## Friday, February 13, 2015

### Chapter 13 Test (Day 112)

Triskaidekaphobia is a word that comes from Greek. It can be broken down as follows: tris means "three," kai means "and," deka means "ten," and phobia means "fear." Thus triskaidekaphobia means "fear of the number thirteen." Many buildings lack a thirteenth floor, and my old apartment building had no apartment 13, because of triskaidekaphobia.

Even some mathematical websites discuss triskaidekaphobia. Mathworld, for example, has a page on this fear:

http://mathworld.wolfram.com/Triskaidekaphobia.html

And the Online Encyclopedia of Integer Sequences, which gives many well-known sequences in mathematics, refers to the "elevator sequence" -- the sequence of natural numbers without 13:

http://oeis.org/A011760

And so, today -- which, of course, is Friday the 13th -- I post the Chapter 13 Test, which consists of thirteen questions. Even the day count, based on a school district where I work, conspires to join in on the day's numerology as today is Day 112 -- and notice that 1 + 12 = 13.

Unlike some of my other plans -- such as the plan to introduce our Fifth Postulate on Day 55 (which was busted up because I switched calendars near that day) -- posting the Chapter 13 Test on Friday the 13th was not intentional. At the start of 2015, I wanted to skip Chapters 8 through 10 in order to get quickly into the similarity and coordinate geometry of Chapters 11 and 12, and save area and volume for right before the PARCC and SBAC. When February began, I wrote out a day-by-day schedule for Chapter 13, and saw that with my fortnightly chapter tests, the Chapter 13 test would wind up on Friday the 13th. Even though I ended up changing my schedule in an attempt to line up my lessons with the geometry student I tutor, I couldn't resist keeping my Chapter 13 test and writing it with exactly a baker's dozen questions.

Well, the Chapter 13 Test will certainly be bad luck -- for the students who didn't study for it!

Meanwhile, it's been a while since I subbed in a math class. Last week, for example, I spent one day in a German class. Fortunately, I only had to play various DVD's in German and so I didn't actually have to speak the language.

But whenever I spend time in a foreign language class, I like to read the classroom text -- not just so I can actually know something about the language, but also so I can learn about the culture. Indeed, many texts often describe the school system in the other country, and this was no exception. Chapter 4 of the text describes the German education system.

Many traditionalists yearn for our school system to be more like European school systems. And I can see why some might like the German system -- students are divided into three "tracks." One track is the vocational path, another is technical, and the third is academic. According to the text, about half of all young Germans are on the vocational track, and another quarter are on the technical track. So only about a quarter of German students attend the academic high school, the Gymnasium. (Right, the German word Gymnasium has nothing to do with the American gym!) Furthermore, the division occurs fairly early -- fifth grade, according to the text.

I can see why this would be attractive to traditionalists. We could offer eighth grade algebra and twelfth grade calculus to those on the academic track without worrying about alienating those students who don't need to know anything higher than fourth grade math for their vocation. And the same is true for other subjects, not just math.

My problem, as I mentioned before, is that with any tracking system, the tracks end up corresponding to class or ethnicity. This is no less true in Germany than it would be if the U.S. had this system. So here is a link to an article discussing the inequities in the German system:

http://www.economist.com/news/europe/21606298-parents-fret-over-how-long-children-should-stay-school-gymnasium-revolt

So blindly switching to a German- or European-style education system won't solve all our problems.

Here's an answer key for the test:

1. a. 90 degrees. I could have made this one more difficult by choosing a heptagon, or even a triskaidecagon, but I just stuck with the easy square.

b. Here is the Logo program:
TO SQUARE
REPEAT 4 [FORWARD 13 RIGHT 90]
END

Notice that the side length is 13. I'll still find a way to sneak 13, if possible, into each problem.

2. a. If a person is not a Rhode Islander, then that person doesn't live in the U.S.
b. If a person doesn't live in the U.S., then that person isn't a Rhode Islander.
c. The inverse is false, while the contrapositive is true.

Notice that Rhode Island is the thirteenth state.

3. y = 10.

4. There is a line MN. (M is the thirteenth letter of the alphabet.)

5. Every name in this list is melodious.

Notice that with all this discussion about Friday the 13th and President's Day, there a day coming up that I've almost forgotten -- Valentine's Day. Since this question from the U of Chicago text is about romance, I decided to keep it for the test today. Apparently Lewis Carroll had never heard of Christian Grey -- a name beginning with a consonant, yet is the hero of a romance that will likely earn big bucks this weekend.

6. The equation has no solution. (This question references both 13, as 13x appears in the expansion, and Valentine's Day, as Val could be short for Valentine.)

7. a. 13, 11, 9 (descending odds).
b. 13, 17, 19 (increasing primes).

8. a = 2, b = 1, c = 3. (Notice that the values in alphabetical order are 213, for today's date 2/13.)

9. kite.

10. I discussed this problem earlier this week. It is the same as the problem from the Glencoe text, except that I only drew half of the figure -- the part where a contradiction appears.

Assume that the figure is possible. Then ABC is isosceles, therefore angles A and C are each 40 degrees (as the third angle of the triangle is 100). Then ABO is isosceles (as it has two 40 degree angles), so AO = BO = 3. Then by the Triangle Inequality, 3 + 3 > 8, a contradiction.

11. Through any two points, there is exactly one line. (This is part of the Point-Line-Plane Postulate.)

12. a. KML measures 13 degrees.
b. K measures less than 167 degrees.
c. L measures less than 167 degrees. (This is the TEAI, Exterior Angle Inequality/_

13. a. Law of Ruling Out Possibilities.
b. You forgot to rule out another possibility -- that nothing bad will happen to you today. Hopefully, this will be true for you.

So happy Friday the 13th, Valentine's Day, and President's Day. I'll see you on Tuesday, when we will begin Chapter 14.