Who says children aren't ready for the more Grimm of the Grimm Fairy Tales? Today I introduced the special right triangles, but I wanted to quickly show my students where the crazy ratios came from. The story I'm about to repeat to you started with "they got divorced", and one student asked, "why does it always have to be about divorce? Why not an assassin?"... And so I give you the final story (picture all the geometry figures that go along with it).
Once upon a time there was this square. He was EVERY SQUARE, so his sides were of length "x" to stand for EVERY SQUARE. Life was grand. Suddenly! An assassin came along and PHSHWOOT sliced that square in half right through the diagonal and ran away with 1/2 the square laughing maniacally. The square was a broken man. He was half the man he used to be. (draw right triangle). What are his angles? (place a big question mark on the hypotenuse). The townspeople were not compassionate about the "square" after the tragic incident. They were more curious as to the length of his scar. (go through process of finding the hypotenuse in terms of x). The End. Or is it?
But wait, no one ever caught the assassin. Over in Equilateral Triangle Land, a hapless EVERY EQUILATERAL was innocently going about his days. His side lengths were 2x. Cue in the music. PHSHWOOT, the assassin strikes again ...... etc, etc. .... The end....
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Tuesday, February 28, 2012
Thursday, February 23, 2012
Drugs, Sex, & Rock-n-Roll
That was the title of today's notes in precalculus in which we were to delve into a revisiting of logarithms. I know, it's REALLY "s, d, & rnr" (as my wise 11th graders kept reminding me), but I thought about the drugs 1st (since my vitamins were sitting on the student desks, and I moved them to under my document camera and thought drugs), then I thought about the population growth model we'd be talking about, and DING, sex .... then it was only a short hop to how we'd also be briefly discussing decibel levels and BOOM, rock-n-roll.
I started class with a cool problem I got at NCTM a long time ago, something to the effect of:
An athlete ingests 16mg of drug at 8am, and has to take a drug test at 1pm. His body metabolizes the drug at a rate of 25% an hour, and to pass the drug test, he can have at most 1mg of drug in his body. Will he pass the drug test? If not then when (hour, minute, second) can he pass? How much could he have taken at 8am to actually pass at 1pm?
I broke it up into parts, and we had good discussions about various things:
* why not be 0mg to pass?
* how do you convert decimal numbers/answers to actual time?
* okay, this may not happen, but think about hospitals and drugs and surgery scenarios.
* what does metabolizing 25%/hour mean?
After this, then we got to sex. I'd looked up the US population as of mid 2011 (311,800,000), and separately found a model for US population, and asked if the model was accurate. That's all I gave them, and had them work things out and back up their reasoning. Good discussions:
* how do they get the models?
* how far off is it when we see the numbers? (% difference)
Then class was almost over, but I'd copied a brief example on how they calculate decibel levels of noise, and I mentioned cilia in the ear and how once it's damaged, it doesn't repair itself and such. Some kids talked about how their dad's or grandfathers were in rock bands or such and had huge hearing loss.
Of course we had a brief review of log rules and such and they did get basic review homework and practice, but it was fun to tease them along.
I started class with a cool problem I got at NCTM a long time ago, something to the effect of:
An athlete ingests 16mg of drug at 8am, and has to take a drug test at 1pm. His body metabolizes the drug at a rate of 25% an hour, and to pass the drug test, he can have at most 1mg of drug in his body. Will he pass the drug test? If not then when (hour, minute, second) can he pass? How much could he have taken at 8am to actually pass at 1pm?
I broke it up into parts, and we had good discussions about various things:
* why not be 0mg to pass?
* how do you convert decimal numbers/answers to actual time?
* okay, this may not happen, but think about hospitals and drugs and surgery scenarios.
* what does metabolizing 25%/hour mean?
After this, then we got to sex. I'd looked up the US population as of mid 2011 (311,800,000), and separately found a model for US population, and asked if the model was accurate. That's all I gave them, and had them work things out and back up their reasoning. Good discussions:
* how do they get the models?
* how far off is it when we see the numbers? (% difference)
Then class was almost over, but I'd copied a brief example on how they calculate decibel levels of noise, and I mentioned cilia in the ear and how once it's damaged, it doesn't repair itself and such. Some kids talked about how their dad's or grandfathers were in rock bands or such and had huge hearing loss.
Of course we had a brief review of log rules and such and they did get basic review homework and practice, but it was fun to tease them along.
Sunday, February 19, 2012
"Other" Life aka GettaLife
It seems I've come across the following sentiment a ton lately: balancing school life and nonschool life in order to not burn out and to not put all your "happiness" eggs in one basket.
I'm having a pretty good year this year, and I think part of it is that every week, I have things OTHER than school to look forward to. So just in case (and it'll always happen at some point) I have a super crappy day, then I can recharge with my nonschool existence.
Let's see ... Tuesdays I have my favorite (and only for now) yoga class at 6pm. I have to follow my new year's resolution and actually leave school by 5:40 in order to make it, but I've been pretty good so far. Thanks to my guardian angel across the hall that comes in and taps at her watch to make sure I don't backslide :).
Wednesdays I have tap dancing and Lindy Hop lessons at night. That's always fun. Either I feel like the galumphing dolt in tap class, or I rock it. Either way, fun. And in Lindy Hop. Social dancing. Fun.
Thursday mornings I treat myself to breakfast out at a popular local restaurant. I've been doing it for 3 years, and the waiters know me, and it feels like home. I read the paper and do the puzzles and ease into the day. Something to look forward to.
Fridays, well, there's most always nachos and liquids to look forward to after school.
Also, our whole math department has the same period off at the end of a day, so we hike it over to a local place for debriefing and caffeine.
And on my daily 1/2 hour commute to and from work, I look forward to either listening to a book on CD (thank you simplyaudiobooks) or learn "Italian Like Crazy". Which reminds me .... Italy! Spring Break! Lucky Dog!
These are many of the things that keep me sane during the crazy times.
I'm having a pretty good year this year, and I think part of it is that every week, I have things OTHER than school to look forward to. So just in case (and it'll always happen at some point) I have a super crappy day, then I can recharge with my nonschool existence.
Let's see ... Tuesdays I have my favorite (and only for now) yoga class at 6pm. I have to follow my new year's resolution and actually leave school by 5:40 in order to make it, but I've been pretty good so far. Thanks to my guardian angel across the hall that comes in and taps at her watch to make sure I don't backslide :).
Wednesdays I have tap dancing and Lindy Hop lessons at night. That's always fun. Either I feel like the galumphing dolt in tap class, or I rock it. Either way, fun. And in Lindy Hop. Social dancing. Fun.
Thursday mornings I treat myself to breakfast out at a popular local restaurant. I've been doing it for 3 years, and the waiters know me, and it feels like home. I read the paper and do the puzzles and ease into the day. Something to look forward to.
Fridays, well, there's most always nachos and liquids to look forward to after school.
Also, our whole math department has the same period off at the end of a day, so we hike it over to a local place for debriefing and caffeine.
And on my daily 1/2 hour commute to and from work, I look forward to either listening to a book on CD (thank you simplyaudiobooks) or learn "Italian Like Crazy". Which reminds me .... Italy! Spring Break! Lucky Dog!
These are many of the things that keep me sane during the crazy times.
Saturday, February 11, 2012
Figuring It Out On Your Own
As I was leaving school on Friday, a student wanted to use my phone and then hang out in the room while she waited for her ride. We chatted for a bit, and our talk turned to grades. I congratulated her on her recent high test score, and she mentioned that she's really proud of herself this year. Her lowest grade is an 82%. She's a sophomore. She's one of my more diligent students, and I wondered out loud why she wasn't in NHS, and she mentioned that she was a slacker her freshman year, and now her GPA reflects that.
I asked what would have helped her do better as a freshman. We batted around ideas. Here were basically all her responses:
* Would it have helped hearing from older students about the importance of grades?
-- No, I'd just tune them out and think they thought they were "all that"
* Would it have helped if adults talked about the importance of GPAs and college?
-- No, bla bla bla, just adult talk.
* Do you think anything would have helped?
-- No, I think I just had to figure it out on my own.
But that makes me wonder. Maybe it doesn't seem like we're getting through at the time, but maybe we're all planting seeds for future actions. Maybe collectively it's just a process everyone has to go through and who knows what will finally get through, so we have to keep trying and not get discouraged if there's not INSTANTANEOUS reversal of bad study habits.
I'm also thinking of a second student this year who's now a junior. This student was a bit flaky her first 2 years. Did the bare minimum and had the grades to prove it. All of a sudden this year, she's in the A and B range. She finally figured out that grades matter and that she IS smart and doesn't have to act the fluff head.
It's nice when you see things change for the better.
I asked what would have helped her do better as a freshman. We batted around ideas. Here were basically all her responses:
* Would it have helped hearing from older students about the importance of grades?
-- No, I'd just tune them out and think they thought they were "all that"
* Would it have helped if adults talked about the importance of GPAs and college?
-- No, bla bla bla, just adult talk.
* Do you think anything would have helped?
-- No, I think I just had to figure it out on my own.
But that makes me wonder. Maybe it doesn't seem like we're getting through at the time, but maybe we're all planting seeds for future actions. Maybe collectively it's just a process everyone has to go through and who knows what will finally get through, so we have to keep trying and not get discouraged if there's not INSTANTANEOUS reversal of bad study habits.
I'm also thinking of a second student this year who's now a junior. This student was a bit flaky her first 2 years. Did the bare minimum and had the grades to prove it. All of a sudden this year, she's in the A and B range. She finally figured out that grades matter and that she IS smart and doesn't have to act the fluff head.
It's nice when you see things change for the better.