INSTRUCTOR AREA

INSTRUCTOR SUPPLEMENTS | TA TIPS | SAMPLE SYLLABUS

INSTRUCTOR SUPPLEMENTS Instructor's Solutions Manual 0-321-06665-0 Written by Gary Rockswold, contains complete solutions to all graphical and numerical exercises. Free to instructors with textbook adoption Instructor' s Testing Manual 0-321-06668-5 Provides prepared tests for each chapter. Free to instructors with textbook adoption. Videotapes 0-321-06833-5 Videos correlate directly to the text. An engaging team of lecturers provide comprehensive coverage of material. Presenters use worked-out examples, visual aids, and manipulatives to reinforce concepts. Videos emphasize the relevance of material to the real world and relate mathematics to students' everyday lives. Can be ordered by mathematics instructors or departments. TestGen-EQ with QuizMaster-EQ Win/Mac Dual Platform CD-ROM 0-321-06831-9 Available in Windows and Macintosh versions. TestGen-EQ's friendly graphical interface enables instructors to easily view, edit, and add questions, transfer questions to tests, and print tests in a variety of fonts and forms. Search and sort features let the instructor quickly locate questions and arrange them in a preferred order. Six question formats are available, including short-answer, true-false, multiple-choice, essay, matching, and bimodal formats. A built-in question editor gives the user power to create graphs, import graphics, insert mathematical symbols and templates, and insert variable numbers or text. Computerized testbanks include algorithmically defined problems organized according to each textbook. An "Export to HTML" feature lets instructors create practice tests for the Web. QuizMaster-EQ enables instructors to create and save tests using TestGen-EQ so students can take them for practice or a grade on a computer network. Instructors can set preferences for how and when tests are administered. QuizMaster-EQ automatically grades the exams, stores results on disk, and allows the instructor to view or print a variety of reports for individual students, classes, or courses. InterActMath Plus Software Available in Windows and Macintosh versions, combines course management and on-line testing with the features of the basic InterAct Math tutorial software to create an invaluable teaching resource. Consult your Addison-Wesley representative for details.

TA TIPS Introduction This is written for teaching assistants and instructors who may be teaching from the text PRECALCULUS through Modeling and Visualization for the first time. This text is designed to be flexible and meet a variety of student and instructor needs. The unifying concept throughout this text is that of a function. The graphing calculator, modeling, and a variety of real-data applications are integrated throughout this unique text. The rule of four (verbal, graphical, numerical, symbolic) is frequently used to represent mathematical concepts. Graphical and numerical interpretations are emphasized. Students are often asked to make conjectures and interpret their results. ORGANIZATION This text has nine chapters and 50 sections. Each chapter contains five or six sections and covers the standard college algebra curriculum with an innovative approach that breathes life into the course. In this text, sections are organized according to mathematical concepts and do not always represent one class day of work. A major goal of this text is to have students understand how concepts in mathematics are related to one another. The authors have found that this format allows for more discussion time when the need arises and has been well received by the students. Spend time answering questions on homework assignments. You may want to discuss certain homework problems even if students do not ask questions. Many times students fail to ask questions even when they do not understand the material. Discussing homework is particularly important early in the course. THE GRAPHING CALCULATOR Try to obtain a graphing calculator viewing screen with an overhead projector so that your calculator viewing rectangle can be seen by students on a large screen. By seeing how you operate a graphing calculator, students will learn more quickly how to use a graphing calculator. You will find that you need this overhead viewing screen most class days. There are many resources for students, teaching assistants, and instructors to learn how to use a graphing calculator. Although the text does not usually spend time on specific keystrokes for a particular graphing calculator, numerous graphing calculator screens with detailed explanations are included throughout the text. There are also technology notes in the text, which point out important concepts involving the graphing calculator. The Graphing Calculator Manual by Stuart Moskowitz provides instruction on specific keystrokes for a variety of graphing calculators. This manual is written specifically for this text and contains examples from the text. Contact your Addison Wesley Longman sales representative for details. There are additional resources at the Web site for this text. One of these resources is a TI-82/83 graphing calculator supplement that explains the keystrokes to solve specific examples from the text. Finally, for detailed information on the features of your calculator, consult your graphing calculator owner's manual. You may or may not choose to emphasize a square viewing rectangle when using a graphing calculator. A square viewing rectangle will result in a square appearing square rather than rectangular and a circle appearing circular rather than elliptical. See page 49 of the text. There are times when it may be simpler for your students not to use a square viewing rectangle. For example, a square viewing rectangle may not be practical when solving applications graphically because real data often varies greatly. One of the most difficult things for students to do with a graphing calculator is to find an appropriate viewing rectangle or window. Sometimes it is important for a student to find their own viewing rectangle, other times it can become a major distraction. This text tends to supply more difficult viewing rectangles to the students. However, it allows ample opportunity for students to find their own viewing rectangles. Setting a viewing rectangle can lead to a worthwhile discussion about domain and range of a relation when making a scatterplot. APPLICATIONS Applications are integrated throughout this text in both the discussions and the exercises. Many times applications are used to motivate mathematical concepts and help students learn how mathematics is used in our society. It is important to present some applications in class. Students learn by watching how the instructor solves problems. Afterwards they are more comfortable trying to solve application exercises on their own. It is difficult for students to master solving application and modeling exercises if they are not discussed in class. However, applications do not have to be done at the expense of skill-building exercises. You will find that there is ample time to work examples involving mathematical skills too. Be sure to discuss the chapter and section introductions with your students. These introductions often set the tone for the coming chapter or section and often discuss real applications, historical events, and give meaning to mathematics. It is not necessary to assign a large number of applications each day, but it is important to assign at least a few applications as part of each assignment. Include one or more applications on every exam. Over time students become more proficient at solving these problems. Select applications that will interest you and your students. If you are interested in the application, it will create interest in your students. Try to strike a proper balance between symbolic skill-building exercises and exercises that involve applications, modeling, and graphical interpretation. You are the expert and in the best position to judge your students' needs. COLLABORATIVE LEARNING OPPORTUNITIES There are many opportunities for collaborative learning in this text. One technique that works well is to use Checking Basic Concepts that occur throughout the text. You might want to allow students to work together the last 15­20 minutes of a period on some of these exercises. Require students to work in groups of 2­5. Have them turn in one paper with everyone's name on it. During this time walk around the room and answer any questions­this is not a test. You will be surprised how much you learn about your students and how they think. Extended exercises or even­numbered exercises can also be used. It generally works best not to assign questions for which they already have the solutions. The authors have found collaborative learning exercises to be most beneficial for both the students and instructor. GETTING STARTED It is essential to get students off to a good start in Chapter 1. The first chapter offers a different approach compared to how most mathematics courses begin. It is intended to generate student interest and give students a different look at mathematics from the start. Instead of initially concentrating on symbolic manipulation skills from intermediate algebra that they may be weak on, students are introduced to some essential mathematical concepts such as functions and graphs. The motivation behind mathematics is discussed. Skill building is emphasized more after Chapter 1. If you have any extra time in your syllabus, spend some of it on the first chapter. Students typically experience success in this chapter and attitudes toward mathematics often change. Students will need to become familiar with their graphing calculators in Chapter 1. Take time to answer questions about graphing calculators in class. You may not always know all the answers­that is normal. With the rapid growth in technology, no one can answer every question. If you are learning the graphing calculator for the first time, concentrate on the essential features that are necessary for students to complete the course. For other questions you might suggest that students consult their owner's manual. Generally, students adapt well to a graphing calculator. Many students have already been exposed to graphing calculators in high school. However, if a student is having genuine difficulty, you may want to suggest that they talk to you during office hours. Collaborative learning is an excellent opportunity for you to help students and for students to help each other with the graphing calculator. The number of calculator skills required in this text are minimal. At the end of the first chapter, students should be able to set a viewing rectangle, graph a function, evaluate mathematical expressions, and make a table, scatterplot or line graph. You may want to have one or more brief quizzes to make sure that students are learning the important concepts in Chapter 1. The following motivation for Chapter 1 should be explained explicitly to students. Society creates data by inventing a variety of number systems to quantify data. To better understand and analyze data, we create algorithms and visualize data using graphs and scatterplots. We invent functions to model data. Once a function is found that models a data set, we can use the function to solve problems and make predictions. Because there is such a wide variety of data, we need different types of functions to model data. Three common types of functions are constant, linear, and nonlinear. In Section 1.5 students are provided with the functions to model data, and in Section 1.6 students use transformations of graphs to create their own functions to model data. THE RULE OF FOUR The rule of four is used consistently throughout this text. It is important that in Chapter 1, students learn what is meant by verbal, graphical, numerical, and symbolic representations of a function. You are probably familiar with graphical and symbolic representations of functions. A verbal representation of a function can be expressed using an algorithm, which is a step-by-step procedure for computing f(x). In this text a numerical representation of a function consists of a table of values. Since a function can have an infinite number of ordered pairs in the form (x, y), most numerical representations are partial numerical representations. Be sure to explain Examples 5 and 6 in Section 1.3 or present similar ones. Graphical, numerical, and symbolic methods can be used to solve equations and inequalities. This begins in Chapter 2 and continues throughout the text. See Example 6 in Section 2.1, Example 6 in Section 3.1, and Example 1 in Section 4.5. Two basic methods to solve equations graphically are the x-intercept method and the intersection-of-graphs method. These graphical methods are explained in Section 2.1. This text uses the intersection-of-graphs method more than the x-intercept method. The intersection-of- graphs method tends to be more intuitive for students when solving equations and inequalities involving real applications. Because of the consistent use of graphical and numerical methods, the graphing calculator will be used most class days. OTHER IMPORTANT FEATURES There are several important supplements for this text that can help you and your students, such as test banks, videotapes, and a Web site. See the preface of this text for details or talk to your Addison Wesley Longman sales representative. The following are some features that are especially helpful. 1. Be sure that students are aware that each section ends with Putting It All Together, which summarizes many of the important concepts presented in the section. 2. Critical thinking exercises occur in each section and can be used for class discussion, group activities, or extra credit problems. Critical thinking exercises usually ask the student to take a concept one step further than has been presented. For examples, see Critical Thinking on pages 32, 56 and 70­71. 3. The exercise sets are designed to be flexible. There are numerous exercises that test a variety of mathematical concepts and skills. This allows an instructor to design assignments that meet their students' needs. Exercises are organized by topic to make it easier to choose an assignment. For example, if you are planning to take two days to cover a section, it is easy to give students a partial assignment on the material that is covered on the first day. If you choose to skip over a topic, the corresponding topics in the exercise set can be easily omitted. If you choose to not emphasize a component of the rule of four, it is easy to adjust the assignment accordingly. For example, if most students have older models of calculators and cannot create tables, you may decide not to assign as many numerical exercises. 4. There is an Instructor's Solutions Manual that contains the solutions to all the exercises in the text, including the Critical Thinking exercises. On the other hand, the Student¹s Solutions Manual does not have solutions for Checking Basic Concepts, Critical Thinking, even-numbered exercises, or Extended and Discovery exercises. 5. The Extended and Discovery Exercises at the end of each chapter can be used for collaborative learning or extra credit problems. One student, after being assigned an extra credit extended exercise, returned to class the next day and said enthusiastically, "It took me about an hour, but I got it!"

SAMPLE SYLLABUS Syllabus for a 4-credit semester course. (57 class days) Day 1: Course policies, Read Sections 1.1 and 1.2. Day 2: Section 1.3 Day 3: Section 1.4 Day 4: Section 1.5 Day 5: Section 2.1 Day 6: Section 2.2 Day 7: Section 2.3 Day 8: Section 2.4, 2.5 (Basics of piecewise functions, midpoint rule, and distance formula) Day 9: Review Day 10: Ch. 1 & 2 Exam Day 11: Section 3.1 Day 12: Section 3.1, 3.2 Day 13: Section 3.2 Day 14: Section 3.3 Day 15: Section 3.4 Day 16: Section 3.4 Day 17: Section 3.6 Day 18: Review Day 19: Ch. 3 Exam Day 20: Section 4.1 Day 21: Section 4.2 Day 22: Section 4.2, 4.3 Day 23: Section 4.3 Day 24: Section 4.4 Day 25: Section 4.4 Day 26: Section 4.5 Day 27: Review Day 28: Ch. 4 Exam Day 29: Section 5.1 Day 30: Section 5.2 Day 31: Section 5.2, 5.3 Day 32: Section 5.3 Day 33: Section 5.4 Day 34: Section 5.5 Day 35: Section 5.6 Day 36: Review Day 37: Ch. 5 Exam Day 38: Section 6.1 Day 39: Section 6.2 Day 40: Section 6.2 Day 41: Section 6.3 Day 42: Section 6.4 Day 43: Section 6.5 Day 44: Review Day 45: Ch. 6 Exam Day 46: Section 7.1 Day 47: Section 7.2 Day 48: Section 7.3 Day 49: Section 8.1 Day 50: Section 8.2 Day 51: Review Day 52: Ch. 7 & 8 Exam Day 53: Section 9.1 Day 54: Section 9.2 Day 55: Section 9.2, 9.3 Day 56: Section 9.3 Day 57: Review for Final Exam

Home | InterAct Math | Chapter Resources | TI Downloads | Course Success | About the Author (c) Addison Wesley Longman 2000