Friday, August 26, 2005

No need to solve for X

Jay Tea over at Wizbang linked to a Boston Globe story about the math question that stumped the most students on the Massachusetts Comprehensive Assesssment System (MCAS) test. Here it is:

Of the people in attendance at a recent baseball game, one-third had grandstand tickets, one-fourth had bleacher tickets, and the remaining 11,250 people in attendance had other tickets. What was the total number of people in attendance at the game?
A) 27,000
B) 20,000
C) 16,000
D) 18,000
Jay provides an extended answer and writes that he had the solution in “30-40 seconds.” Not to brag, but I had it in about one. One-third plus one-fourth makes up more than half of the baseball fans, so the remaining 11,250 comprises less than half. If that share is less than half, the total is more than double 11,250 making (A) the only reasonable answer.

Is that so hard? Still, with paper, pencil and calculator at hand, half of all Massachusetts students missed the question. Considering that random guessing would produce a 25% success rate, the 50% level is a little startling. What would Danica say?

As I like to say, there are three kinds of people in the world: those who can count and those who can’t.


Linda said...

I solved the problem the traditional way, using my Algebra skills, but I like your logical solution better.

Either way, it shouldn't have stumped the students. But, it doesn't surprise me - I teach Physical Science to 9th graders, and MOST of them are freaked out by anything related to fractions, decimals, or long division. Which eliminates all but a few elementary problems.

I'm pretty patient - I show them how to set up the problem, talk them through some examples, and am OK with repeating the instruction over and over for weeks (sometimes months). At some point, it clicks.

It's a great moment.

I referenced your blog post on Technology in Teaching

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