Tuesday, March 13, 2018

Lesson 12-7: Can There Be Giants? (Day 127)

Lesson 12-7 of the U of Chicago text is called "Can There Be Giants?" In the modern Third Edition of the text, giants appear in Lesson 12-5.

Today I subbed in a middle school math class. It's yet another special ed class, but fortunately for me, the subject is math. So there definitely is "A Day in the Life" today. This is obviously in my new school district -- where today is Day 119 -- since my old district is high school only.

8:15 -- I do briefly see the regular teacher (who double checks her lesson plans) before the day begins with homeroom. Ordinarily, homeroom in this district is only about 15 minutes, but once a month, it is extended for a special lesson. The subject is digital citizenship -- more specifically, cyberbullying.

Cyberbullying, of course, is a major issue in many schools, especially middle schools. Indeed, last year at my former charter school, the Monday coding teacher warned students in all three grade levels about cyberbullies. Those lessons were in September -- it's interesting that this district decided to wait until March to talk about online safety.

8:50 -- First period begins. That's right -- first period! Like the other middle schools in the district, this school has a period rotation schedule. I just wrote in yesterday's post about how the daily rotation (1-2-3-4-5-6, then 2-3-4-5-6-1, then 3-4-5-6-1-2 and so on) doesn't line up with days of the week.

But this middle school is different. First period is always in the morning -- only periods 2-6 are involved in the rotation. This has two advantages:

  • First period is always after homeroom -- in fact, the kids' homeroom is always the same as their first period. This way, homeroom can be extended for special lessons (such as cyberbullying) without significantly disturbing the rest of the schedule.
  • Since only five periods rotate, the schedules can now correspond to days of the week. So second period always follows first on Mondays, third period follows first period on Tuesdays, and so on. We don't need Eleven Calendar Reform to make the rotation fit the calendar week.
And so it is now first period. This is an eighth grade math class. The students are working on the laws of exponents, especially power of a power and power of a product (in other words, multiplying and distributing exponents). In my February 26th post, I wrote about an Algebra I class that was also working on the monomial chapter. If they finish, the students are to work on a graphing activity -- a simple one, more like the graphs I mentioned in my November 17th, 2017 than the complicated "Cartesian Cartoons."

9:40 -- First period ends and third period begins, since it's Tuesday. This is a seventh grade class. The students are working on comparing fractions. The students have been taught to cross-multiply, but one student remembers a trick his first grade teacher showed him -- the special case where the denominators or numerators are equal.

10:30 -- The third period students leave for snack. Fourth period is the conference period, so I'm granted a nice long break here.

11:40 -- Fifth period arrives. This is another eighth grade math class.

12:25 -- The fifth period students leave for lunch.

1:10 -- By now, you blog readers should be familiar with the schedules of special ed teachers -- they travel to another classroom to co-teach the same subject (typically a general ed class with a few mainstreamed special ed students). This teacher actually co-teaches two math classes -- and it just happens to be sixth and second periods, the final two classes on Tuesdays. So I spend the rest of the day after lunch in the other teacher's classroom.

This is an eighth grade class. These students aren't learning about exponents -- instead, they're studying functions, domain, and range. The teacher tells me to hole-punch some packets for her, as well as assist one boy who was absent yesterday. Of course, I have to go back to Sarah Carter and her famous DIXI-ROYD mnemonic.

2:05 -- Sixth period ends and second period begins. This is another eighth grade class. This time the teacher has me supervise two boys who fail to do the homework while she has the rest of the class correct each other's papers.

While the teacher gives the main lesson (on slope and rates), I gaze up at a pacing plan for the entire year that she's written on the back board:

Trimester 1:
Integer Operations
Order of Operations
Equations in One Variable
Linear Equations

Trimester 2:
Systems of Equations
Rules of Exponents
Scientific Notation

Trimester 3:
Geometry: Lines and Angles
Pythagorean Theorem
Data: Gathering Data
Graphing & Interpreting Measures of Center

Today is Day 119, so it's near the end of the second trimester. As it turns out, this teacher has checked everything off under "Trimester 2" except Functions -- the current chapter. So apparently, she isn't bound to the order of the textbook.

It's instructive to compare this pacing plan to what I taught my eighth graders last year. My pacing plan was confused because I kept jumping back and forth between the Illinois State traditional text and the Illinois State STEM text, which had two distinct orders.

In particular, in the first trimester I taught NS (Number System) and the first part of EE (Expressions and Equations), following the traditional text. Then I jumped to G (Geometry) the second trimester before wrapping up EE. Of course, I left my old school before the third trimester.

Perhaps this teacher's plan, starting with integers and order of operations, is better. Then again, it's notable that she covered volume even earlier than I did. Presumably, she'll start Geometry as soon as she can get through this functions chapter.

2:55 -- Second period leaves, thus concluding my day.

Let's look at today's focus resolution:

2. Keep a calm voice instead of yelling at students.

Recall that even though classroom management is important, it's awkward to focus on the first resolution on special ed days. The adults who are already familiar with class structures (the aides in the special ed classes and the resident teacher in co-teaching classes) end up running the class.

On the other hand, the second resolution is definitely in play on special ed days. The students often have trouble understanding the material and following directions, and my frustration often leads to my yelling at them. Once again, I must think back to the special scholar (January 6th post).

Let's take a closer look at my fifth period class. During snack and fourth period conference, the aide warns me that fifth period tends to be the worst-behaved class.

So of course, I try to go over the answers to last night's homework, and the class is loud. Some of the students throw small objects (like pencils and erasers) around the room.

As you already know, I lack a strong teacher tone. So when I raise my voice today, it comes dangerously close to turning into a yell and violating the second resolution. I remind the students that they might lose participation points if they continue to talk, and I warn them that they won't be successful next year in high school if they don't take their classes seriously.

Now hold on a minute, you're probably thinking. Regardless of whether my voice crossed the line into yelling, I apparently just repeated two huge mistakes from last year. Some students evidently don't care about losing points or setting themselves up for future failure. What happens is that they don't change their behavior -- then I get so frustrated that my real yelling begins.

But I have two specific reasons for mentioning participation points and high school. First, it's the aide who tells me to warn them with the possible loss of points. Otherwise, I wouldn't have known that the regular teacher even uses a participation points system. If I someday get my own classroom again and implement a participation points system, students will only be able to gain points, not lose them. The loss of points cannot replace an actual punishment.

Likewise, I mentioned high school only because the special ed eighth graders are going on a field trip to the local high school tomorrow. Of course, students from feeder middle schools visit the high school as a sort of orientation for next year. So my mention of high school is in accord with the field trip, on which the students are clearly supposed to plan for their futures. It's one thing to get the kids thinking about high school just before a field trip there -- or to get them thinking about grades right around the time trimester report cards come out (which is now). It's another to rub their futures in their face when report cards and high school are far away, as I did last year. Warning the students about future failure cannot replace a present punishment.

I still fear that I might have gone too far. When I try to warn one of the offenders about high school, he stands up and walks out of the room (where the aide is helping some of the students). It's possible that he perceives my talk as an outright yell, and about the future that he doesn't care about (so he leaves the room not to get help, but just to escape my "yell"). If my talk is perceived as a yell, it might as well be a yell -- and this is what I must avoid in order to fulfill the second resolution.

This class has a second aide, and she's the one who suggests a real punishment -- with fifth period being before lunch today, she recommends a five-minute lunch detention. In the end, security must be called, and the assistant principal is the one who enforces the five-minute detention for two students, a boy and a girl.

I still believe that there's room for improvement here -- especially when the first aide tells me how especially disruptive these two students are today. I can't help but wonder whether an argument could have been avoided if I don't make a big deal about points and especially about high school.

This is what I wrote last year about today's lesson:

Lesson 12-7 of the U of Chicago text is called "Can There Be Giants?" Last year we skipped over this lesson, so I don't have any old worksheets for it. This is one of those "fun lessons" that we can cover if there's time, but in the past we bypassed it to get to 12-8 and the all-important SSS Similarity.

As I wrote above, Lesson 12-7 naturally lends itself to an activity. The whole idea behind it is that while dilations preserve shape, they don't preserve stability. This is because of the Fundamental Theorem of Similarity -- a dilation of scale factor k changes lengths by a factor of k, areas by a factor of k^2, and volumes by a factor of k^3. Weight varies as the volume, or k^3, while strength varies only as the area (as in surface or cross-sectional area), or k^2. Therefore, the answer to the question in the title of the lesson is no, there can't be giants because their k^2 strength, couldn't be strong enough to carry their own k^3 weight.

Notice that the monomial worksheet from today's lesson somewhat fits this lesson. Some of the problems ask the students to find the area of a square or volume of a cube -- with a particular monomial as one side, so that the students can practice squaring and cubing monomials.

Here are the worksheets that I've created for this lesson:

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