**The Department of Mathematics Education**
# EMT 669 Class Home Page

for

Mike Callinan

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
Excel.

**Geometric
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.

**Instructional
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).

**Cedar
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.

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