I'm going to go all Dan up in here and post this for a day or two without comment. (I have no idea if more than a scant few regular commenters are interested in participating...let's look at this as a little experiment.)
Edit: I only made it about 7 hours without commenting. Everything I have to say is in the comments. Let's move on, shall we?
8 comments:
Well first thing the guy's blatantly trying to rip off Ze Frank's style.
@unapologetic: I agree, but it does seem to have one thing different about it; it isn't several years old and a rerun. So I can't harp on him too bad.
As for the video itself, I think it suffers from the problem Dan has pointed out about stock photography of having too much of the photographer in it (he used the example of a parabolic dish from a creative angle). The message seems muddied by his (using the term "his" lightly) style.
Um.
You round 1 to 4 down, and 5 to 9 up, and that accounts for nine out of ten.
Because you round 0 down also. It's just that it doesn't look like you're rounding, because the number doesn't change. But you have to count it in your ratios.
Is this guy for real, or is he trolling?
Using an entirely fair, shouldn't the average of 0+0.1+0.2...+0.9 be the same as 0+0+0+0+0+1+1+1+1+1?
It's 0.45 vs 0.5, so yes, rounding would skim off the top.
I think Kenneth has this one nailed. I just don't know what the students do with it.
He violates the rule of least power, which is fine for vodcasters, but for classroom media you want something that does nothing more than raise a clear question in an uninflected voice and then steps quickly out of the way.
Off the cuff, maybe you tripod a camera in front of a gas pump and film the meter running in fast motion over an hour, which maybe brings up the penny-shaving. Then you film the gas station itself from across the street over an hour, sped up. Have them count the cars, count gas stations, convert units, estimate total profit. Maybe.
Barry I don't think he's for real or trolling. I think he's trying to be funny.
Yep, totally ripping off Ze Frank. Like a dozen other vodcasters. And the kids don't know Ze Frank.
Of course his argument is specious! Sometimes I wonder what people must think of me. :)
But the thing is, I don't know about your kids, maybe it's a sheltered suburban thing, but my kids believe everything they hear on the Internet. They equate possession of a video camera and computer with authority. They are alarmingly uncritical.
I played this to kill a few minutes near the end of the period with something amusing, and to my shock and horror they totally agreed with this guy's logic. "If it's zero, you don't have to round! It doesn't count in things you have to round!" They just didn't think it was a big deal for a few pennies. Maybe I should have seen it coming, but all I could do was stand there with my mouth open and blink at them for a few seconds.
I'm hoping a few of them sensed something was off, and I can get them to try to articulate why it seemed wrong when I bring it up today.
Also, for seeming like such a no-brainer skill, many of them still screw up rounding all the time. Either they just do it wrong, or they round too early while solving a problem, and it throws off their answer. Children have told me cos(60) = .9. Also 7.49 rounded to the nearest unit = 8. Because the 9 makes the 4 a 5, and when it's 5 you round up! Excuse me while I find a wall against which I may bang my head.
On a Regents exam, unbelievably, you lose a whole point for every problem with a rounding error. There are only 87 points available on the exam. It's a big enough concern that I spend at least half a period on it during Regents review. Now at least I will have something a little fun to kick off the discussion.
I know it's not in the same vein as Dan's stuff. (Which, by the way, even though when you see one you're like "Oh! Why didn't I think of that?" I find a real challenge to invent my own.)
Here's a rough rounding lesson that ties into the video at the end (I'm going to say use playing cards but who wants to keep shuffling? Maybe a short computer or calculator program is better):
Put students into pairs and give each pair cards 1-9 of a single suit. Tell each pair to devise a rule to determine who "wins" for each card that may be dealt and their goal is to make the rule as fair as possible. Each card must make someone a winner (5 can't be a tie or a redo). Have students play something like 30 rounds (shuffling cards after each round) and count how many times each person wins.
Have some class discussion about what rules people came up with and how fair they are based on their "experiment". Maybe someone came up with the idea of dealing a 2nd card if the first card is a 5. If not you can do round 2 of the game where each pair gets 2 suits of 10 cards and every time 2 cards will be dealt and there is a rule to determine the winner for each set of 2 cards.
Ideally what students start to see (maybe you go on to 3 cards etc.) is that if you only deal 1 card there is nothing very close to a fair rule. If you deal 2 cards you get closer to fair, 3 cards you get even closer to fair. The rule students are coming up with is the rule for how to round numbers (ie with 2 cards 49 gets rounded down not up to be most fair).
At this point you could show the video and ask the students if they believe the claim. In math 0 and 1 can arise but in the real world nothing will ever be exactly 0 or 1 (throwback to your perfect cube post and discussion) so rounding will always occur. The more decimals you have before you round the closer the rounding rule will be to fair. The computer calculating the cost at the gas pump will have a finite number of digits so there would be some rounding error. Even so the rounding error would still be more like a thousandth of a cent rather than a tenth of a cent given the number of decimals involved before the rounding.
Off: you can add this to the list, probably.
Berkeley parking meter: a math-rich object for WCYDWT http://www.naturalmath.com/index.php?option=com_jd-wp&Itemid=88888996&p=110
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