I’m pretty sure people do actually do Maths based on such situations as the boiling point one. There are several web sites that talk about how to calibrate thermometers based on the boiling point of water at a given altitude.

One even gave this piece of information “The boiling point lowers about 0.6ºC (1ºF) for each 168 meters (550 feet) above sea level” which I think is a nice context for linear graphs.

Oo. Yeah. This all seems really constructive. Let’s do this in the future.

You could also invert the question the other way say “In xyz scenario, which one of these would be most helpful: mean, median, mode, range, or standard deviation?” If you’re lucky, you’ll start an argument during which the students have to explain why their choice is best.

Are there any circumstances when you care about the mean, median, mode, range, and standard deviation of a set of numbers? I can think of contexts where you care about a couple of those, but all of them? That’s hard.

And if I can’t think of a context where the task is necessary, does that mean the task is bad in some way?

We should just make the animals be gelatinous cubes — then the right kind of model is pretty obvious but at least it’s a more entertaining problem: You’re on a dungeon crawl and you encounter two gelatinous cubes, one 4m on a side and one 6m. You have {insert name of coldness spell here — Cone of Coldness I think?}, which will decrease the temperature of the air around one of the cubes to {some temperature} for {some number of seconds}. Which cube will get the most damage from this spell and why? How much damage?

How stuff scales for biology is pretty damn interesting regardless of the shape of the animal, so you can do some simplifications in the modeling. Sure, it would have been nice if you left that part out, and had the students do it as part of their modeling, but its’ not the worst case of pseudocontext I’ve seen.

The chapter on modeling with logarithmic functions from my Algebra II textbook, on the other hand, was complete ass. There wasn’t a *single* problem where the kids had to actually figure out a model – they just verified that the numbers in a given table matched a provided function. I skipped it, because ass. Will hunt down actual real world data sets and have them decide on the models instead.

Nevermind, I answered my own question. Dang Romans. (I knew “rectangle” literally means “right angle”, but I didn’t know the below.)

Carry on, sir.

From etymonline:

rectangle (n.) Look up rectangle at Dictionary.com
1570s, from Middle French rectangle (16c.) and directly from Late Latin rectangulum, from rect-, comb. form of Latin rectus “right” (see right (adj.1)) + Old French angle (see angle (n.)). Medieval Latin rectangulum meant “a triangle having a right angle.”

From le-dictionnaire: Définition du mot :
rectangle

Adjectif singulier invariant en genre
(géométrie) qui possède au moins un angle droit (triangle rectangle)

Nom masculin singulier
(géométrie) figure possédant quatre angles droits et quatre côtés égaux deux à deux