From: Gary Horne (gary@horne.cc)
Date: Sun Jun 29 2003 - 09:03:15 PDT
Date: Sun, 29 Jun 2003 09:03:15 -0700 Subject: Re: pinhole Re: significant figures From: Gary Horne <gary@horne.cc> Message-Id: <3124DFC6-AA4B-11D7-99A7-0030654C6092@horne.cc>
This is a great idea! I love it!
Am I right that we regularly are victim of a sig fig error? I think I
heard that, originally, average body temperature was calculated at 37
degrees celsius (2 significant figures). This was converted to 98.6
degrees Fahrenheit which has 3. Thus, that .6 is misleadingly
accurate. (For example, if the average human body temp is REALLY 37.3
degrees C and just didn't get measured that way, it would convert to
99.14 degrees F)
Perhaps finding errors of accuracy in news reports would be an
interesting application of significant figures.
g
On Sunday, June 29, 2003, at 08:32 AM, Ellen Koivisto wrote:
>
>
> 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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