Today I subbed in a middle school special ed English class. It's in my first OC district, and I've been to this classroom several times before. My last visit was a two-day assignment, the first day of which happened to be Halloween 2019.
Of the three classes that meet today, the first two are eighth grade classes -- and yes, I do recognize a few of these students from last year. The other class is Reading Support. An aide takes over the classes today, so there's no "A Day in the Life."
In the two English 8 classes, it's back to -- you guessed it! -- that big district assessment where students have to write a persuasive essay about a claim. Last year, I happened to avoid English classes in February, but the previous year I subbed mostly English in January and February. That year, the deadline for the assessment was Presidents' Day -- this year, the students appear to be barely starting to learn what a claim is, and so I suspect the actual assessment won't be until March. (And since I still get Google Classroom emails from all the classes I subbed a few weeks ago, yes, at least one of those English classes is starting to teach claims as well.)
The Reading Support class has only a single in-person student, as is typical for the pandemic era. It's a guy, and he's assigned to do work on the Lexia website. The aide takes a few online students and works with them one-on-one.
I sing a few quick songs during the last few minutes of class. These are two of my shortest songs -- first the "Linear or Not" rap that I performed earlier this week, and then "Plug It In." I only have time for short songs after the aide is finished with her lesson.
And as it turns out, today just happens to be the Open House Showcase at this school -- which means that it's my second straight minimum day. Once again, minimum days in this district basically mean that there is no academic support after lunch today.
Today is Elevenday on the Eleven Calendar, so it's my day to focus on communication. I subbed at this school often before the pandemic but not since until today. So I do say hello to the eighth graders I remember from earlier, and I also walk around to visit some of the other teachers.
(Also, I might add that Lessons 10-1 and 10-3 also flow naturally from last month's 8-8 and 8-9. Both the formulas for a circle appear in the surface area formula of a cylinder -- the circumference of a circle leads to the lateral area of a cylinder and the area of a circle leads to the full surface area including the bases.) But some people might point out that this would confuse the students even more. Instead of doing all of the surface area formulas at once (as the U of Chicago does) and all of the volume formulas at once, we'd keep going back and forth between surface area and volume. But another argument is that it's better to do all of the prism formulas at once, then all of the pyramid formulas, and finally all of the sphere formulas.
Volume Postulate:
a. Uniqueness Property: Given a unit cube, every polyhedral solid has a unique volume.
b. Box Volume Formula: The volume of a box with dimensions l, w, and h is lwh.
c. Congruence Property: Congruent figures have the same volume.
d. Additive Property: The volume of the union of two nonoverlapping solids is the sum of the volumes of the solids.
Just as we derived the area of a square from part b of the Area Postulate, we derive the volume of a cube from part b of the Volume Postulate:
Cube Volume Formula:
The volume of a cube with edge s is s^3.
And just as we can derive the area part of the Fundamental Theorem of Similarity from the Square Area Formula, we derive the volume part of the Fundamental Theorem of Similarity from the Cube Volume Formula:
Fundamental Theorem of Similarity:
If G ~ G' and k is the scale factor, then
(c) Volume(G') = k^3 * Volume(G) or Volume(G') / Volume(G) = k^3.
Last year I stopped posting Euclid's propositions at this point, and so I do likewise this year.
Also, last year, today was an activity day. This year, I wish to do an activity for 10-4 instead. But last year's 10-3 activity is easy to convert to a pandemic version -- it involves a video. This is what I wrote last year about that project:
Today's lesson is on surface areas. But recall that back at the end of the first semester, I mentioned Dan Meyer, the King of the MTBoS (Math Twitter Blogosphere), and his famous 3-act lessons. I pointed out how one of his lessons was based on surface area, and so I would wait until we reached surface area before doing his lesson.
Well, we've reached surface area. And so I present Dan Meyer's 3-act activity, "Dandy Candies," a lesson on surface area.
So here's how I'm fixing it for the pandemic. The first page from last year corresponds to the video, so instead I'll just link to the video:
http://www.101qs.com/3038
Then I'll keep the other two pages from last year. One of them asks questions about the video, while the other is my typical lesson page.
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