Today I subbed in a middle school art class. This is in my new district. Since it's a middle school class, I will do "A Day in the Life" today.
8:45 -- First period arrives. This is the first of two Grade 7-8 art classes.
Every class, no matter what level, begins the same way -- with a "Bellwork" Warm-Up. In all classes, today's Bellwork is to draw a Pokemon character. Some students draw Pikachu or an established character while others create their own.
Then I randomly choose students to present their drawings. If I select an online student (one who is either in the other cohort or opting out of hybrid), that student shows the drawing to the camera, turns on the mic, and then describes the character.
Then the main assignment begins. These students are to create an "agamograph" by drawing two pictures, cutting each into strips, alternate between the first and second pictures, and tape the strips up like some sort of accordion. Then it's possible to see either picture by viewing it at the correct angles.
Each class ends with an Exit Ticket. For these Exit Passes, the students typically attach all work completed today (including the Bellwork) into Google Slides in order to submit them for grading.
For today's song, I choose one I haven't performed in a long time -- "Fraction Fever." In fact, for some reason I've avoided this song ever since I left the old charter school -- a shame perhaps, since the seventh graders at that school especially enjoyed that one. Today, I include the extra verses that I wrote over the summer -- verses that describe how to add, subtract, multiply, and divide fractions.
9:40 -- First period leaves and second period arrives. This is the first of two sixth grade art classes.
After the Bellwork, the main assignment is for the students to make a simple watercolor painting. For most of them, this assignment is very simple.
10:30 -- Second period leaves for break.
10:45 -- Third period arrives. This is the second of two Grade 7-8 art classes.
The regular teacher warns me about this class in her lesson plans -- and I can see why. As you might recall from previous posts, the middle schools in this district tend to have the strictest camera rules for online students on Google Meet. This teacher requires that the cameras be on during attendance -- if the camera is turned off, that student loses participation points. And the teacher makes several camera checks throughout the period, again taking away points from those with camera off. Between the camera checks, she says that it's OK for them to turn the cameras off.
So anyway, I take attendance, and most of the students have cameras off. I tell them that I will mark them as non-participating. But then one girl complains in the chat that the regular teacher only counts the second camera check, and so they shouldn't have to have them on during attendance. A few students agree with the first girl.
In past years, especially at the old charter school, this would have been the seeds of an argument. But then I remember something else that the regular teacher wrote -- the chat feature in Google Meet should be turned off during third period! So I immediately disable the chat -- and that, obviously, is the end of the argument.
By the time I reached the second camera check, only two students have their cameras off. Indeed, the class with the most noncompliant students today is first period, not third. (This has occurred often in middle schools in this district -- after first period, fewer students break the camera rule. It might be because after I see too many students with cameras off in first period, I clamp down and enforce the rule more strictly as the day goes on.)
11:40 -- It is now time for tutorial. As in the other middle schools in this district, students are assigned to a particular period for tutorial each day. Today, they are to report to their fourth period class, which for me is the second of two sixth grade art classes.
And as I've been doing during tutorial at other schools, I sing the entire period. Since I already started performing Pi Day songs yesterday, I might as well continue to do so today. And besides -- middle schools in this district follow Hybrid Plan #2, where Cohort A is in-person Tuesday/Thursday. Thus just like the students who attended the high school in-person yesterday, today is the last day that these particular students are on campus until the Tuesday after Pi Day.
I have the students choose among my Pi Day tunes, and these are what they select:
- This Old Pi
- O Number Pi
- Ring the Bells
- Ludolph the Mathematician
- American Pi (Bizzie Lizzie)
- Digit Connection (Bizzie Lizzie)
I won't link to all of these songs this time -- you can find most of them on Google, except for the Bizzie Lizzie songs whose lyrics I've posted earlier on the blog.
No, I don't bring any 7-Eleven pies for the students today. The only reason I was able to yesterday was that I started the day with conference period (when I can see the attendance rosters and decide how many pies to purchase). Middle schools in my new district don't have conference periods this year -- instead, all teachers have sixth period "conference," and all students have P.E. independent study.
It's a shame though that I had sixth graders during my Pi Day tutorial "concert." Sixth graders haven't learned about pi yet -- pi used to be a sixth grade topic under the California pre-Core standards (which expected eighth graders to take Algebra I), but it's now a Common Core 7 topic. Thus my Pi Day songs would have been better appreciated (and understood) if it had been one of the Grade 7-8 classes.
12:10 -- The sixth graders leave for lunch.
12:50 -- The sixth graders return from lunch. I do sing "Fraction Fever" during this period -- just as I do in all the other classes, despite this class getting so many extra songs during tutorial.
1:45 -- Fourth period leaves and fifth period arrives. This is the only Advanced Art class. Of course, only Grades 7-8 are in this class.
While the Bellwork and Exit Ticket are the same for this class as all the others, the main assignment for them is different. The students are wrapping up a project on linear perspective -- which reminds us of Lesson 1-5 of the U of Chicago text. And the new assignment is on drawing faces, on the computer, using a technique called "vectors" -- and vectors are coming up in Lesson 14-5 of our text. Yes, there is a stronger connection between art and math than we might expect at first.
2:35 -- Fifth period leaves, thus completing my day.
Today is Elevenday on the Eleven Calendar. This is the day that I focus on the millennium resolutions and communication skills.
One sixth grade boy is wearing a USC mask. I tell him that I graduated from UCLA, and that our schools are rivals. I continue to play around with this during all of tutorial and fourth period, but he doesn't respond at all. He appears to be quite shy -- either that, or likely he doesn't follow USC sports as closely as some boys his age might. Perhaps there are better ways I could have tried to engage with this young student.
Elevendays are also for improving my communication skills with adults. During lunch, one teacher (more likely an aide for special ed) I see in the staff lounge is wearing a UCLA jacket. She tells me that she didn't go to UCLA -- she only wore it because she likes its colors. But her son is currently a high school junior, and he's strongly considering applying to UCLA by the end of the calendar year.
I also have the opportunity to communicate on Twitter today. One Texas teacher mentions a Pi Day art project where students make -- you guessed it -- agamographs. (That is, unless you guessed that they make Pi Day watercolor paintings.) Of course I reply that I subbed in an art class today that's also making agamographs, though they have nothing to do with Pi Day. (What was I saying earlier about a connection between math and art again?)
Section 12-6 of the U of Chicago text covers the Fundamental Theorem of Similarity. As its name implies, it is the most important theorem related to dilations and similarity. Here is how this theorem is stated in the U of Chicago:
Fundamental Theorem of Similarity (U of Chicago):
If G ~ G' and k is the ratio of similitude, then
(a) Perimeter(G') = k * Perimeter(G) or ...
(b) Area(G') = k^2 * Area(G) or ...
(c) Volume(G') = k^3 * Volume(G) or ...
Notice how I had to rewrite this theorem so that it fits into ASCII. Here the * and ^ symbols denote multiplication and exponentiation, respectively -- these symbols should be recognizable as they appear on TI graphing calculators. The "or ..." sections refer to the text rewriting each equation as a ratio, so that the ratio of the perimeters is k, the ratio of the areas is k^2, and so on, but that is rather awkward to write in ASCII.
David Joyce describes this theorem in his criticism of the Prentice-Hall text:
The proofs are omitted for the theorems which say similar plane figures have areas in duplicate ratios, and similar solid figures have areas in duplicate ratios and volumes in triplicate rations. At least there should be a proof that similar triangles have areas in duplicate ratios; that's easy since the areas of triangles are already known.
Here is the U of Chicago proof:
(a) Perimeter is just the sum of the lengths. Suppose lengths a, b, c, d, e, ...make up the perimeter of G. Then lengths ka, kb, kc, kd, ke, ...make up the perimeter of G'.
Perimeter(G') = ka + kb + kc + kd + ke + ...
= k(a + b + c + d + e + ...)
= k * Perimeter(G)
(b) Let A = the area of G. Then you could think of the area of G as the sum of areas of A unit squares. Then the area of G' is the sum of areas of A squares k units on a side. Since each square in G' has area k^2,
Area of G' = A * k^2 = k^2 * Area of G.
(c) The argument is identical (except with unit cubes). QED
As I mentioned earlier this week, I'm no longer posting old worksheets that mention the Hung-Hsi Wu proof. Thus I'm rearranging last year's worksheets.
Last year's second worksheet is now the first worksheet, since it mentions the U of Chicago version of the Fundamental Theorem of Similarity.
This is labeled as a so-called "activity." Tomorrow is when I'll post my next pandemic-friendly activity.
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