Core 098 - Quantitative Skills

Master Syllabus

November 2007

 

Course Description: This course develops the skills needed for other mathematics courses at King’s College, and emphasizes the organizational and analytical skills required for success in a problem solving society.  Mathematically, this course focuses on the structure of arithmetic and directly relates this understanding to the more theoretical topics of algebra.  Students will review and relearn the fundamentals of real numbers and use this knowledge as a bridge to the abstract concepts of algebra.  The arithmetic and algebraic concepts covered in the course are used to introduce the basics of problem solving and mathematical reasoning.  Topics include; whole numbers and integers, fractions, decimals, and mixed numbers, exponents, roots, simplifying algebraic expressions, solving first and second degree equations, factoring algebraic expressions, and simplifying rational expressions.

 

Introduction:

In any career or life path that you choose, it is likely that you will encounter problems where the solutions are based on mathematical and logical principles.  Therefore, the basic concepts of mathematics are a necessary component of a liberal arts education.  This course is designed to bridge the gap between high school and college mathematics courses.  The emphasis of the course is on relearning known topics and learning new topics for the purpose of understanding and then using this knowledge as a foundation for learning other concepts that are essential for success in future mathematics courses at King’s College and everyday life. 

                                                           

Goals:

1)              Students will understand the rules of algebra and how they extend from the basic principles of arithmetic.

 

2)              Students will become prepared for further mathematics courses at King’s.  Students will gain a firm understanding of the fundamentals needed to perform more complex calculations in advanced classes.   

 

3)              Students will become more comfortable and confident with mathematics and relieve any anxiety by concentrating on linking the known basics of arithmetic to the more abstract concepts of algebra.  Students will begin to appreciate their progression of knowledge in mathematics as an extension of what they already know and not a new and unrelated topic. 

 

4)              Students will learn important steps in organization and problem solving.  While some topics covered in this course may not be encountered by people outside a mathematics classroom, the analytical and procedural skills needed to solve these problems are used daily in any career or life path.    

 

Objectives:

          As a result of taking this course, students will:

1)              Understand and be able to communicate and apply the techniques of mathematics using precise terminology (i.e., be able to “think like a mathematician.”)

 

2)              Perform basic arithmetic operations with real numbers such as addition, subtraction, multiplication, division, factoring, and simplifying expressions.

 

3)              Formulate exponent rules based on past arithmetic examples and simplify expressions using these rules.

 

4)              Apply arithmetic examples of addition, multiplication, and the distributive property to perform operations with polynomials.

 

5)              Employ different methods to factoring polynomials and be able to choose when it is best to use the different methods.

 

6)              Analyze percent application problem solving to find the missing variables.

 

7)              Solve quadratic equations by either factoring or using the quadratic formula. 

 

8)              Recognize the difference between linear, quadratic and rational equations and be able to solve each for the missing variable.

 

9)              Perform operations on rational expressions corresponding to existing rules for numerical fractions.

 

10)           Sketch linear equations and be able to find the linear equation given the point and slope. Sketch quadratic equations by finding the roots and the vertex.

 

Textbook:             

Introductory Algebra, 10th edition, Marvin L. Bittinger,  

Addison Wesley Higher Education, 2006.

 

Assessment:

A) Tests

There will be four in class tests that will be announced at least one week in advance.  The format for these tests will vary depending on the content covered in class.  Since this course is meant to hone your mathematical skills, completing homework assignments, reviews, and practice problems will be the best way to prepare for each exam. You learn math by doing math!   Each test will be worth 15% of the final grade.

 

B)  Final Exam

The primary purpose of this course is for students to walk away with a much improved mastery of the mathematical skills examined in the course.  As a result, the final exam will cover all material from the course.  This exam will be given during finals week at a date and time to be determined by the registrar.  The final exam will be worth 20% of the final grade.

 

C) Homework/ Homework Quizzes:    

·                 Homework is essential for learning mathematics and your success in the course depends on the commitment you make to the daily assignments.  Homework should be brought to class every day, and individual students will take an active roll in checking and correcting their assignment. 

 

·                 Only a limited time will be spent discussing homework from the previous night.  It is the responsibility of the student to see the professor during office hours for additional help on questions that are not answered in class.

 

·                 There will frequently be homework quizzes. These quizzes will consist of questions on homework related topics that have been covered and discussed.

 

·                 Each  homework quiz will be graded on a scale of 0 to 3:

          0 = little or no work related to the problem(s).

          1 = slight knowledge is shown or correct answers are given with insufficient work. 

          2 = clear understanding, but slight mistakes in either reasoning or computation.

          3 = complete understanding and correct computation.

 

·                 If the instructor has the impression that the class is not attempting the homework, then homework may be collected and graded the class after it is assigned.

 

·                 One homework/homework quiz grade during the semester will be dropped.

 

·                 You will be required to visit at least two tutoring sessions during the semester; this will count towards your homework grade.

 

Homework and Homework Quizzes will be worth 10% of the final grade.

 

D) Classroom Participation and Attendance:

·                 You will be graded based on your attendance, involvement, and overall classroom demeanor.  Your grade will benefit from trips to the blackboard, questions asked and answered in class, positive interactions with others, completed homework assignments, homework discussion, and office hour and tutoring visits if beneficial to the learning process. 

 

·                 For each unexcused absence, your final class participation grade will be reduced by 10%. 

 

·                 Other items that will detract from your participation grade are resistance or negative participation as well as any disruption of classroom activities. 

 

·                 Students are expected to attend every class on time and be prepared to discuss the previous night’s homework and be actively involved in classroom discussion.  Remember, attendance plays a roll in your participation grade.

 

·                 If circumstances develop that cause you to miss class (serious personal illness, family emergency, documented school function, etc…) it is required that you contact me as soon as possible in advance of the absence (or A.S.A.P.) to make arrangements to complete any class work.  The absence will otherwise be considered unexcused. You will be responsible to make-up any work missed prior to the next class meeting.

 

·                 Any student failing to follow this procedure on a test date will not be given a makeup test.  Evidence of the reason for absence may be required. 

 

·                 For missed exams due to an excused absence, a MORE CHALLENGING make-up exam will be given.  For missed homework quizzes due to an excused absence, you are responsible for handing in the homework assignment for a grade. 

 

Classroom Participation and Attendance will be worth 10% of the final grade

 

 

 

 

Special Needs:

All students who have a learning disability or a physical handicap should schedule an appointment with the instructor during the first week of class to discuss accommodations for the classroom and/or assignments and examinations.

 

Other Items:

1)              A calculator is helpful and suggested for this course.  Any style of calculator is sufficient. 

 

2)              Students are expected to complete their own assignments.  Refer to the King’s College Students Handbook for the policy on Academic Integrity.

 

3)              Cell phones or other items that may cause distractions in class are not permitted.

 

4)              At certain times I may need to communicate with the class via email.  When I do, I will ONLY use your kings.edu account.  You are responsible for any information sent in this way.

 

Outline (tentative)

The course covers selected topics in the textbook along with supplemented topics.

Problem Solving, Arithmetic, and Pre-Algebra                                 Textbook Section

1)                        Factoring Integers, Least Common Multiples                   R.1

2)                        Addition and Subtraction of Real Numbers                       R.2, R.3, 1.3, 1.4

3)                        Multiplication and Division of Real Numbers                     R.2, R.3, 1.5, 1.6

4)                        Decimals, Real Numbers                                                R.3, 1.2

5)                        Exponential Notation                                                       R.5

6)                        Properties of Real Numbers, Order of Operations            R.5, 1.7, 1.8

TEST  1

Polynomials

7)                        Exponent Rules, Scientific Notation                                 4.1 – 4.2

8)                        Addition and Subtraction of Polynomials                          4.3 – 4.4

9)                        Multiplication of Polynomials                                            4.5 – 4.7

Linear Equations

10)                     Solving Equations: Addition and Multiplication Principle     2.1 – 2.3

TEST  2

11)                     Formulas and Percents                                                   2.4 – 2.5

12)                     Applications of equations                                                2.6

Factoring polynomials and Quadratic Equations

13)                     Factoring Trinomials using FOIL and By Grouping            5.1 – 5.4

14)                     Strategy of Factoring Trinomials                                      5.5 – 5.6

15)                     Solving Quadratic Equations by Factoring                        5.7

16)                     Solving quadratic equations using the quadratic formula   9.3

TEST   3

     Graphing

17)                     Graphing linear equations                                               3.1 – 3.5

18)                     Slope and Applications                                                    3.4

19)                     Graphing inequalities                                                      3.7

20)                     Graphing quadratic equations                                         9.6

TEST   4

Rational Expressions and Equations

21)                     Multiplication and Division of Rational Expressions 6.1 – 6.2

22)                     Addition and Subtraction of Rational Expressions             6.3 – 6.5

23)                     Solving Equations Containing Rational Expressions          6.6

FINAL EXAM