Metric Conversion ChartDate: 07/17/97 at 15:24:29 From: Carrie Brzozowski Subject: Conversion chart Dear Dr. Math, I am an 8th grade math teacher and I teach my students how to convert within the customary system and within the metric system. I want to know if you know of a conversion chart where I can convert from metric to customary and vice versa. Thank you very much. By the way, are you a real person? Carrie Date: 07/19/97 at 01:08:26 From: Doctor Terrel Subject: Re: Conversion chart Dear Carrie, I am a 7th grade math teacher and I also teach my students "conversion" work of various kinds. You say you teach conversion "within" the two systems, but need help "between" the systems. Since I don't know how you teach within a system, that is, exactly what procedure you use (there are several writing methods), I will simply show you how I do it. It is different from the ways shown in my current textbook [UCSMP's Transition Mathematics]. I call it the QFP method. Several people to whom I've shown it like it and do it with their students. Here is a typical example. Change 14 inches to centimeters. First, one must know the basic relation between inches and centimeters: 1 in. = 2.54 cm. Now I ask my kids, "What's the question before us?" Answer: how many centimeters are in 14 inches. So we write: Qstn: ? cm = 14 in. Next, "What fact do we know that connects inches to centimeters? Ans.: 1 in. = 2.54 cm. So we write: Qstn: ? cm = 14 in. Fact: 2.54 cm = 1 in. This presentation begins to look like a "proportion", doesn't it? [This implies the students must have a little background about basic proportion solving; otherwise, this is a good time to teach a little bit about it, because here is a USE for it.] So we write: Qstn: ? cm = 14 in. Fact: 2.54 cm = 1 in. x 14 Prop: -------- = ------ 2.54 1 x = 2.54 * 14 [by cross multiplication, or any other phrase you prefer] x = 35.56 So 14 inches is 35.56 centimeters. Later we discuss whether the 35.56 should be rounded or not. Technically it should, if the 14 in. was a humanly made measurement. No such measurement is ever "exact". Although the in/cm conversion factor is an exact one, it is so by definition; the others, such as mi/km, lb/kg, etc. are not exact. Here I tell my kids to say "about 36 cm" or "about 35.6 cm"; and the "about" is required. Another example with inches/centimeters. Change 45 cm to inches. We proceed as before. Qstn: ? in. = 45 cm Fact: 1 in. = 2.54 cm x 45 Here I like to point out Prop: ------- = -------- the"criss-cross" model is 1 2.54 unnecessary, if we look at the equation cerefully. x/1 = x, so we have x = 45 / 2.54 x = 17.716535 Now the necessity of rounding is more obvious. I suggest an answer statement of "45 cm is about 17.7 in." When I was a lad in the early '50s, studying conversions (usually within the customary system only; we didn't worry about metrics in "them days"), I could never remember whether I should divide or multiply when going from larger to smaller units or vice versa. [And I had no Dr. Math to turn to!] But when I learned about proportions, via slide rules (the predecessor of our calculators today), all my troubles vanished. The proportion "told" me what to do if I could get it set up by what I now call the QFP method. Piece of cake... By the way, QFP works within systems, too, but it is admittedly less useful within the metric system. It's great for converting between unfamiliar monetary systems, though. Now, Carrie, I hope this helps you a little bit. Try it, and let me know. All you need are some more relations between metric and customary units, which can be found in most textbooks, even dictionaries. As to your final question... Asking if Dr. Math is a real person is like asking if Santa Claus exists. As Santa Claus is the collective spirit of many good people doing good things for many others, Dr. Math is a collection of math volunteers ("elves," as it were) dedicated to helping all you kids, young and old, out there with your difficulties in math. Yes, I am a real person. Thanks for asking... -Doctor Terrel, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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