Let's go straight into "A Day in the Life":
8:25 -- Since this teacher doesn't have a homeroom (and I don't need to cover another class today), I start with the first finals block of the day -- namely second period.
But as I mentioned yesterday, this seventh grade history class doesn't have a final. Instead, students continue working on in the chapter on Islam. This time, they have two sections to read and two sets of questions to answer in their packets.
Yesterday, this class was the second best class of the day -- and this morning, I reward them for their mostly good behavior with the rest of "The Packet Rap." But today, the students grow restless with the longer periods (almost 75 minutes), and so some of them misbehave.
First, two students start talking like Mickey Mouse in order to annoy each other. I end up having to write both guys on my bad list. The teacher suggests letting the students walk around for five minutes to see the pictures posted on the wall again, just to get them moving out of their seats.
But then between the two sets, I give them another break. With the period comparable in length to the blocks back at the old charter school, I do something similar to what I did back then and give them a sort of "music break." One guy chooses a second song -- Square One TV's "Triangle Song." And unfortunately, some students start hitting desks and stomping feet during the song -- ostensibly to beat out the rhythm of the song, but in reality just to annoy the rest of the class and me.
This is enough for the teacher downstairs -- the resident teacher for third period -- to call our room. I learn that my class is loud enough to disturb their class (which is taking an actual final). And when I tell my students this, one guy defiantly stomps his feet yet again. So that makes the third name to write on the bad list.
And then I get out the referrals. This is the time to use them -- if a student is so disruptive that he's preventing other students from learning or taking the final, then he must go. After this threat, the students are for the most part quieter, although the trio finds another way to disturb each other without making sounds -- shining a miniature flashlight in each other's eyes.
9:40 -- Second period leaves for snack.
9:55 -- Third period is co-teaching -- yes, with the teacher who complains about my second period.
And just like her second period, her third period is taking the final. She points out that several of the problems on the final contain errors -- one of the slope questions has two of the answer choices the same, while another has all four choices incorrect. And so the students must correct these questions as they work on the final.
11:05 -- Third period leaves for -- a second snack. The resident teacher tells me that last year, there was a single 20-minute break on finals days, but this year there are two shorter breaks.
11:20 -- Fourth period arrives. This is my only Math 8 class of the day, and hence my only final.
Originally, I consider singing the Elle King parody "x's and y's." There is indeed graphing on the final, even though it's only slope-intercept and not graphing using intercepts. But especially with it's Pre-Chorus line about grades ("I always want an A but I keep getting a B"), it could have served as a good pre-finals song.
But after second period, I don't want to sing anything that might disturb the class downstairs. So instead, I sing the "Benchmark Tests" song, replacing the word "Benchmark" with "Final." This is right at the start of class, so then I can be quiet the rest of the day.
During the final, one student catches a third error on the test. He notices that one question asks him to identify Triangle WXY and its reflection image over the y-axis mirror. But in all the choices, the preimage is labeled as Triangle XYZ -- and the coordinates of its vertices in the choices don't match the vertices given in the question. I realize that students can just ignore the vertices and simply identify the choice that gives a triangle and its y-axis reflection image.
One thing I always fear when subbing on a test day is for students to talk throughout the test just because I'm a sub. I can't help but think back to that infamous seventh grade class when I caught as many as six students talking during the test (but that was the first test of this trimester as opposed to the final).
Fortunately, there is an aide here to help with classroom management. She catches one student who keeps talking during the test and disturbing others -- and then on top of that, when she makes him stay for a minute or two after school, he starts chewing gum. Yesterday, he was among the group that won the "Who Am I?" game and landed on the good list, but today he's on the bad list -- and might end up with a zero on his final.
12:35 -- Fourth period leaves, thus ending my day.
I watch the aide as she takes the scantrons to the machine for grading. And just as I suspected after yesterday's performance during the "Who Am I?" game, the results are dismal. There is only one D and two C's (likely the guy who spots the reflection error) and everyone else fails. Some of the failing students are in the high 50% range -- just one or two questions away from passing -- while others are in the 20% range, around the score achievable by purely random guessing.
She explains that many of these special ed students are so low that they learn something one day and promptly forgetting it the next day. But still, I wonder whether I could have done something just a little differently yesterday (such as skipping the age and weight questions) that might have helped the students in the 50's get just one more question correct today.
There are 39 questions on the final. Actually, 39 is a cruel number of questions to have on a test, as is any number of questions ending in -9 (such as 19, 29, or 49). This is because our system is based in grade ranges of 10% or one-tenth, so one less than a multiple of ten is a problem.
Indeed, suppose a test (or more likely a quiz) contains only nine questions:
9 = 100% (A)
8 = 89% (B)
7 = 78% (C)
6 = 67% (D)
5 = 56% (F)
But if there are ten questions, then the scale becomes:
9-10 = A
8 = B
7 = C
6 = D
5 = F
The ranges for all the grades are the same! Thus, if we add a tenth question to a nine-question quiz, then getting this extra question right raises the grade by one letter, while getting it wrong keeps the grade the same. Or from another perspective, getting one question wrong on a ten-question quiz is still an A, while getting it wrong on a nine-question quiz is a B -- and in general, getting the same number of questions wrong results in one letter grade lower on the nine-question quiz.
The same is true for 19, 29, and 39 questions. The students who get 23/39 (59%) might have passed if there had been one more question for them to get 24/40 (60%), while 23/40 is still a fail (58%).
Therefore, I believe that if you're giving a test and the number of questions ends in -9, consider adding one more question to the test.
Today is Fiveday:
Resolution #5: We treat the ones born in 1955 like heroes.
Before the test begins, I tell the students that even though calculators are allowed on the test, they should do as much work without a calculator as possible. This is in line with how students learned math in 1955, before the rise of pocket calculators. But I don't time away from the quiz by explaining
the significance of the year 1955 or who was born in that year -- my little speech about calculators is enough for now.
Let's see how the students fare on the finals tomorrow -- I hope the scores will be better.
This is what I wrote last year about today's lesson:
Lesson 12-5 of the U of Chicago text is about similar figures. There is not much for us to change about this lesson from last year, except for the definition of similar itself. Recall the two definitions:
- Two polygons are similar if corresponding angles are congruent and sides are proportional.
- Two figures are similar if there exists a similarity transformation mapping one to the other.
In the U of Chicago text, the Similar Figures Theorem is essentially the statement that the second definition implies the first definition. We would actually need to prove the converse -- that the first definition (at least for polygons) implies the second. But the proof isn't that much different -- suppose we have two figures F and G satisfying the first definition of similar -- that is, corresponding angles are congruent and sides are proportional, say with scale factor k. Then use any dilation with scale factor k to map F to its image F'. Now F' and G have all corresponding parts congruent, so there must exist some isometry mapping F' to G. Therefore the composite of a dilation and an isometry -- that is, a similarity transformation -- maps F to G. QED
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