Portland Community College | Portland, Oregon

A scientific calculator and access to a graphing utility may be required.

Students are no longer required to have physical graphing calculators in MTH 60, 65, 70, 95, 111, and 112. Where physically possible, instructors will demonstrate using Desmos, GeoGebra, or other online programs in class. Assessments requiring the use of a graphing utility may be done outside of proctored exams.

There is a required notation addendum which may be found at pcc.edu/programs/math/course-downloads.html.

Upon completion of the course students should be able to:

1. Identify the differences between an expression and an equation.
2. Simplify and evaluate algebraic expressions.
3. Solve linear equations and inequalities in one variable, and linear systems in two variables.
4. Identify and interpret the slope as a rate of change in linear relationships.
5. Create linear equations, inequalities, and systems that model contextual situations and use the model to make predictions.
6. Represent linear relationships between two variables using a graph, table, verbal description, and algebraic formula.

Assessment Requirements

1. The following must be assessed in a proctored, closed-book, no-note, and no-calculator setting:
   1. Simplifying expressions
   2. Graphing lines
   3. Solving linear equations and inequalities in one variable
   4. Solving a system of linear equations in two variables
2. At least two proctored, closed-book, no-note 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 fill-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. Application problems must be answered in complete sentences.
4. At least two of the following additional measures must also be used:
   1. Graded homework
   2. Quizzes
   3. Projects
   4. In-class activities
   5. Portfolios

Linear relationships in one and two variables

1. Algebraic Expressions and Equations
   1. Simplify algebraic expressions using the distributive, commutative, and associative properties.
   2. Evaluate algebraic expressions.
   3. Translate phrases and sentences into algebraic expressions and equations, and vice versa.
   4. Distinguish between factors and terms.
   5. Distinguish between evaluating expressions, simplifying expressions, and solving equations.
2. Linear Equations and Inequalities in One Variable
   1. Identify linear equations and inequalities in one variable.
   2. Use the definition of a solution to an equation or inequality to check if a given value is a solution.
   3. Solve linear equations, including proportions, and non-compound linear inequalities symbolically.
   4. Express inequality solution sets graphically and with interval notation.
   5. Create and solve linear equations and inequalities in one variable that model real life situations.
      1. Properly define variables; include units in variable definitions.
      2. State contextual conclusions using complete sentences.
      3. Use estimation to determine reasonableness of solutions.
   6. Solve an equation for a specified variable in terms of other variables.
   7. Solve applications in which two values are unknown but their total is known; for example, a 10-foot board cut into two pieces where one piece is 2.5 feet longer than the other piece.
3. Introduction to Tables and Graphs
   1. Plot points on the Cartesian coordinate system, including pairs of values from a table.
   2. Determine coordinates of points by reading a Cartesian graph.
   3. Create a table of values from an equation or application. Make a plot from the table. When appropriate, correctly identify the independent variable with the horizontal axis and the dependent variable with the vertical axis.
   4. Classify points by quadrant or as points on an axis; identify the origin.
   5. Label and scale axes on all graphs.
   6. Create graphs where the axes are required to have different scales (e.g. -10 to 10 on the horizontal axis and -1000 to 1000 on the vertical axis).
   7. Interpret graphs, intercepts and other points in the context of an application. Express intercepts as ordered pairs.
   8. Create tables and graphs with labels that communicate the context of an application problem and its dependent and independent quantities.
4. Slope
   1. Write and interpret a slope as a rate of change in context (include the unit of the slope).
   2. Find the slope of a line from a graph, from two points, and from a table of values.
   3. Find the slope from all forms of a linear equation.
   4. Given the graph of a line, identify the slope as positive, negative, zero, or undefined. Given two non-vertical lines, identify the line with greater slope.
5. Linear Equations in Two Variables
   1. Identify a linear equation in two variables.
   2. Manipulate a linear equation into slope-intercept form; identify the slope and the vertical intercept given a linear equation.
   3. Recognize equations of horizontal and vertical lines and identify their slopes as zero or undefined.
   4. Write the equation of a line in slope-intercept form.
   5. Write the equation of a line in point-slope form.
6. Graphing Linear Equations in Two Variables
   1. Graph a line with a known point and slope.
   2. Emphasize that the graph of a line is a visual representation of the solution set to a linear equation.
   3. Given a linear equation, find at least three ordered pairs that satisfy the equation and graph the line using those ordered pairs.
   4. Given an equation in slope-intercept form, plot its graph using the slope and vertical intercept.
   5. Given an equation in point-slope form, plot its graph using the slope and the suggested point.
   6. Given an equation in standard form, plot its graph by calculating horizontal and vertical intercepts, and check with a third point.
   7. Given an equation for a vertical or horizontal line, plot its graph.
   8. Create and graph a linear model based on data and make predictions based upon the model.
7. Systems of Linear Equations in Two Variables
   1. Solve and check systems of equations using the following methods: graphically, using the substitution method, and using the addition/elimination method.
   2. Create and solve real-world models involving systems of linear equations in two variables.
   3. Properly define variables; include units in variable definitions.
   4. State contextual conclusions using complete sentences.
   5. Given the equations of two lines, classify them as parallel, perpendicular, or neither.

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 students throughout the course to perform arithmetic operations with fractions and negative numbers without calculators. 

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.