Phil said "I don't have a problem with problems with non-intuitive answers, but
what I don't like about the potato salad problem is that it describes an absurd
situation."
This is really my point. Non-intuitive answers are acceptable - probability in
particular has a way of sneaking up on you. But when it's presented in a
situation with which the student is familiar and throws a curve this way it's
particularly sneaky!
BTW - the plane problem below.. 2h 5 min?
______________________________ Reply Separator _________________________________
Subject: Re: [MATHEDCC] Have you heard this one? Another good proble
Author: mathedcc@archives.math.utk.edu at CCNODE
Date: 4/8/97 12:27 PM
I'm enjoying the potato problem - not because I like the problem itself,
which actually I don't.
I agree with Jack Rotman and others that the answer is 250 lb, a
surprising answer.
But the discussion is more interesting than the answer. A lot of us
feel like our students do when confronted with a new type of word
problem - finding multiple ways to get a number, and afraid that
an answer is not correct. Reinforces my personal opinion that in fact there
is no universal word problem solving method, but that there are classes of
problems, and each has its own techniques for solving.
And I guess we have modeled group problem solving behavior too.
I don't have a problem with problems with non-intuitive answers, but what I
don't like about the potato salad problem is that it describes an absurd
situation. How does someone know that the water went from 99% to 98% water,
overnight or whenever? Take it to a laboratory?
An equally interesting problem, more realistic, might be something
like: A batch of 500 lb. of potato salad is 99% water by weight. After
some time sitting around, the weight decreases by half. How much of
this stuff (I hesitate to call it potato salad at this point) is water,
by weight?
Of course this one is easier to solve, so it doesn't have the benefit
of being a real exercise in problem solving.
I'd be interested in the potato problem if it somehow modeled a more
realistic situation, and I'm sure one exists.
Another non-intuitive problem I like, more "realistic", is the airplane that
can fly at 100 mph in still air. It makes regular sight-seeing trips between
two airports that are 100 miles apart, without landing. On a certain windy
day it flies between the two airports. Going, into a 20 mph headwind, and
coming back it has a 20 mph tailwind. Neglecting turning time, what is the
flight time?
Phil Mahler
Middlesex CC
Bedford, MA
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