The Department of Mathematics Education
EMT 669 Class Home Page
Last modified on March 21, 1996.
Comparison of Means.
This essay compares the arithmetic mean, (a + b)/2, to the geometric
mean, sqr(a + b). The comparison demonstrates that the arithmetic
mean is always greater than the geometric mean except when A and
B are equal, at which time, the two means are equal. The essay
gives an algebraic proof of this comparison and has the capability
of "launching" 2 examples using the Enhanced Version
3 of Geometer's Sketch Pad and another example using Microsoft
Ratio. This document examines how specific situations
involving proportions can be useful in leading to generalizations
in which valid rules can be stated. We will begin with a specific
instance of a constant geometric ratio and from this we will try
to arrive at a general case.
Unit. This unit, called "Save or Play", was
given to a Cedar Shoals High School Pre-Algebra class to teach
them how to manipulate equations and a variable on a spreadsheet
(Excel, in this example).
Shoals Unit. This unit, called "Save or Play",
was a one-day unit given to a Cedar Shoals High School Pre-Algebra
class. The objective was to teach them how to manipulate equations
and a variable on a spreadsheet (Microsoft Excel, in this example)
and also give them a valuable lesson for their future.