Discipline: Mathematics
Originator: James Namekata
Riverside Community College District
Integrated Course Outline of Record
Mathematics
52
MAT-52 : Elementary Algebra |
College:
Lecture Hours:
90.000 Outside-of-Class Hours: 180.000 Units: 5.00 Grading Methods: Pass/No Pass Letter Grade |
Course Description
Prerequisite:
None
Course Credit Recommendation:
Non-Degree Credit
Examines the four basic operations of real numbers without the use of any calculating device. Variables will be covered as they are involved in polynomials, fractions, linear equations, quadratic equations, systems of equations, inequalities, exponential and radical expressions, and absolute value. Factoring, graphing, and word problem applications will also be included. 90 hours lecture. (Non-degree credit course. Letter grade, or Pass/No Pass option.)
Short Description for Class Schedule
Study the four basic operations applied to real numbers, to include applications to real world problems along with the concepts of algebra and its uses.
Entrance Skills:
Before entering the course, students should be able to demonstrate the following skills:
Course Objectives:
Upon successful completion of the course, students should be able to demonstrate the following activities:- Simplify expressions using the properties of real numbers.
- Simplify expressions using the properties of exponents.
- Simplify polynomial, rational and radical expressions.
- Divide polynomials.
- Factor polynomials.
- Solve linear, quadratic, polynomial, rational and radical equations.
- Solve linear systems of equations in two variables using substitution and elimination.
- Solve and graph linear inequalities in one and two variables.
- Solve applications using linear, quadratic and rational equations and systems of linear equations.
- Graph lines.
- Graph linear inequalities in two variables.
- Write equations of lines using the slope-intercept and the point-slope form.
- Simplify expressions involving whole numbers, integers and rational numbers.
- Simplify expressions using the order of operations.
- Simplify algebraic expressions involving polynomials.
- Translate expressions and equations into algebraic symbols.
Student Learning Outcomes:
Upon successful completion of the course, students should be able to demonstrate the following skills:- Simplify algebraic expressions using correct mathematical symbols and language.
- Factor polynomials.
- Identify and apply appropriate methods to solve linear, quadratic, rational, and radical equations.
- Critical Thinking: Students will be able to demonstrate higher-order thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
- Solve applications that require writing and solving equations. Communicate solution in the context of the problem.
- Communication Skills: Students will be able to communicate effectively in diverse situations. They will be able to create, express, and interpret meaning in oral, visual, and written forms. They will also be able to demonstrate quantitative literacy and the ability to use graphical, symbolic, and numerical methods to analyze, organize, and interpret data.
- Graph linear equations.
- Simplify numerical expressions involving whole numbers, integers and rational numbers.
- Critical Thinking: Students will be able to demonstrate higher-order thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
Course Content:
- Real number operations
- Addition of real numbers
- Subtraction of real numbers
- Multiplication of real numbers
- Division of real numbers
- Properties of real numbers
- Simplifying algebraic expression using real numbers
- Order of operations with real numbers
- Linear equations and inequalities in one variable with applications
- Solving linear equations using the addition principle
- Solving linear equations using the multiplication principle
- Solving linear equations using the addition and multiplication principle
- Solving formulas for specific variables
- Application problems with percentages
- Solving linear equation application problems
- Solving linear inequalities
- Solving linear inequality application problems
- Graphs of linear equations and inequalities
- Graph linear equations with two variables by x-y tables
- Graph linear equations using the x- and y- intercepts
- Graph linear equations by using the slope and y-intercept
- Write linear equations by using the slope and y-intercept
- Write linear equations by using the slope and a point
- Write linear equations by using two points on a line
- Graph linear inequalities
- Systems of linear equations and applications
- Solving systems of equations with two variables using graphing methods
- Solving systems of equations by the substitution method
- Solving systems of equations by the elimination method
- Solving application problems of system of equations
- Exponents and polynomials
- Product rule of exponents
- Quotient rule of exponents
- Negative exponent rule
- Power rule of exponents
- Product to a power rule of exponents
- Quotient to a power rule of exponents
- Scientific notation
- Addition of polynomials
- Subtraction of polynomials
- Multiplication of polynomials
- Special product of multiplication
- Operations of polynomials with several variables
- Division of polynomials
- Factoring polynomials
- Factoring the GCF from a polynomial
- Factoring by grouping methods
- Factoring trinomials in the form ax^{2}+bx+c=0 with a=1
- Factoring trinomials in the form ax^{2}+bx+c=0 with a≠1
- Factoring perfect square trinomials and difference of squares
- Rational expressions and equations
- Simplifying rational expressions
- Multiplying rational expressions
- Division of rational expressions
- Addition of rational expressions
- Subtraction of rational expressions
- Simplifying complex rational expressions
- Solving rational equations
- Solving applications of rational equations
- Radical expressions and equations
- Simplifying radical expressions
- Multiplication of radical expressions
- Division of radical expressions
- Addition of radical expressions
- Subtraction of radical expressions
- Solving radical equations
- Quadratic equation
- Solving quadratic equations by factoring
- Solving quadratic equations by the square root property
- Application of solving quadratic equations
- Solving quadratic equations by using the quadratic formula
Methods of Instruction:
Methods of instruction used to achieve student learning outcomes may include, but are not limited to, the following activities:
- Class lectures, discussions, and demonstrations of the four basic operations as applied to real numbers and polynomials as well as rational and radical expressions, graphing linear equations and inequalities, factoring polynomials, and evaluating algebraic expressions. Delivery of content may take place in an on-line/distance education setting.
- Drills and pattern practices utilizing hand-outs and/or computer-based tools in order to assist the students in mastering the techniques involved in applying the algebraic principles and techniques to the solution of applications, the four basic mathematical operations as applied to real numbers and polynomials as well as rational and radical expressions.
- Provision and employment of a variety of learning resources such as videos, slides, audio tapes, computer-based tools, manipulatives, and worksheets in order to address multiple learning styles and to reinforce material.
- Pair and small group activities, discussions, and exercises in order to promote mathematics discovery and enhance problem solving skills.
Methods of Evaluation:
Students will be evaluated for progress in and/or mastery of student learning outcomes using methods of evaluation which may include, but are not limited to, the following activities:
- Evaluation of written homework assignments and/or computerized homework assignments for correct application of algebraic principles as well as the correct use of symbols and vocabulary of algebra.
- Evaluation of quizzes and midterm/final examinations for conceptual understanding as well as correct technique and application of algebraic principles, the four basic mathematical operations as applied to real numbers and polynomials as well as rational and radical expressions, graphing linear equations and inequalities, factoring polynomials, and evaluating algebraic expressions.
- Assessment of classroom discovery activities for content knowledge and conceptual understanding.
Sample Assignments:
Outside-of-Class Reading Assignments
- Read and analyze text, examples, and notes covering topics such as evaluating algebraic expressions and solving equations.
Outside-of-Class Writing Assignments
- Use the symbols of algebra while solving application problems.
Other Outside-of-Class Assignments
- Problem sets that require students to perform arithmetic operations on expressions, solve equations, or graph equations.
Course Materials:
All materials used in this course will be periodically reviewed to ensure that they are appropriate for college level instruction. Possible texts include the following:
- Bittinger. Introductory Algebra. 12th Pearson Education, 2015.
- Sullivan. Elementary Algebra. 4th Pearson Education, 2018.
- Tussy & Gustafson. Elementary Algebra. 5th Brooks Cole, 2013.
- (In addition to the textbooks listed, instructors may also choose open source textbooks which often come at little or no cost to the students such as OpenStax Elementary Algebra) https://openstax.org/details/books/elementary-algebra
Codes/Dates:
CB03 TOP Code:
1701.00 - Mathematics, General
CB05 MOV Transfer Status: Non-Transferable (C)
CB05 NOR Transfer Status: Non-Transferable (C)
CB05 RIV Transfer Status: Non-Transferable (C)
CB05 MOV Transfer Status: Non-Transferable (C)
CB05 NOR Transfer Status: Non-Transferable (C)
CB05 RIV Transfer Status: Non-Transferable (C)
Board of Trustees Approval Date:
04/16/2019
COR Rev Date:
04/16/2019