Fundamentals of Algebra
Updated February 17, 2012
- Semester Credit Hours: 3
- Lecture Hours per Week: 3
- Lab Hours per Week: 1
- Contact Hours per Semester: 64
An introductory algebra course designed to increase proficiency in the mathematics of the real number system, linear equations and inequalities, functions and their graphs, quadratic equations, exponents, and radicals. Will not meet graduation requirements. (3-3-1)
Basic Intellectual Compentencies in the Core Curriculum
- Critical thinking
- Computer literacy
Perspectives in the Core Curriculum
- Establish broad and multiple perspectives on the individual in relationship to the larger society and world in which he/she lives, and to understand the responsibilities of living in a culturally and ethnically diversified world.
- Stimulate a capacity to discuss and reflect upon individual, political, economic, and social aspects of life in order to understand ways in which to be a responsible member of society.
- Develop a capacity to use knowledge of how technology and science affect their lives.
- Develop personal values for ethical behavior.
- Use logical reasoning in problem solving.
- Integrate knowledge and understand the interrelationships of the scholarly disciplines.
Core Components and Related Exemplary Educational Objectives
- To apply arithmetic, algebraic, geometric, higher-order thinking, and statistical methods to modeling and solving real-world situations.
- To represent and evaluate basic mathematical information verbally, numerically, graphically, and symbolically.
- To expand mathematical reasoning skills and formal logic to develop convincing mathematical arguments.
- To use appropriate technology to enhance mathematical thinking and understanding and to solve mathematical problems and judge the reasonableness of the results.
- To interpret mathematical models such as formulas, graphs, tables and schematics, and draw inferences from them.
- To recognize the limitations of mathematical and statistical models.
- To develop the view that mathematics is an evolving discipline, interrelated with human culture, and understand its connections to other disciplines.
Instructional Goals and Purposes
Panola College's instructional goals include 1) creating an academic atmosphere in which students may develop their intellects and skills and 2) providing courses so students may receive a certificate/an associate degree or transfer to a senior institution that offers baccalaureate degrees.
General Course Objectives
The goal of this course is to increase academic proficiency in expression of mathematical solutions, mathematical reasoning, and mathematical understanding.
Specific Course Objectives
I. NUMERIC REASONING
1.) To perform computations with and to compare real numbers.
2.) To use estimation to check for errors and reasonableness of solutions.
II. ALGEBRAIC REASONING
3.) To explain and differentiate between expressions and equations using words such as “solve”, “evaluate”, and “simplify”.
4.) To recognize and use algebraic field properties, concepts, procedures, and algorithms to combine, transform, and evaluate expressions.
5.) To explain the difference between the solution set of an equation and the solution set of an inequality.
6.) To recognize and use algebraic field properties, concepts, procedures, and algorithms to solve equations.
7.) To interpret multiple representations of equations and relationships.
8.) To translate among multiple representations of equations and relationships.
III. GEOMETRIC REASONING
9.) To recognize and apply right triangle relationships.
10.) To make connections between geometry and algebra.
IV. MEASUREMENT REASONING
11.) To find the perimeter and area of two-dimensional figures.
12.) To determine indirect measurements of figures using Pythagorean Theorem.
13.) To recognize whether a relation is a function.
14.) To recognize and distinguish between linear and quadratic functions.
15.) To understand and analyze features of a function.
16.) To algebraically construct and analyze linear and quadratic functions.
17.) To apply linear and quadratic function models to real-world situations.
18.) To develop a linear or quadratic function to model a situation.
VI. PROBLEM SOLVING AND REASONING
19.) To analyze given information, formulate a plan or strategy, determine a solution, justify the solution, and evaluate the problem-solving process.
20.) To formulate a solution to a real-world situation based on the solution to a mathematical problem.
21.) To use a function to model a real-world situation.
VII. COMMUNICATION AND REPRESENTATION
22.) To use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
23.) To use mathematical language to represent and communicate the mathematical concepts in a problem.
24.) To use mathematics as a language for reasoning, problem solving, making connections, and generalizing.
25.) To model and interpret mathematical ideas and concepts using multiple representations.
26.) To summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
27.) To communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, graphs, and words.
28.) To create and use representations to organize, record, and communicate mathematical ideas.
29.) To explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
30.) To connect and use multiple strands of mathematics in situations and problems.
31.) To connect mathematics to the study of other disciplines.
32.) To use multiple representations to demonstrate links between mathematical and real-world situations.To know and understand the use of mathematics in a variety of careers and professions.
General Description of Each Lecture or Discussion
Disability Considerations (ADA and 504)
As mandated by Section 504 of the Rehabilitation Act and rights protected under ADA, students with disabilities may not be discriminated against and are afforded equal access to services offered by the College. If you have a disability, you are not required to disclose the disability to your professor; however, if you wish to gain services or modifications, you must see Teresa Washington-Brooks and provide proper documentation. As the Disability Support Service Coordinator, you can reach Teresa through email, at firstname.lastname@example.org, by telephone at 903-693-1123, or in her office in the Miller Administration Building.
Withdrawing from a course
It is the responsibility of the student to withdraw or drop a course. A student interested in doing so should consult the Academic Calendar to determine the last day to drop. Be advised that according to legislation, students in the state of Texas will only be allowed to drop 6 courses over the tenure of their academic endeavors. Think carefully and meet with the instructor before withdrawing from any course. However, if you do not drop the course and you stop attending, you will likely receive an F for the course.
Students are expected to be respectful of the beliefs of others. This includes sensitivity to cultural, familial, language, and manifestations of dress indicative of a global community. Further, students are expected to maintain standard classroom decorum which includes taking turns in speaking, not talking out, attacking other students or faculty either physically, verbally, or emotionally. All language and comments should be appropriate for a community college classroom. Virtual etiquette will not deviate from that required in face to face instruction. Distractions to the concentration of fellow students should be avoided. This includes arriving late or leaving early. Cell phones and other electronic devices should not be in use during lecture. These items should not be visible during class and should be turned off or placed on vibrate.
After studying the material presented in lectures and labs, the student should be able to complete all learning and performance objectives with an average of 70% competency in all assignments, tests, and assessments. Upon completion of this course, the students will be able to:
- Operations with Real Numbers and Introduction to Algebra – Demonstrate skills in simplifying and evaluating numeric and algebraic expressions using the Order of Operations, Commutative, Associative, Additive and Multiplicative Identity, Additive and Multiplicative Inverse, and Distributive properties. Identify terms, numerical coefficients, and like terms and simplify expressions by combining like terms.
- Solving Affine Equations and Inequalities – Identify linear equations and define the terms solution and equivalent equations. State the four properties of equivalent equations and use them to solve linear equations. Write word phrases and sentences as mathematical expressions and equations. State the properties of equivalent inequalities and use them to solve linear inequalities. Graph intervals on a number line.
- Algebraic Expressions and Polynomials – Define the terminology of exponential notation and use integer exponents exponents to rewrite and evaluate expressions. Use the rules of exponents to simplify expressions. Identify the terms and coefficients of a polynomial expression. Define the terms monomial, binomial, trinomial, and polynomial. Add, subtract, and multiply polynomials.
- Factoring and Solution of Quadratic Equations by Factoring – Define the concept of “factoring” a number or expression. Find the greatest common factor of a given list of integers or polynomial expressions. Factor a polynomial by dividing out the greatest common factor of its terms. Factor polynomials by grouping. Factor trinomials including perfect square trinomials. Factor polynomials using the difference of two squares. State the Principle of Zero Products and use it to solve quadratic and higher degree polynomial equations by factoring. Translate real-world situations into quadratic equations in order to solve problems involving area, perimeter, consecutive integers, and the Pythagorean Theorem.
- Linear Equations in Two Variables and Analytic Geometry – Define the terminology in the Cartesian Coordinate System including axes, quadrants, ordered pairs, and origin. Graph ordered pairs as points in the coordinate plane and determine in which quadrant a point is located. Graph linear equations and functions by completing a table of ordered pairs. Define the terms x- and y-intercepts, determine the x- and y-intercepts of a linear equation, and use the intercepts to graph the linear equation. Define the term slope and determine the slope of a line when given a graph, table, or two points that lie on the line. Graph a line given its slope and a point. Given the slope and y-intercept of a line, write the equation of the line in slope-intercept form. Graph a line using the slope-intercept form of its equation.
- Functions – Define and recognize functions. Use function notation and evaluate a function for a given input value. Recognize and use multiple representations of functions such as equations, tables, graphs, and sets of ordered pairs.
- Roots and Radical Expressions – Find the square root of a number. Find selected higher order roots of a number. Decide whether a given root is rational or irrational. Simplify radical expressions using the Product Rule. Solve quadratic equations using the square root property.
Methods of Evaluation
Four Major Exams** 50%
Homework/Math Lab/Quizzes 15%
Comprehensive Final Exam 25%
**Note: There will be no make-up exams. If you miss an exam, your Final Exam percentage will be used as a substitute for the missing grade. If you do not miss any exams, your one lowest Exam grade will be replaced by the Final Exam percentage provided it (the final exam percentage) is higher and you have not exceeded the maximum number of allowed absences in the class.
Texas Success Initiative (TSI)
You must have a C or better to complete your TSI requirements or pass the MATH Section of the Accuplacer. Students who pass the MATH Section of the Accuplacer can choose to withdraw from the course immediately and receive either their current grade or a W or they may choose to finish the semester and receive the grade earned based on the grading schedule.
Letter Grades for the Course will be assigned as follows:
A: 90 < Average < 100
B: 80 < Average < 90
C: 70 < Average < 80
D: 60 < Average < 70
F: 00 < Average < 60
Q: 00 < Average < 70 (and meets guidelines below)
Q GRADE: Students who fail to master the educational objectives of the course but complete the semester showing progress in the discipline will be assigned a Q grade. This grade will prevent a student from receiving a grade of D or F. To receive this grade a student:
- Must have no more than 5 absences to a MWF class or no more than 3 absences to a TR class.
- Must have no more than 5 unresolved tardy marks.
- Must have completed at least 90% of assigned work.
- Must not have violated the Academic Dishonesty policy published in each Developmental Education Syllabi.
If a student is awarded a “Q” they must repeat the same course the next long semester or retake and pass a TSI assessment before the next long semester begins. The repeated class will receive the grade earned, but the “Q” from the previous semester will not be amended. Students who are TSI deficient in two or more areas may not skip a semester if a grade of “Q” is attributed.
Receiving a “Q” can only occur once per developmental course.
For each section covered in lecture there will be an assignment on My Math Lab.
Your teacher may require you to keep a notebook in which you show work on all problems assigned. Work should be labeled by section and problem number. Homework notebooks will be turned in on exam day for grading. If the notebook is not turned in, or if it is disorganized, could result in a grade of 0. A calendar is provided to help you keep track of the assignments. Although the homework will be graded on exam day, you should work on the assignments immediately following the lecture over each lesson
Your teacher may give graded quizzes throughout the semester. These will be done on My Math Lab and may be done anywhere you have access to the internet. However, in order to receive a grade for a quiz, you must turn in a hand written record of your work on the problems. This can be done in your homework notebook or on a separate sheet of paper. You are on an honor system to do the work on your own. Quizzes will be set to turn off at the due date and time. After that time, you will not be able to take the quiz and you will receive a grade of 0. In the case of an extreme emergency, see me to discuss the possibility of a make- up quiz.
Exams are scheduled in advance and every effort should be made to attend class on exam day. In the case of an extreme emergency please speak with me to arrange making up the exam prior to your next class meeting. If you do not make up the exam prior to the next class, a grade of 0 will be assigned.
However, I will replace your lowest exam grade with your grade on the final (if it is higher) and you do not exceed the maximum number of allowed absences in the class. This can take the place of a missed exam if necessary.
Students are required to be in attendance every class day and attendance will be recorded. As a student you are allowed to have 5 absences in MWF classes, and 3 in TR classes. I will not differentiate between excused and unexcused absences with the exception of those due to school related business. The only absences that an institution considers “excused” are those absences necessitated by institutional constraints or obligations. If you experience an emergency that necessitates a review of this policy, I am more than willing to consider, but it must be a legitimate emergency. Attendance is important to student success and every effort should be made to attend class regularly. Coming to class late is detrimental to your success as well as disruptive to the concentration of other students. You should avoid being late to class unless it is an extreme emergency. If you do arrive late, please see me after class to discuss the reason and to change your attendance from absent to tardy. You should also note that 3 tardies will count as an absence to class.
The student handbook has this to say about attendance…”Regular and punctual attendance of classes and laboratories is required of all students. When a student has been ill or absent from class for approved extracurricular activities, he or she should be allowed, as far as possible, to make up the work missed. When an instructor feels that a student has been absent to such a degree as to invalidate the learning experience, the instructor may recommend to the Vice President of Instructional Affairs that the student should be withdrawn from the course.”
Academic Dishonesty will not be tolerated at any level. Academic Dishonesty is defined as the act of or an attempt to pass off someone’s work as your own. It also includes resubmitting work that you submitted in a previous course. Likewise, sharing answers with others, or bringing in unapproved outside resources into an exam is considered a breach of academic honesty. Additionally, the use of cell phones to send, receive, or retrieve any material related to assignments or assessments in the course during the class is also considered a breach.
Should a professor find a student in the act of being dishonest, the student will be subject to an automatic zero for the assignment. Repeated attempts or acts of dishonesty may result in the dismissal from the course with a grade of F attributed.
Text, Required Readings, Materials, and Supplies
My Math Lab Pearson Prentice Hall. (Online Computer Access Code)
1. My Math Lab Access Code (Included in the purchase of a new book, it can also be purchased separately online)
2. Consistent access to computer
3. Canvas (Provided by Panola College)
5. Scientific Calculator
6. Other materials as assigned by the instructor.
Technical Skill Requirements
To be successful in this course, students should be able to
1) Use a web browser
2) Access and use Canvas
3) Access and use Microsoft Office or appropriate word processor
4) Use email for communication
5) Attach and send documents as email attachments
6) Download and install appropriate plug-ins as determined by system needs.
Students are required to spend the equivalent of 1 lecture hour (50 minutes) per week
in the math lab (MAR 102) and participation in the math lab will be included in calculating
the semester average for this course. Students must sign in and attendance will be
monitored. This time is designed to be utilized studying/practicing skills taught
in the developmental mathematics classes. An instructor or tutor will be present
in the lab at scheduled times to provide assistance and individual instruction. NOTE: IF YOU DO NOT ATTEND LAB 70% OF THE REQUIRED TIME, YOU WILL FAIL THE COURSE.