MTH 091 Algebraic Literacy

Lecture Hours: 4
Credits: 4

Develops the skills and procedures necessary to manipulate algebraic expressions, solve equations in one variable, and graph equations in two variables. The course is designed primarily to prepare students for precalculus.

Prerequisite: Placement into MTH091; or completion of XMTH5001A with a grade of C or better; equivalent course as determined by instructor; or consent of instructor.
Student Learning Outcomes:

Use mathematical problem solving techniques involving algebraic expressions, algebraic equations and graphing.
Create mathematical models of abstract and real world situations using algebraic expressions, algebraic equations and graphing.
Use inductive reasoning to develop mathematical conjectures using algebraic expressions, algebraic equations and graphing.
Use deductive reasoning to verify and apply mathematical arguments involving algebraic expressions, algebraic equations and graphing.
Make mathematical connections to, and solve problems from, other disciplines using algebraic expressions, algebraic equations and graphing.
Use oral and written skills to individually and collaboratively communicate mathematics using algebraic expressions, algebraic equations and graphing.
Use appropriate technology to enhance mathematical thinking and understanding, to solve mathematical problems, and to judge the reasonableness of results involving algebraic expressions, algebraic equations and graphing.

Content Outline

Real Numbers
- Subsets of Real Numbers
  - Whole Numbers
    - Prime Numbers
    - Composite Numbers
  - Integers
  - Rational Numbers
    - Fraction Representations
    - Decimal Representations
  - Irrational Numbers
- Operations With Real Numbers
  - Addition & Subtraction
  - Multiplication & Division
  - Powers & Roots
- The Real Number Line
  - Absolute Value of a Real Number
  - Inequality between two Real Numbers
Algebraic Expressions
- Vocabulary
  - Constants & Variables
  - Operations & Inverse Operations
  - Expressions & Equations
- Simplify Equivalent Expressions
  - Use Commutative & Associative Properties
  - Combine Like Terms
  - Distributive Property
    - Distribute Signed Numbers
    - Distribute Monomials
    - Distribute Binomials
  - Properties of Exponents
- Evaluate Expressions
  - Substitute Given Numbers for Variables
  - Use the Order of Operations
Elementary Equations
- Solve One-Step Equations
  - Use the Addition Principle
  - Use the Multiplication Principle
  - Use the Definition of Square Roots
- Solve Multi-Step Equations
  - Use Inverse Operations in the Reverse Order
- Solve Formulas for Specified Variables
Intermediate Equations
- Solve Multi-Step Linear Equations
  - Equations involving Distribution
  - Equations involving Combining Like Terms
  - Equations with Variables on Both Sides
- Solve Multi-Step Nonlinear Equations
  - Equations involving the Zero Factor Property
  - Equations involving Factoring
  - Equations involving Roots
  - Equations requiring the Quadratic Formula
- Solve Equations with the Variable in Unusual Locations
  - Equations where X is in the Subtrahend
  - Equations where X is in the Denominator
  - Equations where X is in the Exponent (Guess & Check) 
Graphs of Two Variable Equations
- Introduction to the Cartesian Coordinate System
- Create Graphs from Tables of Values
- Linear Equations
  - Slope
  - Intercepts
  - The Slope-Intercept Form
- Quadratic Equations
  - Vertex
  - Intercepts
  - Use Graphs to Solve Equations
  - Use Technology to Graph Equations