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.

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.

• Å·ÖÞ±­¾öÈü¾º²Âapp_Å·ÖÞ±­×ãÇòÍø-Ͷע|¹ÙÍø basic algebraic skills necessary to accurately simplify and evaluate expressions.
• Complete assignments, projects, test or quiz problems, and class activities which apply algebra to real-life situations.
• Show an understanding of multiple representations of linear and non-linear 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, closed-book, no-note, and no-calculator 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, 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 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.

1. Take-home examinations
2. Graded homework
3. Quizzes
4. Projects
5. In-class activities
6. Portfolios

THEMES:

1. Number sense

2. Algebraic Manipulation

3. Graphical understanding

4. Problem solving

5. Effective communication

6. Critical thinking

7. Applications, formulas, and modeling

SKILLS:

1. REAL NUMBERS
   1. Review prerequisite skills, signed numbers, and fraction arithmetic
   2. Simplify arithmetic expressions using the order of operations
   3. Evaluate powers with whole number exponents and integer bases
   4. Simplify arithmetic expressions involving absolute values
   5. Order real numbers along a real number line
   6. Classify numbers as natural, whole, integer, rational, irrational, and/or real numbers
2. VARIABLES AND EXPRESSIONS
   1. Simplify algebraic expressions
   2. Evaluate algebraic expressions
   3. Recognize equivalent expressions and non-equivalent expressions
   4. Distinguish between evaluating expressions, simplifying expressions and solving equations
   5. Translate from words into algebraic expressions and vice versa
   6. Apply the distributive, commutative, and associative properties
   7. Recognize additive and multiplicative identities and inverses
   8. Distinguish between factors and terms
   9. Apply the product rule, product to a power rule, and power-to-a-power rule to expressions with natural number exponents emphasizing the logic behind these rules of exponents
3. GEOMETRY APPLICATIONS
   1. Evaluate formulas and apply basic dimensional analysis
   2. Know and apply appropriate units for various situations; e.g. perimeter units, area units, volume units, rate units, etc.
   3. Memorize and apply the perimeter and area formulas for rectangles, circles, and triangles
   4. Memorize and apply the volume formula for a rectangular solid and a right circular cylinder
   5. Find the perimeter of any polygon
   6. Evaluate other geometric formulas
   7. Use estimation to determine reasonableness of solution
4. LINEAR EQUATIONS AND INEQUALITIES IN ONE VARIABLE
   1. Identify linear equations and inequalities in one variable
   2. Understand the definition of a solution; e.g. \(2\) is a solution to \(x\lt 5\); \(3\) is the solution to \(x+1=4\)
   3. Distinguish between solutions and solution sets
   4. Recognize equivalent equations and non-equivalent equations
   5. Solve linear equations and non-compound linear inequalities symbolically
   6. Express inequality solution sets graphically, with interval notation, and with set-builder notation
   7. Distinguish between a solution to an equation (e.g. The solutions is \(2\).) and an equivalent equation (e.g. \(x=2)\)
5. GENERAL APPLICATIONS
   1. Create and solve linear equations and inequalities in one variable that model real life situations (e.g. fixed cost plus variable cost equals total cost)
      1. Properly define variables; include units in variable definitions
      2. Apply dimensional analysis while solving problems
      3. State contextual conclusions using complete sentences
      4. Use estimation to determine reasonableness of solution
   2. Apply general percent equations (\(A=PB\))
   3. Create and solve percent increase/decrease equations
   4. Create and solve ratio/proportion equations
   5. 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
6. 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
7. INTRODUCTION TO TABLES AND GRAPHS
   1. Briefly review line graphs, bar graphs and pie charts
   2. Plot points on the Cartesian coordinate system; determine coordinates of points
   3. Classify points by quadrant or as points on an axis; identify the origin
   4. Label and scale axes on all graphs
   5. Create graphs where the axes are required to have different scales (e.g. Slope of 10 with scale of 1 on the \(x\)-axis and a different scale on the \(y\)-axis.)
   6. Interpret graphs in the context of an application
   7. Create a table of values from an equation emphasizing input and output
   8. Plot points from a table
8. LINEAR EQUATIONS IN TWO VARIABLES
   1. Identify a linear equation in two variables
   2. Emphasize that the graph of a line is a visual representation of the solution set to a linear equation
   3. Find ordered pairs that satisfy a linear equation written in standard or slope-intercept form including equations for horizontal and vertical lines; graph the line using the ordered pairs
   4. Find the intercepts given a linear equation; express the intercepts as ordered pairs
   5. Graph the line using intercepts and check with a third point
   6. Find the slope of a line from a graph and from two points
   7. 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
   8. Graph a line with a known point and slope
   9. Manipulate a linear equation into slope-intercept form; identify the slope and the vertical-intercept given a linear equation and graph the line using the slope and vertical-intercept and check with a third point
   10. Recognize equations of horizontal and vertical lines and identify their slopes as zero or undefined
   11. Given the equation of two lines, classify them as parallel, perpendicular, or neither
   12. Find the equation of a line using slope-intercept form
   13. Find the equation of a line using point-slope form
9. Applications of linear equations in two variables
   1. Interpret intercepts and other points in the context of an application
   2. Write and interpret a slope as a rate of change (include units of the slope)
   3. Create and graph a linear model based on data and make predictions based upon the model
   4. Create tables and graphs that fully communicate the context of an application problem and its dependent and independent quantities
10. LINEAR INEQUALITIES IN TWO VARIABLES
    1. Identify a linear inequality in two variables
    2. Graph the solution set to a linear inequality in two variables
    3. 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.