Introduction
Today is the winter solstice, the shortest day of the year. The solstice officially occurred at 1:47 PM here in the Pacific time zone.
This is the third Yule Blog post, but I'm doing the fourth prompt from Shelli's list today. That's because there are 18 prompts for only 12 days, so I'll be skipping some of the prompts. (Notice that the post titles will be counted out of 12 while the prompts are numbers out of 17, so this is Yule Blog post #3/12 and Yule Blog prompt #4/18.)
Yule Blog Prompt #4: My Faves of 2022...(Lesson, Activity, Tool, Memory, Strategy, Anything)
Well, that one's easy. This is a Geometry blog, so my favorite lesson was a Geometry lesson. And so far, there was only one Geometry lesson in my Math I class -- transformations, covered in Chapter 3. So it's a priori my favorite lesson of 2022.
But before I discuss how my favorite lesson went this year, let me say a little about office politics. Last year, I didn't have to think about office politics -- I was one of only two math teachers at our tiny magnet school, and the two of us taught different levels of math. But now I'm part of a large math department at the main high school, and so politics have come up, especially with regards to Math I.
There is a head of the Math I curriculum team (or CT), but he's the leader in name only. There's a teacher on special assignment (or TOSA), and he's made math decisions for Math I in the district. (I know what you're thinking -- aren't we the only comprehensive high school in the district? Yes, but some eighth graders who are Calculus-bound are taking Math I, and so the middle schools also matter.)
With all of this confusion at the top, there are four of us who are going our own way, so to speak. It's noteworthy that the four of us are neighbors, while the CT leaders work in another building. Sometimes I ask my neighbors for worksheets or other ideas on how to teach the material, and so I believe it's best to follow their lesson pacing.
In particular, the CT leaders told us that the district Benchmark tests (the last two weeks in October) should count as a midterm, and so they should be included in the students' grades. But my neighbors disagreed -- instead, the district test wouldn't count, and instead a separate midterm would be given on DeltaMath two weeks later. Since they sent me a copy of the midterm topics as well, I decided to follow my neighbors and give the separate midterm. But this left me with a tough decision -- what to teach between the district test and the new midterm.
The first day of school after the district test was Halloween. I was originally planning on starting Chapter 3, my favorite chapter, that day -- and indeed, I'd already set up a Halloween worksheet on graphing and transformations. So I assigned this to my students anyway. The next day, I found a Linear Art project on Desmos, and I assigned it as filler between the district test and midterm. I've already discussed this extensively on the blog -- as it turned out, my neighbors decided to assign it after the midterm as a full-blown project, which took us to Thanksgiving break.
I blogged that I would start transformations in earnest after the Turkey Day break. But as I pointed out, transformations is only part of Chapter 3 of the CPM text -- 3.1 is transformations, 3.2 is on solving equations with fractions ("Fraction Busters"), and 3.3 is on adding and multiplying polynomials.
The Math I leaders told us to focus on transformations, and that's what I started to do on Cyber Monday and Giving Tuesday. But my neighbors (two of whom wrote the final exam) had a different idea -- they would cover Chapter 3 in reverse, starting with polynomials and ending with transformations.
And so that's how the office politics went in my CT. For most of the semester, I'd follow my neighbors, not the CT leaders, in deciding what to teach and when. In Chapter 3, I'd already started transformations and so I was out of sync with my neighbors.
Of course, I'd been itching to teach transformations ever since Halloween, and so I'd been patient in waiting until Thanksgiving. As it turns out, I needed to wait one more week to stay with my neighbors.
An Alternate Chapter 3 Pacing Plan
While each of my neighbors differed slightly in their pacing plans, I diverged from all of them. Here's what my Chapter 3 might have looked like if I'd stayed closer to my neighbors.
Monday, November 29th: Adding Polynomials. This is a straightforward lesson. A Desmos activity was already set up, with pictures of donuts used to represent algebra tiles. (Ring donuts represented x^2, bar donuts x, and donut holes 1.) Students would fill out a worksheet based on the Desmos lesson.
First Block of Week: Multiplying Polynomials. There was another Desmos activity set up. But there was also a huge distraction in fourth period -- the World Cup. Team USA was playing its last match of group play during that time.
One of my neighbors didn't even bother competing with the World Cup, and so neither did I. Instead, I could have quickly shown them a few examples during halftime, and then left them on their own. If they chose to watch the match instead of work, then that's on them. I could go around the room to help individual students on the lesson.
Second Block of Week: Review for Quiz. In reality, I did give a quiz this week -- but on this alternate timeline, the quiz would have been on polynomials. This is the day that both Mexico and Argentina played, and so I could do this the same way -- pass out the review worksheet during halftime and then it's up to the students to work.
But after the Group C matches ended and sixth period began after lunch on Wednesday, there was another problem that I mentioned on the blog -- the Wi-Fi outage, that lasted through Thursday. And due to the quirky schedule, Wednesday was second block for fourth period but first block for sixth. Of course, I couldn't have predicted the Wi-Fi outage, but I should have anticipated the World Cup. As it happened, contingencies to help get through the Cup might have got us through the outage too.
For example, I might have decided not to do Desmos in fourth period on either World Cup day. Instead, I could have assigned some multiplication problems and had them copy them into their notebooks. This would have worked out in sixth period during the outage. And of course the review worksheet could have been printed at home on Tuesday, so that no Internet would have been necessary.
Friday, December 2nd: Quiz on Lesson 3.3, Polynomials. This quiz would be on DeltaMath, since by now the Wi-Fi outage was fixed.
Monday, December 5th: Fraction Busters. This is the day we should have returned to Desmos after the Wi-Fi outage.
First Block of Week: Reflections and Translations. This is when we'd finally get to my favorite topic. In fact, on Monday, one my neighbor teachers set up two packets -- one on reflections and translations, the other on rotations -- and one of my other neighbors made the copies for all of us (in reality, all of us except me, since I'd already taught this).
In these packets, the students were given grids to perform the transformations, but no coordinate planes were set up on the grids. As I mentioned before, this is a better way to teach this topic -- after all, many students are confused by coordinates, indeed, and the U of Chicago text doesn't use coordinates to teach transformations at all. (Instead, in reality I'd already given out a worksheet the previous week -- one that did use coordinates to teach transformations.)
Recall that fourth period was also the day of the principal's observation (so instead of fraction busters, this would have been the lesson of observation). The principal had told me that he wanted to see some sort of technology used during his observation. So this would have been a good day to give the Desmos activity on transformation golf (instead of the previous week). The only difference is that the kids would not have seen rotations yet. But that's OK -- a rotation is the composite of two reflections, and so any Desmos problem that required a rotation could have been solved using two reflections instead.
The other thing about the packet is that the only written work that I grade is in their notebooks. The reflection/translation packet contained about five pages. So the students would have had to cut out the edges and glue them into the notebooks. The kids likely would have dropped scraps of paper, scissors, and glue onto the floor -- right in front of the principal.
Instead, an alternative would have been to do the work in packets, and then turn them in. Then the next day, when the principal isn't there, uh --
Second Block of Week: Rotations. I would hand back the packets and have them glue some of the pages into their notebooks before handing out the rotation packets.
Notice that in fourth period, this second block was on my birthday, December 7th. The "Who Am I?" game could still be played, with my age and weight as the first two questions. The tricky part is that the worksheet was based on graphs. So I'd have to check the groups to see whether which ones were drawing the correct graphs, and the race questions would be to find which group drew them the fastest.
In sixth period, my birthday would have been the first block of the week. Thus the "Who Am I?" game would have been based on the reflection/transformation worksheet day instead of the rotation sheet -- rotations are the trickiest transformation and hence should be taught last. The only difference is that I might have saved the transformation golf Desmos for the next day (and then rotations would have been one of the allowable moves).
Friday: December 9th: Hero Quiz. So the Hero Quiz would be on transformations -- and like my other Hero Quizzes, it would be on paper.
There are several ways I could have done this Hero Quiz. I could hand out half-sheets of graph paper and ask the students to perform two transformations. I also could have had two questions, but only one a transformation and the other a fraction buster.
An interesting quiz would have been two transformations -- a reflection and a translation, except that after performing the reflection, they must translate the image (or vice versa). This would transform the original pre-image by the composite of a reflection and a translation -- that is, a glide reflection. So it would have been an interesting way to show the students the oft-forgotten isometry.
In any case, after the Hero Quiz, the students should begin reviewing for the final exam (which is what I asked them to do anyway on the original timeline).
A Sneak Peek at Chapter 4
As I mentioned on the last day before winter break, Chapter 4 will be a Statistics chapter. I don't want to think that much about the new chapter, not yet. But here's what I do know -- there's supposed to be another project in that chapter. The project might be tied to a real-world topic, such as basketball or some other sport (where there are plenty of Stats, of course).
I'm not quite sure when that project will be given. There's an old second semester pacing guide posted on Google Classroom -- the project is listed as an unnumbered week between Week 1 and 2 of the second semester.
But there's one thing I do know -- I'll return to following my neighbor teachers and their pacing plan. In particular, I'll give the Chapter 4 project whenever they do so. Even after having taught Stats at the old magnet school last year, I'll still rather follow my colleagues when it comes to the Chapter 4 project.
The next chapter with some Geometry content is Chapter 7, on congruence. Originally, Chapter 7 was listed as one of the key chapters of the Math I course, but that's since been replaced by Chapter 4. So I can already predict what might happen -- we end up spending extra time in Chapter 4 (and perhaps 5 and 6), and Chapter 7 gets squeezed near spring break, just as Chapter 3 was squeezed.
Even so, I must avoid the temptation of starting Chapter 7 before my colleagues. After all, I started Section 3.1 before the others, and by doing so, I missed out on some excellent transformation packets (that were superior to anything posted on the old pacing guide). I'd much rather spend one week on teaching the chapter well than start it early but teach it less effectively. And my more experienced neighbors might be able to help me with the material if I wait for them to begin, no matter how eager I might be to get to the Geometry chapters.
The battle lines have been drawn -- and my loyalty is to my closest neighbor teachers, since they are best positioned to help me teach the lesson effectively. In the end, my ultimate loyalty must be to my young freshman students. As I wrote back in my Thanksgiving posts, I must continue to check for understanding in order to ensure student success in this critical year of their education.
Rapoport Question of the Day
On her Mathematics Calendar 2022, Rebecca Rapoport writes:
1/sqrt(2) * cbrt(27)sqrt(98)
The key to solving this question is to regroup the multiplication:
cbrt(27)sqrt(98)/sqrt(2)
= cbrt(27)sqrt(49)
= (3)(7) = 21
Therefore the desired answer is 21 -- and of course, today's date is the 21st. I choose to write about this question since we did recently discuss some square and cube roots in Chapter 5 of the Math III text.
Conclusion
One other participant in Shelli's Yule Blog challenge is Nancy Swank. Let's compare her Slope Dude lesson to what I taught my own Math I students:
http://frauswank.blogspot.com/2022/12/my-favorite-lesson-of-2022-yule-blog.html?m=1
I won't quote the website, because it speaks for itself. Swank's slope lessons were superior to my own, which is why her students learned it much more effectively than my own Math I kids.
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