But this teacher has one class that isn't P.E. -- instead it's seventh grade science. So we can at least do our usual comparison between this class and my so-called "science" class at the old charter school.
Anyway, like most science lessons these days, today's assignment is on Chromebooks. This lesson is on chemical and physical properties.
Now here's where the confusion between the old California and new NGSS standards (specifically the Preferred Integrated model) come in. Under the old California standards, this would considered part of physical science, an eighth grade lesson. Apparently, under the new NGSS standards, this is a seventh grade lesson.
I mentioned how that year at the old charter school, Grades 7-8 would been have grandfathered into the old California standards, while only sixth graders got the new NGSS standards. Thus I would have taught this to my eighth graders. My counterpart at the sister charter taught this unit around the time that my car broke down (and I had that unexpected "sub day"). She actually taught it to her seventh graders -- not because she was trying to integrate her science class, but because she'd been provided with a copy of the Illinois State Physical Science text, but not the Life Science text.
At some point after that "sub day," I did try to teach this lesson to my eighth graders -- making it one of the (way too few) science lessons that I taught them. I'm not quite sure how much they got out of that lesson -- adding an online component (from either the Illinois State or Study Island websites) would have enhanced my lesson.
Recall that I now have a focus resolution -- one of my New Decade's Resolutions. And I'm using my new Eleven Calendar to choose my focus resolution. Since today is Fiveday in my new Calendar, here is my focus resolution:
Decade Resolution #5: We treat the ones born in 1955 like heroes.
Of course, my New Decade's Resolutions are designed for math classes, and so it's difficult to follow this resolution today. Perhaps I could have mentioned it in science class, but the students mainly focus on their Chromebook assignments today. Chromebooks didn't exist in 1955. And in P.E. class, there's not much reason to think about Bill Gates, Steve Jobs, or Tim Berners-Lee.
Today, the students are supposed to play something called "Lightning Basketball" in the gym, but I'm not quite sure what "Lightning Basketball" is. Throughout the day, I gather that this game requires two balls on one-half court. Two players take turns shooting while the other students line up.
The last period of the day isn't the worst today, but it's in this class when I have enough information to conclude that the kids are just playing freestyle rather than the "Lightning" format. I tell the students that if I see too many of them failing to follow instructions and play Lightning, then the class would receive a punishment. There are eight basketballs, and so I distribute two balls to each of the four side half-courts in the gym. If I see any number of balls other than two on a single court, then I conclude that they aren't really playing Lightning.
About halfway through the period, I see one half-court with three or four balls. So I tell the guys playing there to pass the extra ball to another court with only one ball. One student asks, "Can we just play free?" and upon my negative response, he adds, "Why not? No one else is playing Lightning!"
That crosses the line. If "no one" is following the instructions to play Lightning, then everyone truly deserves the punishment. I collect the balls and have the students sit on their P.E. numbers until it's time to get dressed. While they are sitting there, I decide to invoke 1955 in explaining why they deserve their punishment. Instead of the techno-kings, I consider basketball players born in 1955.
(Notice that with basketball players on, say, the high school team, I shouldn't have to tell them the importance of practice. But eighth graders are sometimes as unmotivated to work hard in P.E. as they are in their math classes.)
Anyway, the players born in 1955 would have been in their primes in the 1980's -- around the time of the Showtime Lakers. The star of this era, Magic Johnson, was born in 1959, although he did have a teammate (Mychal Thompson, the father of current Warrior Klay) who was born in 1955. So I tell the students to imagine if the Showtime Lakers decided to goof off during practice the way the students do today -- how many championships would they have won? And we don't even need to go back to the 1955 generation -- if, say, LeBron James and his teammates goofed off in practice, would the Lakers now be first in the conference or last?
(Ironically, the real LeBron James misses practice today due to an illness. Yet he's cleared to play in tonight's game.)
Another of my new resolutions refer to singing. I wrote that I most likely wouldn't sing during P.E. classes, and I don't today. (Some students during the punishment try to get me to sing, but I don't reward them with songs during punishment time.) I do indeed sing in the science class -- as I usually choose during a physical science lesson, it's "Earth, Moon, and Sun."
Lecture 2 of Michael Starbird's Change and Motion is called "Stop Sign Crime -- the First Idea of Calculus," and here is an outline of this lecture:
I. Calculus has two fundamental ideas (called the derivative and the integral) -- one centered on a method for analyzing change; the other, on a method of combining pieces to get the whole.
II. The following stop sign is a modern-day enactment of one of Zeno's paradoxes of motion. [To make a long story short, a driver named Zeno runs through a stop sign, then claims that the car isn't moving at the instant the car reaches the stop sign.]
III. Officers Newton and Leibniz produce additional evidence. [Basically, the cops show where the car was at 1 minute, 0.1 minute, 0.01 minute after reaching the stop sign, indicating that the average speed over each interval is 1 mile per minute.]
IV. The idea of instantaneous speed is the result of an infinite amount of data.
V. Knowing the position of a car at every moment allows us to computer the speed at every moment.
VI. The first idea of calculus, the derivative, quantifies the idea of instantaneous speed.
Starbird's key idea -- the particular "word of the day" -- in this lecture is that the derivative is the measure of change. He summarizes his story of the driver and cops in the following chart:
p(t) = t
Avg. speed from t = 1 to t = 2 is 1 mile/min.
Avg. speed from t = 1 to t = 1.1 is 1 mile/min.
Avg. speed from t = 1 to t = 1.01 is 1 mile/min.
Avg. speed from t = 1 to t = 1.001 is 1 mile/min.
Avg. speed from t = 0.99 to t = 1 is 1 mile/min.
Instantaneous speed at t = 1 is 1 mile/min.
The professor quotes a definition of motion from Aristotle (384-322 BC), after Zeno stated his paradoxes: "Motion is the fulfillment of what exists potentially, in so far as it exists potentially. We can define motion as the fulfillment of the movable qua movable."
Starbird repeats the calculations for a car that is getting faster as it reaches the stop sign:
p(t) = t^2
Avg. speed from t = 1 to t = 2 is 3 mile/min.
Avg. speed from t = 1 to t = 1.1 is 2.1 mile/min.
Avg. speed from t = 1 to t = 1.01 is 2.01 mile/min.
Avg. speed from t = 1 to t = 1.001 is 2.001 mile/min.
Avg. speed from t = 0.99 to t = 1 is 1.99 mile/min.
Instantaneous speed at t = 1 is 2 mile/min.
Instantaneous speed at t = 0.7 is 1.4 mile/min.
Instantaneous speed at t = 1.4 is 2.8 mile/min.
Instantaneous speed at t = 2 is 4 mile/min.
Instantaneous speed at t = 3 is 6 mile/min.
And he ends all of these calculations by giving a simple velocity function:
v(t) = 2t
Thus Starbird defines his word for the day, DERIVATIVE:
(p(t + delta-t) - p(t))/(delta-t), as delta-t approaches 0
This is what I wrote last year about today's lesson:
Lesson 8-6 of the U of Chicago text is called "Areas of Trapezoids." In the modern Third Edition, areas of trapezoids appear in Lesson 8-5.
Today is the first lesson of the second semester, and this is the lesson I've been bringing up for a while now. The digit pattern tells us that we should begin with Lesson 8-6. But the first semester finals took place on Days 83-85, thus blocking Lessons 8-3 through 8-5. Our challenge is to cover the missing material from Lessons 8-3 to 8-5, especially triangle area in Lesson 8-5. So let's dive in.
In Lesson 8-3, the Area Postulate tells us that area satisfies four properties. Three of these are Uniqueness, Congruence, and Additivity. The fourth is the rectangle formula, A = lw. But by starting with Lesson 8-6 today, we're essentially postulating the formula not of a rectangle, but of a trapezoid:
A = (1/2)h(b_1 + b_2)
So now all we need to do is derive formulas for the parallelogram, rectangle, and triangle. The area of the parallelogram is easy, since today's Lesson 8-6 already provide for this. Last year I wrote:
- The text uses inclusive definitions, so a parallelogram is a trapezoid. If you're wondering why there's a section for areas of trapezoids but not of parallelograms, this is why. Recall that the most useful fact about a trapezoid that isn't isosceles is its area formula.
Thus we find the area of a parallelogram by using the trapezoid formula. For the parallelogram, both bases are equal, so b_1 = b_2 implies:
A = hb
And now you might notice that a rectangle is a parallelogram, so now we have the rectangle formula as well. Notice that the variables here are A = hb instead of A = lw, but there's nothing stopping us from calling the dimensions of a rectangle "base" and "height" instead of "length" and "width."
This leaves us only with the triangle area -- the subject of Lesson 8-5. I think that there are three different ways to proceed at this point:
- Follow the missing Lesson 8-5 precisely -- branch into three cases depending on whether the triangle is right (half a rectangle), acute, or obtuse.
- Since we have a parallelogram area formula, just take half a parallelogram. This is how some other Geometry texts present the area of a triangle, specifically those that teach a parallelogram formula before a triangle formula.
- Consider a trapezoid with a base of length 0. It's easy to imagine how as the base of a trapezoid approaches zero, the trapezoid's area approaches the triangle's.
The third method is the most interesting to me, since it means that a single formula works for all the shapes that we're teaching today. But I suspect that the second method will be the easiest for the students to understand. The first method, which requires three cases, is a bit much on a day when we're giving the areas of so many other shapes. In any case we obtain the formula:
A = (1/2)hb
For today's lesson, I'll take last year's Lesson 8-6 worksheet. I won't change it, so it means that the vocab term "triangulated polygon" is meaningless, and so the answer to #2 must now change from the old (c) to this year's (b).
It also includes a "review" question on triangle area, but it's not "review" at all. We might consider this question to be sufficient, but to be safe, let's add an extra worksheet from the old Lesson 8-5 to today's post. Polygon area is one of the more important lessons of the course.
And that's all I have to say today. No, I can't even find a contrived reason to start writing about computer music again. (Even though I have more to say about 16-bit music, it's all useless unless I have a 16-bit player.)
So I guess that's all, folks!
So I guess that's all, folks!
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