Lesson 3
Exponential Growth
Class: Math II
Time: One 50minute class
Overview:
This lesson will help students model the real world situation using the knowledge of inverse variation or exponential functions.
Objectives:
The student:
1. will learn how to fit an inversevariation function to real world data by trial and error.
2. will use residuals to judge how well a function fits data
3. will use residuals to improve the fit of a function
NCTM Standards:
Understand patterns, relations and functions.
Use Mathematical models to represent and understand quantitative relationships.
identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships;
use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts.
draw reasonable conclusions about a situation being modeled.
GPS Standards:
Prerequisite Skills:
Students should be able to graph exponential functions. Students should be able to use function transformations (dilations and translations) and fit an exponential function by trial and error.
Fathom Prerequisites: Students should be able to
Create attributes defined by formulas
Make a scatter plot of two attributes
Add least square line
Graph a leastsquares line
Make a residual plot
Fathom Skills: Students will learn how to
Use a residual plot to recognize a better function model.
Materials Needed
Activity Worksheet: Worksheets to be distributed at the beginning of the class.
Computers with Fathom 2 along with survey feature
A sheet of notebook paper
Activity: During the activity student will work in pairs and the teacher will begin the activity by distributing the worksheet and demonstrating the beginning of the activity by taking a sheet of paper and folding it into half and asking students how many folds they see and what fraction of the total area does each part represent. Teacher may draw a table on the board or over head display to show how to record the number of folds and rectangles. And directing the students to work in pairs, teacher will go around the class room assisting and scaffolding students in completing the task.
Assessment:
Students will be assessed on the basis of classroom discussion, participation, ease of technology use, completion of task and involvement in the activity.
Evaluation:
Student worksheet will be evaluated based on the following rubric.
Rubric for Modeling the nonlinear data
Question 



Points 
Completion of task 
The student completes the task (45 pts)

The student miss two to three questions(23 pts) 
The student does not complete the task. (01 pt) 

Mathematical Concepts 
Explanation shows complete understanding of the mathematical concepts used to solve the problem(s). (45 pts) 
Explanation shows substantial understanding of the mathematical concepts used to solve the problem(s). (23pts) 
Explanation shows very limited understanding of the underlying concepts needed to solve the problem(s) OR is not written. (01pts) 

Explanation/ Justification of reasoning 
Explanation is detailed and clearly justifies. (45 pts)

Explanation is clear but does not justify. (23 pts) 
Provides little or no explanation (01pt) 

Type of graph chosen 
Graph fits the
data well and makes it easy to interpret. (45 pts) 
Graph is adequate and does not distort the data, but interpretation of the data is somewhat difficult. (23 pts)

Graph seriously distorts the data making interpretation almost impossible (01 pt) 
