If I had a dollar for every time a student in a math class has asked me "how do I use this in real life?" I'd have a paycheck. But, like it says in the song, "if I had a million dollars, I'd be rich."

I'm asked this most often by Algebra 2 and Geometry students, so here are three things I can show them.

(1) The Rule of 72. Which states, in probably over-simplified form:

"If you take the number 72, and divide it by your interest rate, the result is the number of years it takes for the principal to double."

That's a pretty good simulation of compound interest there, especially for rates around 15% or less. This way students can see how fast a credit-card balance can balloon up, without their having to fool around with the formulas. Once they get the idea, the formulas don't seem so bad.

(2) The break-even point. This is a simulation of a system of two linear equations:

- One is for the money a company brings in via sales. You assume a length of time before the sales kick in (x-intercept) and a sales rate per month (slope).

- The other is for the company's expenses. You translate salaries, leases, utilities, insurance, marketing, etc. into a rate per month (slope) with a fixed value (y-intercept).

The point where the two lines intersect is the break-even point. The area to the lower-left shows loss; the area to the upper-right shows profit. If the students' imagined companies start making money right away, they haven't thought the problem through. Apart from that, any Algebra 2 student can do it.

(3) The blind robot arm. This takes three cardboard tubes (at least two paper-towel size; the other can be smaller), three rubber bands and a pencil. But it takes a minute to put this together.

- It works best if two of your tubes are of different diameters. Because what you will do is cut two slots in each tube and pass a rubber band through each slot. (WyzAnt really needs to allow images here.) One tube on the outside, one on the inside, with a rubber band passing through both. Repeat with the other two bands, so you are surrounding each tube with rubber bands. When you turn the inner cardboard tube, you stretch the three rubber bands until they meet at the center.

- The stretched rubber bands can be used to grab the pencil from a desk or table-top. This becomes your robot hand.

- BUT. The third tube is the scope - the robot vision - that you use to find the pencil.

The experiment works best with two students - one to look through the scope and the other, blindfolded, to operate the hand. The students must judge distances and angles without seeing everything at once, but seeing everything they need to retrieve the pencil. And this is how a live robot arm works.

Students who survive these lessons generally don't ask me about "real life" again. :-)