HW / track-meet metaphor

word problem words: 80% -> restore 125% example

x^2-4<=0

basketball metaphor -- few rules, many games; many paths to hoop

write down what you do know; view improves
- Hiking metaphor
- Very shot problem -- do in head.
- Short problem -- short hike.  See the stop sign; walk toward it.
- Longer problem -- can't see goal.  maybe over next hill.
  Write down what you do know & simplify -- like climbing to top of next
  hill and now you *can* see your destination.
- Very hard problems -- you don't even know what to do.  Write down what you
  do know; draw a picture; simplify; use techniques from other problems you've
  seen; guess; check; ... .

- write what you *do* know and what you *don't* know.

  > For the former, split into useful and not, as much as you can tell.
    E.g. the name of the town is Maple Grove -- so what?

  > For the latter, split into what you need to find, and what you don't need
    to find.  Example: Ce^kx problems where you only need to find k, not C.

- what *kind* of curve, before writing down eqn

problem-solving list
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units: dimensional analysis
- helps w/ setting up problems
- helps w/ spotting errors

curve fit: # points & # params -- e.g. mx+b, Ce^kx
- check w/ calc'r!  always! tbl & grf

# decimal places:

- usu. 3 for final answer; retain lots for intermediate calculations

- retain hundredths of percents for interest-rate calculations

- careful rounding 1.000001 down to 1.0 for exp growth problems -- ln(0)!

- rough rule of thumb: # DP out ~ # DP in.  Full answer requires numerical
  analysis which is past freshman math.  Give an example w/ two lines;
  suggest that outerr vs. inerr deps on slope of func.