CCOG for MTH 63 archive revision 63
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 Effective Term:
 Winter 2014 through Spring 2014
 Course Number:
 MTH 63
 Course Title:
 Introductory Algebra  Part III
 Credit Hours:
 3
 Lecture Hours:
 20
 Lecture/Lab Hours:
 20
 Lab Hours:
 0
Course Description
Addendum to Course Description
 Students will be evaluated not only on their ability to get correct answers and perform correct steps, but also on the accuracy of the presentation itself.
 Application problems must be answered in complete sentences.
Intended Outcomes for the course
1. Recognize and differentiate between linear and quadratic patterns in ordered paired data, graphs, and equations.
2. Use variables to represent unknowns in quadratic problems, create a quadratic equation that represents the situation, and find the solution to the problem using algebra.
3. Be prepared for future coursework that requires the use of basic algebraic concepts and an understanding of functions.
Outcome Assessment Strategies
Assessment shall include:
 The following must be assessed in a proctored, closedbook, nonote, and nocalculator setting: simplifying expressions; binomial and trinomial factoring; extracting roots; solving quadratic equations by factoring and using the quadratic formula; and graphing quadratic functions.
 At least two proctored closedbook, closednote examinations (one of which is the comprehensive final). These exams must consist primarily of free response questions although a limited number of multiple choice and/or fill in the blank questions may be used where appropriate.
 Assessment must include evaluation of the student’s ability to arrive at correct and appropriate conclusions using proper mathematical procedures and proper mathematical notation. Additionally, each student must be assessed on their ability to use appropriate organizational strategies and their ability to write conclusions appropriate to the problem.
 At least one of the following additional measures:
 Takehome examinations
 Graded homework
 Quizzes
 Projects
 Inclass activities
 Portfolios
Course Content (Themes, Concepts, Issues and Skills)
THEMES:
 Functions
 Graphical understanding
 Algebraic manipulation
 Number sense
 Problem solving
 Applications, formulas, and modeling
 Critical thinking
 Effective communication
SKILLS:

WORKING WITH ALGEBRAIC EXPRESSIONS
 Understand nonvariable square roots
 Simplify using the product rule of square roots
 Recognize like radical terms
 Rationalize denominators
 Estimate square roots
 Understand nonvariable square roots

FACTORING POLYNOMIALS
 Factor the greatest common factor from a polynomial
 Factor a polynomial of four terms with the grouping method
 Factor trinomials that have leading coefficients of 1
 Factor trinomials that have leading coefficients other than 1
 Factor the difference of squares
 Recognize and factor the sum and difference of cubes

QUADRATIC EQUATIONS IN ONE VARIABLE
 Solve quadratic equations by using the zero product principle (factoring)
 Solve quadratic equations by using the square root property (see Section 1.1)
 Solve quadratic equations by using the quadratic formula (see Section 1.1)
 Make choices about the appropriate method to use when solving a quadratic equation
 Understand that the solutions satisfy the original equation by checking the solutions
 Distinguish between a linear and a quadratic equation and be able to solve both kinds of equations when mixed up in a problem set
 Create and solve realworld models involving quadratic equations
 Properly define variables; include units in variable definitions
 Apply dimensional analysis while solving problems
 State contextual conclusions using complete sentences
 Use estimation to determine reasonableness of solution

QUADRATIC EQUATIONS IN TWO VARIABLES
 Identify a quadratic equation in two variables
 Create a table of solutions for the equation of a quadratic function
 Emphasize that the graph of a parabola is a visual representation of the solution set to a quadratic equation
 Graph quadratic functions by finding the vertex and plotting additional points without using a graphing calculator
 Algebraically find the vertex, axis of symmetry, and vertical and horizontal intercepts and graph them by hand
 The vertex as well as the vertical and horizontal intercepts should be written as ordered pairs
 The axis of symmetry should be written as an equation
 Determine whether quadratic functions are concave up or concave down based on their equations
 Create, use, and interpret quadratic models of realworld situations algebraically and graphically
 Evaluate the function at a particular input value and interpret its meaning
 Given a functional value (output), find and interpret the input
 Interpret the vertex using proper units
 Interpret the vertical intercept using proper units
 Interpret the horizontal intercept(s) using proper units

RELATIONS AND FUNCTIONS
 Use the definition of a function to determine whether a given relation represents a function
 Determine the domain and range of a function given as a graph or as a table
 Apply function notation in graphical, algebraic, and tabular settings
 Understand the difference between the input and output
 Identify ordered pairs from function notation
 Given an input, find an output
 Given an output, find input(s)
 Interpret function notation in real world applications
 Evaluate the function at a particular input value and interpret its meaning
 Given a functional value (output), find and interpret the input
ADDENDUM:
MTH 63 is the third term of a threeterm sequence in beginning algebra. One major problem experienced by beginning algebra students is difficulty conducting operations with fractions and negative numbers. It would be beneficial to incorporate these topics throughout the course, whenever possible, so that students have ample exposure. Encourage them throughout the course to get better at performing operations with fractions and negative numbers, as it will make a difference in this and future math courses.
Vocabulary is an important part of algebra. Instructors should make a point of using proper vocabulary throughout the course. Some of this vocabulary should include, but not be limited to, inverses, identities, the commutative property, the associative property, the distributive property, equations, expressions and equivalent equations.
The difference between expressions, equations, and inequalities needs to be emphasized throughout the course. A focus must be placed on helping students understand that evaluating an expression, simplifying an expression, and solving an equation or inequality are distinct mathematical processes and that each has its own set of rules, procedures, and outcomes.
Proper usage of equal signs must be stressed at all times. Students need to be taught that equal signs are used to communicate multiple ideas and they need to be taught the manner in which equal signs are used to communicate these ideas.
Equivalence of expressions is always communicated using equal signs. Students need to be taught that when they simplify or evaluate an expression they are not solving an equation despite the presence of equal signs. Instructors should also stress that it is not acceptable to write equal signs between nonequivalent expressions.
Instructors should demonstrate that both sides of an equation need to be written on each line when solving an equation. An emphasis should be placed on the fact that two equations are not equal to one another but they can be equivalent to one another.
Instructors should demonstrate and emphasize the importance of performing operations in a vertical format. Equal signs must be used when changing the form of an expression. Examples of a vertical format are as follows:
13x+715x=55⋅13x+17x=515x+715x=1215x=45x 3x2−15x−18=3x2−5x−6=3x+1x−6
The distinction between an equal sign and an approximately equal sign should be noted and students should be taught when it is appropriate to use one sign or the other.
The manner in which one presents the steps to a problem is very important. We want all of our students to recognize this fact; thus the instructor needs to emphasize the importance of writing mathematics properly and students need to be held accountable to the standard. When presenting their work", all students in a Math 65 course should consistently show appropriate steps using correct mathematical notation and appropriate forms of organization. All axes on graphs should include scales and labels. A portion of the grade for any free response problem should be based on mathematical syntax.
The concept of functions should be covered before quadratic equations", and continually revisited. Use quadratic equations as an example of a function to reinforce the use of function notation, and the concepts of domain and range throughout the course.
Instructors should remind students that the topics discussed in MTH 60 and MTH 65 will be revisited in MTH 95 and beyond, but at a much faster pace while being integrated with new topics.