Bone Density Math and Logarithm Introduction
Exponential and logarithm graph.Copyright 2006 Kristyn Shaffer, Vanderbilt University
In their reading from activity 1 of this unit, students should have discovered the term "logarithm." It is at this point that they begin their study of logarithms. Specifically, students examine the definition, history and relationship to exponents; they rewrite exponents as logarithms and vice versa, evaluating expressions, solving for a missing piece. Students then study the properties of logarithms (multiplication/addition, division/subtraction, exponents). They complete a set of practice problems to apply the skills they have learned (rewriting logarithms and exponents, evaluating expressions, solving/examining equations for a missing variable.) Then they complete a short quiz covering what they have studied thus far concerning logarithms (problems similar to the practice problems). They consider how what they have learned moves them closer to answering the unit's challenge question.
Students learn the equation needed to calculate bone mineral density, which is a calculation that biomedical engineers make all the time. Through this lesson, students come to realize that they have not learned all the necessary math skills in order to calculate bone mineral density but gain the motivation to learn about logarithms.
After this lesson, students should be able to:
- Define logarithms as exponents.
- Rewrite logarithms as exponents and vice versa.
- Apply the properties of logarithms (products, quotient, power and equality) to solve equations.