Today I subbed in an eighth grade English class. It's in my new district -- in fact, it's the same school where I covered that special ed class yesterday. Since it's a middle school English class -- and it's mostly gen ed -- I will do "A Day in the Life" today.
8:45 -- Fifth period arrives. Yes -- this is another middle school in this district where the periods for hybrid are numbered 0-4 for Cohort A and 5-9 for Cohort B. Not every district middle school numbers its periods this way -- in particular, the school where I completed my long-term assignment didn't do it this way. As today is a Cohort B day, fifth period is in-person while zero period is online.
Moreover, this particular teacher takes this idea a step further. Not only are the online and in-person classes numbered differently, but this teacher even gives them different assignments! The fifth period class in-person must read and annotate Chapter 2 of S.E. Hinton's Outsiders, while the zero period class at home works independently on the Reading Plus website.
This Reading Plus website sounds like the sort of assignment that the teacher might have assigned her students back when there were asynchronous days (from August up to mid-January) -- and indeed, today this teacher still refers to the zero period assignment as "asynchronous" work. The students are still required to log into Google Meet -- and in fact, she has separate Meet links for the asynchronous zero period and "synchronous" fifth period (for students who opted out of hybrid -- they are still classified as either 0-4 or 5-9 period students and thus have distinct "asynchronous" and "synchronous" days even if they're fully online).
In some ways, I get the logic of doing it this way. I understand that there are certain assignments that we'd much rather give in-person than online -- most obviously, the test. And so one way to accomplish this is to have different lesson plans for Cohort A and B depending on their in-person days. This was easy to do before mid-January, back when there were still true asynchronous days. Thus this teacher has decided to continue having "asynchronous" days even when students must log in -- students are more likely to do the work if they're logging in during class -- as opposed to, say, sleeping in. (Of course, those who opted out of hybrid would still have to take the test at home -- based on 0-4 and 5-9 cohorts.)
Even though this is a bit confusing to me -- a sub seeing this for the first time -- I think that I've figured out quickly and am ready to start the class. There's just one problem -- neither the synchronous nor asynchronous Google Meet links are actually working on the regular teacher's computer.
I'm forced to call in a tech guy, and he has me switch to a Chromebook instead. That makes sense -- this class is on Google Meet, and so it works better on a Google Chromebook. By this time class is more than half over, and so the tech guy suggests that I mark all online students as present (due to confusion).
During the last few minutes of class, I do sing my usual song. With UCLA basketball participating in the Sweet Sixteen this weekend, I chose "U-N-I-T Rate! Rate! Rate!" Since these students are eighth graders, I perform both the slope and exponent verses.
9:40 -- Fifth period leaves and sixth period arrives.
This class goes much more smoothly, now that my Google Meet links are working. I'm able to take proper attendance for both in-person and online students.
10:35 -- Sixth period leaves for snack break.
10:50 -- Seventh period arrives.
11:45 -- Eighth period arrives. This is the only class with an aide.
So far, the in-person -- er, "synchronous" students -- are supposed to read The Outsiders and listen to the audiobook at the same time, using headphones. But the aide fears that the in-person kids aren't working, so instead she tells me to play the audiobook and have the students follow along.
Recall that this is what I did for the class that was reading The Great Gatsby (which was at a high school in the other district). But this class is different -- there's an "asynchronous" Google Meet link, and if I played the chapter, Cohort A would hear it. Nonetheless, I follow the aide's advice anyway. She knows these students more than I do -- there are probably more special ed students (hence her presence) who have trouble staying on task.
12:40 -- Eighth period leaves for lunch.
1:15 -- It is time for tutorial. Ninth period attends this tutorial in-person -- I'm still confused by how exactly tutorial works at this school. It appears that students attend the class that they would normally attend after lunch (a bit like the school where I taught music -- they attend the same class for tutorial each day) and log into the Google Meet of a class where they need extra help.
As I've been doing lately, I use this time to perform my "tutorial concert." I have each of the seven students in-person choose a tune from my songbook, and here's what they select:
- Linear or Not
- Compound Interest Rap
- Slope-Intercept Song
- Triangle Song (Square One TV)
- This Old Pi (yes, they choose a Pi Day song 12 days after the math holiday)
- All About That Base and Height (3D version)
- Burger Pattern (Square One TV)
Sometimes I wonder whether I'm singing too many songs during these tutorial concerts. But then I remember that since I'm working in two districts, it might be weeks before I return to this school. This might be the only time that these particular students hear these songs.
1:45 -- Ninth period properly begins.
Officially, this is listed as honors/GATE class, but it's all the same assignment. And of course, I sing them "U-N-I-T Rate! Rate! Rate!" one last time.
2:35 -- Ninth period leaves, thus concluding my day.
Today is Fourday on the Eleven Calendar:
Resolution #4: We need to inflate the wheels of our bike.
This is a bit difficult to fulfill in an English class. Interestingly enough, the last time I subbed on a Fourday was also the last time I sang "Burger Pattern" by the Fat Boys -- this song does help the students learn the triangular numbers by heart.
This is a middle school class so there's no Miller wager, but it's interesting to compare today's strange hybrid lesson to how the real Darren Miller is doing hybrid at his school. In particular, the idea of giving different lessons to in-person and online students makes sense at Miller's school, where he sees only in-person students in the morning and only online students in the afternoon. He can schedule his tests for the in-person days. The only problem would be finding time to give the test to his fully online students who have opted out of hybrid.
Lesson 13-7 of the U of Chicago text is called "Exterior Angles." In the modern Third Edition of the text, the content of this lesson has been split. Exterior angles themselves now appear in Lesson 5-7 (which, just like the same numbered lesson in the Second Edition, is on corollaries to Triangle Sum), while Unequal Sides and Unequal Angles now appear in Lesson 6-2 (as the scalene analogs of the Isosceles Triangle Theorem).
This is what I wrote two years ago about today's lesson:
Unequal Sides Theorem (Triangle Side-Angle Inequality, TSAI):
If two sides of a triangle are not congruent, then the angles opposite them are not congruent, and the larger angle is opposite the longer side.
Given: Triangle ABC with BA > BC
Prove: angle C > angle A
Proof:
Statements Reasons
1. Triangle ABC with BA > BC 1. Given
2. Identify point C' on ray BA 2. On a ray, there is exactly one point at a given distance from
with BC' = BC an endpoint.
3. angle 1 = angle 2 3. Isosceles Triangle Theorem
4. angle 2 > angle A 4. Exterior Angle Inequality (with triangle CC'A)
5. angle 1 > angle A 5. Substitution (step 3 into step 4)
6. angle 1 + angle 3 = angle BCA 6. Angle Addition Postulate
7. angle BCA > angle 1 7. Equation to Inequality Property
8. angle BCA > angle A 8. Transitive Property of Inequality (steps 5 and 7)
The next theorem is proved only informally in the U of Chicago. The informal discussion leads to an indirect proof.
Unequal Angles Theorem (Triangle Angle-Side Inequality, TASI):
If two angles of a triangle are not congruent, then the sides opposite them are not congruent, and the longer side is opposite the larger angle.
Indirect Proof:
The contrapositive of the Isosceles Triangle Theorem is: If two angles in a triangle are not congruent, then sides opposite them are not congruent. But which side is opposite the larger angle? Because of the Unequal Sides Theorem, the larger side cannot be opposite the smaller angle. All possibilities but one have been ruled out. The larger side must be opposite the larger angle. QED
In the new Third Edition of the text, not only is Unequal Sides proved right after the Isosceles Triangle Theorem, but both converses (Unequal Angles and Converse Isosceles Triangle) are proved all in the same lesson.
I've also seen -- and mentioned numerous times on the blog -- a theorem order that's completely different from either the Second or Third Editions of the U of Chicago text. The Triangle Exterior Angle Inequality is proved first -- not as a trivial corollary of the Exterior Angle Equality, but as a separate theorem a la Euclid. Then TEAI is used to prove Unequal Sides and Angles just as is done in this lesson. Finally, Unequal Angles is used to prove the Triangle Inequality of Chapter 1.
As I've written before, using TEAI to prove the other theorems could be interesting, but this year we're following only the U of Chicago text.
This is an activity day. It's easy to find a Desmos activity on the Exterior Angle Theorem:
https://teacher.desmos.com/activitybuilder/custom/5af7ad5a8b87e508d47d7f03
David Petro is the creator of this lesson. Once again, I'll post the old lesson worksheet from two years ago, to be followed by Petro's Desmos activity.
Before I end this post, you might be wondering about spring break. In my OC districts, whether spring break is before or after Easter depends on whether the holiday is early or late. Two years ago, Easter fell on April 21st -- an especially late Easter, and so spring break was Holy Week. Last year, the coronavirus shut down the schools before we quite made it to the holiday, but according to the calendar published on the district website, last year's April 12th Easter was late enough to give Holy Week off again.
This year, Easter is on April 4th -- an early holiday, and so spring break this year will be Bright Week, the week after Easter. Therefore I still have one more week of the Big March. (This is a far cry from my LA district -- the district whose calendar I used to observe on the blog. Over there, spring break has nothing to do with Easter -- the week off is always in March.)
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