Today, of course, I only perform this song in my fourth period Math I class. As you can see by the titles of these blogposts, I've jumbled up the lesson order again, moving back to Lesson 5.2.2 of the CPM text after having already covered 5.2.3.
And I've already given the Desmos lesson for 5.2.2, -- explicit formulas for geometric sequences. So instead, today I follow my neighbor Math I teachers and show the students some problems directly from this lesson of the CPM text.
With no Desmos lesson to get through, I have my first VNPS session in a long time. The first question asks students to consider the arithmetic sequence -9, -5, -1, 3, 7, ..., and analyze it, both in a table and on a graph. So I have the kids draw these in groups on the board before doing so in notebooks. Yes, that's right -- after starting geometric sequences, the text suddenly jumps back to arithmetic sequences.
There are a few more things I want to say about how sequences are taught these days. The traditional notation for sequences has been a_n, with the n written as a subscript (which, of course, makes it more difficult to render here in ASCII). But ever since the advent of the Common Core, more emphasis is being made on sequences as functions -- indeed, the text I used as a student teacher used f (n) to denote the nth term of a sequence. (Since when do we as teachers want to replace A's with F's?) Anyway, the CPM text appears to favor the notation t(n) -- with t standing for term. In many ways, the new function notation is in line with what the TI calculators have been using for years -- u(n), along with v(n) and w(n), are used for sequences.
I enjoy doing VNPS because it gets more students to participate. Of course, in some groups only one student is doing all the work on the board while the others are just talking. But that's a far cry from most lectures when I call on a single student -- often it's a struggle to get that one kid to answer the question, while all the other kids are ignoring us.
The next two CPM questions are more difficult for the students. That's because they ask questions that relate to Chapter 1 and 2 topics on which the kids have been struggling all along. Can any term of the sequence -4, -1, 2, 5, 8, .., equal 42 (which requires plugging in a number and solving), is the graph of a sequence continuous or discrete (domain and range), if the 5th and 50th term of a sequence are known, how can one find an equation (slope)?Despite all this, I believe that the students learn a bit more in today's lesson than they would have if I'd just stuck to notebooks.
You might notice that today's post is labeled as a single-day post (Day 107). That's because tomorrow is Open House, which counts as a special "Day in the Life" post. As I've blogged before, "Open House" at high schools have turned into "Showcases" whose target audiences are prospective eighth graders. Even here in my district with only one comprehensive high school, some families might consider sending their kids to local private schools until they learn what our school has to offer.
Friday becomes the minimum day associated with Open House. This isn't the old monthly minimum day, and so it does not count as "A Day in the Life." This is one reason for the Hero Quiz this week -- there won't be time for a full quiz on the short day.
(Recall that last year, Open House was cancelled. This was due to the sudden loss of two days after winter break due to the COVID surge, so we couldn't afford to have a minimum day.)
Today is Fourday on the Eleven Calendar:
Resolution #4: We start our Warm-Ups and the main lesson promptly.
I do attempt to cut down my Warm-Up times in all classes today -- especially fourth period, in order to allow enough time for VNPS.
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