## Thursday, May 31, 2018

### SBAC Practice Test Questions 25-26 (Day 176)

Today on her Mathematics Calendar 2018, Theoni Pappas writes:

It's 3 pm. At 3:?? pm the [minute] hand will have traveled 186 degrees.

(Pappas has a typo here -- she writes "second" where "minute" is intended.) In 60 minutes the minute hand travels 360 degrees, so we can write a proportion:

x/186 = 60/360
x/186 = 1/6
6x = 186
x = 31

So the answer is 31 minutes -- and of course, today's date is the 31st. Technically this is a Geometry problem since it involves angles and degrees, but it's also an Algebra problem.

Today I subbed in a seventh grade special ed class. Math is indeed one of the subjects I cover today, and so I am doing "Day in the Life" today. But the two main math classes aren't until the end of the day, and so bear with me while I discuss what happens the rest of the day. The focus resolution for today will be the fourth resolution, on warm-ups, since they're a part of the math classes today.

8:15 -- This is the middle school that starts with homeroom and first period everyday. The teacher I subbed for had first period conference -- except that I must cover for another teacher who calls for a sub late. The other sub doesn't arrive until first period is almost over, and so I cover what turns out to be a digital video class. The students already have projects to work on, so all I do is make sure that they don't start playing games or YouTube on the computers.

9:20 -- Just before first period ends, the other sub arrives. At this time, there's an announcement that the school is now on a "rainy day schedule." So it's time for me to explain California weather once again, since today is a rainy day (viz. a so-called "California 'Snow' Day").

Last year, I explained that snow is almost nonexistent at sea level in Southern California. As for rain, it usually occurs only between late October and early May. The exception is the so-called "May Gray" and "June Gloom." This refers to a marine layer consisting of low clouds, fog, and drizzle. I usually don't consider "May Gray" or "June Gloom" to be a true rainstorm since it usually falls in the morning and is gone by noon (though earlier this month the rain stayed an entire day).

My second/fifth grade teacher was born in Washington State. She once told the class that in her hometown, the schools let students have recess in the rain since there's so much precipitation. It's only here in California where if there's a little rain, outdoor recess is cancelled. Yet even I was surprised that the middle school declared a rainy day schedule after a mere morning drizzle.

In elementary schools, a rainy day schedule means no outdoor recess. Here at this middle school, rainy days mean no nutrition break, and instead of a single lunch there are two lunches, A and B. In theory, this means that there's more room to eat indoors or in a covered area, since only half the students eat during either lunch. All periods on a rainy day schedule are a few minutes off of the regular schedule except for first, which is why the schedule must be declared so early.

9:25 -- All periods except for first rotate at this school. On Thursdays, fifth period is after first. All special ed teachers co-teach at least one period -- and in fact, this regular teacher co-teaches two classes, both fifth and sixth period.

Fifth period is a science class. Whenever I sub for science -- especially middle school science -- I lament my failure to teach science properly last year. The students are working in the final unit of the year, which is the engineering design process. This is a brand new unit that's part of the Next Generation Science Standards.

These students take a test on engineering. Then they watch The Bee Movie, since there was a recent project where they design a bee hotel. (And yes, I know that tonight is a very different type of bee -- the National Spelling Bee.) The resident teacher is also out -- and instead another sub is there. He explains that he used to work in industry as an engineer, and so he's able to tie the lesson to his former job experience. (He was also recently long-term sub for a math class, and so some of the students recognize him.)

10:20 -- Sixth period I co-teach a math class. (Notice that I still haven't actually taught my own math class yet -- that's just the luck of the period rotation.) These seventh graders are learning about volume and surface area. The resident teacher uses nets of prisms to introduce surface area. The U of Chicago Geometry text is a bit similar -- nets appear in Lesson 9-7, and then Lesson 10-1 uses nets to explain surface area.

11:20 -- Some students head for lunch -- but I don't, as I'm scheduled for second lunch. Along with losing both conference period and nutrition, it means that I have four straight classes without a break.

The second period class, my first special ed class, is science. These students are also working on engineering, but this time they are to use Chromebooks to look up the definitions of words related to the engineering design process (including engineering, design, and process).

12:15 -- It is finally time for lunch.

1:00 -- Third period is the first of two special ed math classes. Unlike science (where the special ed students are more or less at the same point as the gen ed kids), this math class is well behind. The students are just now learning about circumference. Recall that I spotted a gen ed seventh grade class at this same school learning this lesson around Pi Day.

Here's how the special aide and I run this class. Let's watch for the fourth resolution:

1:13 -- We complete the Warm-Up -- the aide stamps their homework while the students answer six perimeter questions (all regular polygons). One student at a time goes up to the document camera to answer one of the Warm-Up questions -- the worksheet is placed in a dry-erase packet and then placed under the camera.

1:19 -- We finish going over the homework. The main lesson begins about a third of the way into the period.

1:45 -- We finish the main lesson (actually I teach most of it), with the students completing the notes in their notebook. The students are given the last 10-11 minutes to do the homework.

This is something I must keep in mind as I prepare for my summer school Algebra I class. Then again, the fact that my class is computer-based would affect the pacing of my class.

2:00 -- Fourth period is the last math class. Checking the clock, I notice that the pacing for this period isn't quite as good as the previous class -- perhaps because this class is slightly more talkative. Thus time management is affected into classroom management.

2:55 -- Fourth period ends and I go home.

Let's get back to music and the 18EDL scale:

The 18EDL scale:
Degree     Ratio     Note
18            1/1         white D
17            18/17     umber D#
16            9/8         white E
15            6/5         green F
14            9/7         red F#
13            18/13     ocher G
12            3/2         white A
11            18/11     amber B
10            9/5         green C
9              2/1         white D

How can we make music in this scale? Well, we notice that this scale contains a minor triad on the root, just as 12EDL does. The main difference is that 12EDL has a perfect fourth, while 18EDL lacks this white fourth. In exchange, 18EDL has a neutral sixth (which might go better in a minor scale than the supermajor sixth) and a minor seventh (as opposed to no seventh at all in 12EDL).

But 18EDL also has a supermajor third and hence a supermajor triad, 18:14:12 (or 9:7:6). Since 18EDL is the first EDL to have any sort of major triad, we can think of this as the supermajor EDL.

One use of the prime 17 is to make a fully diminished seventh chord, 10:12:14:17 (otonal). In Mocha, we might try playing the corresponding utonal diminished chord, 17:14:12:10. This chord can join the root supermajor triad as the start of a riff (D supermajor, D#dim7). But the next chords that are part of that riff (Em, A) aren't playable in Mocha. We've been using our utonal chords for descending rather than ascending, and so maybe D#dim7 could lead into D supermajor.

On the guitar, we might play D supermajor as D ordinary major. There's a way to finger D#dim7 on the guitar (take a D7 chord and add a "lute index finger" for D#), but this is difficult to play.

Possible 18EDL root notes in Mocha:
Degree     Note
18            white D
36            white D
54            white G
72            white D
90            green Bb
108          white G
126          red E
144          white D
162          white C
180          green Bb
198          amber A
216          white G
234          ocher F
252          red E

Question 25 of the SBAC Practice Exam is on inequalities:

A student earns \$7.50 an hour at her part-time job. She wants to earn at least \$200.

Enter an inequality that represents all of the hours (h) the student could work to meet her goal. Enter your response in the first response box.

Enter the least whole number of hours the student needs to work to earn at least \$200. Enter your response in the second response box.

This is a first-semester inequality problem. Inequalities appear in Chapter 5 of Glencoe, and so it's the last topic we'll cover this summer:

7.50h > 200
h > 13 1/3

So the inequality is 7.50h > 200 ("at least" = "greater than or equal to") and the smallest whole number value that satisfies it is 14 hours.

Question 26 of the SBAC Practice Exam is on comparing statistics:

Michael took 12 tests in his math class. His lowest test score was 78. His highest test score was 98. On the 13th test, he earned a 64. Select whether the value of each statistic for test scores increased, decreased, or could not be determined when the last test score was added.

(The possible stats are standard deviation, median, and mean.)

Stats appears in the last chapter of Glencoe Algebra I, and so this is a second-semester question. The other summer teachers don't like how Edgenuity requires students to find standard deviation by hand!

Anyway, the mean must decrease because Michael's last test score is lower than that of any previous test that he has taken. The standard deviation must increase when that low value is added. But we can't be sure about the median. The median of 12 values is the mean of the 6th and 7th value, but the median of 13 values is the 7th value (the old 6th value before the 64 happened). So median could decrease if the original 6th test is less than the 7th -- but the median could stay the same if the original 6th and 7th scores were equal. (It's impossible for the median to increase here!)

SBAC Practice Exam Question 25
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.

SBAC Practice Exam Question 26
Common Core Standard:
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

Commentary: The inequality I wrote for h can be solved as early as Lesson 4-6 of the U of Chicago Algebra I text. Meanwhile, stats isn't covered in the text at all, except for Lesson 1-2 where mean and median appear, but not standard deviation.

Note that I'm posting two additional Geometry pages from today's subbing. One is a Kuta Software worksheet about Nets of Solids from the gen ed class. (I've posted Kuta Software on this blog before, since anyone can access the free trial pages.) The other is a half-sheet with a circumference, diameter, and radius from the special ed class.