Google says $1-$4 an hour depending on engine size. Even with childhood obesity I suspect school bus engines are on the low side, let’s say $30 to idle from 4pm one day to 7am the next. So far it is fun but trivial arithmetic.

What gets interesting is estimating the cost of getting the things started if we let them drop to ambient temperature — diesels are not like gas engines, so we prolly cannot get them started without heating them externally which will take so long that (a) the cost of the mechanic getting them started blows away the fuel cost and (b) we are adding the risk cost of kids standing in the cold waiting for buses that are not coming.

At this point $30 a bus (a dollar a kid) looks like — well, let;s just say the district and its fleet mechanics knew what they were about.

Here’s a fun one: some Europeans I met said the law required them to turn their cars off at a red light. I asked if anyone had worked out how much extra fuel it cost to restart an engine compared to idling — starting takes quite a gulp. They all yelled out the answer together. Left as an exercise.

-kt

The question burning in my mind is ‘was it worth it,’ but the modeling gets hopelessly complex to the point where you would have to give kids too much information. They would have to account for the cost of a mechanic to fix a bus that won’t start, find some way to measure the cost of a kid not getting to school because the bus won’t start, etc, and then take the probability of that happening into account…not the kinds of calculations that are readily approachable

It seems like this could lose ‘authenticity’ really quick with kids that might not have engaged that question. You could take a great context and blow it pretty quickly that way

As a lower middle school task (Grade 6 or 7), we could get pretty hands-on with the question ‘how much did that cost’

Take the kids outside, let them start the bus and monitor the gas level for thirty minutes of idling (or do it in a video yourself), and then scale that for the overnight and the size of the fleet. Multiply by the cost of gas and you’re there. I would want to let kids make assumptions about the size of the fleet, the hours each bus was left on, and the cost of gas. Discuss how the assumptions affect the model.

Sounds like gwe are hitting SMP.4 there as well as some pretty in-depth ratio analysis…

“What was the cost of this idling bus decision – economically, environmentally, and socially?”

If students can prove that the optimal choice would be to declare a snow day it would answer why they should learn algebra.

I jokingly submitted “The amount of black ice formed from the exhaust pipes when water is generated from combustion.” on Twitter as a terrible question. It’s bad for the reasons Dan just described (basically a poor camouflage for calculations).

I don’t have a problem with students needing to search online for info, as long as they’ve been training to sort through all of the bad info they get. I know Language Arts teachers have to teach kids to do this now, and maybe it’d be good for some math/science training too.

Maybe it’s better (like Sammy said) to leave the question at “Is it worth it?” so that the kids can decide how to define the question. But then, it still could be a poor mask for doing calculations.

An interesting question is this: how do you know whether you’re right? The more interesting question is this: did the *adults* do the math?

Somewhere in the bowels of the the school (county?) office, is there an excel spreadsheet? It takes a few variables – number of busses in the fleet, gallons per hour, cost of diesel, cost of a snow day, and spits out a yes or no.

An intriguing (if high risk?) exercise would be to divide the students into groups. Have them discuss what variables would go into that spreadsheet and why. Have each of the groups write a letter to the district office explaining what factors they think are relevant and why, and asking for a response explaining how the actual *adults* made that decision.

If it turns out that the adults do, in fact use some sort of math, then you can have the students play with it and try to understand why the adults did what they did. If not, maybe have the students propose something?

re Molly: “I”m not sure calculating the cost would actually be the point!”
Too often, our reflex in math is “what’s the answer? Am I right?”
Calculating the cost is simply the period at the end of the sentence. The glory lies in the sentence, in the construction, in the overcoming of itchy, scratchy puzzlement that happens up to the period that ends the sentence that brings the problem to closure.
The idling bus problem is thick with potential. You can spend lots of time just estimating and defending and revising. Every step of the problem is begging you to critique the reasoning of your peers.
As an ancillary to this you might have a mini lesson called How cold is cold?”(here come integers)
We keep math questions sequestered in discrete chunks of calculations because those are the ones that bring the fastest closure.
I think someone commented on the Magic Octagon, or some other one with, “great, where’s the lesson?” The lesson is in your ability to see and hear and dream up the long and diversified narrative that can spin out of such problems.
What’s kind of shape was that hand holding?, How did you know? Draw an octagon, draw a regular octagon, how many degrees are in an octagon?, Hey, how do you use a protractor, and on and on unto a full problem.

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