That's the Way Mr. Chips Crumbles

This is usually where I write the paragraph that makes it appear as if I’m writing about one topic, before I swerve into the real topic. But first, a confession: my jones is getting the best of me. I made it for a couple weeks drug-free, but I’m back on the ‘roids. Next thing you know I'll be skulking in dark alleys looking to score....

One of my qualifications for writing a blog is the variety of my life experiences. OK, I'll be honest, my primary qualification is that I have an Internet connection, or at least that’s the only commonality I’ve found among the other blogs I’ve read. Even the ability to write a coherent (or interesting) sentence in English, or any other language, is not a prerequisite.

Anyway, I’ve done everything from working backstage at a tiger show to cleaning toilets as a church custodian, not necessarily in increasing order of fascination. But much of my career was spent teaching math.

One of the reasons I quit was because I probably got more affirmation and positive feedback from the tigers than I did from the students (or my colleagues), but there were at least three notable episodes that still give me a slightly warm & fuzzy feeling.

The first was during my abbreviated high school teaching career. I had an honors-level Algebra II class, and for a unit on systems of equations, I asked them to write their own word problem using three equations with three variables. One young lady asked me, “Does it have to come out even?” I suggested that she change her numbers slightly to make it "come out", and she said, “But then it wouldn’t rhyme!” She had written her word problem in verse, a rare instance of my being faced with excess creativity.

The second instance was in a Calculus II course – the highest level I ever attained. There was a local high school student taking the course. There was no single tipoff, but slowly I recognized this kid was sharp… in all likelihood, smarter than me. Not to sound pompous, but in the low-level courses I usually taught, it was unusual to catch that flash of intelligence. He made me raise my game; I knew if I wasn’t absolutely on top of what I was discussing, he’d catch me.

And one pretty minor episode that nonetheless still tickles me: in a math for non-majors course, we were talking about “number tricks” -- like, take a number, add 3, double it…. So I had them pick their own number and follow along as I went through the steps on the overhead, and when I unveiled the last line – “The answer is 5” – there was an audible and almost unanimous gasp. Made me feel like David Copperfield or something.

I was reminded of that earlier this week when a friend sent me a link to a number trick on the Web. Once you've checked it out, you might be interested to know how it works:

• If the digits of a 3-digit number are a, b, and c, the value of the number is 100a+10b+c.
• Scramble the digits, for example ‘bca’, which has the value 100b+10c+a. If you subtract one from the other (assume ‘abc’ is larger, it doesn’t affect the conclusion), you get 99a-90b-9c.
• Since I can rewrite this as 9(11a-10b-c), it’s clear this number is a multiple of 9 (or divisible by 9, if you prefer).
• From number theory, here’s the deal about numbers divisible by 9: the sum of their digits is also divisible by 9. So if you tell me all but one of the digits, I can subtract that sum from the next-larger multiple of 9 to find the missing digit. Note the insistence that you don’t omit a zero; if I leave out a zero, you can’t tell whether the missing one should be a zero or a 9.
  

Example: 286, reshuffle to 628. Difference is 342. Sum of the digits is 9, so if you tell me any 2 digits I can subtract from 9 to find the missing one.

Example 2: 8594, reshuffle to 4859. Difference is 3735. Sum of the digits is 18; if you give me 335, sum is 11, 18-11=7.

So as you can see, your high school algebra teacher was right: algebra is vitally important to … let me think... no, I was right the first time -- it's the Foundation of the Universe.