Organs and Artificial Organs

CONTENTS OF CURRICULUM UNIT 11.07.10

  1. Unit Guide
  1. Rationale and Introduction
  2. Content Objectives
  3. Overview of the Circulatory System
  4. Dimensional Analysis Calculation Demonstrating Heart Reliability
  5. Introduction to Units of Measure
  6. Dimensional Analysis of Graphical Data: Ventricular Pressure vs. Volume Graph
  7. Dimensional Analysis for Evaluating Potential Power Sources for an Artificial Heart
  8. Dimensional Analysis does Problem Analysis
  9. Student Background and Challenges
  10. Strategies
  11. Classroom Activities and Lesson Plans
  12. Standards Alignment
  13. Teacher and Student Resources
  14. Endnotes
  15. Bibliography

Dimensional Analysis: A Mathematics Tool to Dissect the Circulatory System

Richard Cordia Taylor

Published September 2011

Tools for this Unit:

Guide Entry to 11.07.10

In the fall of 1999, NASA announced that it had lost the $125 million Mars Climate Orbiter because the scientists guiding the satellite made their calculations using metric measures, while the computer controlling the orbiter had been programmed using English units. Through all the years of design, testing, and simulations, no one had sensed that anything was wrong until the craft disappeared. Units are what give numbers meaning. Attach the wrong units to the numbers and even the most precise calculation is worthless. As medical technology develops new therapies to replace malfunctioning organs in our bodies as we age or injure ourselves, there will be questions as to performance, longevity, and reliability of those replacements. Will engineers look at the data in precisely the correct way to give them that extra insight? When engineers design these organs, will they make the same mistakes that NASA made, getting all the big pieces of data correct but missing the most basic consideration of knowing what the numbers mean? This unit will guide students into a way of approaching data and getting a feel for what numbers say so that little considerations like the meaning of the numbers get their due.

(Developed for Calculus AP/AB and AP/BC, grades 10-12, and Algebra I Support, grades 9-10; recommended for Algebra I, Geometry, Algebra II, Trigonometry, Calculus, Physics, Chemistry, and Biology, High School grades 9-12 [also appropriate for Middle School])

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