High School: Number and Quantity
2. Define appropriate quantities for the purpose of descriptive modeling.
You've assigned your math class a set of word problems. One of the questions ends with, "How many people voted for candidate Jones?" Fingers fly over calculators as your students try to determine the correct answer. After a minute or two, Tommy raises his hand and announces his answer: 4,602.28
Everything inside of you wants to scream, "Are you out of your mind, Tommy boy? A closer answer would be 4 because at least it would be possible! How on earth could a candidate receive 28 hundredths of a vote?"
Okay, breathe. Poor Tommy has made the kind of error that drives math teachers like you to the brink of insanity. He's given an answer that makes absolutely no sense.
Whatever else math is or isn't, it is always logical. Answers should always make sense. Math frequently relies on general knowledge—concepts that we assume are known by everyone over the age of about seven—along with a healthy dose of common sense (not you, Thomas Paine).
The problem, of course, is that people have a tendency to ignore both common sense and the knowledge that they possess. Particularly when calculators are involved, there's the tendency to run with the answer you're given. That ignores one very basic principle: the calculator answers the question you ask, not the one you intended to ask. Every answer, every step along the way, should always be reality-based. Make sure your students know that.