Since math is one of the classes I subbed for today, I will do "A Day in the Life" today, despite their being a special aide to help with classroom management. And the fact that the regular teacher has both math and science reminds me of my failings at the old charter school two years ago. So of course I'll compare today's teacher to myself from two years ago.
8:15 -- The day begins with homeroom and announcements.
8:20 -- This is the middle school where all classes rotate -- but as it turns out, the rotation begins with first period, and all the periods meet in numerical order.
Like many special ed teachers, this teacher has one period of co-teaching -- and as it turns out, the period of co-teaching is first period. This is an eighth grade math class. (That's another reason why I did "A Day in the Life" today, so that I can discuss the co-teaching math class.)
And yes, I warned you last week that this was coming up soon -- the math Performance Task. The eighth graders spend the entire period on the district Performance Task.
Of course, I don't post details about the district assessment here on the blog. Instead, I'll create a similar problem with different numbers:
Part I. You have a budget of $600 to host a birthday party at Magic Mountain. The fun center charges a flat rate of $50 plus $25 per guest for the party.
a) Fill in the T-table.
Guests Cost
0 $50
10
20
30
40
b) Graph the data (guests on x-axis, cost on y-axis).
c) Write and solve an equation to find the maximum number of guests you can invite.
Part II. Write a paragraph using complete sentences. Include a claim (What is the maximum number of guests you can invite?), evidence (two pieces from Part I to support the claim), and your reasoning.
Scoring rubric: One point for the claim, two points for evidence, one point for reasoning.
The first thing we notice is that the scores are on a 4-point scale. Again, this mimics the actual SBAC Performance Task.
The actual district assessment mentions another amusement park. I decided to change this to Magic Mountain, which hosted my old charter's eighth grade graduation party last year (though not two years ago, when I was a teacher there).
I didn't invent the prices, but instead obtained them from the following website:
http://www.magicmountainfuncenter.com/east/birthday-parties/?alttemplate=TextPage-Mobile
Unfortunately, I didn't realize that this link is not our Magic Mountain theme park. Instead, this "Magic Mountain" is in Ohio. (I should have realized it when the water park mentioned at the link is called "The Beach" rather than Hurricane Harbor.) But I like the prices mentioned at the link, and so I decided to use this to set up your Performance Task anyway.
The values I chose for your task come directly from this link. To make it easier, I selected the "Mega Magic Birthday Party Package" and rounded the dollar amounts to whole numbers in order to avoid the common ".99" ending for prices. Unlike the district assessment problem, this site specifies a minimum of eight guests. But since 8 * 25 = 200 anyway, I just ignored the eight-guest minimum and used only the $50 "non-refundable deposit" as the "flat fee" mentioned in your task.
When the resident teacher assigns this task to her first period class, she keeps track of how many students get the right answer. Of the 29 test takers, eleven give the correct answer of 22 guests, seven of them answer 20, and the remaining eleven give a different answer altogether.
It's obvious how seven students obtain the answer 20. They fill in the T-chart, where multiples of ten for the independent variable are already supplied. They see that 20 guests are under budget while 30 guests are over budget, and so they conclude that 20 is the correct answer. The graph scale is also given in multiples of ten on the x-axis as well.
Of course, traditionalists would prefer to skip everything in this task except Part 1c, where the problem is solved using an equation. Traditionalists nonetheless believe that T-tables and graphs are worth teaching, but when it's time to solve problems, equations rule.
While the students are taking the test, I notice a schedule for the next two weeks written on the board:
Monday, March 18th: Taco Cart CER
Tuesday, March 19th: District Performance Task
Wednesday, March 20th: Measuring Angles with Protractors, WS #83
Thursday, March 21st: Parallel Lines Cut by a Transversal, Vocab, WS #84A
Friday, March 22nd: Parallel Lines Cut by a Transversal, WS #84
Monday, March 25th: Angles and Triangles, WS #85
Tuesday, March 26th: Vertical and Adjacent Angles, WS #86
Wednesday, March 27th: Interior and Exterior Angles of Polygons, WS #87
Thursday, March 28th: Interior and Exterior Angles of Polygons, WS #88
Friday, March 29th: Angles Review, WS #89
Here "CER" (in "Taco Cart CER") refers to Claim, Evidence, Reasoning -- in other words, the three components of the Performance Task. Thus yesterday's assignment is merely preparation for today's district assessment.
From the rest of this pacing plan, it's obvious that we're now in the G (Geometry) strand. Indeed, last week the student took a quiz on the Pythagorean Theorem -- the resident teacher grades these quizzes during the Performance Task. As I wrote last week, many middle school math classes reach the G strand right around Pi Day.
This is a Geometry blog, so let's look at these lessons in more detail. I find it unusual that parallel lines cut by a transversal would be taught before vertical angles, since of the two main parallel lines results (Corresponding and Alternate Interior Angles), one is usually proved from the other using vertical angles. Likewise, the Angles and Triangles lesson (when I assume that Triangle-Sum is taught) appears before adjacent angles (linear pairs), even though the "180" appearing in the proof of Triangle-Sum ultimately goes back to linear pairs. Then again, the eighth grade G strand isn't proof-based in the same way that high school Geometry is (supposed to be).
I actually wonder whether it's better to teach the 8.G strand earlier in the year, and save the EE and F strands for right now, since these standards appear on the Performance Task.
9:15 -- Second period arrives. This is the first seventh grade math class of the day. Fortunately, these students are not doing a Performance Task today. (Otherwise I might have skipped "A Day in the Life" today if nothing other than the district assessment was happening today.)
We begin by going over last night's homework. I notice that there are several errors in the teacher's answer key, and so I write the names of students who catch and correct them on my good list.
The main lesson today is on classifying triangles. Students learn how to classify triangles by their sides (equilateral, isosceles, scalene) or by their angles (acute, obtuse, right). The students take their vocabulary notes on a "foldable" that's actually included in an interactive notebook.
Another worksheet for classwork/homework is inserted in the notebook -- Worksheet #85 (which we abbreviate as WS #85). Here are some questions included on this worksheet:
1. Classify each triangle by its sides and by its angles.
7. True or false. A triangle can be isosceles and right.
13. Find the value of x in Triangle ABC if Angle A = 94, Angle B = 47, and Angle C = x.
Once again, even though the seventh graders are in the G strand near Pi Day, they aren't actually learning about circle measurement now. (I believe that only honors seventh graders get the pi lesson near Pi Day.)
10:10 -- Second period leaves for snack.
10:20 -- Third period arrives. This is the other seventh grade math class of the day.
11:15 -- Third period leaves and fourth period arrives. This is a seventh grade science class.
These students are required to take a test. The entire lesson in on Discovery software. The students use the first 20 minutes of class to study the online lessons, and then the remaining time is for taking the online test. The unit is on populations in ecosystems.
12:05 -- Fourth period leaves for lunch.
12:50 -- Fifth period arrives. This is officially a seventh and eighth grade science class. but after the daily silent reading period, eighth graders take the same populations test as the seventh graders.
2:00 -- Fifth period leaves and sixth period arrives. This is an eighth grade math class.
Once again, there is no Performance Task in this class. Just like the seventh graders, the eighth graders begin with a vocab "foldable" for the interactive notebooks, in Cornell notes format. The students must define terms such as "parallel," "perpendicular," and "transversal." Notice that this corresponds to this Thursday's lesson in the first period co-teaching gen ed class.
The assignment is also numbered WS #85. Some of the questions include:
1. Classify Angles 2 and 4 as alternate interior, alternate exterior, or corresponding.
7. The parallel lines are cut by a transversal. Find the value of x.
a. Angles 1 and 2 are corresponding angles, Angle 1 = 45, and Angle 2 = x + 25.
b. Angles 3 and 4 are alternate interior angles, Angle 3 = 2x, and Angle 4 = 80.
You might notice that there's also a WS #85 in the co-teaching class, even though today's lesson corresponds more to WS #84. I suspect that different teachers count the assignments differently, but the count is nearly equal in both classes. (Today is Day 124 in this new district, so out of 124 days, 85 assignments were given. There are probably several days when no assignment is given, such as the first week of school, test days, days near long breaks, and so on.)
2:55 -- Sixth period arrives, but I'm assigned after-school supervision duty.
3:05 -- My duty ends, and so I finally go home. It was a tough day, especially since this teacher has all six periods without a conference period.
Let's compare this teacher's schedule to my own two years ago at the old charter. Neither one of us has a conference period. But today's teacher has at most four preps, since sixth graders don't attend the middle school -- they go to elementary school instead. Likewise, my counterpart at the sister charter didn't have to teach eighth graders. I, on the other hand, would have had to teach six preps since all three grades needed both math and science. This is part of the reason I failed that year.
And indeed, I'm not sure whether this teacher has eighth grade science as a separate prep. The fifth period class had both seventh and eighth graders, but the eighth graders took the same test as the seventh graders in both classes.
The test is on populations and ecosystems. This is the seventh grade unit I tried to teach during "Science Week"-- a last-ditch effort to teach science before I left the school.
Since this class was special ed, I can't help but think back to the special ed students at the old charter school -- especially the special scholar. She was one of my strongest critics, especially regarding the way I taught (or didn't teach) science. And so I ask myself, if I had run my science class two years ago the way the regular teacher does today -- fulling embracing the online Illinois State text -- how would the special scholar have responded?
Well, I'm not quite sure. Today, one student has particular trouble with the online test. He wants the special aide to read the test to him -- or better yet, allow him to use headphones so that he could listen to the computer read out the questions. The aide gives in and reads him the questions, but even then, he is distracted. He keeps making noises and trying to visit other websites. The aide and I agree to write his name on my bad list for fifth period -- and he continues to be disruptive during the sixth period math class.
The special scholar was the same. She often didn't feel like writing or typing either. She appeared to be hoping for something more hands-on, like her cousin's Edible Cell project. Thus I can't be sure how she would have reacted to a science class taught like today's. (And I don't know whether Illinois State, like Discovery, provides the option of pronouncing the words out loud.)
Other students have trouble with the online interface as well. Two students in fourth period end up with very low scores on the actual test when they were supposed to be taking the practice test. One other guy is kicked out of the website and receives a score of "Incomplete," with no possibility of completing the test. And even though there are 20 questions, the test calculates percentages out of 21 because the 21st question is "constructed response." I have one student check the CR question -- apparently they're supposed to draw a diagram (of, I believe, a food web) on the computer.
Lesson 13-3 of the U of Chicago text is called "Ruling Out Possibilities." In the modern Third Edition of the text, ruling out possibilities appears in Lesson 11-1.
This is what I wrote about Lesson 13-3 last year:
Here are a few things that I want to point out. First of all, some texts refer to the Law of Ruling Out Possibilities in Section 13-3 by another Latin name, modus tollens. Here is a link to the Metamath reference to modus tollens.
http://us.metamath.org/mpegif/mt4.html
As we can observe in the proof at the above link, modus tollens is essentially modus ponens (The Law of Detachment) applied to the contrapositive (Law of the Contrapositive, or contraposition.)
Section 13-3 is another section that lends itself to an activity, since many of its questions are actually logic problems, like the ones that often appear in puzzle books. But unfortunately, today isn't an activity day.
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