Course Content and Outcome Guide for MTH 60 Effective Fall 2015
 Course Number:
 MTH 60
 Course Title:
 Introductory Algebra  First Term
 Credit Hours:
 4
 Lecture Hours:
 30
 Lecture/Lab Hours:
 20
 Lab Hours:
 0
 Special Fee:
 $6.00
Course Description
Introduces algebraic concepts and processes with a focus on linear equations and inequalities in one and two variables. Emphasizes applications, graphs, formulas, and proper mathematical notation throughout the course. A scientific calculator may be required. The TI30X II is recommended. Prerequisites: MTH 20 and (RD 80 or ESOL 250). Recommended that MTH 20 be taken within the past 4 terms. The PCC math department recommends that students take MTH courses in consecutive terms. Audit available.Intended Outcomes for the course
Upon completion of the course students should be able to:
 Simplify and evaluate algebraic expressions.
 Represent a quantity with an algebraic expression for a given situation.
 Use a variable to represent an unknown in a linear problem, create a linear equation or inequality that represents the situation, and find the solution to the problem using algebra.
 Distinguish linear and nonlinear relationships between quantities represented by two variables when given a graph, table, verbal description or algebraic formula.
 Identify and interpret the rate of change in linear data, construct a model and use the model to make predictions.
Outcome Assessment Strategies
 Develop basic algebraic skills necessary to accurately simplify and evaluate expressions.
 Complete assignments, projects, test or quiz problems, and class activities which apply algebra to reallife situations.
 Show an understanding of multiple representations of linear and nonlinear relationships in a variety of forms through the use of activities, exam
problems, projects and/or discussions.  Participate in, and contribute to, class discussions and activities.
 Take all scheduled examinations.
Assessment Requirements:
1. The following must be assessed in a proctored, closedbook, nonote, and nocalculator setting:
 arithmetic with signed rational numbers
 simplifying expressions (including exponential expressions)
 graphing lines
 solving linear equations and inequalities in one variable
2. At least two proctored, closedbook, nonote examinations (one of which is the comprehensive final) must be given. These exams must consist
primarily of free response questions although a limited number of multiple choice and/or ll in the blank questions may be used where appropriate.
3. Assessment must include evaluation of the students ability to arrive at correct conclusions using proper mathematical procedures and notation.
Additionally, each student must be assessed on their ability to use appropriate organizational strategies and write appropriate conclusions. Application
problems must be answered in complete sentences.
4. At least two of the following additional measures must also be used.
 Takehome examinations
 Graded homework
 Quizzes
 Projects
 Inclass activities
 Portfolios
Course Content (Themes, Concepts, Issues and Skills)
THEMES:

Number sense

Algebraic Manipulation

Graphical understanding

Problem solving

Effective communication

Critical thinking

Applications, formulas, and modeling
SKILLS:
 REAL NUMBERS
 Review prerequisite skills, signed numbers, and fraction arithmetic
 Simplify arithmetic expressions using the order of operations
 Evaluate powers with whole number exponents and integer bases
 Simplify arithmetic expressions involving absolute values
 Order real numbers along a real number line
 Classify numbers as natural, whole, integer, rational, irrational, and/or real numbers
 VARIABLES AND EXPRESSIONS
 Simplify algebraic expressions
 Evaluate algebraic expressions
 Recognize equivalent expressions and nonequivalent expressions
 Distinguish between evaluating expressions, simplifying expressions and solving equations
 Translate from words into algebraic expressions and vice versa
 Apply the distributive, commutative, and associative properties
 Recognize additive and multiplicative identities and inverses
 Distinguish between factors and terms
 Apply the product rule, product to a power rule, and powertoapower rule to expressions with natural number exponents emphasizing the logic behind these rules of exponents
 GEOMETRY APPLICATIONS
 Evaluate formulas and apply basic dimensional analysis
 Know and apply appropriate units for various situations; e.g. perimeter units, area units, volume units, rate units, etc.
 Memorize and apply the perimeter and area formulas for rectangles, circles, and triangles
 Memorize and apply the volume formula for a rectangular solid and a right circular cylinder
 Find the perimeter of any polygon
 Use a triangle with side lengths given, write the ratios for sine, cosine, and tangent
 Evaluate other geometric formulas
 Use estimation to determine reasonableness of solution
 LINEAR EQUATIONS AND INEQUALITIES IN ONE VARIABLE
 Identify linear equations and inequalities in one variable
 Understand the definition of a solution; e.g. \(2\) is a solution to \(x\lt 5\); \(3\) is the solution to \(x+1=4\)
 Distinguish between solutions and solution sets
 Recognize equivalent equations and nonequivalent equations
 Solve linear equations and noncompound linear inequalities symbolically
 Express inequality solution sets graphically, with interval notation, and with setbuilder notation
 Distinguish between a solution to an equation (e.g. The solutions is \(2\).) and an equivalent equation (e.g. \(x=2)\)
 GENERAL APPLICATIONS
 Create and solve linear equations and inequalities in one variable that model real life situations (e.g. fixed cost \(+\) variable cost equals total cost)
 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
 Apply general percent equations (\(A=PB\))
 Create and solve percent increase/decrease equations
 Create and solve ratio/proportion equations
 Solve applications in which two values are unknown but their total is known; for example, a 50 foot board cut into two pieces of unknown length
 Create and solve linear equations and inequalities in one variable that model real life situations (e.g. fixed cost \(+\) variable cost equals total cost)
 LITERAL EQUATIONS AND FORMULAS
 Solve an equation for a specified variable in terms of other variables
 Input values into a formula and solve for the remaining variable
 INTRODUCTION TO TABLES AND GRAPHS
 Briefly review line graphs, bar graphs and pie charts
 Plot points on the Cartesian coordinate system; determine coordinates of points
 Classify points by quadrant or as points on an axis; identify the origin
 Label and scale axes on all graphs
 Create graphs where the axes are required to have different scales (e.g. Slope of 10 with scale of 1 on the \(x\text{axis}\) and a different scale on the \(y\text{axis}\).)
 Interpret graphs in the context of an application
 Create a table of values from an equation emphasizing input and output
 Plot points from a table
 LINEAR EQUATIONS IN TWO VARIABLES
 Identify a linear equation in two variables
 Emphasize that the graph of a line is a visual representation of the solution set to a linear equation
 Find ordered pairs that satisfy a linear equation written in standard or slopeintercept form including equations for horizontal and vertical lines; graph the line using the ordered pairs
 Find the intercepts given a linear equation; express the intercepts as ordered pairs
 Graph the line using intercepts and check with a third point
 Find the slope of a line from a graph and from two points
 Given the graph of a line identify the slope as positive, negative, zero, or undefined. Given two nonvertical lines, identify the line with greater slope
 Graph a line with a known point and slope
 Manipulate a linear equation into slopeintercept form; identify the slope and the verticalintercept given a linear equation and graph the line using the slope and verticalintercept and check with a third point
 Recognize equations of horizontal and vertical lines and identify their slopes as zero or undefined
 Given the equation of two lines, classify them as parallel, perpendicular, or neither
 Find the equation of a line using slopeintercept form
 Find the equation of a line using pointslope form
 Applications of linear equations in two variables
 Interpret intercepts and other points in the context of an application
 Write and interpret a slope as a rate of change (include units of the slope)
 Create and graph a linear model based on data and make predictions based upon the model
 Create tables and graphs that fully communicate the context of an application problem and its dependent and independent quantities
 LINEAR INEQUALITIES IN TWO VARIABLES
 Identify a linear inequality in two variables
 Graph the solution set to a linear inequality in two variables
 Model application problems using an inequality in two variables
MTH 60 is the first term of a two term 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.
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 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.
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 60 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.
There is a required notation addendum and required problem set supplement for this course. Both can be found at spot.pcc.edu/math.