What is algebra? One person might conceive of algebra as generalized arithmetic. In this sense, it is manipulating symbols or performing mathematical operations with letters instead of numbers. To someone else, the process of algebra involves finding unknown values by factoring, solving equations, or solving word problems. On a third level, algebra is perceived as a mathematical language that can be used to model and communicate real-world problems. In fact, algebra is all of these!
The foundations of algebra are the rules of arithmetic, which are generalized by using symbols and letters. The resulting rules of algebra are used to rewrite algebraic expressions and equations in new, more useful forms. The ability to rewrite algebraic expressions and equations is the common skill involved in the three major components of algebra--simplifying algebraic expressions, solving algebraic equations, and graphing algebraic functions.
Intermediate Mathematics is the independent study equivalent of Math 002 (Intermediate Mathematics) at the University of Kansas. The course is designed and recommended for students who have recently taken an introductory algebra course or have had two years of high school algebra and need a refresher course. You should be able to do arithmetic with signed numbers and have some experience solving linear algebraic equations. It is extremely important for you to accurately assess your background to determine the course best suited for your ability level. You are much more likely to enjoy mathematics and experience success if you start at the proper level and then continue through the proper sequence without an extended interruption in your study.
In recent years, technological advances have made powerful computational and graphical abilities available through the use of affordable hand-held calculators. Proficient use of a graphing utility is increasingly needed for advanced course work in mathematics and the sciences. It is very likely that you will be using a graphing utility in any subsequent course you take in mathematics. This course fully integrates the use of a graphing calculator, making precision and visualization both accessible and efficient for the student.
Intermediate Algebra: A Graphing Approach. Demana, Waits, Clemens, and Greene, Addison Wesley, 1994.
A graphing calculator is required. The TI-82 or TI-83 is recommended. Graphing calculators can be purchased at office supply stores and many discount stores. The TI-82 may be ordered through the Kansas Union Bookstore with your text. To be usable for this course, a grapher must have the features listed below.
This course incorporates the use of a graphing calculator throughout for concept development, for discovery learning, and for problem solving. The interplay between algebraic and graphical methods for solving problems involves three ideas. This approach is stated as follows:
The course begins with a review of the basic numerical properties and solutions to equations in one variable, followed by solutions and graphs of linear equations in two variables. Systems of equations and inequalities in one and two variables, as well as absolute value relationships, are explored both algebraically and graphically. The second half of the course concentrates on integer and rational exponents, polynomial arithmetic, rational expressions, and radicals. Complex numbers are introduced. The course concludes with solution and graphing techniques for radical and quadratic equations. Application problems are interwoven into all topics of the course and the function concept is included throughout.
This course consists of eight lessons, eight required writing assignments, a midterm exam, and a final exam. Both the midterm and the final will be supervised, and the use of notes, books, and writing assignments is not permitted. Proficient use of a graphing calculator will be expected. You must pass the final to pass the course.
Each lesson covers five or six sections of the text. The study guide includes a brief summary of the topics covered in each lesson, objectives describing the major concepts you should have learned by the end of the lesson, and a list of the main calculator skills emphasized in the lesson. Make sure that you have mastered all of these concepts before you begin the writing assignment.
Each lesson also contains a list of practice problems from your text that should be completed, but not submitted for a grade. These problems should be treated like homework. Each set includes drill exercises, which help gain mastery of key skills, and extension exercises, which encourage creative problem solving. Most practice sets will also include some exercises on translating words to symbols and making connections with previously learned material. You will find a few exercises that require written explanations. It is extremely important for you to complete these practice problems before you begin the writing assignment.
You are encouraged to read each section of your text carefully, study the examples provided, and try the grapher explorations before you attempt the practice problems for that section. This careful preparation will be a key to success as you study independently. Check your answers to the practice problems with the solutions provided in the back of the book. Once you have mastered these practice problems, you are ready to complete the writing assignment for that lesson found in this guide.
Top of Page | Bottom of PageEach writing assignment contains twelve questions (worth three points each) that should be completed without referring to your textbook or your notes. One or two of the questions may require written explanations in addition to, or in place of, algebraic solutions. For many people, writing in a mathematics course is an unfamiliar process. Refer to Appendix A for examples of how to treat a written exercise in this course.
The writing assignment should be worked neatly. Each page should include your name, the lesson number, and the course name. Partial credit is given for partially correct solutions. It is extremely important that you show all work required for the completion of each problem. One point is deducted for answers that are not completely simplified.
When the graded assignment is returned to you, read the comments and rework any problems not receiving three points. It is important to resolve all misconceptions before proceeding to the next lesson. Concepts not mastered will be obstacles to completing subsequent lessons.
Do not complete and submit writing assignment II until the first writing assignment has been returned to you. Thereafter, you may submit assignments without waiting for previous ones to be returned to you, but you may submit no more than three assignments in any seven-day period. Be sure to include an Independent Study cover sheet with every completed assignment.
Each lesson also includes a set of flashcard questions. Memorizing the answers to these questions will give you the factual information you will need to complete the practice problems and writing assignments.
Begin by making your own flashcards from the flashcard questions and answers located in each lesson. To make your flashcard, copy the question on one side of an index card and the answer on the other. Most of the learning takes place in transferring the information to cards. Once you have made your deck of flashcards for a given lesson you are ready to begin studying them. This involves going through each card and learning the answer. Since these are fundamental concepts, it is important not only that you know them but also that you can recall them quickly. After you have studied the flashcards, have a friend test you. You should be able to answer them with very little hesitation (approximately one card every three to six seconds).
Use the flashcards to prepare for every writing assignment. If you study the flashcard concepts, you will take less time to prepare for the writing assignment and will be more likely to retain the information and succeed in this course.
The key to successful completion of this course is consistency! Once you begin the course, it is extremely important for you to interact with the material on a regular basis. Very little is accomplished with infrequent marathon sessions. Extended periods with no practice will result in your forgetting much of what you had previously mastered. Concepts learned in each lesson are necessary for comprehending future lessons.
The more algebra problems you work, the better you will become at working them. Don't expect to understand every new topic the first time you see it. Sometimes you will understand everything you are doing, and sometimes you won't. That's just the way things are in mathematics. The process of understanding algebra takes time. Working the exercises in the text will help you to gain proficiency. The practice will help you to complete the writing assignment without referring to your notes or text. If you need more practice, work additional problems from the text. Remember, you will eventually need to perform on proctored exams where notes and texts are prohibited.
To prepare efficiently, complete the following steps:
The midterm is a supervised exam over Lessons I-IV. It consists of 30 questions worth 6 points each. All work must be shown in order to receive credit for an answer. Partial credit will be given.
The final examination is a supervised, comprehensive exam taken after you have taken and received a grade for the midterm exam and all eight writing assignments have been completed. The final contains 40 questions worth 6 points each. All work must be shown in order to receive credit for an answer. You must pass the final (132 points or more out of 240 points) in order to pass the course. The grading formula that appears in the next section applies only if you pass the final.
You will be assigned both a numerical and a letter grade for your writing assignments and examinations. Be sure to bring your graphing calculator to both the midterm and final exams. You will not, however, be allowed to use your text, study guide, or any other aids.
Your course grade will be determined by the following:
Writing assignments (8 @ 36 pts.): 288 pts.
Midterm exam: 180 pts.
Final exam: 240 pts.
Total: 708 pts.
Grading Scale:
A = 637-708 points (90%-100%)
B = 566-636 points (80%-89%)
C = 460-565 points (65%-79%)
D = 389-459 points (55%-64%)
F = 0-388 points (0%-54%)
Use the form at the end of this guide to record your progress as you work through the course.
Ingrid Peterson is the assistant director of the algebra program at the University of Kansas. She has taught mathematics at both the high school and community college levels. She has a B.A. and M.A. in mathematics education and is currently pursuing a Ph.D. in mathematics education at the University of Kansas. She is originally from Lindsborg, Kansas, and resides in Lenexa, Kansas, with her husband, two teenagers, cat, and dog. Her interests include reading, music, hiking, antiquing, and spending time with her family.
Carol Lucas is originally from Carthage, Missouri, and currently resides in Lawrence, Kansas. She is the director of the algebra program at the University of Kansas. She holds a B.S. in education and an M.A. in mathematics from Southwest Missouri State University and is currently working on her Ph.D. in mathematics education at the University of Kansas. She has taught mathematics at the high school level and at both Southeast Missouri State University and Southwest Missouri State University. Her interests include reading (science fiction and mysteries), travel, and spending time with her son, Sean (6).