Today I subbed in a middle school cooking class. It's in my new district. Since it's a middle school class, I will do "A Day in the Life" today.
There is something unusual about this assignment, though. It's split between two different schools, and I must travel from one school to the other. If this sounds familiar, it is -- that's right, one of the two schools is the school where I completed my assignment. Recall that upon the return from winter break, our school rearranged the entire schedule in order to accommodate a certain teacher. Well, this is that teacher.
8:10 -- The day begins with -- yes, second period. No, it's not because "first period" means zero period (since that's in the other district anyway). It's because this is one of the reordered classes that was made to accommodate today's teacher.
Here's what happened with the schedule -- cooking is an elective that most students don't take, so the cooking teacher wouldn't have a full class load if she only worked at one school. Thus a deal was made for her to work at two different schools.
When hybrid began in the fall, it was originally decided to have a block schedule, with odd periods on certain days and even periods on the others. This turned out to be convenient for the cooking teacher -- she could teach odd periods on one campus (my long-term school) and even periods on the other.
Then administrators realized that the block schedule was ineffective during hybrid -- the students weren't learning as much as they could be. Thus the schedule was changed to that all periods meet everyday -- but unfortunately, naively scheduling all periods in order would force the cooking teacher to go back and forth between her two schools (which are located about ten miles apart).
The solution was to reorder the classes so that all even periods occur before all periods -- the official order is now 2-4-1-3-5. (Sixth period is independent study P.E. at district middle schools.) This is why I start today with second period.
Second period is an advanced cooking class, although today "advanced" matters little, since all classes are baking the same thing -- chocolate muffins. This is another one of those classes where the regular teacher is running the classes from home, so all I need to do is supervise and make sure the kids don't burn themselves or the school. One girl gives me one of her muffins.
9:05 -- Second period leaves and fourth period arrives. It's a beginning cooking class.
This is the class with the most discipline issues (semi-expected since it's a lower-level class). Some kids start chasing each other, hitting each other with potholders, and just playing around in general. Of course, the regular teacher sees it all and knows exactly who is doing what.
10:00 -- Fourth period ends. Two girls haven't finished their muffins yet -- unfortunately, they don't realize that their oven is turned off until it's too late. The previous class is supposed to leave their ovens on so that they're preheated for the next class, but the first class is smaller -- this pair just happens to choose the unused oven.
As they wait out the last few minutes, I sing the only song that I perform at this school. Admittedly, songs are often awkward on days when the regular teacher is Zooming in from home. I choose "Solving Equations," a cumulative song for which I can keep adding verses until the oven timer goes off.
After the girls leave, it's time for me to travel to the other school -- my long-term school.
11:00 -- I arrive at the second school.
When the new schedule was announced early last month, I was wondering why we couldn't keep first period the same and change the other classes -- that is, 1-3-2-4-5 instead of 2-4-1-3-5. Then only two classes would have to change.
Now that I'm covering for the cooking teacher, I can appreciate why the even periods have to be taught before the odd periods. The school day starts over half an hour earlier at the even period school than the odd period school. This gives her 30 extra minutes to get to the second school and still have a full load of five teaching periods.
Indeed, tutorial has been arranged in order to maximize her travel time. When I arrive at the second school, it's still the last few minutes of tutorial. Students are supposed to attend a certain period each week for tutorial -- if this works out to be the cooking class, those students go to the library instead.
11:05 -- The snack break begins as usual.
11:20 -- Third period begins -- no, not first period, but third. That's because while both schools have rearranged their classes to 2-4-1-3-5, my long-term school decided to renumber those periods 1-2-3-4-5 while the first school retained the numbering 2-4-1-3-5. Thus this teacher officially has two fourth period classes (one at each school) and no first period -- and this can be a bit confusing for her (ironic, since the class reordering was done solely for her benefit).
This is also a beginning cooking class, and it's the only class with an aide. As it turns out, it's the same aide I had from September to January during the long-term! She'd told me that she covered three classes, with two of them being my math classes. I never realized until now that her third class was in fact a cooking class.
This class is much better behaved than the corresponding class at the first school. I strongly suspect it's due to the presence of the aide. One guy gives me another chocolate muffin.
This leaves me with some more time for performing a song. I don't want to sing "Solving Equations" again, since I've already performed it in November during the long-term and yes -- I do recognize a few students from that long-term.
Since I still receive Canvas emails from my long-term, I know that the eighth graders are studying volume while the seventh graders have a lesson on surface area this week. This means that a good song to play is "All About That Base and Height," my Meghan Trainor parody:
Chorus:
Because you know I'm all about that base,
'Bout that base and height.
I'm all about that base,
'Bout that base and height.
I'm all about that base,
'Bout that base and height.
I'm all about that base,
'Bout that base base base base.
1st Verse:
Yeah, it's pretty clear, I really want to,
Calculate your volume, volume, like I'm suppose to do.
'Cause I got that formula that all the students chose.
Just plug in all the right values in all the right places.
See that base! That's the area of the top.
We know the height, come on now make it pop.
If you got your calculator, 'lator, just multiply 'em,
'Cause every cubic inch is perfect from the bottom to the top.
Pre-Chorus:
Hey prisms, cylinders, don't worry about your size,
'Cause students all know the formula to find it right.
You know for the whole volume, it's just V = bh,
And for lateral area, it's L.A. = Ph.
(to Chorus)
2nd Verse:
I'm bringing area back! Go ahead with lateral
Area! Naw I'm just playin'. I know you
Want surface area! Then I have to tell you
First find lateral area then add the bottom and the top.
(to Pre-Chorus)
12:10 -- Third period leaves and fourth period arrives. This is the second of two advanced classes. I also sing "All About That Base and Height" for them.
1:05 -- Fourth period leaves for lunch.
1:45 -- Fifth period begins -- but this isn't a cooking class. Instead, it's an ASB class. It provides a second reason why our schools reordered the classes to 2-4-1-3-5 instead of 1-3-2-4-5 -- her fifth period class is here at my long-term school, along with her other odd periods.
As is typical for ASB, students go in and out of class doing their own projects and posters. I still find a way to sing "All About That Base and Height" for this students -- indeed, all three periods at this school have kids from my former long-term.
2:35 -- Fifth period ends, thus completing my day of teaching.
3:00 -- Before I leave campus, I meet with the regular teacher from my former long-term. He tells me that his mother has completely recovered from her cancer -- and she's also received both doses of the coronavirus vaccine.
Today is, I believe, the first time I've ever subbed a full-fledged cooking class. I believe that I once covered a self-contained special ed class where one of the skills the students get is cooking. (This was before the year I worked at the old charter school.) It's definitely the first time I ever had to work two half-days on different campuses.
Of course, it's especially interesting to return to my long-term school and see my former students and colleagues once more. I hope I get to come back to this school soon -- particularly on a Tuesday or Thursday, since I don't see that cohort in-person on today's visit.
Today is Nineday on the Eleven Calendar:
Resolution #9: We pay attention to math as long as possible.
This doesn't really come up today. I will point out that one guy -- a student I recall from the long-term as someone who almost never does his math work -- is the first (along with his partner) to finish his chocolate muffins, and in the advanced class to boot. If he's not motivated to do math, at least he's hopefully found something that he is motivated to do, namely bake.
By the way, the official name of this class is "Culinary Arts" at one of the two schools (and something more complicated at the other). A more traditional name of the class is "Home Economics" -- and in the old days, mainly girls take Home Ec. Today's classes are more gender-balanced, but girls are definitely the majority in the advanced classes -- neither has more than two boys in-person today. (I did mention that I took a one-quarter Home Ec class as part of a seventh grade Exploratory Wheel.)
Today on her Daily Epsilon on Math 2021, Rebecca Rapoport writes:
What is the difference of the areas of the non-overlapping portion of the squares?
[Here is the given info from the diagram: the two squares have side lengths 7 and 5.]
It's been a long time since I've posted a Rapoport problem. There are several Geometry questions on the calendar in February, but nearly all of them are on weekends or other non-posting days (including the long Presidents' Day weekend).
Notice that I don't give the area of the overlapping region -- or whether the overlapping region is even a rectangle (which it appears to be from the diagram). Let's see why not -- if the area of the overlapping region is x, then the remaining portion of the larger square has area 49 - x and the remaining portion of the smaller square has area 25 - x. Thus the difference between them is:
(49 - x) - (25 - x) = 49 - x - 25 + x = 49 - 25 = 24
Therefore the desired difference is 24 square units -- and of course, today's date is the 24th.
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.
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