Today was the last day of school before "Winter Break", and I got to lead the class. It was great!
Something I learned: Saying "Yo!" or "Word!" or "I'm-a get ma shizzle ON!" etc is a very easy way to get the attention of grade ten students. Indeed! One student, in particular, was embarrassed for me :). But it works. It's so outrageous, that they immediately cease all other activity and turn their heads.
We went over the kids' exam first (as planned here). Half the class got less than 50%. The average was 53%. We got through the first two pages before recess. I wanted to finish quickly so we'd have time for their "presents" afterward, so I just picked one of the hyperbolas to graph. They actually stayed the first minutes of recess to see it through.
Recess.
After, I handed back their tests. Not happy. I copied down a summary of How to Complete the Square; after, I gave them the flow-chart.
Handed out the "presents": condensed notes on sketching conics; and "Why Conic Sections are Cool!". Talked about "formula sheets", study guides, condensed notes.
I passed around my first "formula sheet" I ever made. It has taped edges to prevent tearing; sprayed with hairspray to prevent graphite smudging (write in graphite so that you can erase and position everything better); everything is labeled; colour and indents help titles to pop out... Only two things about this are dumb: One, I used pencil crayons, which the hairspray dissolved. Two, I spent too much time making it. On the next formula sheets, I smarted up. No colour, no tape; but the indents keep everything orderly.
I told them about speaking "Ukrainian Math Wizard", and (let's call him) Vasil, my prof for Honours Calculus.
Then, I gave them the One Million Beans problem (but with fixed values), saying that if anyone could solve and prove it, I'd bring doughnuts next class (solution below). The top students (grade-wise) couldn't get it, but two girls who were interested but determined they could not figure it out ended up solving it! Well, not necessarily proving it, but close enough. So I owe them doughnuts next class (January 12).
While they were working on it, I told them an Engineers vs. Mathematician joke; they're on the train, one ticket... They laughed--they got it! Just before class ended, I told them the joke about Mathematicians reducing everything to problems they've already solved whereas Engineers can solve "new" problems with originality. If they don't get it now, I'm sure they'll get it later!
Proof of "One Million Beans" Problem
We know that after the beans have been moved back and forth, each jar still contains P number of beans. Now let's look at the number of red and green beans in each jar:
Jar A has
Set up equality:
| P = P | Number of beans in Jar B = number of beans in Jar A. |
| (P - m) + n = (P - n) + m | Cancel (P) on both sides. |
| - m + n = - n + m | |
| 2n = 2m | Cancel (2) on each side. |
| n = m |
| | n - m | = 0 |
for all Natural m, n, P, Q < P.
Okay, I have to get up early tomorrow, then work an 8-hour shift. Sigh. Shouldn't have committed to it...
But I'll mention quickly:
I've been blessed with amazing Math teachers over the years, which probably explains a lot about me. Hopefully, this will allow me to pass along that experience to others.
One student remarked how great it was to have a teacher who didn't mumble (which is especially funny because my father teaches the level below and some kids had him last year). Another said I was exciting and that she was having fun. A few others generally remarked that I explained well and was interesting.
And these are the three (recent) things that have made me feel so worthwhile, in chronological order:
- 1. Finding out my army-boss has harassment issues (it's not everyone--and we're not necessarily bad untrained privates!).
2. My army-boss telling me I look good (dress/deportment).
3. Hearing that the kids enjoyed my teaching.
--Charissa
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