Math 106 --- Elementary Algebra
Catalog Description
A study of the real number system, first degree linear equations and inequalities, polynomial expressions and equations, factoring, radicals, quadratic equations, and the quadratic formula, interpretation of graphs, and problem solving techniques. Small group work and exploratory activities (including the use of the graphing calculator) are involved in this course.
Special notes or advisories: Graphing calculator required, TI-83 recommended.
Prerequisites:
Math 375 or 376 with a grade of "C" or better (or equivalent), or appropriate score on the math placement exam.
Describe representative skills without which the student would be highly unlikely to succeed: Understanding the properties of real numbers. Possess the ability to:
- Add, subtract, multiply and divide whole numbers, integers, and rational numbers.
- Evaluate algebraic expressions with one or more variables.
- Simplify polynomial expressions (add, subtract and multiply).
- Solve linear equations.
- Apply the five step problem solving process to solve applications (word problems).
- Plot points on the Cartesian coordinate system.
Course Learning Outcomes:
What should the student be able to do as a result of taking this course? State some of the objectives in terms of specific, measurable student accomplishments.
- Read, write, and speak accurately about mathematical ideas using correct mathematical notation.
- Apply the mathematics they have learned to real world problems and applications.
- Use graphs and the graphing calculator to explore mathematical concepts and to verify their work.
- Demonstrate competency in the required prerequisite skills for intermediate algebra.
- Demonstrate the characteristics of an effective learner.
- Read and use function notation correctly.
- Perform symbolic manipulations that will support success in the other outcomes.
Course Content
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Themes: What themes, if any, are threaded throughout the learning experiences in this course?
- Critical thinking.
- Problem solving.
- Symbol manipulation.
- Use of Technology.
- Graphing and Data Analysis.
- Communication.
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Concepts: What concepts do students need to understand to demonstrate course outcomes?
- A systematic, step-wise problem-solving process.
- The presentation of mathematical solutions in a logical coherent structure, including the use of fundamental writing skills, grammar, and punctuation.
- Use of the graphing calculator as a fundamental problem-solving tool.
- Problem-solving skills learned in class are applicable in many different areas outside of the classroom.
- The recognition that proper symbolic manipulation is an important tool in multiple problem-solving situations.
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Issues: What primary issues or problems, if any, must students understand to achieve course outcomes.
- The differences between solving an equation, simplifying an expression, and evaluating an expression.
- The concept that a graph of an equation is a set of all ordered pairs that satisfy the equation.
- The concept that factoring is the inverse of applying the distributive property.
- The limitations of technology.
- The connection between mathematics and the "real world."
- The role of the student in becoming a successful learner.
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Skills: What skills must students master to demonstrate course outcomes?
- Graphing calculator:
- Graph a function
- Adjust the viewing window in order to identify all salient features of the graph
- Trace
- Find intersections and zeros
- Generate a table
- Approximate solutions to equations
- Troubleshoot calculator error messages
- Interpret scientific notation
- Algebraic Expressions:
- Identify
- Simplify
- Evaluate
- Translate word phrases into algebraic expressions
- Linear Equations:
- Identify
- Solve
- Check solutions
- Graph solutions on a number line
- Clear fractions and decimals to solve an equation
- Translate sentences into a mathematical equation
- Solve a formula for a specified variable
- Linear Inequalities in a single variable:
- Identify
- Solve
- Check solutions
- Graph solutions on a number line
- Clear fractions and decimals to solve an inequality
- Translate sentences into a mathematical inequality
- Graphing:
- Graph and read ordered pairs in the Cartesian plane
- Create a table of points that satisfy an equation
- Create a Cartesian coordinate system on graph paper
- Scale and label axes appropriately
- Plot data points from a table on the coordinate system
- Interpret data from a graph
- Linear Equations in Two Variables:
- Graph a line given the x- and y-intercepts
- Graph a line given the equation in slope-intercept form
- Graph a line given the equation in standard form
- Graph a line through a given point with a specific slope
- Determine the slope of a line given its graph
- Graph vertical and horizontal lines
- Determine the x- and y-intercepts of a line
- Write the equation of a line given a slope and a point on the line
- Write the equation of a line through two given points
- Write the equation of a vertical or horizontal line
- Identify characteristics of parallel and perpendicular lines
- Calculate rates of change, with appropriate units, from a written problem or a graph
- Identify and interpret the slope as the rate of change
- Solve or interpret application problems using linear equations
- Systems of linear equations:
- Solve systems of two equations and two unknowns
- Graphically
- Using elimination
- Using substitution
- Solve application problems
- Solve systems of two equations and two unknowns
- Functions:
- Identify a function
- Identify domain and range
- Represent functions
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- Graphically
- Numerically
- Algebraically
- Descriptively, in English
- Compare different interpretations of a function
- Read and write function notation
- Evaluate functions
- Determine relations as functions using the Vertical Line Test
- Integer Exponents:
- Simplify and evaluate exponential expressions
- Use properties of exponents
- Read, write and solve problems using scientific notation
- Polynomials:
- Identify polynomials
- Evaluate polynomial expressions
- Add, subtract, and multiply polynomials
- Divide a polynomial by a monomial
- Factoring:
- Determine common factors and greatest common factors
- Factor by grouping
- Recognize and factor special products
- Factor trinomials
- Solve polynomial equations by factoring
- Rational Expressions and equations
- Simplify rational expressions with monomial denominators
- Add, subtract, multiply and divide rational expressions with monomial numerators and denominators
- Solve direct and indirect variation problems
- Radical expressions and equations
- Simplify square roots of numbers (exact and decimal approximations)
- Simplify radicals by factoring out perfect square factors
- Pythagorean Theorem
- Quadratic Equations:
- Solve quadratic equations by factoring and/or by using the Quadratic Formula
- Solve application problems involving quadratic equations
- Graphing calculator:
Represenative Learning Activities
What will the students be doing (i.e., Listening to lectures, participating in discussions and/or group activities, attending a field trip, etc.)? Relate the activities directly to the Course Learning Outcomes.
- Listening to lectures.
- Participating in group activities or assignments.
- Participating in in-class assigments or discussions.
- Completing online activities on the computer.
Assessment Tasks
How will the student show evidence of achieving the Course Learning Outcomes? Indicate which assessments (if any) are required for all sections.
- Representative assessment tasks:
- In class exams.
- Assignments that offer an opportunity to express mathematical concepts in writing.
- Quizzes.
- Group projects or other in-class activities.
- Portfolios.
- Individual projects.
- Required assessments for all sections – to include but not limited to:>
- At least two proctored, closed-book examinations, plus a comprehensive final examination.
Examples of Appropriate Texts or Other Readings
- Author: Bittinger, Ellenbogen, Johnson; Title: Elementary and Intermediate Algebra, Graphs and Models, Second Edition; Date 2003
- Author: Tussy, Gustafson; Title: Elementary and Intermdiate Algebra, Third Edition; Date 2005
- Author: Dugopolski; Title: Elementary and Intermediate Algebra, 2nd Edition; Date 2005