PCC/ CCOG / MTH

Course Content and Outcome Guide for MTH 70

Course Number:
MTH 70
Course Title:
Review of Introductory Algebra
Credit Hours:
4
Lecture Hours:
30
Lecture/Lab Hours:
20
Lab Hours:
0
Special Fee:
$6.00

Course Description

Review of algebraic concepts and processes with a focus on linear equations and inequalities in one and two variables, functions, linear systems, properties of exponents, polynomials, and quadratic equations. Applications, graphs, functions, formulas, and proper mathematical notation are emphasized throughout the course. A scientific calculator is required. The TI-30X II is recommended. Prerequisites: (MTH 63 or MTH 65) and (RD 80 or ESOL 250) Audit available.

Intended Outcomes for the course

  • Use a variable to represent an unknown in a simple linear problem, create a linear equation that represents the situation, and find the solution to the problem using algebra.
  • Recognize a linear pattern in ordered paired data collected or observed, calculate and interpret the rate of change (slope) in the data, create a linear model using two data points, and use the observed pattern to make predictions.
  • Recognize and differentiate between linear and quadratic patterns in ordered paired data, graphs, and equations.
  • Use variables to represent unknowns in linear or quadratic problems, create a linear system or quadratic equation that represents the situation, and find the solution to the problem using algebra.
  • Be successful in future coursework that requires the use of basic algebraic concepts and an understanding of functions.

Outcome Assessment Strategies

 Assessment shall include:

  1. The following must be assessed in a proctored, closed book, no-note, and no-calculator setting: simplifying expressions, factoring quadratic binomials and trinomials, solving linear and quadratic equations, solving systems of linear equations, and graphing linear and quadratic functions.
  2. At least two proctored closed-book examinations (one of which is a 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.
  3. Assignments that offer an opportunity to express mathematical concepts in writing. Assessment should be made on the basis of using correct mathematical syntax, appropriate use of the English language, and explanation of the mathematical concept.
  4. At least two of the following additional measures must also be used:
    1. Take-home examinations
    2. Graded homework
    3. Quizzes
    4. Projects
    5. In-class activities
    6. Portfolios

Course Content (Themes, Concepts, Issues and Skills)

 Themes:

  • Functions, with special attention to linear and quadratic functions
  • Algebraic manipulation of expressions
  • Problem solving
  • Graphing
  • Number sense
  • Critical thinking
  • Effective communication

 

Skills:

  1. RELATIONS AND FUNCTIONS
    1. Use the definition of a function to determine whether a given relation represents a function
    2. Determine the domain and range of a function given as a graph or as a table
    3. Apply function notation in graphical, algebraic, and tabular settings
      1. Understand the difference between the input and output
      2. Identify ordered pairs from function notation
      3. Given an input, find an output
      4. Given an output, find input(s)
    4. Interpret function notation in real world applications
      1. Evaluate the function at a particular input value and interpret its meaning
      2. Given a functional value (output), find and interpret the input
  2. LINEAR EQUATIONS AND FUNCTIONS
    1. Solve linear equations and inequalities in one variable
    2. Graph linear functions
      1. Graph a linear function by finding the intercepts
      2. Graph a linear function given its slope and the vertical intercept
      3. Graph a linear function given its slope and a point on the line
    3. Determine the slopes of lines from equations and graphs and interpret their significance as rates of change
    4. Determine linear functions
      1. Find an equation for a linear function given a graph of the function
      2. Find an equation for a linear function given two points
      3. Find an equation for a linear function given a verbal description of a linear relationship", first identifying the independent and dependent variables
    5. Solve systems of linear equations in two variables
      1. Solve systems by graphing
      2. Solve systems by the substitution method
      3. Solve systems by the addition (elimination) method
    6. Applications of linear equations of one variable, linear functions, and systems of linear equations
  3. QUADRATIC EQUATIONS AND FUNCTIONS
    1. Review polynomial operations, laws of exponents, and factoring polynomial expressions
      1. Factor expressions having a greatest common factor
      2. Factor binomials
        1. Differences of squares
        2. Sums and differences of cubes
      3. Factor trinomials with leading coefficients of 1 as well as leading coefficients not 1
      4. Factor multivariable expressions.
    2. Solve quadratic equations in one-variable
      1. Solve quadratic equations using the square root method
      2. Solve quadratic equations by factoring
      3. Solve quadratic equations using the Quadratic Formula
        1. Simplify and approximate nonvariable square roots
    3. Graph quadratic functions
      1. Graph a quadratic function from an equation by creating a table and plotting points
      2. Graph a quadratic function by finding the axis of symmetry", the vertex and the intercepts
      3. Use and interpret quadratic models of real world situations algebraically and graphically
        1. Evaluate the function at a particular input value and interpret its meaning
        2. Given a functional value (output), find and interpret the input
        3. Interpret the vertex using proper units
        4. Interpret the vertical intercept using proper units
        5. Interpret the horizontal intercept(s) using proper units
  4.     LITERAL EQUATIONS AND FORMULAS
    1. Solve an equation for a specified variable in terms of other variables
    2. Input values into a formula and solve for the remaining variable

ADDENDUM:

The purpose of the MTH 70 class is to prepare students to be successful in MTH 95. Several topics in MTH 95 require that students have much more than an introductory understanding of MTH 60/65 material. For instance, students must be able to recognize and quickly factor quadratic expressions if they are to successfully understand rational expressions, the quadratic formula and completing the square in MTH 95. Algebraic concepts covered in MTH 70 will be used in MTH 95 with the expectation that students know and understand them. 

One major problem experienced by introductory algebra students is difficulty conducting operations with fraction and negative numbers. This is the most likely reason that they find themselves in such a course. Thus, 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, factors, terms, equations, expressions and equivalent equations.

The difference between expressions and equations 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 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:

            1 3 x + 7 15 x = 5 5 ‹… 1 3 x + 1 7 x = 5 15 x + 7 15 x = 12 15 x = 4 5 x                              3 x 2 ˆ’ 15 x ˆ’ 18 = 3 x 2 ˆ’ 5 x ˆ’ 6 = 3 x + 1 x ˆ’ 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 MTH 70 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 introduced at the beginning of the course and continually revisited. Use linear and quadratic equations as examples of functions to reinforce the use of function notation, as well as the concepts of domain and range throughout the course.

Instructors should remind students that the topics discussed in MTH 70 will be revisited in MTH 95 and beyond", but at a much faster pace while being integrated with new topics.