MIT Stem Pals
March-April 2015

Orders of Magnitude
From Richard C. Larson

Dick LarsonSTEM education should include a healthy dose of students learning to estimate orders of magnitude in various settings. And it’s best if these estimates are with pencil and paper, not calculators, since experience has shown that relying on calculators reduces a student’s intuition for identifying decimal placement errors.

We have BLOSSOMS lessons that feature orders of magnitude, including “How Big Is a Mole? Do We Really Comprehend Avogadro’s Number?”, and “The Power of Exponentials, Big and Small”.

Any teacher who reads the news can find examples from daily life that bring up orders of magnitude. And the math of daily life can often lead to related aspects of science and then to serious policy discussions.

reservoirOne of my favorites: Twice in the past three years the City of Portland Oregon has emptied an open reservoir because someone was found urinating in it. This is 38 million gallons of water dumped from a Mount Tabor reservoir because of a 19-year-old male’s one-time urination. The human bladder has capacity for up to 24 ounces of urine, but the urge to urinate comes when the bladder is about 25% filled. Even at the upper bound of 24 ounces, since one gallon equals 128 ounces, the maximum amount of urine from this event is 24/128 = 18.75% of one gallon.

A wonderful science/math project, in line with the objectives of both Next Generation Science Standards (NGSS) and Common Core Standards, would be to assign students to perform an analysis of this situation. Did it make sense for the City of Portland, Oregon twice to dump 38 million gallons of drinking water because of a one-time human urination event? The students need not limit their analyses to numbers, fractions, densities and percentages. They can “work out of the box” and research the types of birds and animals whose habitat includes the Mount Tabor reservoir environment (biology). For example, the Portland Audubon society reports that about 200 species of birds make the Portland area part of their living environment during the year. And, representing mammals, we understand that Portland has coyotes, raccoons, deer, skunks and more. Students could “ballpark” estimate the volume of bird and animal waste that must routinely find its way into the reservoir, apparently with no negative effects on the humans who drink the (treated) water. Then they need to examine the water treatment (chemistry) and its effectiveness (biology). They could compare their estimates of biological waste from natural sources to that on the one-time human urination event—and draw conclusions. Then, it they wanted to expand their research, they could estimate the total area in square miles of open reservoirs in the U.S. today, estimate the volume of bird, animal and other biological waste that enters these systems, and reach a conclusion as to whether this is alarming or an acceptable risk.

I can't wait to see their work! In fact, we will publish the best two or three student analyses that are submitted to STEM Pals!

Richard Larson is the Mitsui Professor of Engineering Systems at MIT. He is also the Director of MIT LINC and the Principal Investigator of MIT BLOSSOMS.

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