# Teacher's Commentary

### Lesson:

**Exponential Fit Using Statistical Methods of Analysis**

### Level:

This lesson is intended for high school students who are either in,
- A statistics class
- An Algebra II or Pre-Calculus class

It is necessary that the student have a background working with exponential and logarithmic functions. There is a review section included with the lesson along with review exercises, however it is limited in its scope and is intended only for review.

### Materials:

The student must have access to these materials to do this lesson,
- Knowledge of and access to Microsoft Excel
- Access to a browser supporting inline images such as Netscape. This can be downloaded from
Netscape.
- A color monitor
- A bag of M&M's or Skittles

### Comments

The most noticeable difference between this lesson to others similar to it is the method of finding the best fitting curve. Often students have no conceptual understanding of terms such as variance, covariance and correlation. These terms do not appear anywhere in this lesson. They only see the formulas to calculate these terms and have no feeling for what they mean. The method presented in this lesson of manipulating b to find the best fit gives the student a firmer understanding of the concept of the best fit. Here they can see that they are trying to minimize the error lines from the curve to the data. In the other method using covariances and standard deviations to find the slope of a logarithmic transformation, gives no indication of the concepts at hand.

### NCTM Standards

The standards suggest an increased emphasis on statistics and this lesson certainly provides this. Many of the headings listed in the statistics strand are directly addressed in the lesson. For instance, students should be able to construct and draw inferences from tables and graphs, they should use curve fitting to predict from data, conduct experiments and interpret the outcomes. Also, data transformations should be introduced which they are here.

Any comments or suggestions will be greatly appreciated. I can be reached through the
MSTE Webmaster