Author Description

Introduction This is a graphing calculator resource book designed to help students explore applications of mathematics. The book is intended for use in secondary school mathematics courses. The book is designed to be duplicated by the teacher, either by photocopying or making transparency masters. The material was created to help answer student questions such as, Why are we learning this; and;When will we ever use this? With this resource book you can continue to show them why they are learning a topic and specific examples of where it is used. For example, the material does not reteach the definition and initial work with graphing the sine function. It does, however, provide a quick review of graphing the sine function and how different coefficients affect the shape of the sine graph, an intuitive introduction to finding a sine regression equation, and a practical example of where these techniques are used. In short, we believe that skill maintenance can be imbedded in concept exploration, applications and technology use. The material was created to accompany the standard graphing calculator, but most of the activities can be adapted to other graphing calculators or computer-based applications. The programs can even be converted for use with other calculators by consulting the manuals for each machine. Organization This book is divided into six basic parts. The first section, Basic Calculator Activities, covers the elements that help students become familiar with their calculator and its various popular functions. The second section, Number Patterns, studies basic number sequences that can be replicated on the graphing calculator. In the third section, students begin exploring and analyzing data through games that have been designed to illustrate common ideas. Students will explore common algebraic formulas in the fourth section, Algebra Exploration, by playing games that deal with single-variable equations and averages. The fifth section, Geometry, teaches students about the various components of shapes as well as the Pythagorean Theorem and the geometric principles that come into play in GPS technology. The last section of the book, Probability, teaches students about the issues that influence the likelihood that certain events will occur. Because the material is both specific and open-ended, all students will benefit from using these activities. Students who work carefully are guided by the worksheets to make generalizations that go beyond the scope of standard textbook lessons. Each exploration is designed to be used as a guide. Many of the worksheets also provide important key stroking tips to save time. These explorations can be used in several ways. One way is to assign individuals or small groups to work with a particular experiment for a short interval of time. Several of the lessons can be divided so that groups of students can do individual parts of the lesson and then put the parts together for final analysis by the whole class. The time you allot to a given experiment will vary depending on both student background and interest. Many lessons start with a series of questions or examples that create student interest in the problem. This is often followed by discussion designed to clarify the initial questions and shape the direction the lesson will take. Frequently, multiple solutions are possible and multiple strategies for arriving at those solutions are encouraged. Many extra challenges involving further research and programming are also provided. A concept can also be introduced to or reviewed by an entire class by using a projector. Most student difficulties are caused when they encounter grammar and syntax problems associated with finding options on the powerful graphing calculators that are currently available. Calculator hints are provided on many pages to help k