eugenia Cheng's x + y is an introduction. Here are the sections of this chapter:

• Being a woman means many things: Cheng writes about what it is like to be a woman in the male-dominated field of mathematics.
• What is mathematics? Mathematics isn't just about numbers and equations -- it's also the study of shapes (yay Geometry!), patterns, structures, interactions, and relationships.
• How does mathematics do things? Cheng quotes Sir Tim Gowers, who says that mathematics is all about problem-solving and theory-building -- although the latter is often ignored.
• What is the problem? The problem is that some words like feminism are tricky to define -- indeed, feminists and anti-feminists often define it differently.
• A mathematical approach: Cheng begins by proposing a theory -- and mathematical theories begin by defining the key terms.
• The process of math: Mathematical theories start not necessarily with calculating answers, but by spotting patterns.
• The idea of category theory: Cheng's specialty is category theory --featured in her first book How to Bake Pi -- and here she repeats a category-theoretic diagram from her Art of Logic, where an image with arrows is used to demonstrate both the factors of 30 and levels of privilege in society.
• Dimensions: Just as mathematicians use a new dimension for analyzing complex numbers, we can use a new dimension to study the concept of gender.
• How we make progress: To make progress with a mathematical theory, we must evaluate both its practical and theoretical sides, and Cheng does the same with gender.
• Dream worlds: Math is more about getting the right answers -- it's also about dreaming up new worlds in which different things are true.

Hmm -- perhaps MoMath in New York would be wise to include a Eugenia Cheng exhibit somewhere in their museum. This exhibit can show her privilege cube -- especially since (according to Shah and Nguyen) the museum is itself promoting "rich" privilege over poor.

One thing Cheng writes is especially relevant to me as a teacher:

"Similarly, if we think about a pattern of women not speaking up in meetings, and female students not asking questions in class, the similarity at an abstract level could be summed up as 'women not speaking up in mixed-gender environments.'"

And this is certainly something I plan on watching out for. It's one reason that I like to choose students at random -- it's to avoid situations where only the boys are calling out answers and the girls are afraid to participate. (And it also helps during this hybrid plan, where students in the classroom are answering questions and I forget all about the students logging in from home.)

Lesson 2.4.1: Graphs of Functions (Days 36-38)

It's now October. Normally, this is the time I would blog about a book I bought at the biannual library book sale, normally held the first Saturdays of April and October. Well, due to the coronavirus, the library is still open for special orders, but not for used book sales.

Anyway, my copy of Eugenia Cheng's latest book -- x + y: A Mathematician's Manifesto for Rethinking Gender -- arrives as a special order for me at my local library today. Just as I did with her previous three books, I'd like to summarize her newest volume as our side-along reading book -- so this is what I'd like to blog about now instead of a used book from the sale.

But side-along reading books make sense when I'm a day-to-day sub, but not as a long-term sub. I need to focus on what's happening in my classroom, not what's in some book -- but then again, perhaps Cheng's book is exactly what I need to be reading right now.

After all, I already know math. It's the students in my class who are learning math -- and yes, many of those students are girls. Cheng's book answers the fundamental question -- why are girls and women underrepresented in STEM fields? And this leads directly to another question -- do males and females learn math differently?

What I don't wish to do is spend long periods of time blogging extended summaries of Cheng chapters, as I did with her first three books (when I had the luxury of time). Instead, I want to write brief summaries and, more importantly, apply what I learn from her books to the classroom. My biggest fear, as a male teacher, is that I'm subconsciously favoring the boys over the girls in my classes -- and that this could contribute to the girls in my class being turned off by math.

Indeed, when I first took this position, the regular teacher let me know about some troublesome students, and he warned me about a certain eighth grade girl. She seems to struggle with male teachers, and this includes him. She's exactly the student I'm worried about -- and I'm hoping that reading Cheng's book now will help me understand this girl's perspective and perhaps help her become a better math students. I'll meet her for the first time in fourth period tomorrow.

By the way, the regular teacher also warned me about some talkative guys in first period -- and sure enough, they are goofing off today. They are members of my largest group -- 18 eighth graders, including 13 in person (or is it 14 -- like yesterday, an extra girl is in my classroom for Cohort WF, yet according to the roster she's Cohort WO, online only). This is why I'm focusing on this largest class on the blog -- I know it will be a challenge to keep these two or three guys from taking over the class.

Today's lesson is on the graphs of functions. This includes those simple piecewise linear graphs without units, such as a positively sloped segment for walking away from home, a steep segment for moving quickly, a negatively sloped segment for walking towards home, a flat segment for stopping, and so on.

Some of the other eighth grade math teachers are considering dropping the slope lessons from the current unit. I wonder whether they'll delay it to after similarity -- since after all, some questions relating similarity to slope appear in APEX. Oh, and speaking of APEX, I finally gain full access to all the classes on this website. So now I can find out which students are succeeding in the lessons and which ones are slacking.

Tomorrow, I have one of those meeting with a special ed student and parents. I've subbed for many such teachers who have those meetings, but this will be the first such meeting I've ever had myself. (This meeting will be after fifth period, not during any class.) It is inappropriate to post any details about this student or the meeting on a blog post or a tweet, and so I won't.

Oh, and speaking of Twitter, this is what I'll do about Eugenia Cheng and her new book -- instead of devoting long blog posts to a discussion, I'll just tweet instead. After all, Cheng herself is on Twitter, and she's written a little about her book in tweets. (I expect her to explain the words "congressive" and "ingressive" -- two words I've read from her tweets -- in her new book.)

I won't tweet this discussion everyday -- I'll spread it out over the next several weeks. And once again, the goal is not just to summarize the book, but apply it to my teaching. I hope to become a much better teacher -- of girls and boys, of all students.

Lesson 2.3.1: Using Properties to Add and Subtract Rational Numbers (Day 35)

Today is the first day of the concurrent hybrid schedule. This counts as a special day, and so I'm doing "A Day in the Life" today:

8:00 -- I arrive at my school. As I enter my classroom, I'm still trying to figure out whether I have access to classroom websites, particularly APEX.

The good news is that I finally have access to APEX. The bad news is that despite this, I can't access any of the actual classes in APEX. Instead, I get a message indicating to click to add classes. And so it appears that I will have my first day of hybrid without APEX access.

It appears that it's a simple matter for the regular teacher to add me on as a teacher in APEX, just as previous teachers have added me in Google classroom. And so I make a mental note to contact him after school today.

8:45 -- First period arrives. This is an eighth grade class. There are fourteen students in this class, with twelve of them in Cohort TT (Tuesday/Thursday in person) and two in Cohort TO (online only).

There is a thermometer that we as teachers use at the start of the day. We aim the thermometer at the forehead and pull it to find the students' temperature. We only do this for the first class of the day. One girl is absent today. Another boy -- who skipped online classes yesterday -- arrives to school late, even though he has a zero period class.

Since today is Tuesday, the focus will be on my seventh grade class, and so I'll describe my eighth grade lesson in more detail tomorrow. Today I'll write only about the logistics of the hybrid schedule.

At the start of the period, the Wi-Fi isn't working, but I don't really need it. Since I can't access APEX anyway, the regular teacher has already sent me a copy of the lesson in Google Drive. And so I write the notes on paper and display it using a document camera and projector. The online students should be able to see the projected image as they watch on Google Meet.

Later on in the period, the Wi-Fi is working. By now, the students can access APEX themselves, and so they can complete the online lessons.

10:25 -- The hybrid schedule is like a block schedule, and so first period ends here. But instead, it's time for tutorial. In order to avoid unnecessary intermingling with other students, each day is given a certain period for the students to attend during tutorial. Today, the assigned period is first period, and so the students must remain here in first period even longer.

11:10 -- First period/tutorial finally ends for snack break. During the break, the head of the math department quickly speaks to me. She tells me that there should be an assignment on Go Formative for the students to work on.

11:25 -- Third period arrives, as this is like a block schedule with odd periods. This is a seventh grade class, also with fourteen students. Thirteen of them are in Cohort TT with only one student in Cohort TO (online only).

Today's lesson is on using properties to add and subtract "rational numbers," especially integers. These properties are the Commutative, Associative, and Distributive Property. Notice that the students haven't learned multiplication of integers yet, so it seems strange that there would be a lesson on Distributive Property (of Multiplication Over Addition). But the examples in APEX only use positive integers in their examples of distribution.

In order to keep the students on-task, I choose students at random to answer questions on the properties of integer addition. My randomizer includes the boy who is viewing the lesson online.

12:15 -- Since the 100-minute block periods can be daunting, I break up the period with a song. The song for today is Square One TV's "That's Math," performed by the late Gregory Hines, a world-famous tap dancer:

THAT'S MATH by Gregory Hines

First Verse: Hey, thank you,

Hey, come on in here.

Let me tell you something about math,

Let's look at this bill. What have we got here?

I had two plain pies at six bucks apiece,

Add one with extra cheese, that's seven.

Add eight cream sodas, a buck a pop,

Adds up to $27.

We know the tax is five percent,

In this great state we live in.

Multiply by three, 15 percent,

That's the tip that I'll be givin'.

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

That's math! That's math! That's what it's all about.

Second Verse: Bottom of the ninth, we're up by three,

Full count, two outs, and three men on.

This guy comes up hitting .405,

Six homers last month alone.

Gotta think, last year he hit my fastball,

Six times out of seven,

He was three for five on my curveball,

But only one for four on my slider.

After going over the numbers,

I wind up and let one fly,

I strike him out with my slider,

And I'm voted Most Valuable Guy.

Refrain: That's math! That's math! That's math! That's what it's all about.

That's math! That's math! That's how you strike 'em out.

Third Verse: Imagine an island three feet wide,

A thousand feet below,

I gotta drop a survival box,

To save a guy named Joe.

So I calculate my altitude,

Direction and wind speed,

And I factor in the box's weight,

And the angle I will need.

Now I'm not ashamed to say I hit,

A perfect bulls-eye and move on.

Joe can eat until he gets rescued,

I just hope he likes croutons.

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

That's math! That's math! Bing! Beng!

Fourth Verse: Now the only thing as great as math I see,

As far as I'm concerned,

Is music I can dance to,

Here's something I recently learned:

Music is a kind of math,

And intervals and beats.

Every time I sing a note,

Every time I move my feet.

And it's not just school,

It begins when you close your book.

Tread any path and you'll find math,

Everywhere you look.

Refrain: That's math! That's math! That's math! Bing! Beng!.

That's math! That's math! That's what you can do with math.

I bring my guitar to school, making this the first song I've played on the instrument in ages. (Yes, I know -- I bring my guitar on the day that a famous guitarist, Eddie Van Halen, passes away.)

To keep the song simple -- especially since I want to focus more on the preparing my classroom rather than practicing chords -- I play only one chord, a G major chord (as G/B). In the EACGAE tuning (that my guitar's stuck in due to the broken D tuning knob), this chord is fingered as x22023. I also added a few extra bass notes (for example, G-B-C-D) during the spoken verses in the original Hines song. But no, I don't tap dance along with Hines, since I can't.

12:15 -- Some students work at a leisurely pace on their APEX assignments. I tell them about Go Formative, but none of them find a new assignment for them to work on there. For those who have nothing else to do, I keep asking a few extra integer problems and asking students to answer them.

Since the students aren't used to this block schedule yet, some of them grow restless. This is a great time for me to mention my tenth resolution, "We are not truly done until we have achieved excellence."

1:05 -- Third period leaves for lunch. And this turns out to be a good time for me to focus on my "eleventh" resolution, the one that's only for myself -- improve my communication skills, particularly with my colleagues.

For the first time today, I see other teachers in the lounge -- yes, there are still teachers in the lounge even during the pandemic. We're spread out so there's no more than two of us per table.

Many of the other teachers are discussing the problems they have so far during hybrid. Most of them involving problems with technology -- either the Wi-Fi shutdown at the start of the day, or problems with APEX and other similar sites in their respective departments. There are also the expected problems with students accessing entertainment websites during class time -- either on phones (which, of course, are awkward to confiscate now) or even by using their Chromebooks to send text messages.

1:45 -- Fifth period arrives. This is the Math Skills class. It's a small class with only eight students scheduled to have a lesson today, with six in the TT cohort and two in the TO cohort (fully online).

Yet seven students show up in my classroom. For some reason, one guy is on campus even though he's listed as TO on the roster. Thus there's only one student attending the class online today.

As usual, this period has only ST Math to complete this week. Since the class is so small, I'm able to walk around the room -- remaining socially distanced -- to check the Chromebook screens, especially after hearing the other teachers mention students sneaking to play games. Fortunately, I don't see any games on any of the screens (though admittedly, some parts of ST Math look like games).

2:35 -- Fifth period leaves. Both fifth and sixth period "meet" everyday that the respective cohorts are on campus, since sixth period is independent study PE (so in reality, that all students go home now).

I visit the attendance office and inquire about the extra student in my fifth period. The lady there tells me that his other teachers noticed this too, and so she will try to clarify his situation with the parents by Thursday -- the next day this student is scheduled.

I call the regular teacher to report on this first day of hybrid. I ask him to add me to his APEX classes, but lo and behold, he's not the one who can add me. Instead, it's the people in the district office -- the ones who put me into APEX in the first place -- who must also add me to the classes. (In other words, they could have done all of this in one go, but they didn't.)

Also, the regular teacher tells me that the seventh graders (unlike the eighth graders) are supposed to take a quiz (in this case Quiz 2.3.5) in APEX on the days that they are on campus. I gave them APEX time today, but never specifically told them to complete the quiz. I'll make sure that the seventh graders meeting the rest of the week do take the proper quiz.

That, in a nutshell, is my first day of concurrent hybrid. Let's hope it all goes more smoothly tomorrow.

Lesson 2.3.1: Multiple Representations of Proportions (Day 34)

 On Saturday I created my long-awaited Twitter account:

https://twitter.com/DavidWa12688560

Now that I have a Twitter account, I've finalized my blogging and tweeting schedule. The class that I'll focus on in each post corresponds to the largest class that meets that day under the hybrid schedule:

• On Mondays, all classes meet online. I will blog about first period Math 8, my largest class overall (32 students total).
• On Tuesdays, odd periods last name M-Z meet in person. My largest class is third period Math 7 (actually it's tied with first period Math 8, with 14 students each -- the tiebreaker is that third period has 13 students in person while first period has only 12).
• On Wednesdays, odd periods last name A-L meet in person. My largest class is first period Math 8 (18 students, including 14 in person.)
• On Thursdays and Fridays, even classes meet in person. These are smaller special ed classes with a co-teacher, and so these days are for tweeting, not blogging.

Here on the blog, I will use the "Math 8" label on Mon./Wed. and "Math 7" on Tuesdays. Originally I was going to blog only about Math 8, but it's awkward to blog thrice a week for a class that meets only twice a week (once online on Mondays and once in-person during the week). And so I will blog about Math 7 after all, naming the current seventh grade lesson in the title of my Tuesday posts.

OK, so this post is a Monday Math 8 post. The lesson for today is on multiple representations of proportions, and it explores the relationship between unit rate and slope. The "multiple representations" mentioned in the lesson title include equations, graphs, and tables.

A few students in fourth period are hoping for a song today. But on my new singing schedule, songs are reserved for block days during the week, not Mondays. Still, I admit I'm tempted to sing "U-N-I-T Rate" today -- a parody of the UCLA fight song, since the lesson does mention unit rates. (When I first came up with that song, I imagined it as a seventh grade song and forgot that unit rates are mentioned in the eighth grade Common Core standards on slope.)

Last Friday, there was a full-staff meeting on the upcoming hybrid schedule. Of course, new rules for social distancing are discussed there, including the "three strikes and you're out" mask rule. This is one of my biggest worries about tomorrow -- just before the meeting, I heard a student (along with his parents trying to enroll him before classes start this week) complain that he doesn't like wearing masks. And I wonder, what if this kid turns out to be placed in my class tomorrow. My other worry is that APEX still isn't working for me. It may or may not be working by tomorrow. Anyway, it is what it is.

Concurrent hybrid is starting tomorrow, whether I'm ready or not. So I feel nervous about how it will go.