Introduction to algebraic concepts and processes with a focus on linear equations and inequalities in one and two variables. 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 20 and RD 80 (or ESOL 250). Audit available.
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
Use a variable to represent an unknown in a simple linear problem at home or in an academic or work environment, 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 at home or in an academic or work environment, 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.
Be successful in future coursework that requires an understanding of the basic algebraic concepts covered in the course.
Outcome Assessment Strategies
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, and 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 fill in the blank questions may be used where appropriate.
3. 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.
4. At least two of the following additional measures must also be used
a. Take-home examinations
b. Graded homework
e. In-class activities
Course Content (Themes, Concepts, Issues and Skills)
Applications, formulas, and modeling
1.1Review prerequisite skills – signed number and fraction arithmetic
1.2Simplify arithmetic expressions using the order of operations
1.3Evaluate powers with whole number exponents; emphasize order of operations with negative bases
1.6Identify numbers as elements of the subsets of the real numbers
2.0VARIABLES AND EXPRESSIONS
2.1Simplify algebraic expressions
2.2Evaluate algebraic expressions
2.3Recognize equivalent expressions and non-equivalent expressions
2.4Distinguish between evaluating expressions, simplifying expressions and solving equations
2.5Translate from words into algebraic expressions and vice versa
2.6Apply the distributive, commutative, and associative properties
2.7Recognize additive and multiplicative identities and inverses
2.8Distinguish between factors and terms
2.9Apply the product rule, product to a power rule, and power-to-a-power rule to expressions with positive integer exponents emphasizing the logic behind these rules of exponents
3.1Evaluate formulas and apply basic dimensional analysis
3.2Know and apply appropriate units for various situations; e.g. perimeter units, area units, volume units, rate units, etc
3.3Memorize and apply the perimeter and area formulas for rectangles, circles, and triangles
3.4Memorize and apply the volume formula for a rectangular solid and a right circular cylinder
3.5Find the perimeter of any polygon
3.6Evaluate other geometric formulas
3.7Use estimation to determine reasonableness of solution
4.0LINEAR EQUATIONS AND INEQUALITIES IN ONE VARIABLE
4.1Identify linear equations and inequalities in one variable
4.2Understand the definition of a solution; e.g. 2 is a solution to x < 5; 3 is the solution to x + 1 = 4
4.3Distinguish between solutions and solution sets
4.4Recognize equivalent equations and non-equivalent equations
4.5Solve linear equations and non-compound linear inequalities symbolically
4.6Express inequality solution sets graphically, with interval notation, and with set-builder notation
4.7Distinguish between solutions to equations and equivalent equations (e.g. “The solution is 2.” vs. “x = 2”)
5.1Create and solve linear equations and inequalities in one variable that model real life situations (e.g. fixed cost + variable cost equals total cost)
5.1.1Properly define variables; include units in variable definitions
5.1.2Apply dimensional analysis while solving problems
5.1.3State contextual conclusions using complete sentences
5.1.4Use estimation to determine reasonableness of solution
5.2Apply general percent equations (A = PB)
5.3Create and solve percent increase/decrease equations
5.4Create and solve ratio/proportion equations
5.5Solve 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
6.0LITERAL EQUATIONS AND FORMULAS
6.1Solve an equation for a specified variable in terms of other variables
6.2Input values into a formula and solve for the remaining variable
7.0INTRODUCTION TO TABLES AND GRAPHS
7.1Briefly review line graphs, bar graphs and pie charts
7.2Plot points on the Cartesian coordinate system; determine coordinates of points
7.3Classify points by quadrant or as points on an axis; identify the origin
7.4Label and scale axes on all graphs
7.5Interpret graphs in the context of an application
7.6Create a table of values from an equation
7.7Plot points from a table
8.0INTRODUCTION TO FUNCTION NOTATION
8.1Determine whether a given relation presented in graphical form represents a function
8.2Evaluate functions using function notation from a set, graph or formula
8.3Interpret function notation in a practical setting
8.4Identify ordered pairs from function notation
9.0LINEAR EQUATIONS IN TWO VARIABLES
9.1Identify a linear equation in two variables
9.2Emphasize that the graph of a line is a visual representation of the solution set to a linear equation
9.3Find 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
9.4Find the intercepts given a linear equation; express the intercepts as ordered pairs
9.5Graph the line using intercepts and check with a third point
9.6Find the slope of a line from a graph and from two points
9.7Given 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
9.8Graph a line with a known point and slope
9.9Manipulate 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
9.10Recognize equations of horizontal and vertical lines and identify their slopes as zero or undefined
9.11Given the equation of two lines, classify them as parallel, perpendicular, or neither
9.12Find the equation of a line using slope-intercept form
9.13Find the equation of a line using point-slope form
10.0Applications of linear equations in two variables
10.1Interpret intercepts and other points in the context of an application
10.2Write and interpret a slope as a rate of change
10.3Create and graph a linear model based on data and make predictions based upon the model
10.4Create tables and graphs that fully communicate the context of an application problem
11.0LINEAR inequalities IN TWO VARIABLES
11.1Identify a linear inequality in two variables
11.2Graph the solution set to a linear inequality in two variables
11.3Model 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.
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.
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 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.