Mathematics

Syllabus

Mathematics 65 - Elementary Algebra

Effective Fall 2006

Text:   Elementary Algebra, Concepts and Applications, 7^th Edition, Bittinger/Ellenbogen Addison Wesley Publishers 

Ancillaries for the Instructor:

            Annotated Instructors Edition                          ISBN: 0-321-23385-9

            Complete Solutions Manual                             ISBN: 0-321-26955-1

             Printed Test Bank and Resource Guide            ISBN: 0-321-26956-X

            Computerized Test Bank                                  ISBN: 0-321-26948-9

            Answer Book                                                  ISBN: 0-321-26953-5

            Adjunct Support Manual                                  ISBN: 0-321-29446-7 

Ancillaries for the Student:

            Student Solutions Manual                      ISBN: 0-321-26954-3

            Student Video                                       ISBN: 0-321-26952-7

            Digital Video Tutor                               SBN: 0-321-26951-9

Note:  Instructor Joe Berland has written supplementary materials for this textbook. Each section for which there are materials is marked with an asterisk. Pages are attached to this syllabus on which a description is given of what is discussed in the supplementary material for each section. All the supplementary material is optional. See Alice to obtain an electronic or a hard copy of the supplement.

Chapter 1   Introduction to Algebraic Expressions

Hours: 8. The document “Fundamental Concepts” is in the supplementary materials. It is important to teach this material here if you are going to use the supplementary material for many other sections. It takes about two hours of class time. 

Chapter 2  Equations, Inequalities, and Problem Solving

Hours: 10 

Chapter 3  Introduction to Graphing

Hours: 7 

Chapter 7  Systems and More Graphing

Hours: 6 

Chapter 4  Polynomials

Hours: 10 

Chapter 5  Polynomials and Factoring

Hours: 10 

Chapter 6  Rational Expressions and Equations

Hours: 9 

Chapter 8  Radical Expressions and Equations

Hours: 2.  In Section 8.2, define square root and simplify square roots of constants only.  Students need to be able to use square roots in solving quadratic equations. 

Chapter 9  Quadratic Equations

Hours: 2

Total hours: 64 

In this chart 1 “hour” corresponds to a 50-minute class session.  This course meets for a total of  77-83 “hours” (depending on holidays) during the semester.  So this schedule leaves you 13-19 “hours” for review, collaborative, and exams.  If you have extra time, add more depth to the course rather than covering new topics. 

Since very few of our classes still have 50-minute class sessions, it is useful to note that

the textbook chapters neatly divide the course into 8 parts.  So you’ll spend about two

weeks each on chapters 1,2,3,7; a little more than two weeks each on chapters 4,5,6;

and about a week on chapters 8 and 9. 

If  you choose to give an exam after each chapter, you would be giving an exam about every two weeks.  Many instructors like to give major exams less frequently, interspersed with shorter quizzes or tests.  An example would be: 

Quiz 1:  Chapter 1

Exam 1: Chapters 1 and 2

Quiz 2:  Chapter 3

Exam 2:  Chapter 3 and 7

Quiz 3:  Chapter 4

Exam 3:  Chapters 4 and 5

Quiz 4:  Chapter 6.1 – 6.5

Exam 4:  Chapters 6 and Sections 8.1, 9.1, 9.3

Kolb  Revised 6/2004

Stubblebine  Revised 3/2005

Revised Joe Berland, Fall 2006

DESCRIPTION OF SUPPLEMENTARY MATERIALS 

Fundamental Concepts 

What is division? Division by zero is undefined (meaningless). Concept of set. Definitions of constant, variable, expression. Domain of an expression. Equivalent expressions. Definition of equation. Solutions to equations. Domain of an equation. Equivalent equations. Exercises. 

I highly recommend beginning the course by spending about two hours on this material. Much of the remaining supplementary materials involves extensions and reinforcements of the ideas in “Fundamental Concepts,” most especially the concepts of domain and equivalence. 

Section 1.1 

Ordered pairs and ordered n-tuples in general. Domain of expressions with more than one variable. Exercises. 

Section 1.2 

Discussion of commutative, associative, and distributive laws using the concepts of domain and equivalent expressions. 

Sections 2.1 and 2.2 

Discussion of addition and multiplication principles of equality using the concepts of domain and equivalent equations. 

Section 2.3 

Supplemental discussion of a text example, discussing the equivalence of the equations formed when solving a literal equation. 

Section 2.6 

Discussion of addition and multiplication principles for inequalities using the concepts of domain and equivalent inequalities. 

Sections 3.2 and 3.3 

Meaning of the graph of an equation. Meaning of graphs that are lines. Deducing that if the graphs of ,  and  are lines, then the graph of  

(A and B not both zero) is a line. What is the graph of  when A and B are both zero? 

Section 3.6 

Discussion of slope and parallel lines, correcting errors in the text. 

Section 3.7 

Derivation of the point-slope form, correcting the errors and gross incompleteness of the derivation in the text. Deriving the slope-intercept form from the point-slope form. 

Sections 7.2 and 7.3 

Justification of the number of solutions to systems of linear equations using the concept of equivalent systems, when using substitution or elimination. 

Section 5.6 

Discussion of the principle of zero products, using the concept of equivalent statements. 

Section 6.6 

Deeper discussion than in the text on why extraneous roots do or do not occur in rational equations, using the concepts of domain and equivalent equations. 

Section 8.1 

Domain of an expression with a square root. 

Section 9.1 

Discussion of the principle of square roots, using the concept of equivalent equations. 

Section 9.3 

Stating the quadratic formula with a  properly restricted lead coefficient and using the language of equivalent equations.