Today I subbed in a high school honors Algebra I class. It's in my LA County district. Since it's a math class, I'm definitely doing "A Day in the Life" today.
8:30 -- Second period arrives. (With this district's 4 * 3 plan, all periods are even this quarter.)
The class is learning to solve quadratic equations. The students begin with a Pizzazz worksheet on equations that be solved by taking the square root of both sides. This sets them up for an Edpuzzle on completing the square.
Once again, I'm off to a slow start in this class. There is a desktop in the classroom but it's never been set up for Zoom -- and trying to install Zoom produces only error messages. I wait for a Chromebook to be sent down to my room.
When it arrives, there's just enough time for me to take attendance, announce the assignment, and then sing my song for today. Since the lesson is about square roots, I sing an old "Roots" song from my days at the old charter school. I don't recall whether this song was waiting for a new EDL-based tune or not, but I do have my old songbook when an old version of the tune.
By the way, you might wonder why I didn't sing this song during my long-term job, when the eighth graders were also studying simple square and cube roots. It's because that lesson was squeezed in between the district Benchmarks and the semester final exam. The entire lesson was covered in a day -- a Monday, when all students had an online minimum day and I didn't sing at all.
I'll post the lyrics that I sing today. A full music post involving the song might come at some point:
ROOTS
Square root of 1 is 1,
Hey, this is so much fun.
Square root of 4 is 2,
So here's what we should do.
Square root of 9 is 3,
So let's all come and see.
Square root of 16 is 4,
So please show us some more.
Square root of 25 is 5,
And now I feel so alive,
Square root of 36 is 6,
So now there ain't no more tricks.
Today, I sing each line of the song twice (beginning with "Square root of 1 is 1"). This is in anticipation of converting this song into a call-and-response. I don't tell any students to repeat any lines today, but I might when the pandemic has waned (since group singing might not be considered safe now anyway).
After the thirty minutes of Zoom have ended, I start doing some problems from the worksheet. I also call on two in-person students to do a problem on the board.
At the end, I sing more for the in-person kids. The first is "GCF Song" -- a song that I often sing in Algebra I classes during or near the factoring chapter. (Meanwhile, I doubt this class has made it to the Quadratic Formula yet, so I don't get to sing the "Pop Goes the Weasel" parody.)
The other is "Sign of the Times." Ever since four years ago at the old charter school, I'd been hoping to perform this Square One TV song on Cinco de Mayo. But then I left the charter and never made it to May at all. The next two years, Cinco de Mayo fell on the weekend, and of course last year the Mexican holiday was during the pandemic closure. Thus today is finally my first opportunity to sing the song on the fiesta day.
9:40 -- Second period leaves for first snack.
9:55 -- Fourth period arrives.
As usual, now that Zoom is working, I organize this class a little better. I do three problems before the Zoom kids log off. Then I have every in-person student do a problem on the board. I don't change the singing pattern though -- Zoom gets only "Roots," while in-person hears the other two songs as well.
11:05 -- Fourth period leaves for second snack.
11:20 -- Sixth period arrives.
This is the period when my resolution comes in. Today is Elevenday on the Eleven calendar, and so it's time to focus on communication skills. I listen to the students, including one girl and one guy who are really having trouble with these questions. In particular, these two students try to perform the square root step out of sequence in a problem like (x - 2)^2 = 25, and are even more confused if there's a constant factor in front of the parentheses. (Notice that this sort of equation is just like a multi-step linear equation studied in eighth grade or first semester Algebra I, except now one of the steps is a square root. Hmm -- perhaps the "Solve It" song could have been helpful here too.)
12:30 -- Sixth period leaves. I don't need to stay for academic support this time -- originally, the regular teacher was going to Zoom in today, with my presence needed to watch the in-person kids (and so he would have done the academic support). Thus my contract is only for 12:30 today -- and the office manager tells me that I'm free to leave.
Because it is a test day, today is a traditionalists' post. Even though she's not a traditionalist, I will begin with MTBoS Queen Fawn Nguyen, who makes her first math post in nearly six months:
https://www.fawnnguyen.com/teach/math-newsletters
It’s okay that there are 6 weeks left of school when I decide to revive a monthly math newsletter that I’d created for my district last year but stopped when the pandemic hit. I’ve been busy!
The newsletter posted here is interesting. Of course, it has nothing to do with traditionalism -- the first item is "Number Talks," which are the opposite of traditionalism (especially that second open-ended question, which traditionalists hate).
So instead, I'll write more about cheating, which really is a traditionalist concern. Even when I sub in a class for one day, I often continue to get email notification from Canvas or Google Classroom. In particular, I know that the Geometry teacher I covered for a week in January just gave the Chapter 11 Test to her students. The test has 25 questions on volume and surface area, and so it corresponds roughly to the Chapter 10 Test that I posted here for the U of Chicago text.
In her email, she explains how she is grading her test. The test is online, and Canvas automatically assigns a percentage grade, so each question is worth 4%. But then students must submit their work -- and if the work isn't acceptable, she deducts points from the test score. There is no partial credit -- if there's not enough work, then the student receives 0/4 for that question. Many students have been shocked to find out that their actual test score is one letter grade -- or even two letters -- lower than what the computer originally told them it was.
The teacher also writes that, just as we might expect, the deductions have been much greater for the students who have opted out of in-person learning. In each of the four periods of Geometry, the average test grade for in-person students is a C, but for online, the averages in each period have ranged from the 60's down to the 40's.
Thus like the traditionalists, this teacher would agree that in-person learning is much more effective than online learning. Unlike some traditionalists, she is not a zero-percenter (that is, someone who believes that the coronavirus risk rounds to 0%). After all, I did cover her class for one week in January right when the two-day hybrid began (and I believe the pandemic was a factor in her absence).
And so, as usual, this problem doesn't have a simple solution. It's difficult to balance the apparent superiority of in-person learning with the extra health risks. Even in the fall, it's likely that many parents won't want to send their students to school for in-person learning. But it will be hard to prevent online math students from wanting to cheat by Googling for answers to test questions.
Oh, and by the way, here's another example of the perfect being the enemy of the good. We know some parents might be willing to send their students to school in-person for five days but will opt out of a hybrid of 1-4 days per week. Well, I also read that some parents might even opt out of five days, if there's no before or after school care for working parents. On one hand, the extended care is an extra hassle (and an extra opportunity to spread the virus), but for some working parents it's a deal breaker.
Recall that just before the pandemic last year, I blogged about a Senate proposal to have the school day go from 8 AM to 6 PM. And I mentioned the original proponent of that bill -- it was then-Senator (and now Vice President) Kamala Harris. (I don't know whatever came of that bill.)
Here are the Chapter 15 Test answers:
1. 144pi - 288 square units.
2. 178 degrees.
3. Arc DE = 65 degrees.
4. Many answers are possible, for example Angle A = 47.5 degrees.
5. 14 degrees.
6-7. These are visual, so I can't put the answers here.
8. 21.
9. a. (-2, 9). b. 7. c. Many answers are possible. To find lattice points on the circle, we go right, left, up, and down seven units, to obtain (5, 9), (-9, 9), (-2, 16), and (-2, 2).
10. a. (0, 0). b. sqrt(72). c. This time, sqrt(72) = 6sqrt(2), so we can go diagonally to find lattice points on the circle, to obtain (6, 6), (-6, 6), (6, -6), and (-6, -6).
11. This is the complete the square question -- included because such problems are on PARCC!
x^2 + y^2 - 8y = 9
x^2 + y^2 - 8y + 16 = 25
x^2 + (y - 4)^2 = 25
So this gives us:
11. a. (0, 4). b. 5. c. (5, 4), (-5, 4), (5, 9), and (5, -1).
12. a. A circle with radius 20 feet. b. 40pi feet.
13. Draw any circle.
14. About 1.68%.
15. 15.
16. Cavalieri's Principle. Take that, traditionalists!
17. a. When the line and circle intersect in a point. b. When the line is perpendicular to the radius at the point of tangency. PARCC contains a few tangent problems, and all of them appear to involve angle measures, so that right angle is important.
18. a. 36 degrees. b. 18 degrees. PARCC also contains problems on inscribed angle measure -- possibly in the same question as tangents.
19. a. About 2.5 or 2.6 cm. b. The ratio to the circumference to the diameter is -- what else -- pi. We see that we estimate pi as either 3.08 or 3.2 using this measurement. Interestingly enough, 3.14 is almost exactly halfway between these two estimates.
20. a. 24 square units. (The height is 4, using the Pythagorean Theorem) b. About 38.5 square units.
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