Today I subbed in a middle school history class. This is in my new district. Since it's a middle school class and it's not special ed, I will definitely do "A Day in the Life" today.
8:15 -- First period arrives. This is the first of three seventh grade World History classes. The class begins with a short duck and cover drill (for earthquakes) during the first few minutes.
It turns out that this was one of those middle schools where Cohort A attends periods 0-4 and Cohort B attends periods 5-9. But once all classes started meeting everyday on January 19th, these classes were simply renumbered as the traditional periods 1-5 -- although the old numbered periods 0-9 are still used on the attendance log. (Contrast this with another middle school in this district, where students still refer to the classes as periods 0-9.)
Also, today is a Cohort B day, like all Wednesdays and Fridays for middle schools in this district. They don't shift the entire week forward a day ahead of the Friday holiday, unlike the other district. And moreover, at this school, Monday was an online day like any other Monday. Since all classes meet everyday now, they felt there's no need to follow the Friday schedule on Monday just to make everything even (so now Cohort A is in-person twice this week, but Cohort B is in-person only once).
Like the seventh graders in yesterday's district, these students are studying feudal Japan. They have two assignments to complete on Kahoot, a website I haven't used in previous classes so far.
The song for today is still the "Row Row Row Your Boat" parodies on mean/median/mode and adding signed numbers. And this is the third day this week of handing out Valentine's prizes -- although since I have a full gen ed class, I don't just hand them out to anyone. Instead, students must earn their prizes -- the first few in-person students who show me a score of at least 10,000 points on Kahoot gets rewarded.
For some reason, this class is the most talkative class by far. It could be because I arrived without having access to Canvas or Google Meet and had to wait for a tech guy to arrive -- the students started talking from the beginning of class and proceeded from there. It appears that the class normally starts each day with a Warm-Up, but no such Warm-Up was provided for today.
9:10 -- First period leaves and second period arrives. This is the second of three World History classes.
In this class, all of the students who receive the Valentine's reward are girls.
10:00 -- Second period leaves for break.
10:20 -- Third period arrives. This is the third of three seventh grade World History classes.
In this class, all of the students who receive the Valentine's reward are boys -- almost as if to make up for only girls earning it in the previous class.
11:10 -- Third period leaves and fourth period arrives. This is the first of two sixth grade history classes.
Once again, I rarely teach sixth graders these days, mainly because sixth grade is still considered elementary school in the other district. Sixth graders also study World History, although it's more ancient than what's studied in seventh grade. The cutoff between sixth grade and seventh grade history is roughly the BC/AD line -- BC in sixth grade, AD in seventh grade. Indeed, the Roman Empire is often split between the two grades (its rise in sixth grade and its fall in seventh).
Today, the students have a quiz on ancient India, including the two major religions that began in that country, Hinduism and Buddhism. The quiz is taken on Canvas and scored automatically, and so I give out the Valentine's reward to the top students who earn 36 or 38 out of 40 points.
Because it's a quiz, I'm especially strict with the "camera on" rule today. I write down the names of two boys who refuse to turn on the cameras.
Meanwhile, when one girl turns her camera on, I see that she is riding in a car. I notice that this girl earns only 14 out of 40 on the quiz. I wonder whether she's distracted by the car ride, and so I take note of this for the regular teacher.
When many students have finished the quiz, I sing the "Row Row Row Your Parodies" to them.
12:00 -- Near the end of fourth period, the earthquake drill from this morning continues -- this time, the evacuating portion of the drill begins. Students must report to their homeroom class -- that is, their first period (the one labeled 0 or 5 on the rosters -- in this case 5 for Cohort B).
12:20 -- Officially this is tutorial, but that's mostly taken by the drill. Since there are a few minutes left in class, I have the students choose some extra songs for me to sing. One girl chooses "Rudolph the Statistician" -- even though it's not Christmas, a stats song pairs nicely with the "Measures of Center" song that I perform earlier. Fortunately, one boy chooses a song that's more appropriate for Valentine's Day, "Count the Ways."
12:30 -- The students leave for lunch.
1:10 -- Fifth period arrives. This is the second of two sixth grade World History classes.
By now I've run out of Valentine's candy, and so these students get only pencils. It's a shame, since three students in this class earn perfect scores on this quiz (while no one gets 40/40 in fourth period). Maybe in fourth period, when running low on candy, I should have said "candy for perfect scores only," so that I could have saved the candy to for the top scorers in fifth period.
Two girls have nothing else to do after finishing the quiz, and so they start working on math. I notice that they are working on one-step equations -- and since this class doesn't get candy, I make it up to them by singing an extra song for this class. Of course, I sing "Solve It."
2:00 -- Fifth period leaves. As is usual for middle schools in this district, sixth period is independent study P.E., and so the students and I leave after fifth period.
Today is Sixday on the Eleven Calendar:
Resolution #6: We ask, what would our heroes do?
Once again, this doesn't really come up. I tell the two sixth grade girls about how mathematicians solve equations, but both of them seem to understand their assignment without much help from me. Of course, again I can say that the heroes we pay homage to in History 7 are the Japanese -- let's say the samurai, since they were definitely heroic.
Lesson 10-7 of the U of Chicago text is on the volumes of pyramids and cones. And of course, the question on everyone's mind during this section is, where does the factor of 1/3 come from?
The U of Chicago text provides two ways to determine the factor of 1/3, and these appear in Exploration Questions 22 and 23. Notice that without the 1/3 factor, the volume formulas for pyramid and cone reduce to those of prism and cylinder, respectively -- so what we're actually saying is that the volume of a conic surface is one-third that of the corresponding cylindric surface. So Question 22 directs the students to create a cone and its corresponding cylinder and see how many conefuls of sand fill the cylinder. The hope, of course, is that the students obtain 3 as an answer. This is the technique used in Section 10.6 of the MacDougal Littell Grade 7 text that I mentioned in last week's post as well. (By the way, I just realized that I mentioned four different math texts in last week's post!)
But of course, here in High School Geometry, we expect a more rigorous derivation. In Question 23, students actually create three triangular pyramids of the same base area and height and join them to form the corresponding prism, thereby showing that each pyramid has 1/3 the prism's volume. But this only proves the volume formula for a specific case. We then use Cavalieri's Principle to show that therefore, any pyramid or cone must have volume one-third the base area times height -- just as we used Cavalieri a few weeks ago to show that the volume of any prism, not just a box, must be the base area times height.
I decided not to include either of the activities from Questions 22 or 23. After all, there will be an activity tomorrow and I wish to avoid posting activities on back-to-back days unless there is a specific reason to.
No comments:
Post a Comment