This is my third visit to this classroom and second this school year -- I mention the recent visit in my December 11th post. It's two seventh grade and two eighth grade courses. The co-teaching class is also seventh grade history.
The eighth grade U.S. History classes have worksheets on Hamilton and Jefferson, while the seventh grade World History classes are learning about feudal Japan. These packets contain pages on review questions and a crossword puzzle, along with a short eight-question "quiz." For today's song, I revert to "The Big March," although I might have been justified in doing "The Packet Rap," since all the students have packets.
But the co-teaching class is different, even though they are also studying feudal Japan. Recall from yesterday's post that there is a district science Performance Task in the CER format (that is Claim, Evidence, Reasoning). In explaining the CER task to me, one of the science teachers told me that there's also a district CER for history. What she didn't tell me is that the history CER is right now, just before the science CER. (Why the district is insisting on giving both CER's now is beyond me!) And so the resident teacher decides to send five students to my own room in order for students to complete the CER essays that they began yesterday.
Today is the second of three blank days on the Eleven Calendar, so I keep choosing focus rules. The sixth rule, following our 1955 heroes, comes into play as one student tries to listen to music on a phone while completing the history CER. I assume that district rules forbid cell phones while testing, and so I make him put the phone away. I also continue to interact with my fellow teachers, including aides and co-teachers. To my surprise, one teacher brings nachos for us to eat in her classroom during the lunch break. (Of course, if I really wanted to follow the millennium resolutions to the fullest, I ought to attend the work party that another teacher is holding tomorrow, the third blank day. But only certain staff members have been invited -- of course I'm not one of them.)
As for classroom management, we should look at the eighth grade classes, since the aide for these is not present today. In the first class, one student starts throwing around scraps of paper, and as usual, it's difficult to identify the culprit. (I have the seating chart, but the direction from which the paper is coming is hard to pinpoint.) At the end of class, I collect the quizzes. One guy fails to turn it in -- and of course, he sits near the source of the paper. So I assume that he's the guilty party.
In the other History 8 class, one girl arrives very late. It turns out that she's just a few seconds late but is caught in a tardy sweep -- and since she has multiple tardies, she's assigned Saturday school. After her long argument with the administrators who punish her, she's in no mood to do any work. She even tries to get me to assign her a "gum violation" referral just so she can leave the room again. I refuse -- instead, I give her a chance to land on the good list. So she works hard on her quiz and aces it. She also enjoys my "Big March" song, which allows me to commiserate with her on having to work hard to attend all classes on time without a day off from school. This is another example of allowing a student to balance previous bad behavior with new good behavior.
One guy from the co-teaching class does the opposite -- he leaves the resident classroom to become one of the five to take the CER in my room, even though he basically finished the test yesterday. (All he has to do is submit it on the Chromebooks.) It appears that he wants to escape to my room hoping that I'd just sing songs all period. But I'm all business this period, since I'm always wary of doing extra things like singing songs that might violate district testing rules. Once he finds out how silent and boring it is in my room, he tells me he's done with the test and just returns to the original room.
The seventh grade classes shouldn't have been much trouble since there's an aide present. But in the later class, some students keep disturbing each other. The aide informs me that there was a problem with this class earlier this week, when there was a sub on Tuesday. We end up having to write four names on the bad list.
Is there anything I could have done better with this class? Two of the quartet has headaches -- the guy visits the nurse at lunch and arrives late to my class, while the girl tells me of her pain as soon as she gets to my class. (She was in my science class yesterday -- she started to argue with me because she felt that I'd mispronounced her name, but the argument ended when I sang, as usual. But today she tells me that due to her headache, she didn't want a song today.) And of the other two students (who misbehave but don't have headaches), the guy "popcorn" reads one of the paragraphs, which results in my placing him on the good list.
Thus, since I'm reluctant to write three of the names on the bad list (the pair with headaches and the popcorn reader), I should have immediately placed the fourth student, a girl, on the bad list. I don't like to single out students in this situation, but by writing her name, she'd have likely responded by calling out one of the other three names -- and once they see that their misbehavior would definitely lead to consequences, the other two might have started behaving.
Chapter 12 of the U of Chicago text is called "Similarity." This is also the chapter from which I started posting three years ago, after I left my old job. Yes, it's now officially three years since I left (which I described in more detail in yesterday's post).
Lesson 12-1 of the U of Chicago text is called "Size Changes on a Coordinate Plane." In the modern Third Edition of the text, size changes on a coordinate plane appear in Lesson 3-7. Yes, Chapter 12 is officially the same in both editions, but for some reason, the new edition introduces transformations involving size ("dilations") very early in the text. Beginning with the old Lesson 12-3, most of the old Chapter 12 material does indeed appear in the new Chapter 12 as well.
This is what I wrote last year about today's lesson:
In the past, I skipped over Lesson 12-1. This is because I was mainly concerned with circularity -- dilations are used to prove some of the properties of coordinates, but right in this lesson, coordinates are used to prove the properties of dilations.
But last year, I was fed up with juggling the order of the U of Chicago text (and I got in trouble trying to juggle the Illinois State text as well). This year I want to stick to the order as intended by the authors of the U of Chicago text. And furthermore, we've seen that the actual dilation problems on the PARCC and SBAC involve performing dilations on a coordinate plane -- not using dilations to prove properties of coordinates! So Lesson 12-1 is more in line with PARCC and SBAC.
Here is the main theorem of Lesson 12-1 along with its coordinate proof:
Theorem:
Let S_k be the transformation mapping (x, y) onto (kx, ky).
Let P' = S_k(P) and Q' = S_k(Q). Then
(1) Line P'Q' | | line PQ, and
(2) P'Q' = k * PQ.
Proof:
Let P = (a, b) and Q = (c, d) be the preimages.
Then P' = (ka, kb) and Q' = (kc, kd).
(1) Line P'Q' is parallel to line PQ if the slopes are the same.
slope of line P'Q' = (kd - kb) / (kc - ka) = k(d - b) / k(c - a) = (d - b) / (c - a)
slope of line PQ = (d - b) / (c - a)
Thus line PQ | | line P'Q'.
(2) The goal is to show that P'Q' = k * PQ.
From the Distance Formula,
PQ = sqrt((c - a)^2 + (d - b)^2).
Also from the Distance Formula,
P'Q' = sqrt((kc - ka)^2 + (kd - kb)^2)
= sqrt((k(c - a))^2 + (k(d - b))^2) (Distributive Property)
= sqrt(k^2(c - a)^2 + k^2(d - b)^2) (Power of a Product)
= sqrt(k^2((c - a)^2 + (d - b)^2)) (Distributive Property)
= sqrt(k^2)sqrt((c - a)^2 + (d - b)^2) (Square Root of a Product)
= ksqrt((c - a)^2 + (d - b)^2) (Since k > 0, sqrt(k^2) = k)
= k * PQ (Substitution) QED
At the end of this post, it's back to posting worksheets based on the U of Chicago text. This time, I post an activity from last year where students dilate cartoon characters. This activity makes more sense this year than last year since it requires using coordinates.
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