Tuesday, December 13, 2005

2 more days! . . . and my ramblings on teaching and tutoring math :)

I haven't had a great deal of time for blogging recently. At least, not time to write some deeper posts that require time and effort. It took me 4 days just to post a brief review of the Narnia movie. I am still planning a more detailed response to queries about Chronicles of Narnia/Lord of the Rings/Harry Potter, but I haven't been able to work on it much. In the meantime, make sure to check out Lane Keister's response to the concerns about C.S. Lewis that are raised by Keepers of the Faith. He provides a kind yet solid response to concerns about C.S. Lewis. Also on my blog draft list is a post on Santa Claus, which I would like to post sometime during the Christmas season. Other posts also drafted and waiting to be completed.

These past few weeks, but especially the past week, have been busier than before, with extra students added to my tutoring schedule (Am I supposed to do miracles with a student's math average with 3 weeks before finals?) and the excitement of friends in town for Narnia. I've also been working a bit on Christmas presents and finishing So Much More, so I could return it when our friends came down. Then we had Christmas cookies to make and decorate to bring to Ashley's on Saturday after her church's Christmas program, plus another Christmas program to attend on Sunday evening. Then I decided to make cookies for my students tomorrow, so more baking and icing today.

I'm almost done with the semester! I have one more day of teaching tomorrow, followed by three tutoring sessions afterwards, then miscellaneous paperwork and two more tutoring sessions on Thursday. Then I'm done until January :). Yay! I am thankful for the program for which I teach, and for my tutoring students, but I am ready for a break. Two weeks ago after 5 tutoring sessions in one day (until 8:00, which is unusual) I had nightmares all night long that I was tutoring geometry and trying to explain proofs to a student who did not have a clue how to do a proof. All in all, though, if I must earn an income (part-time though it is), I'm thankful I can do it with my favorite subject :). I still haven't found the time in my classes to explain the wonders of 144, but I'll have to make time sometime this year. Perhaps I'll have time tomorrow in Geometry, as we are not doing a great deal. . . I also have a geometry student begging for me to explain to him why we cannot trisect an angle with a compass and straightedge, but I have tried to explain that vector spaces are a little beyond the scope of a high school geometry course. . .

While I'm on the subject of math, I have a semi-random math thought of the day. I've been trying to lay low with my geeky math posts, but I've held back long enough. I say "semi-random math thought" because it is a little related to a project (read Christmas present) my family is working on right now. I first had this thought back in the spring, but it resurfaced this evening during a family math conversation.

Did you know that 0.4999999999. . . (ellipses denote repeating infinitely) rounds to 1? :-D I was quite delighted when I realized this earlier this year. I love collecting random fun facts about math. It looks like it should round down to zero (assuming we are rounding to the nearest integer), as it begins with a 4 in the tenth place. But the key here is that 0.4999999999. . . is exactly 1/2.

There are a few ways to show this. I will provide two.

(1) 0.3333333. . . is exactly 1/3, undisputed as far as I know. This means that 3 times 1/3 must be 0.9999999. . . . As 3 times 1/3 is 1, we know that 0.9999999. . . is equal to (not just approximately) 1. Now if 0.99999999. . . is equal to 1, than 0.09999999. . . is equal to 1/10, which means that 0.4 + 0.099999999. . equals 0.49999999. . . and also 4/10 + 1/10, or 5/10, or 1/2.

(2) Let n = 0.4999999. . .
Then 10n = 4.99999999. . .
10n - n = 4.99999. . . - 0.4999999. . . which equals 4.5, or 9/2
10n - n also equals 9n, so 9n = 9/2
Solving for n gives n = 1/2

To complete the explanation as to why 0.49999999. . . rounds to 1, we must merely note that since 0.499999999. . . repeating is exactly 1/2, it must round up to 1, as per standard rounding rules. :-D

Isn't mathematics beautiful? *becomes teary-eyed*

I'll close with a picture demonstrating what happens to poor unguarded pieces of paper in our house. This particular work of art was created by Mother Dear on the back of an old envelope.

6 comments:

Michelle said...

Susan,
I am jealous as I have no mathematical gene anywhere in my body. It is during homeschooling your 7th grader and realizing that you can't figure out their math problem that this becomes a blaring issue. I am thankful for math gurus such as yourself. For it is your kind to whom I will seek out and pay lofty sums to sometime in the near future. :)

Adrian C. Keister said...

Ah, yes. The lovely ambiguities of the decimal system. Hey, at least they're not as bad as polar coordinates, right?

Nice, fun post.

In Christ.

Susan said...

Well, Michelle, I'm certainly glad the Lord didn't give us all the same talents :).

I like polar coordinates, Adrian :), although they are a pain to graph unless I have special polar graph paper which, when available, is pretty nifty.

The ambiguities of the decimal system are why my math students are required to keep their answers in fractions! They of course think I am rather cruel for this, as well as for my ban on calculators :).

Esther said...

The ambiguities of the decimal system are why my math students are required to keep their answers in fractions! They of course think I am rather cruel for this, as well as for my ban on calculators :).

I think I would find you cruel as well.

With loving thoughts,
~ Esther, who always said that whoever thought a little girl should do math was mean! ;)

Susan said...

Hehe, I'll take that in a loving way, Esther. I'd find you a cruel cross-country coach, I'm sure ;).

So why shouldn't little girls do math? Aren't girls, as well as guys, supposed to love God with our heart, soul, strength, and mind? Math is just as useful to gals, even those not planning to enter a career path, especially ones who plan to homeschool. . . :)

Esther said...

Good. I'd never say anything in an unloving way. It's just because of my love for you that I could actually say that! ;)

And, yes, I completely agree with you. I didn't mean to imply that I was saying it was only unfair to little girls. In fact, I felt it was unfair to ANY child, regardless of age or gender. I just detested math THAT much! ;)

I don't hate it as much now. Hey, I even passed accounting this semester...enjoyed it...and am looking forward to the next class. That's saying a lot for me!