Preface

About this book

This book contains 26 projects designed to supplement a high school or college precalculus course. The mathematical topics used in these projects are, for the most part, those that are typically taught in a traditional precalculus course. Many of these projects combine several different precalculus topics and serve as a reminder to students that mathematics does not always come in neat self-contained packets of 20 similar questions. Our objectives in preparing these materials were the following: Present concepts from different viewpoints -- Students will see concepts presented from verbal, graphical, numerical, as well as symbolic points of view.

Emphasize writing skills -- Students will be asked questions requiring them to explain a concept and how it applies to the given problem.
Use technology where appropriate -- Students will be encouraged to use a graphing calculator as a tool to assist in both the understanding of concepts and as an aid in problem solving.
Encourage the use of collaborative learning -- By working in small groups, students have the opportunity to share ideas, learn from each other, and learn to communicate mathematically.
Stress the application of mathematics to other disciplines -- These problems are derived from a wide variety of disciplines and are based on realistic data.

Teachers' notes and an answer key accompany each project. These contain not only detailed solutions for each project, but also topics with which students should be familiar before attempting the project, "pitfalls" which students may encounter, and suggestions for ways to extend the project.

How these projects should be used

Through using these materials ourselves and through extensive field testing we have learned from our mistakes as well as from the things we have done correctly. We offer the following suggestions.

You should work through the project yourself before you assign it. You will learn ahead of time about any difficulties that may arise, and will be better prepared to help your students.
Most of these projects work best when students work on them in groups rather than alone.
Beware of not assigning the whole problem. Most of these projects were designed in such a way that no question should be skipped. Each part is important for the students to either successfully answer the next question or for them to see the "big picture." There are a few projects that have portions that may be omitted. These are noted in the project's teachers' notes.
Set a deadline for each project. Be sure to give your students an adequate amount of both class time and homework time to complete each project. In the table of contents, we have given a rough estimate of what an appropriate amount of class time should be for each project.
Hand out the project the day before the students will be working on it in class. Have them read through it, jotting down ideas on how to solve the problem and any questions they might have. This will allow the students to use class time to deal with the difficulties of the project rather than to obtain an initial understanding of the questions.
Set appropriate expectations for your students, show them how they can be reached, and hold them accountable. Give them examples of how detailed you expect their answers to be, how they should display their graphs, how to show why something is true, etc. Also explain to them that they should take pride in their work. What they turn in should be rewritten or typed from their original work, much like a term paper.
As you circulate around the room while the students work on the project, make sure you ask them questions as well as answering their questions. Find out how they are thinking and problem solving.
Make these projects an important part of your class and be sure your students know this. Including questions on exams that relate to the projects will help communicate their importance.

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