Skowhegan Area High School
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Math III Unit 1
Multiple Variable Models

In this unit students are expanding their understanding of algebraic relations to include models in which more than two variables are involved. By the end of this unit students should have a good understanding of a variety of means for exploring different multiple variable situations through the use of tables, graphs, and symbolic representation.
Lesson 1: In this lesson students will explore how the changes in one variable affects the values of other variables.
Lesson 2: Students will work with multiple variable situations that involve algebra, geometry, and trigonometry. In the second lesson students solve problems involving the law of Sines and the law of Cosines.
Lesson 3: The investigations involve two or more output variables related to the same input variable. The students explore such systems of equations and determine algebraic models, tables, and graphs for them. Student will also explore inequalities related to these systems.
Lesson 4: Linear programming is used to motivate interest in and to show one reason for graphing linear inequalities. Students will be discovering the feasible region for linear programming problems, what the boundaries are of the region, and finally the best solution is always a vertex of the region.

Objectives:

• To develop an understanding of and the ability to solve problems involving multiple variable relations where one equation relates more than two variables.
• To develop the ability to solve mulitiple variable equations for one variable in terms of the other variables.
• To model situations with systems of equations and inequalities where two or more output variables are related to the same input variables, and to apply those systems to solve problems.
 "Text paraphrased from CPMP Math 3A, Math 3 Unit 1, pages T1 and T1A"

Maine Learning Results (MLR):
E3, G4, H3, H4, I