So I’m looking at this ladder and I’m wondering why they positioned the spreader at that exact height off the base and at that exact length.

I know that OSHA and ANSI each have lengthy manuals governing every dimension of a ladder. I figure there must be some kind of specification for those spreaders, something involving angles, geometry, maybe some trig if I’m lucky.

Maybe I’ll ask the students where they’d find the spreader on a 15-foot tall ladder and at what length. Then I’ll go find a 15-foot ladder and photograph it to verify their answer.

Or maybe we’ll develop an algorithm together, converting our intuitive sense that this ladder isn’t safe into a formula for the safe construction and placement of a spreader.

It Got Away

So I check the OSHA manual for stairways and ladders. Nothing on spreaders. Then I call Werner Ladder Co. to see if they have some kind of internal specification on the spreaders. Two days later, an engineer calls back to tell me that, nah, the spreaders are pretty much irrelevant to safe ladder usage. They only exist, this guy tells me, to guide the sides of the ladder to a specific location, at which point your body weight – not the spreader – keeps the ladder’s position fixed.

So I’m in Colchester, VT and I’m noticing the license plates.

Three letters followed by three numbers. Every time. The second you fix a format like that, you’re dealing scarcity. Just like in Costa Rica, I’m wondering, “How many license plates are available?” I’m also wondering, “Is it possible to determine the order in which those plates were issued? Can we guess it?”

Then one of the teachers at the school where I’m facilitating the workshop mentions that the first license plate issued was “AAB100” and that Vermont only recently issued “F-----.” Now we’re on our way to a timeline and we’re dealing with the much more interesting question, “When will they run out?”

I needed data. I needed to know when the first license plate in the series was issued and I needed to know what license plate they last issued. I got way more than that.

I called the Vermont Department of Motor Vehicles, which pinballed me around between various confused functionaries until I reached a person who e-mailed me a trove of data, including the one-, two-, and three-letter combinations they don’t allow under any circumstances on their plates. (NSFW, I suppose.) Now we have a scarcity problem with prurient appeal.

So here’s the question:

If AAB100 was issued in January 1990 and if EYT100 was issued in July 2009, when is Vermont going to run out of plates?

You’d have to calculate the total possible plates, excluding the disallowed combinations while respecting the DMV’s various constraints. (eg. you’ll never find a zero in the hundreds place; “FU----” is disallowed while “-FU---” is allowed.) You have to gather some data on yearly issuance of plates. The better the model’s fit (ie. if exactly 60,000 plates are issued every year) the better our mathematical investigation will focus on our targeted skills.

It Got Away

Alas, the model is all over the place.

[BTW: I changed the chart type per Tom’s recommendation.]

So maybe you reduce the data to a single average of 77,229 plates per year and proceed as planned. Maybe you leave the problem at “how many license plates are available?” and set aside the issue of time. Both options kind of bummed me out, though, so I scrapped this one.

So here’s a feature: the WCYDWT lessons that got away from me. It’s important to me you know that for every WCYDWT lesson I spitshine and post on this blog there are dozens that never got off a list of ideas I keep and several more that got off the list and didn’t pan out. This is my eulogy for the latter group, but don’t mistake these posts as accidents of my curriculum development process. They are the process itself. If I don’t chase these paths all the way to their conclusions, I’m pretty sure I’ll stop seeing them altogether.

For instance, here’s a picture of the menu of my favorite coffee shop, Red Rock Coffee.

Here’s a reconstruction of the menu. (Click for higher resolution.) Notice the description of the last drink. “The most caffeine for your money.”

This is pretty great. You have a ton of data on the board: ounces and shots and price. Have your students write some ideas down about how best to measure “the most caffeine for your money.” Obviously dollars and shots need to figure in there somewhere, but you probably ought to divide the dollars by shots and then by ounces because one shot poured over twelve ounces of milk has a different effect than one shot poured over twenty ounces of milk.

Reagan : Russians :: Me : Coffee Shop Proprietors. “Trust but verify.”

And would you look at those lying liars? You get more shots for less cash poured over fewer ounces with a large Cafe Americano – not with the advertised Red Eye. “Math exposes corrupt marketing” is one my favorite angles on mathematical investigation.

It Got Away

Except my wife pointed out to me that the Red Eye isn’t a shot poured over water (like the Americano) or milk (like the latte). It’s poured over coffee. It’s caffeine poured over more caffeine. Which sunk my battleship.

Just watch your step, Red Rock Coffee.