Monday, May 20, 2019

SBAC Practice Test Questions 19-20 (Day 170)

Today I subbed in a middle school special ed history class. Most classes have a special aide, and so there's no need for "A Day in the Life" today.

The day actually begins with eighth grade reading, and then the rest of the day is history. The eighth graders who take U.S. History are learning about the Industrial Revolution, though there is also a period of co-teaching gen ed students who are researching the Civil War. Meanwhile, the seventh grade World History classes are learning about the Renaissance.

As often happens, the aide leaves before the last period of the day, since many of them have part-time schedules that end at 2:00. Thus classroom management matters the most in this class, which is a seventh grade class. It turns out that both seventh grade classes have behavior problems, even the period with the aide.

The problems begin after lunch, when two students ask for a restroom pass. But the regular teacher requires the students to use printed restroom passes -- and unfortunately, neither has a pass.

Lately, I've been trying to avoid the argument that often occurs when I tell students that they should have used the restroom during lunch -- I just let them go even if it's seconds after lunch. But the exceptions are when multiple students ask and I don't want to let more than one out at a time, or when the regular teacher has a strict restroom pass policy -- and both of these apply today. So this time, I do ask one of them why he didn't go at lunch. His excuse is one that I'm starting to hear more often -- he's at detention the whole time and doesn't have time to go.

To me, this isn't a valid excuse. Look at it this way -- if I were a young middle school student and knew that I'd get lunch detention and no time to use the restroom, the first thing I'd do is change my behavior and try to get zero detentions the rest of the year. Of course my behavior wasn't perfect -- so if by chance I received a lunch detention, I would use the restroom before reporting to detention. My basic assumption was that if I ask a teacher to go to the restroom, the teacher would always say no -- so I'd go to the restroom as often as possible without needing to ask. This meant going to use it everyday during lunch, even if I didn't have to go. Note that I'm writing this on the blog, but no, I don't say any of this to the guy today, since it would lead only to an argument.

But the second guy does have a restroom pass -- but it's for a different classroom. In the end, the aide lets both students go to the restroom even though they don't have passes. Then again, this brings up the second problem with this encounter -- the fact that two students who need to go to the restroom yet neither has a pass.

It's possible that both guys have already used their passes this trimester. But as I saw two years ago at the old charter school, more often than not, students lose their passes before using them. Back then, I decided to let students earn the passes -- they get one for each A grade earned on a quiz or test. This included Dren Quizzes, where everyone should be getting an A and a restroom pass.

Yet many students asked to go to the restroom and told me that they'd lost their passes -- even on the next day after I know the student earned an A, or the next day after a Dren Quiz. Then of course an argument would occur -- the student tells me that it's an emergency and so I'm wrong to deny them restroom access, even though all they had to do was not lose the pass they earned.

At some middle schools where I've subbed, restroom passes are handled inside the daily planner that they are supposed to bring everyday. But this still led to arguments -- a student asks to go to the restroom, claims it's an emergency, yet didn't bring a planner to school.

The only way to avoid this completely is to have a restroom policy that doesn't require the student to bring anything to school, so one bringing nothing but clothes on the back can go. This means that I, the teacher, must keep track of the passes myself. Whether it's "one pass per A earned" or a fixed "two passes per trimester, three passes per semester," I must either write down the passes used on a sheet of paper or a computer file.

I know that I won't like this -- I could be in the middle of a Warm-Up or lesson, and a student asks for a pass. So I must interrupt my lesson and look for the clipboard or file where I keep track of points, and then the other students start talking and I lose control of the class. But it's the only way to have a restroom policy that doesn't require students to bring or show me anything.

Of course, there will always be a time when a student who's already used all allotted passes asks to go and tells me I'm wrong to deny the request. But at this point, I want at least to avoid arguments where the passes are merely lost rather than used.

At first, I don't plan on mentioning to the regular teacher that two students go to the restroom without showing me valid passes. But then the two guys spend the rest of the period and fail to do any work at all in the class -- they can't even answer five multiple choice questions in 35 minutes. One guy gives a very lame excuse -- he's supposedly unable to open the packet!

And so I write them down on the bad list with a full explanation of their excuses. Obviously, earning straight A's, or all A's and B's, isn't a priority for these two students. Of course they're likely the type of student who would earn a lunch detention, but it's also likely that they're the type of student who asks for restroom passes, even when they don't need to go, because they don't want to be in class.

During the next period -- after the aide has left -- one girl asks to go to the restroom, and of course, she doesn't have a pass. After what happens in the previous class, I start to argue -- which is wrong, since it violates both my "no arguments" and "avoid mentioning the past" resolutions.

And so I correct myself. This girl, unlike the earlier two guys, appears to be a hard worker -- and it's no longer the period right after lunch. So I let her go -- and while I tell her that I must inform the teacher that she violated his restroom policy by going without a pass, I won't put her on the bad list.

But I must still write down two bad names. Near the end of class, two students -- a girl and a guy -- start chasing each other around the room, even though both have answered the first five questions on their assignments.

I believe that today I make a critical distinction that helps me with management. Some rules are "student vs. teacher" rules, such as the restroom policy. But other rules are "student vs. student" rules where the misbehavior harms another student. This includes chasing each other around the room, bullying, fighting of course, and even talking so loudly that another student complains.

To avoid arguments effectively, it's best to use another criterion besides "student vs. teacher" when deciding whether to write a name on the bad list. Thus I write the two restroom guys on the bad list because they also fail to do any work, while I don't call the girl bad because she does her work. On the other hand, for "student vs. student" rules I write the names even if they did the work, because someone might get hurt. That's why I leave the names of the chasing girl and guy.

Let's change the subject here. Last week was the finale of the TV show The Big Bang Theory. The final episode revealed the last name of one of the main characters -- Penny Hofstadter. Notice that I've mentioned the name "Hofstadter" a lot on the blog in the past month, and so I wonder whether my blog will get extra hits from Big Bang Theory fans, even though I was writing about author Douglas Hofstadter, not Penny.

There is an indirect relationship between Penny and Douglas Hofstadter, and thus their common last name is not a coincidence. First of all, on the show Penny is married to character Leonard, and so Hofstadter is his last name. So in some ways the big reveal that Penny simply has her husband's last name is a cop-out. About 15 years ago, famous diva Madonna wrote a children's book under the name "Madonna Ritchie." But at the time she was married to Guy Ritchie, and so she avoided revealing her actual maiden name (which is Ciccone). And six years ago, Beyonce's "Mrs. Carter Tour" is a similar cop-out, except that Jay-Z's last name isn't generally known either, so in the end, she really revealed his last name. (Her maiden name is Knowles.)

OK, so now we know that Big Bang Leonard's last name is Hofstadter. Now the writers of the show have informed us that he was named for a physicist, Robert Hofstadter, since he and the other main characters on the show are physicists. And Robert's son is Douglas, the author. This completes the link between character Penny and author Douglas Hofstadter.

Recall that I was never a real fan of The Big Bang Theory. But I have mentioned it on the blog due to its connection to physics and math -- certainly much more than that other much hyped finale that aired in the past few days. Flying dragons like Drogon have nothing to do with science.

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

Question 19 of the SBAC Practice Exam is on solving equations:

Consider this solution to a problem:

Problem: -4(6 - y) + 4 = -4
Step 1: -24 - 4y + 4 = -4
Step 2: -20 - 4y = -4
Step 3: -4y = 16
Step 4: y = -4

In the first response box, enter the number of the step where the mistake is made.
In the second response box, enter the correct solution to the problem.

This is a strong first semester Algebra I problem. The original problem has lots of negative signs, and so the obvious error to search for is a sign error. And sure enough, there is a sign error right away -- -4 times -y should be 4y, not -4y. So the step that contains the mistake is step 1.

The solution is easy to correct. All we have to do is change all the signs on y:

Problem: -4(6 - y) + 4 = -4
Step 1: -24 + 4y + 4 = -4
Step 2: -20 + 4y = -4
Step 3: 4y = 16
Step 4: y = 4

Both the girl and the guy from the Pre-Calc class correctly answer Step 1 for this question. But only the girl correctly identifies the solution y = 4. The guy just writes -4 = y for the solution again, even though it's implied that the solution is not -4.

Question 20 of the SBAC Practice Exam is on solving equations:

Consider a sequence whose first five terms are: -1.75, -0.5, 0.75, 2, 3.25

Which function (with domain all integers n > 1) could be used to define and continue this sequence?

A) f (n) = (7/4)(n - 1) - 5/4
B) f (n) = (5/4)(n - 1) - 7/4
C) f (n) = (7/4)n - 5/4
D) f (n) = (5/4)n - 7/4

Because this is an arithmetic sequence, this is also considered to be first semester Algebra I. The first thing we notice is that the terms are listed as decimals, but the choices are all fractions. So the students must convert between decimals and fractions. There is an embedded calculator available, but that assumes that the students know how to use it to make the conversion. I used the calculator (powered by Desmos!) to divide to convert fractions to decimals. Some calculators can convert decimals to fractions, but I don't see that option on this calculator. So the first step would be to divide to convert 5/4 (a major 3rd!) and 7/4 (a barbershop 7th!) to fractions.

We find out that the first term -1.75 is -7/4 and the common difference is -1.25 or 5/4. But we can't use the first term unless we use the (n - 1) version of the formula, f (n) = f (1) + (n - 1)d. Plugging in to this formula, we obtain f (n) = -7/4 + (n - 1)5/4, which is rewritten as f (n) = (5/4)(n - 1) - 7/4. So the correct answer is B).


And as for the girl and the guy from the Pre-Calc class, neither one answers this question -- since for some reason, it didn't print on the SBAC Practice packet! At least this packet is much better than what I had at the old charter school two years ago -- where none of the SBAC Practice problems could print.


SBAC Practice Exam Question 19
Common Core Standard:
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

SBAC Practice Exam Question 20
Common Core Standard:
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Commentary: Distributing a negative sign correctly appears in Lesson 6-9 of the U of Chicago Algebra I text. But the method of finding explicit formulas in Lesson 6-3 -- finding the phantom "zeroth term," doesn't work for Question 10. Instead, students must know and be able to use the formula f (n) = f (1) + (n - 1)d, which most likely appears in later texts based on the Common Core, such as Glencoe and Edgenuity.



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