Introduction
Today is Epiphany, marking the end of the Twelve Days of Christmas on the Christian Calendar. On the mathematical calendar, it is Phi Day, celebrating the number (1 + sqrt(5))/2 -- a value that's also known as the golden ratio.
For many people of Hispanic descent, today is Dia de los Tres Reyes -- Three Kings Day.
Yule Blog Prompt #16: What Worked (and What Didn't) in 2022
Hmmm, let's see -- you already know that the chapter I looked forward to the most was Math I Chapter 3, on transformations. Within that chapter, one lesson I particularly liked was the November 30th Desmos activity, on Tetris Transformations.
Indeed, in comparing that activity to the previous Desmos activity -- Transformation Golf -- there's a reason I like the Tetris one more. The Tetris one is a bit more realistic -- in that game, players really do translate and rotate the tetrominos in order to win. The golf one directs students to translate, rotate, and reflect a "ball" so that it fits in the "hole" -- but the "ball" is really an asymmetrical tetronimo. Had the ball been a real circle, one could win the game via translations only and never reflect the ball.
Notice that the Transformation Golf activity in the U of Chicago Geometry text (Lesson 6-4) is a more realistic example of reflections. No one reflects the ball -- instead, the course is reflected, and then by aiming the ball where the image of the hole is, the ball will bounce off the wall and land in the hole. So this is why, based on how the Desmos activities were set up, I like the Tetris one better.
But Shelli's question here isn't which activity I liked -- it's what worked in 2022. And I must admit that in the end, the Tetris activity didn't work with my students. The main reason it didn't work was timing.
In fourth period, this was one of the lessons I gave during the World Cup, when I knew that many students were paying more attention to the Mexican and Argentinian teams in Qatar. I decided that I'd rather have a Desmos activity than attempt to teach a regular lesson during the matches. And then in sixth period, the soccer games were over -- but then there was a power outage. The blackout lasted into the next day, so that second period didn't get the Desmos lesson on Tetris either.
Once again, if I had followed my neighbor teachers, transformations wouldn't have been taught until the following week, so the World Cup and blackout wouldn't interrupt the lesson. But the lesson was reduced to a packet. The packet was superior to the worksheet that I'd given my own kids, but then it would leave no time for any Desmos activities.
The only way to make these Desmos lessons work better would have been for the Math I department to treat Chapter 3 with more respect. Instead, most of the semester was spent on Chapters 1-2, and transformations were relegated to the last week of the semester.
I know how I'd improve these lessons in future years, and I even know what songs I'd perform those days -- parodies of The Simpsons (for Transformation Golf, referring to the classic episode when Bart goes mini-golfing) and Tetris them songs. But I won't be able to do so unless the department allows more time for Chapter 3 in Math I.
Still, looking at these lessons and seeing what worked and didn't work prepares me for Chapter 4, when I hope more of my lessons will work. Since this is one of my last winter break posts, I want to look ahead to the new semester. Today's post will be all about the second semester of Math I in general, and Chapter 4 in particular.
But before we begin, let's look at one lesson that did work -- from my Ethnostats class. Since Math I Chapter 4 is a Stats chapter, looking at old statistics lessons will help me prepare as well.
An Ethnostats Lesson That Worked in 2022
Believe it or not, one of the best lessons I had at the old magnet school was something that originally didn't work (due to technology), then ultimately worked on a sub day. And it's on interpreting data and correlation, so it's ultimately related to Math I Chapter 4 as well.
I wrote about it on the old Stat blog in February. I will cut-and-paste it here below:
Let me start by describing what is going on in this class, going all the way back to last Wednesday when I received the fateful COVID test. My original plan had been to start the first project of the semester (in lieu of a chapter test). It's another project that goes back to my Ethnostats predecessors -- the students were to read the New York Times interactive article "Money, Race, and Success." They would enter the name of our district and several other districts around the nation, and observe the correlation between percentage of students who are white and number of grade levels they are behind.
But unfortunately, although I was able to access the article on my computer, the students hit a paywall when they tried to read it. So instead, I changed the assignment to answering the review questions at the end of Chapter 12 -- which they'd normally do before a quiz or test. I eventually figured out that if I type in the name of the article in a Google search, then I can see the article. But if I create a link to the New York Times in Google classroom, that's when the paywall appears.
So on Friday, the day of the sub, I finally assigned the project. The students kept track of their data in their Stats Scrapbooks (interactive notebooks). As it turns out, the sub that day has a math background as he's working on his credential. It's always lucky when a math teacher gets a math sub (though there weren't much calculation in the assignment -- it's just recording and interpreting data).
Previewing Math I Chapter 4
Let's look at the pacing guide to see what the upcoming plan for Chapter 4 looks like. First of all, recall that the Math I department chair has shown us his own pacing guide. Both of them devote two weeks to this chapter, although one of them lists the Stats project as an unlabeled week (not Week 1 or 2). I suspect that in reality, it's going to take closer to three weeks to complete the chapter. I will try to stay within a week of the chair's pacing guide, just as I did first semester.
Since the chair places the project between "Week 1" and "Week 2," I'll base the following with "Week 1" the first week, the project the second week, and then "Week 2" the third week. But keep in mind that I'm starting the project when my neighbors begin it, rather than when any pacing guide says to start it.
Week 1 Monday: Nothing.
This pacing plan was originally written last year. But one thing has changed since last year -- recall (from the old Stats blog) that the second semester started on Wednesday, not Monday, due to a COVID surge and a last-minute decision to require COVID testing at a pharmacy. This year, the semester will begin on a Monday as usual, leaving a hole in the schedule.
It appears that teacher-blogger Sarah Carter is planning a 2023 Challenge this year, similar to last year's 2022 Challenge (and similar ones in other years). So I can do this on Monday as well.
Week 1 Block 1: Lesson 4.1.0, Fit Fights
This is a Desmos introducing lines of best fit. I assume the lesson number 4.1.0 means that it's merely an introduction to the material in Section 4.1 of the CPM text.
Week 1 Block 2: Lesson 4.2.2, Correlation and Association
This is a Desmos on the difference between correlation and association. Last year, I taught that correlation is for quantitative data, and association is for qualitative data. Correlation coefficients appear in this lesson.
Week 1 Friday: Section 4.1 Quiz
This is on DeltaMath. Originally I was considering making the first quiz of the new semester be a Hero Quiz, because the students might not have learned enough for a full quiz yet. But this guide suggests that the kids will be ready for a true quiz after all.
Week 2 Block 1 (after MLK holiday): Chapter 4 Project (Part 1)
OK, now let's get to the project. It appears that last year, a Desmos was set up for a project where kids collect data from around the class or school, and that the data should be related to the topics from the first week (lines of best fit, correlation, association). But in a Math I teachers meeting before winter break, the chair and TOSA discussed having a project that's related to sports data instead.
That's why it's imperative that I not start any project until I see other teachers doing so. The last thing I want to do is start a project based on this Desmos, ask the students to go around and survey others to collect data, and then suddenly tell them that they should forget about the surveys and just use the sports data.
By the way, if the project ends up being on sports data, then it will be similar to the Ethnostats project from February that I listed above -- we give the students the data and they interpret any correlations they see in the data. If they must collect data instead, then it becomes similar to the data collection project from earlier in the Ethnostats class. (That project worked too -- the only reason I didn't list earlier is because it was still 2021, so it's not an example of something that worked in 2022.)
Week 2 Block 2: Chapter 4 Project (Part 2)
This might end up being the first day of the project again, depending on other teachers. The new version of the project might have a completely different Desmos set up for it, or it might not have a Desmos component at all. Whatever it contains, I must follow my new Resolution #6 and make sure that I implement all components of the project.
Week 2 Friday: Chapter 4 Project (Part 3)
I notice that there is no Chapter 4 Test -- like Chapter 2, the project is the test. I might end up giving a Hero Quiz this week depending on how the project is going. And the project will likely count as 50 points, and weighted under the Chapter Tests category (25% of the grade).
Week 3 Monday: Lesson 4.1.1, Charge!
This is a continuation of the previous week's lesson on lines of best fit. It is on Desmos, which is often tricky to do on a Monday.
Week 3 Block 1: Lesson 4.1.4, Residuals and LSRL
This is a Desmos on lines of best fit and residuals between the actual and predicted data.
Week 3 Block 2:
Two possible assignments are given here. One is a Polygraph on Desmos, labeled as a "quiz." The other is a worksheet -- apparently, my predecessor was absent that day and left this for the sub. (Maybe he tested positive for COVID in early 2022, just before I did.)
If I do give the Polygraph that day, I likely won't call it a "quiz." There was a similar "quiz" in Chapter 3 that only confused the students.
Week 3 Friday: Section 4.2 Quiz
This is a DeltaMath quiz, so I will give this one. And this ends the chapter -- once again, there is no Chapter 4 Test due to the project.
Looking ahead in the semester, if I stay within a week of the pacing guide, then Chapters 5-6 will be covered by spring break, allowing us to reach Chapter 7 -- the next Geometry chapter -- after the break.
Also, I notice that there are three district Benchmarks in the year. Only one was given in the first semester, so two are given in the second semester. Recall that there was a huge discussion over whether those should count as a midterm grade. With two Benchmarks in the semester, the midterm question will be even trickier.
Conclusion
Let's conclude our Phi Day post with our usual Phi Day song, courtesy Michael Blake:
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