Real world questions and story problems
Story problems are generally:
translate into arbitrary equation, then solve equation.
"""
And then the people talking about "real
world problems" make up a book where you have a swimming pool...that's
conically shaped. And of course it's getting filled at 2 gallons per second. And of
course because it's the real world, you desperately want to know what the
volume of the water is at 30 seconds.
"""
What's the underlying point of "real world" questions?
- motivation: students care more
(fun EG: computing road camber so cars don't flip,
or computing Superman's torque)
- *intuition*: giving equations with *meaning*:
so you can (easily!) judge if the answer "looks right"
Crucially, *you need to explicitly encourage this intuition*.
It's not enough to give a question and expect people to see the intuition:
you should give questions and explicitly ask
"what *should* the answer look like?"
(big/small, positive/negative, etc.)
This is the deeper point behind "estimation" questions.
EG of estimation:
what's 61*42?
Well, it should be a bit *more* than 60*40 = 2400
(more precisely: about 60*40 + 3*50 = 2550)
(indeed it's 2564)
Subtler EG: what's 61*39?
It should be *very slightly* less than 2400 (2379)
...and 59*41 is *very slightly* more than 2400 (2419)
Deeper point here: linear vs. quadratic term
Also: not just "estimate", but notion of the *type of error*
(smaller/bigger: about how much?)