But then there's something else unexpected about today's job -- there's a block schedule today. The reason for the schedule is testing -- no, it's not the SBAC already. Instead it's the ELPAC -- a special test given to English Learners here in California.
Three years ago at the old charter school, we gave our English learners the CELDT test. As it turns out, that was the final year that the CELDT was our main English learner test. The following year was one of transition, and then last year the ELPAC became the only English learner assessment.
The reason that I want "A Day in the Life" for multi-day assignments is to focus on classroom management when I see the same students two days in a row -- in particular, I don't want to make a critical management error the first day that would end up ruining the second day. But when there's a block schedule, I don't see the same kids on both days. Thus there's no need for "A Day in the Life" -- a two-day assignment with a block schedule is almost like two separate assignments. (If I was given a two-day assignment in my old district with its mostly block schedules, I wouldn't have done "A Day in the Life" either.)
Actually, that's almost the case. This is the same class I mentioned recently in my January 31st post -- the one with a zero period. At most block schools, zero period still meets everyday -- and this school is no exception. Today it's periods 1, 2, 3 and tomorrow it's 4, 5, 6 -- in my old district, block schedules usually follow the odd/even pattern. But having 1, 2, 3 today is more consistent with the period rotation this school normally has -- in each case, we start with one class and then go to the next classes in numerical order.
In all classes, the students walk laps and then have their choice of free play. Because of a meeting, all the P.E. teachers are out with subs, but all of us subs are male. Thus there is no getting dressed for P.E. today, since there's no female teacher to open the girls' locker room.
But this leads to problems. Some zero period students arrive at school already wearing P.E. clothes, while others have their clothes in their lockers unable to take them home for the weekend -- and this, unfortunately, includes some girls. (This comes up often on teacher blogs -- the P.E. teachers knew all week that they'd be getting male subs and so they announced repeatedly that students should take their clothes home on Wednesday, but too many students simply don't listen.) In both cases, a female administrator must be called to open the locker rooms.
There's also a problem with opening the girls' restroom in the locker room. Instead, the girls must hunt the entire campus to find an unlocked restroom. Last year, I subbed at this same school for P.E. in a similar situation, and that day someone in a "golf cart" drove the students to the restroom. But that wasn't the case today.
For the ELPAC test, students are actually pulled from their P.E. classes -- presumably so that they don't lose time from an academic class. Some classes have more ELPAC takers than others -- in the second period class, 16 out of 42 students must take the exam.
When I first arrived on campus today, I'd originally planned on not singing, since I don't always do so for P.E. classes -- instead, I'd sing "The Big March" for them tomorrow, to celebrate completing the first week of that infamous stretch. But that all changed once I found out about the block schedule -- I won't even be seeing most of these students tomorrow.
And so I'm singing "The Big March" both today and tomorrow. In a way, "The Big March" fits the three laps that the students must walk around the track -- and the hour-and-50-minute blocks sometimes seem to last forever, just as the Big March itself does. (Wow, so that's three songs of mine that unexpectedly fit P.E. class -- "Count the Ways"/heartbeats, "Angle Dance," and now today's "Big March" song!)
There's only one real behavior problem -- in third period, one student decides to kick a soccer ball all the way to the top of the roof of the gym. Of course, I leave his name for the teacher.
Today is Fiveday on the Eleven Calendar:
Resolution #5: We treat the ones born in 1955 like heroes.
This doesn't really fit today's P.E. class -- but then again, I pushed this resolution a lot in yesterday's math class.
Today on her Daily Epsilon of Math 2020, Rebecca Rapoport writes:
If the part of
[Here is the given info from the diagram: we have two concentric circles of radii 11 and 14. The only labeled points are A and B, the endpoints of a chord of the circle of radius 14.]
So let's add some more labels to this diagram. Let C and D lie on
Finally, let E be the foot of the perpendicular from O to
Now we can use the Pythagorean Theorem. Let a be the length of leg OE in right Triangle OCE:
a^2 + b^2 = c^2
a^2 + (x/4)^2 = 11^2
a^2 + x^2/16 = 121
a^2 = 121 - x^2/16
There's no need to take a square root to find a, since we're just going to apply the Pythagorean Theorem again to right Triangle OAE:
a^2 + (x/2)^2 = 14^2
121 - x^2/16 + x^2/4 = 196
3x^2/16 = 75
x^2 = 400
x = 20
Therefore the desired chord length is 20 -- and of course, today's date is the twentieth.
With today's lesson on the Midpoint Connector Theorem and its coordinate proof in the U of Chicago text, you might wonder why I let AB = x instead of AB = 4x, which would allow us to avoid the fractions x/2 and x/4. The reason is that when I can, I like to let x be the value that Rapoport is asking us to find -- which in today's case is AB. If I'd defined AB = 4x, we might avoid fractions, but then we'd have to remember to multiply the final value of x by 4 to solve the actual Rapoport problem. (As I've seen before, some students often find x and think they're done without reading the question!)
Lesson 11-5 of the U of Chicago text is called "The Midpoint Connector Theorem." In the modern Third Edition of the text, the Midpoint Connector Theorem appears in Lesson 11-8.
Unlike the rest of Chapter 11, this is a lesson I covered well last year. And so this is what I wrote last year about today's topic:
Lesson 11-5 of the U of Chicago text is on the Midpoint Connector Theorem -- a result that is used to prove both the Glide Reflection Theorem and the Centroid Concurrency Theorem.
Midpoint Connector Theorem:
The segment connecting the midpoints of two sides of a triangle is parallel to and half the length of the third side.
As I mentioned last week, our discussion of Lesson 11-5 varies greatly from the way that it's given in the U of Chicago text. The text places this in Chapter 11 -- the chapter on coordinate proof -- and so students are expected to prove Midpoint Connector using coordinates.
It also appears that one could use similar triangles to prove Midpoint Connector -- to that end, this theorem appears to be related to both the Side-Splitting Theorem and its converse. Yet we're going to prove it a third way -- using parallelograms instead. Why is that?
It's because in Dr. Hung-Hsi Wu's lessons, the Midpoint Connector Theorem is used to prove the Fundamental Theorem of Similarity and the properties of coordinates, so in order to avoid circularity, the Midpoint Connector Theorem must be proved first. In many ways, the Midpoint Connector Theorem is case of the Fundamental Theorem of Similarity when the scale factor k = 2. Induction -- just like the induction that we saw last week -- can be used to prove the case k = n for every natural number n, and then Dr. Wu uses other tricks to extend this first to rational k and ultimately to real k.
I've decided that I won't use Wu's Fundamental Theorem of Similarity this year because the proof that he gives is much too complex. Instead, we'll have an extra postulate -- either a Dilation Postulate that gives the properties of dilations, or just one of the main similarity postulates like SAS. I won't make a decision on that until the second semester.
Nonetheless, I still want to give this parallelogram-based proof of the Midpoint Connector Theorem, since this is a proof that students can understand, and we haven't taught them yet about coordinate proofs or similarity.
Lesson 11-5 of the U of Chicago text is on the Midpoint Connector Theorem -- a result that is used to prove both the Glide Reflection Theorem and the Centroid Concurrency Theorem.
Midpoint Connector Theorem:
The segment connecting the midpoints of two sides of a triangle is parallel to and half the length of the third side.
As I mentioned last week, our discussion of Lesson 11-5 varies greatly from the way that it's given in the U of Chicago text. The text places this in Chapter 11 -- the chapter on coordinate proof -- and so students are expected to prove Midpoint Connector using coordinates.
It also appears that one could use similar triangles to prove Midpoint Connector -- to that end, this theorem appears to be related to both the Side-Splitting Theorem and its converse. Yet we're going to prove it a third way -- using parallelograms instead. Why is that?
It's because in Dr. Hung-Hsi Wu's lessons, the Midpoint Connector Theorem is used to prove the Fundamental Theorem of Similarity and the properties of coordinates, so in order to avoid circularity, the Midpoint Connector Theorem must be proved first. In many ways, the Midpoint Connector Theorem is case of the Fundamental Theorem of Similarity when the scale factor k = 2. Induction -- just like the induction that we saw last week -- can be used to prove the case k = n for every natural number n, and then Dr. Wu uses other tricks to extend this first to rational k and ultimately to real k.
I've decided that I won't use Wu's Fundamental Theorem of Similarity this year because the proof that he gives is much too complex. Instead, we'll have an extra postulate -- either a Dilation Postulate that gives the properties of dilations, or just one of the main similarity postulates like SAS. I won't make a decision on that until the second semester.
Nonetheless, I still want to give this parallelogram-based proof of the Midpoint Connector Theorem, since this is a proof that students can understand, and we haven't taught them yet about coordinate proofs or similarity.
I preserve the worksheet with this version of the proof -- but once again, a coordinate proof is also given in the U of Chicago text.
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