Choosing a Unit of Measurement
Date: 05/06/2002 at 21:05:08 From: Karen A. Olenych (Mrs. O.) Subject: Proper unit of measurement to use when measuring butterflies Hi! I am a second-grade teacher at a DeSoto County, Florida elementary school. My students just took the County's math assessment and faced this question (worded something like this): If Sue were to measure the length of all the butterflies in her collection, which would be the best unit of measurement for her to use? a-millimeter b-centimeter c-kilometer I observe butterfly and moth biology for a hobby and could not figure this one out for myself so went home and consulted some standard field guides including Audubon's, Peterson's, Simon and Schuster... Some of the guides gave approximate wingspans in centimeters, while some did in millimeters. I expressed this fact to my County administrators, thinking there was a problem with the answer choices to the question. The County claimed the test question was valid because in math, generally, the unit used to measure an object is the one that is the smallest possible unit where the object is not less in length than the unit in question.... I think I am getting the wording mixed up here... For example, by this argument, one would measure a car's length in yards, not inches, feet, or miles. The county also said that second graders were not responsible for understanding measurement in millimeters. I need to check on that too. I am surprised that they did not care to invalidate the question. Some of my students chose cm and some chose mm. Please send me some sort of help for this situation. I am looking for an outside, objective opinion. Thanks!
Date: 05/06/2002 at 22:28:26 From: Doctor Douglas Subject: Re: Proper unit of measurement to use when measuring butterflies Hi Karen, and thanks for writing. I'm not exactly sure I understand you here. If the object is *not* less in length (emphasis mine), then we should always choose the smallest unit (e.g. micron, or nanometer, or even smaller) possible. I think probably what is meant is that one should choose the *largest* unit such that the unit (e.g. yard) fits at least once into the object (e.g. car). Having said this, I don't believe that this rule is the best one to use. In my opinion, one should use the units that give the most convenient numbers, or are consistent with what other people use. In other words, while it is true that cars might be "best" measured in yards (and give nice, small numbers such as 3.18 yards), what is often relevant is how that object compares to OTHER objects in various contexts: How many (thousands of) feet to the toll booth? Is my car too big for my garage? Am I parking too close to the stop sign? Here it becomes clear that feet are probably more convenient than yards, because of the variety of contexts in which we need to know the dimensions of cars. After all, it's rare that we're driving a car on a football field. Now, what would be "most convenient" for the measurement of butterflies and moths? Here I would probably lean toward cm, because to adequately measure the spread in different sizes, the cm seems to be the most natural unit in that most butterflies and moths that I know are somewhat bigger than a centimeter. However, if there were a multitude of butterflies with wingspans under one cm (or perhaps we are interested in their sizes at various stages in their growth), then I would probably lean toward using mm. I think the County question is poorly written, because both cm and mm seem to be natural choices. If instead the mm is changed to "micron" or something quite a bit smaller than a butterfly, then the "correct" answer would be clear. - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/
Date: 07/16/2002 at 23:42:17 From: Doctor Peterson Subject: Re: Proper unit of measurement to use when measuring butterflies I agree with Dr. Douglas that millimeter and centimeter are both perfectly reasonable units for this case. It's not clear to me whether the problem deals with length or wingspan, but in either case most butterflies will probably be in the range from a centimeter or two to ten or twenty centimeters at the most; and in that range, both units will give small numbers that are reasonably easy to handle. In my mind the "best" unit would be one for which all commonly found values will be greater than 1 (to avoid needing small numbers like 0.43, where the decimal point is easy to miss. But also, in many cases, I would like a unit that gives reasonable precision without needing a decimal point at all. I might prefer to say 12 mm rather than 1.2 cm. Moreover, for some purposes centimeters are to be avoided. The SI metric system recommends keeping to powers of 1000, avoiding "centi-": How Many? A Dictionary of Units of Measurement - Russ Rowlett http://www.unc.edu/~rowlett/units/prefixes.html The prefixes hecto-, deka-, deci-, and centi- are widely used in everyday life but are generally avoided in scientific work. Contrary to the belief of some scientists, however, the SI does allow use of these prefixes. So rules besides the "small number" rule may make us choose millimeters rather than centimeters, just as Dr. Douglas pointed out that we should use whatever units are commonly used by others. In particular, if, say, the wingspans of eagles are typically in the tens of centimeters, we would not choose to use dekameters, both because that is a rarely used unit, and because eagles are likely to be compared to, say, sparrows, which would certainly be measured in centimeters or millimeters. If this much can be said about a problem, then it is certainly too ambiguous! -Doctor Peterson http://mathforum.org/dr.math/
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