Overview of Mathematical Models with Applications

Mathematical Models with Applications is a course for high school students with a minimum prerequisite of Algebra I. This course is intended to reinforce, broaden, and extend the mathematical knowledge and skills acquired in algebra. This course is not intended to be a low-level course. To the contrary, the mathematical content of this course should be appropriate for a college-bound curriculum. The course should build on the mathematical background of the students yet stretch their knowledge toward topics studied in Geometry and Algebra II.

The primary purpose of this course is to use mathematics as a tool to model real-world phenomena in science, finance, music, and art. Science should include not only the biological and physical sciences, but the social sciences as well. Finance should include growth models (e.g., situations involving simple and compound interest rates), saving-up models (e.g., investments, insurance, and retirement plans) and paying-off models (e.g., automobile loans and house loans). Patterns and functions can be used to model musical pitches and scales while geometric transformations can be used to describe such musical concepts as transposition, inversion, and retrograde. Geometric transformations can also be used to model perspective drawings, frieze patterns, quilting patterns, and tessellations, while inversions can be used to model anamorphic art drawings. Through these various situations, prior mathematical knowledge will be expanded and new mathematical knowledge will be developed.

In developing these models students might gather data using something as simple as a meter stick or as sophisticated as an electronic data-collection device with a microphone. Students are expected to have access to various types of technology including graphics calculators, data-collection devices, spreadsheets, dynamic geometry programs, and the Internet as tools for collecting, displaying, and interpreting information. The classroom environment should be student centered and activity orientated. The teacher should serve as a facilitator and guide for the students, not merely a disseminator of information. Students should be allowed to use a variety of problem solving strategies and approaches to problems. Through the use of the various applications and interesting problem settings it is hoped that the students will be motivated to continue their study of mathematics in future courses.

If this course is taught in the manner intended, the students should have the opportunity to reinforce all the exit-level TAKS objectives, maintain and extend their algebraic and geometric skills, and find mathematics both useful and enjoyable.