LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK MATHEMATICS DEPARTMENT Fall 2014

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1 1 LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK MATHEMATICS DEPARTMENT Fall 2014 MAT 097: Algebra 6 Lecture Hours, 2 Educo Lab Hours, 2 Tutoring Lab Hours, 0 Credits Catalog Description This course has a problem solving approach that emphasizes the importance of mathematical reasoning in addressing real-world problems drawn from diverse disciplines. Topics include arithmetic (signed numbers, fractions, decimals and percents), linear equations and inequalities, basics of geometry, functional concepts, linear function and its graph, polynomial algebra, radical expressions, and the quadratic formula. Applications to linear and quadratic model are featured. The course is intended for students with little or no algebra background. Instruction Objectives During this course, the instructor expects to: 1. Provide students with the arithmetic skills necessary to solve real world problems involving whole numbers, fractions and decimals. 2. Familiarize students with proportional reasoning, enabling them to solve a wide variety of applied problems, and providing a natural introduction to solving one variable equations. 3. Develop the students number sense, providing them with skills in estimation and unit analysis. 4. Thoroughly reinforce students' signed number skills, not only in performing arithmetic operations but also in the settings of exponents and scientific notation. 5. Familarize students with the basics of plane geometry, in particular providing them with formulae for calculating the areas and perimeters of familiar geometric figures, and with the Pythagorean Theorem. 6. Introduce students to numerical/algebraic relationships between two variables, fostering their ability to visualize these relationships as graphs in the xy-coordinate plane. 7. Reinforce and expand students' equation-solving abilities: linear equations in one and two unknowns, absolute value equations, and linear inequalities. 8. Provide the student with the skills necessary to construct graphs from linear equations and to deduce linear equations from graphs of straight lines. 9. Enable students to solve systems of linear equations graphically and algebraically and to appreciate the diverse applications involving such systems.

2 2 10. Introduce students to functional concepts: elementary examples, table functions, inputoutput model, domain and range, and vertical line test. 11. Reinforce the laws of exponents in the more general setting of signed numbers. 12. Provide students with the skills required to carry out arithmetic operations on polynomials, factoring, and division. 13. Familiarize students with the algebra of radical expressions and teach them how to solve elementary radical equations. 14. Introduce students to quadratic functions and provide them with a powerful tool for finding the zeros of such functions: the quadratic formula. Performance Objectives At the conclusion of this course, students will be able to: 1. Solve real life problems requiring a full range of arithmetic skills. 2. Solve challenging real life problems involving ratios, proportion and percents. 3. Perform estimates, and therefore to judge whether more elaborately and precisely calculated solutions to problems are numerically reasonable. 4. Make calculations with signed numbers in a variety of different settings. 5. Compute areas and perimeters of basic two-dimensional geometric figures, and to use the Pythagorean theorem to find the length of the third side of a right triangle given the lengths of two other sides. 6. Appreciate elementary numerical/algebraic relationships between two variables and to understand how such relationships can be visualized as planar graphs. 7. Solve elementary equations in both one and two variables as well as linear inequalities. 8. Understand/master algebra fundamentals as generalizations of arithmetic, thus establishing a base upon which to build the sequel course, MAT Appreciate the interplay of algebra and geometry in drawing graphs of straight lines and deriving linear equations from straight line data. 10. Solve systems of linear equations pose in a variety of real-world settings. 11. Understand the power and versatility of the function concept in tabular as well as algebraic settings, and perform elementary tests to decide if a given relationship between two variables is indeed a function. 12. Use laws of exponents appropriately in various algebraic settings. 13. Perform arithmetic operations on polynomials, including factoring, and division 14. Combine and simplify radical expressions and solve elementary equations involving radicals. 15. Grasp the basics of quadratic functions and compare to the (first degree) linear case, and finally use the quadratic formula to find the zeros of such (second degree) equations.

3 Texts: Pre-Algebra (6th edition EDUCO International, Inc.) Man M. Sharma (MAT 095) Beginning Algebra (6th edition EDUCO International, Inc.) Man M. Sharma (MAT 096) 3 Evaluation The purpose of a grading system is to give you, the student, and anyone else reading your transcript an accurate record of your performance in this course. The role of the Mathematics Department is to provide a fair, valid, and reliable structure for assessing your achievement. Note: This is a combined MAT 095/096 course. The first segment of the course (weeks 1-5) will cover MAT 95 material and the second segment (weeks 6-12) will cover MAT 096 material. In each of the two segments the students will be evaluated in the following categories: MAT 095 Categories Online Homework Online Quizzes Lab Worksheets Instructor s Exams Departmental Midterm Exam Departmental Final Exam 5 % 15 % 25 % 35 % Only the students who pass the MAT 095 segment with a total score of at least 74% AND a score of at least 60% on the MAT 095 Final Exam will continue with the MAT 096 segment. The students who fail the MAT 095 segment will continue with the MAT 095 content until the end of the semester. The students who continue with the MAT 096 segment will be evaluated in the following categories: MAT 097 Categories Total MAT 095 score 35% MAT 096 Online Homework MAT 096 Online Quizzes MAT 096 Lab Worksheets MAT 096 Instructor s Exams MAT 096 Midterm Exam CUNY Algebra Final Exam 4 % 3 % 3 % 35 %

4 4 Explanation of Grading Standards 1. Online Homework. Daily online assignments will be given. It is very important that you do them because they reinforce the concepts learned in that section. 2. Online Quizzes You will be required to take quizzes and tests online. It is important that you are aware of deadlines, because after these deadlines the computer will not allow you to take the test. 3. Instructor s Exams Your professor will develop and administer several tests during the course of the semester before the Departmental exams. 4. Lab Worksheets You will meet in the Math Lab (E-215) two hours every week and work on lab sheets containing problems that will enhance your computational skills. You are encouraged to work together and learn from each other. Should you need further assistance, you may ask the lab assistants or bring your questions up with the professor in class. These sheets must be handed in to the lab assistants at the end of the hour. They will then be placed in your professor's folder for review. 5. Departmental Midterm Exams. One 1 hour departmental midterm online exam consisting of 15 multiple choice questions will be given in each of the segments. 6. CUNY Final Exam The CUNY final exam for each of the two segments will be cumulative online exam. Each exam will consist of 25 multiple-choice questions. Attendance Maximum number of absences will be 18 hours. Unexcused absences beyond this maximum will result in a grade of WU or F. Academic Integrity This class will be conducted in compliance with LaGuardia Community College s academic integrity policy. In order to pass this course, you must have a) passed the MAT 095 segment, b) a score of at least 60% on the CUNY Final Exam, c) a total average score of at least 74%, d) no more than 18 hours of unexcused absences, e) completed all assignments and quizzes, tests, departmental exams, and all lab sheets. A student who has not reached the level required to pass the course, but has satisfactorily completed all assigned work, demonstrated satisfactory progress toward the goal of the course, and met attendance requirements may obtain an R grade. Otherwise the student obtains an F grade. Note: Calculators and other electronic devices are NOT allowed in this course.

5 5 COURSE OUTLINE Texts: Pre-Algebra (6 th edition, EDUCO International, Inc.) and Beginning Algebra (6th edition, EDUCO International, Inc.) by Man M. Sharma The following syllabus is a guide for classroom instruction. It is subject to change based on the College s academic calendar. EDUCO on-line homework and quizzes are date sensitive and must be activated by the instructor. These assignments should be coordinated with the appropriate class work material. Week Lesson Topic Section Whole Numbers (Review). Integer, opposites, absolute value. Addition and subtraction with integers. Multiplication and Division with Integers. Exponents, Order of Operations. Lab #1 Translations; Simplifying and Evaluating Expressions. Computing Averages. Solving Equations with Integers Lab # Instructor s Test #1 Applications using integers. Basic Geometry: Perimeter and Area Multiples, and Factors. Prime Factors. Least Common Multiples. Lab #3 Equivalent Fractions. Comparing Fractions. Introduction to Mixed Numbers. Translating Ratios, Rates, Percents to Fractions Addition and Subtraction with Fractions. Lab # Addition and Subtraction with Fractions. Multiplication and Division with Fractions Order of Operations with Fractions Equations with Fractions and Proportions Lab #5 Problems with Fractions Problems with Fractions (cont.) Problems with Ratios and Proportions (continued) Review for MAT 095 Departmental Midterm MAT 095 Departmental Midterm S1.6

6 Lab #6 Reading and Writing Decimals, Rounding Decimals. Operations on Decimals. Decimals and Fractions. Scientific Notation. Decimals and Fractions Lab#7 Equations with Decimals. Applications with Decimals Square Roots and the Pythagorean Theorem Review Instructor s Test #2 Lab #8 Applications to Geometry. Area of a Circle, Circumference. Percents, Changing Percent to Decimal or Fraction, Changing Fraction or Decimal to Percent. Solving Percent Problems. Lab #9 Solving Percent Problems (cont.) Plotting Points: Linear Equation in Two Variables and its Graph Solution of Linear Inequalities Exponents Lab #10 Review MAT 095 Departmental Final S S1.8 S Operations with integers Operations with fractions (including LCD) Translating statements to mathematical Expressions Linear equations (in one variable) Lab #11 More on Solving Linear equations Applications of linear equations Literal Equations. Absolute Value Equations. Linear Inequalities Lab #12 Linear Equations in Two Variables Linear Equations in Two Variables Graphing Linear Equations. Slope. Equations of a Line. Lab #13 Solving Systems of Linear Equations Graphically Substitution Method. Addition Method. Applications of the System of Linear Equations. Lab #

7 Instructor s Test #3 Introduction to Relations and Functions: Functional Notation, Domain, Range and Vertical Line Test. Exponents & Polynomials Rules of Exponents. Integer Exponents. Lab #15 Polynomial Addition & Subtraction. Polynomial Multiplication. Special Products. Polynomial Division: by monomials only Lab #16 Factoring Greatest Common Factor (GCF). Factoring by Grouping. Factoring Trinomials Special Factorization (Difference of two Squares, etc.) Review MAT 096 Departmental Midterm Lab #17 Solving Quadratic Equations by Factoring. Applications of Quadratic Equations. Lab #18 Roots (Square roots only) Finding roots Multiplication and division of roots Addition and subtraction of roots Lab #19 Rationalizing the denominator Quadratic Equations Square root property Solution by Quadratic formula Lab #20 Instructor s Test #4 Review Decimal numbers Percents Ratios and proportions Scientific notation (including word problems) Cumulative review for the CUNY Final CUNY Algebra Final Exam

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