From: Ellen Koivisto (igneous@earthlink.net)
Date: Sun Jun 29 2003 - 08:32:13 PDT
Date: Sun, 29 Jun 2003 08:32:13 -0700 Subject: Re: significant figures From: Ellen Koivisto <igneous@earthlink.net> Message-Id: <DB87206C-AA46-11D7-B68F-000A959C38A8@earthlink.net>
Something like this works best if the students have experience with
cooking, though any practical measuring skills in real-world
circumstances will do (carpentry for example.) And, if you're
particularly sadistic, you can combine studying sig figs with the need
to convert from one unit to another -- I usually do.
Give students a cookie recipe, such as for chocolate chip cookies.
This recipe uses teaspoons, tablespoons, cups, cubes and/or ounces, a
pinch, and eggs and a bag as measuring units. Now give each student a
different measuring device. One gets a 1/2 teaspoon, one gets a single
cup measure with no graduations, one gets a graduated pint measure, one
gets a teaspoon, one gets to use only their hands, etc. They don't
even have to try to make the cookies. They just have to look at the
recipe and their measuring device (and have some experience cooking)
and then try to figure out what their cookies would be like if they
made them using only the one measuring device.
The conclusion to lead them to is that your measurement can't be better
than your measuring device. A student can certainly eyeball the
ungraduated pint measure and use a calculator and say that the
miniscule amount of baking soda she put in there is 2.16 x 10^-3 pints,
but she can't prove it using the measure she's got. This leads to the
point that, when calculating using measured amounts, you can't have an
answer that's better than your worse measuring device. If your worst
measuring device only allows you one sig fig, only one number that you
actually measured and that you're sure of or can pretty fairly
estimate, then any calculations you do using that number can only end
up with an answer of one sig fig.
Usually a fairly interesting discussion follows this prompt and I
always get at least one student who says then that the smallest
measuring unit is the best one to use. That's when you have them
measure the longest hallway in the school using different measuring
units. One group measures it in meters, one in centimeters, one in
millimeters, one in inches, one in yards, one in miles, one in body
lengths, one in strides, and one in hand spans. The groups with the
easiest measuring tasks have time to measure more than once, to
standardize their method of measuring to analyze how accurate and how
precise their measurements are, and to compare measurements (I love it
when they do conversions because they want to.) The groups with the
smaller and less standard units have less time because their task is so
time consuming and because they have to figure out just exactly what
their unit is and how to measure with it. Then we put all the results
on the board, analyze them together as a class, figure out how to
convert them so we can compare them, and then try to figure out just
how long the hallway really is.
The whole point of this set of exercises is to get the students
thinking about the numbers they're going to be throwing around all
year. It seems to work.
Ellen Koivisto
SOTA, San Francisco
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