Saturday, November 5, 2011

Million-dollar division problem

When pressed, I'll reluctantly admit to be a sucker for reality shows.  While catching up on The Amazing Race, I came across this scenario.

Brian and Ericka are presented with a choice: Construct 12 hookahs or weigh out $500,000 worth of gold using the current price per ounce.  They choose the latter (wouldn't you?).  They find themselves in a room with a lot of gold, a scale, and a screen telling them the up-to-the-minute price: $934.75 per ounce.



The first thing they need to figure out is what to do with the numbers $500,000 and $934.75.  Fortunately they are able to answer this (another team had a harder time), but now they're stuck with a long division problem, something with which former Miss America doesn't feel confident: "My American education has dumbed me down to use a calculator for everything."  Plus, the rate just changed: $941.25/oz.



Now, take a moment to appreciate that a long-division problem is standing between them and their goal of winning $1 million.  Ericka had a point: how many students are graduating high school with competency in arithmetic?  I'm guilty of allowing too much calculator use in my classroom as well, having uttered justifications like, "It lets students stay focused on the higher-order concepts..."  This may be true and appropriate at times, but my students would have benefited from more arithmetic thrown into the mix.



Have your students work against the clock, giving them a new divisor every so often.



Poor Brian and Ericka eventually gave up - is that what your students would do?

2 comments:

  1. So how do you do long division quickly? I'm an English teacher who tutors for a living. There aren't many teaching jobs in Vancouver for English majors and I find myself teaching more and more math these days. I keep telling myself there's no such thing as a dumb student, only a lazy one. Some of the students I teach have learning disabilities and are so demotivated by the daunting task of either simple double digit multiplication or division that they don't want to do it. They are already in high school, and a grade level behind. How do you deal with that other than patiently encourage them to practice more?

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    1. Granted, the division problem above is extremely tedious. But this is just a quick motivator - not an end unto itself. Personally, I don't care for arithmetic much, and I think it's much more valuable for students to be able to estimate well (this is not to say that double-digit multiplication isn't an important skill, but too much rote at a time will kill anyone's enthusiasm), so I do a lot of estimation problems to keep them going. Show a picture of a display of cans at the grocery store - "how much do you think this display weighs?" Give them some time and resources to get a good estimation. "Oh, by the way, I don't know the answer" Have them present their thinking. To build proficiency with arithmetic, speed drills are helpful (and short), especially if they can see their progress over time. Think about why they're being lazy - what would they rather be doing? Can you work that into a problem? Most importantly, find applications that you find interesting - if you don't care about the process, the kids won't either. I like worldometers.info to get me thinking about possible problems.

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