Class of 2022 Challenge (Days 87-88)
Today is the first day of the second semester. Therefore I'm doing "A Day in the Life," for the special day "first day after winter break." (Note -- on the blog calendar, today is Day 87 -- but that's counting the two unexpected PD days as Days 85-86. Then again, if two days are added to the end of the year in June to make up for these two missed days, then I'll retroactively label this as Day 85.)
8:00 -- First period begins. As expected, today's schedule is just like an all-classes Monday. I don't have a first period -- and luckily, we didn't have a bunch of teachers call in sick. So I don't need to cover any extra classes today.
9:00 -- Second period begins. This is the first of two Ethnostats classes.
Recall that earlier, I was considering doing the One Word Challenge that Shelli promotes -- perhaps even on Desmos. But instead of Shelli, I decided to go with Sarah Carter. Each year on the first day after winter break, Carter posts a Year Challenge based on the dates of the year. Here's the link to her 2022 Challenge page:
https://mathequalslove.net/2022-challenge/
Today was the first day of the new semester. I issued my students the 2022 Challenge to get their brains re-engaged in doing math without having to jump straight into content on day one.
The goal of the challenge is to use the digits in 2022 (2, 0, 2, and 2) exactly one time each along with any mathematical symbol or operation of your choosing to create expressions equivalent to the numbers between 1 and 100.
So this is like the Four Fours challenge all over again! When I first read about Four Fours as a young elementary school student (reading the TI-34 calculator manual), it never occurred to me that it's an activity for students to do. Yet that's exactly what Carter has done here.
One thing that makes 2022 tricky is that all four digits are even -- and three of those digits are 2's. So the hardest part is trying to get an odd number out of these even digits. I showed the students three ways to do so:
- 2/2 = 1
- 2^0 = 1
- 0! = 1
Indeed, Carter tells us that she allows factorials in the 2022 Challenge for the sole purpose of 0! = 1 as a way to obtain an odd number from just one digit.
I tried to make my class today look as much as Carter's as possible. Notice that in order to remind her students about factorials, she began her lesson with a Warm-Up -- a factorial question from ACT. So apparently, most of her students are juniors preparing to take the ACT. My students are mostly seniors who should have already taken a college entrance exam, if any. So instead of an ACT question, my Warm-Up just asks them to find 1!, 2!, 3!, 4! -- and then I remind them what 0! is. Also, I called my activity the "Class of 2022 Challenge" in order to celebrate those graduating seniors.
I tell the students that the winning class will get cookies, just like Carter's classes. Second period is the only class not affected by COVID-related absences -- all four students are present. The class set the bar by finding 30 expressions. Some of the more interesting ones include:
- 15 = 2^2^2 - 0!
- 17 = (2 + 2)^2 + 0!
- 40 = 20/0! * 2
For the Exit Pass, I was originally considering using some questions from the actual Rapoport Calendar, as both Monday's and Tuesday's questions involve factorials. But school was cancelled both days -- and the Rapoport problem for January 12th has nothing to do with factorials. So instead I just wrote one of the possible expressions for 12, namely 22/2 + 0!
9:55 -- Second period leaves for nutrition.
10:15 -- Third period arrives. This is the AP Calculus class.
This is the first class of mine that's hit hard by absences. Of the six students enrolled in the class, half of them are absent. Indeed, I know this coming in, as one girl had sent me an email warning me that she's going to be out.
This class really came up with some interesting answers. Coming in, I'm assuming that the only use of factorial would be 0!, since 2! = 2 is just a waste. But here's what this class finds:
- 24 = (2 * 2)! * 2^0
- 26 = (2 * 2)! + 2 + 0
- 36 = ((2 + 2^0)!)^2
- 48 = (2 * 2)! * 2 - 0
In the end, though, this class can only tie second period with thirty expressions. While their responses for 26, 36, 48 are impressive, they miss numbers like 15, 25, 40 that second period gets.
11:15 -- Third period leaves and fourth period arrives. This is the second Ethnostats class.
Fourth period is my largest class with thirteen students, but three of them are absent. This class is able to beat the earlier classes by finding 32 expressions. It's the only class that uses a square root:
- 40 = sqrt(20^2) * 2
- 81 = ((2 + 0!)^2)^2
12:10 -- Fourth period leaves for lunch.
12:45 -- Fifth period arrives. This is my newest class, Trigonometry.
The old general Stats class had four students -- this one has three, as the special ed guy dropped. Also, the lone girl in the class is absent, leaving me just two guys in the class.
Thus this class is at a disadvantage with just two students. But it also has an advantage -- recall that one guy in this class is also in second period Ethnostats! After second period ended, I tell him to toss his 2022 Challenge paper in the trash -- he can contribute to the fifth period score, but only by memory, not by looking at his second period paper.
As it turns out, the fifth period duo is able to find 34 expressions. The guy from both second and fifth remembers all of his expressions (except 40), to which the other guy adds some of the expressions involving (2 * 2)! that Calculus has found earlier. So fifth period wins -- and that means I only have to buy cookies for two students tomorrow.
At the end of class, the principal comes in to lead us to the bookroom, where we get our Trig texts. So now I can finally write more substantially about what my Trig text will look like:
Here are the eight chapters of the text:
- The Six Trigonometric Functions
- Right Triangle Trigonometry
- Radian Measure
- Graphing and Inverse Functions
- Identities and Formulas
- Equations
- Triangles
- Complex Numbers and Polar Coordinates
Most of the skipped questions are on special right triangles -- 30-60-90 and 45-45-90 triangles. I believe that I need to remind the students about these explicitly, so I'll briefly mention them as part of tomorrow's lesson where we begin Section 1.2, on the coordinate plane. In addition, I'll need both graph paper and graphing calculators for the main Section 1.2 lesson.
By the way, there exists a Desmos version of the 2022 Challenge:
https://teacher.desmos.com/activitybuilder/custom/619f8c7ce086f304c7509afa
Indeed, I was considering using Desmos for the lesson today, but I don't. One problem is that many students don't arrive at school with their Chromebooks fully charged -- and we want to skip using the class set of Chromebooks in order to avoid needless touching during the pandemic. So I just hand out the assignment on paper, which can be easily thrown away afterward.
1:40 -- Fifth period leaves. Sixth period is conference.
2:50 -- There is a quick after school meeting on Google Meet. The principal asks each teacher in turn how our day goes.
3:15 -- The meeting ends, thus concluding my workday.
I wish now to return to a habit I established on the old blog -- discuss one of the New Year's Resolutions (that is, the Honor Code) and how I enforced the rule in my class today. And I choose the resolution based on the Eleven Calendar that I described in my New Year's Day post. For example, today is Tenday on the Eleven Calendar, so let's look at the tenth resolution:
Resolution #10. We treat others the way we want to be treated.
The students for the most part were respectful as they help each other on the tenth resolution. Also, notice that the principal tries to be respectful to us teachers, since the after school meeting was mainly about asking about our day and getting us accustomed to the school day after winter break. For that matter, I tried to respect my students by easing them back into class with the 2022 Challenge.
I'm tempted to use Desmos tomorrow in Trig class, for the One Word Challenge. As I mentioned in my most recent post, the Desmos version is also about graphing lines -- which ties in directly to the graphing they're doing in Section 1.2. Also, in the first Advisory class tomorrow, there is a Google Slide assignment where students have a Google Slide assignment to reflect on the year 2021 in review. One of the slides is about "One Word" -- but apparently, that one word is to describe the recently completed 2021, not the year 2022 to come (as Shelli's One Word does).
And that is how my first day after winter break goes. I'm now blogging on even days when my Ethnostats class meets (since this is a Stats blog), so my next post will be Friday.
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