MIT Massachusetts Institute of Technology

The Art of Approximation in Science and Engineering: How to Whip Out Answers Quickly

Stephen M. Hou
Ph.D. Candidate
Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139 USA

The purpose of this learning video is to show students how to think more freely about math and science problems. The lesson presents some concepts in ways that students might not have seen in school. In particular, scientific calculations can be tedious and long. Many textbooks and teachers emphasize getting exactly the right answer. But sometimes getting an approximate answer in a much shorter period of time is well worth the time saved. This video explores techniques for making quick, back-of-the-envelope approximations that are not only surprisingly accurate, but are also illuminating for building intuition in understanding science. This video touches upon 10th-grade level Algebra I and first-year high school physics, but the concepts covered (velocity, distance, mass, etc) are basic enough that science-oriented younger students would understand. One class period is needed to complete the lesson and required materials include a blackboard and chalk. If desired, teachers may bring in pendula of various lengths, weights to hang, and a stopwatch to measure period. Examples of in- class exercises for between the video segments include: asking students to estimate 29 x 31 without a calculator or paper and pencil; and asking students how close they can get to a black hole without getting sucked in.

Stephen Hou enjoys learning new things and teaching a variety of subjects. He is a recipient of the Goodwin Medal, MIT's highest award for excellence in teaching by a graduate student.

The website of Dr. Sanjoy Mahajan, the Associate Director of the MIT Teaching and Learning Laboratory, has many relevant materials, including a draft of his textbook on approximation in math and science.

Calculation tips from the Math Forum of Drexel University.

This site comes from BEATCALC and provides a few simple rules for doing mental math tricks faster than they can be done using a calculator.

"Telling lies to describe truth: Do we emphasize the importance of 'the art of approximations'  to the students?" An article by Prof. M. Jagadesh Kumar, Chair Professor, Dept. of Electrical Engineering, Indian Institute of Technology, New Delhi

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