Today on her Mathematics Calendar 2019, Theoni Pappas writes:
Find the circumference of a circle with area 196/pi.
Well, we clearly use the two Chapter 8 formulas, A = pi r^2 and C = 2pi r:
A = pi r^2 = 196/pi
r^2 = 196/pi^2
r = 14/pi
C = 2pi r
C = 2pi(14/pi)
C = 28
Therefore the desired circumference is 28 -- and of course, today's date is the 28th.
Today I subbed in a high school Spanish class. This isn't two-way immersion like Tuesday's middle school class -- instead, it's three sections of AP Spanish and two sections of Spanish III.
This is a multi-day assignment, since this teacher has been out since Tuesday. (She's so sick that she's lost her voice -- a huge problem in a foreign language class.) On that first day, both classes had a written assignment, but since then it's been mostly free days. She was hoping to play that movie I've seen in so many previous Spanish classes -- McFarland USA -- but it won't play. (There is no DVD player, so we had to rely on YouTube Movies -- but it doesn't work today.)
During tutorial (i.e., every single class), I help out some students in math. Just as I wrote last week, all classes -- Geometry, Algebra II, and Pre-Calculus -- seem to be in their trig chapters now.
And finally, today is the day of the Chapter 11 Test. All those other things might be fun, but this is a Geometry blog, so I must post the test -- sorry.
Today is a test day -- hence a "traditionalists" post. I don't have much to say due to so many other recent traditionalists' posts, so let me repeat something I wrote last year on the day of the Chapter 11 Test:
On the other hand, I read anecdotes from traditionalist homeschooling parents about how their second grader learned fifth grade math effectively via direct instruction. I don't consider this to be a valid argument that the fifth grade math standards should be written from a purely traditionalist view -- because fifth graders, more than second graders, will start questioning why they have to learn how to compute with fractions. [2018 update: This isn't discussed at the traditionalist link above, but notice that one commenter wrote "homeschool" as the only rational response to progressive pedagogy.]
But this does mean that the traditionalists' favored standard algorithms and memorization of basic math facts are to be taught as soon as possible, and not delayed a year as in Common Core. One common complaint among traditionalists is that students are never made to memorize basic multiplication facts. Questions such as six times nine or seven times eight should be considered very easy questions that take no more than a second to answer. But not only do many people consider such problems to be difficult, but it has become fashionable to consider those who have difficulties with such problems to be normal and those who find such problems easy to be outliers -- nerds.
It's often pointed out that people would feel deeply ashamed to admit that that can't read at a third grade level, yet are proud to admit that they can't do third grade math. Since I've stated that third grade math is something that students should have learned traditionally -- that is, have memorized -- I should do something about it in my classes.
The thought is that, rather than have those who find single-digit multiplication to be easy be outliers who get the label nerd, it's those who can't multiply by the time they reach middle and high school who should be considered outliers -- just as someone who can't read at a third grade level is taken to be an outlier. But of course, it's improper for me, a teacher, to start calling my students derogatory names such as idiot, no matter how low their understanding of math is.
So I need a word that criticizes the student, yet is proper for me to use in a classroom. Well, since I want my word to have the opposite effect of the word nerd, I briefly mentioned at the end of one of my posts a few months back that I made up my own word, by spelling the word nerd backwards, to obtain "dren."
My plan is to use my new word "dren" in such a way to make it sound as if a "dren" is not what a student wants to be. For example, when we reach the unit on area, students will need to multiply the length and width to find the area of a rectangle. So I might say something like, "A dren will have trouble multiplying six inches by nine inches. Luckily you guys are too smart to be drens, so you already know that the area is ...," and so on. Similarly, if a student, say, starts to reach for a calculator to perform the single-digit multiplication. I can say, "You're not a dren. You know how to multiply six times nine ...," and so on.
Notice that in these examples, I don't call anyone a dren directly. But every time I say the word "dren," I want to be annoying enough so that the students will want to do what it takes to avoid my having to say that word.
I coined the word "dren" to be the word nerd spelled backwards. But ironically -- according to my new Simpsons book -- the word nerd is already spelled backwards! Originally, the word was "knurd," which is drunk spelled backwards. The net result is that my word "dren" is basically just an abbreviation of drunk. Of course, the word drunk isn't a word that I should use in the classroom!
Last year, I wrote about I might strengthen my anti-dren crusade. I can tell math classes that there are three types of students -- "smart," "almost smart," and "dren." Now I don't teach drens -- I choose to work at your school because the students are all "smart" or "almost smart." Those who are struggling with a concept are "almost smart" until they master the concept. This extends the idea from three years ago that I don't call any student a "dren" directly. Every student who works hard is at least "almost smart" -- and I regret having never said this to the "special scholar" two years ago.
Here are the answers to today's test.
1. Using the distance formula, two of the sides have the same length, namely sqrt(170). This is how we write the square root of 170 in ASCII. To the nearest hundredth, it is 13.04.
2. The slopes of the four sides are opposite reciprocals, 2 and -1/2. Yes, I included this question as it is specifically mentioned in the Common Core Standards!
3. Using the distance formula, all four sides have length sqrt(a^2 + b^2).
4. Using the distance formula, two of the medians have length sqrt(9a^2 + b^2).
5. 60.
6. From the Midpoint Connector Theorem,
7. From the Midpoint Connector Theorem,
8. 4.5.
9. (0.6, -0.6). Notice that four of the coordinates add up to zero, so only (3, -3) matters.
10. At its midpoint.
11. 49.5 cm. The new meter stick goes from 2 to 97 cm and we want the midpoint.
12. Using the distance formula, it is sqrt(4.5), or 2.12 km to the nearest hundredth.
13. sqrt(10), or 3.16 to the nearest hundredth.
14. 1 + sqrt(113) + sqrt (130), or 23.03 to the nearest hundredth.
15. sqrt(3925), or 62.65 to the nearest hundredth. (I said length, not slope!)
16. -1/2. (I said slope, not length!)
17. (2a, 2b), (-2a, 2b), (-2a, -2b), (2a, -2b). Hint: look at Question 5 from U of Chicago!
18. (0, 5).
If you want, you can add the following questions, as the equation of a circle is still missing:
In 19-20, determine a. the center, b. the radius, and c. one point on the circle with the given equation.
19. (x - 6)^2 + (y + 3)^2 = 169
20. x^2 + y^2 = 50
Here are the answers:
19. a. (6, -3) b. 13
Possible answers for c: (19, -3), (18, 2), (11, 9), (6, 10), and so on.
20. a. (0, 0) b. 5sqrt(2)
Possible answers for c: (5, 5), (-5, 5), and so on.
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