This course is designed to strengthen studentsâ€™ fundamental math skills and their ability to use basic principles of algebra to analyze and represent proportional and non-proportional linear relationships. Students apply operations to situations involving rational numbers and develop a more sophisticated way of dealing with word problems by utilizing these skills. Students encounter topics that they will see again in Algebra and Geometry courses.

# Mathematics

The courses offered by the Mathematics Department at Stratton Mountain School provide a foundation in logical reasoning and problem solving. Once students reach the study of Geometry, courses are offered on both a normal and an honors track. Students following the normal track will reach the level of pre-calculus or math analysis. Students following the honors track will reach the level of calculus. The minimum graduation requirement is three years of study in the field of mathematics.

Technology plays an important role at all levels of our math program. Many teachers utilize different forms of media to make their material more accessible during our busy winter season. From making movies of lectures to sharing pencast videos of homework problems, all of our teachers strive to make their curriculum travel easily for our student athletes. Students use TI-83 and TI-84 graphing calculators both to facilitate and to complement their studies. In all classes, teachers emphasize the proper use of technology so that students use it to enhance their study of mathematics rather than depend on it excessively.

This course is designed as an introduction to Algebra from both a traditional and a graphical approach. It stresses the fundamental properties of real numbers, operations with real numbers, and the solution of linear equations and inequalities. Topics also include absolute value, solving systems of equations, and operations with quadratic and other polynomial equations. The overarching goal of Algebra I is to develop in students both ease and accuracy in all sorts of algebraic manipulations. Algebra I is recommended for those whose background in Algebra (for example, in solving and factoring quadratic equations) is not strong. **As a foundational course in high school mathematics, it is required for those who have not had a full year of Algebra I or for those who score below 65% on the placement test.**

In the Geometry course, students are introduced to Euclid’s postulates and theorems as the basis for an axiomatic logical system. The underlying qualities of such a system have application beyond mathematics to research of many kinds and even to the study of the law. Students explore Geometry through both inductive and deductive reasoning and through constructions. Because of the sequential placement of the course between Algebra I and Algebra II, there is frequent reference to algebraic connections. Topics of investigation include logical reasoning, angle and line relationships, parallel and perpendicular lines, triangles and other polygons, congruence, and similarity. Students learn to use area, volume, and probability to solve real-life problems. Emphasis is placed on the deductive nature of this branch of mathematics, and on the use of algebra in solving a variety of geometry problems. **The course is open to students who have completed a full year of high school algebra and who score above 65% on the End of Algebra I placement test.**

The Honors Geometry Course is centered on problem solving rather than on topics. The content, which consists of a combination of geometry with algebra and trigonometry, is presented in a series of problem sets, in which each problem is designed to be an exploration. Important theorems, rather than being formally presented, become apparent as students work through problems. The course emphasizes the development of problem-solving skills, and the different attempts students make on problems and their ability to explain them and make connections with other material is just as important as their getting the correct answer. **Open to students who earned a 90% or higher in Algebra I or scored exceptionally well on the placement test**.

The Algebra II course develops and extends many of the concepts encountered in Algebra I and Geometry courses. The main objective of the course is to deepen understanding of the concept of mathematical function, which is central to higher math courses such as Pre-Calculus and beyond. During the course, we revisit linear functions and look in depth at quadratic, polynomial, radical and rational functions. We analyze the behavior of these functions and develop the tools to solve a variety of equations involving them. Emphasis is placed on learning to apply these concepts to solve real world problems. Topics also include systems of equations and complex numbers. **The course is open to students who have completed full year courses of both algebra and geometry.**

Honors Algebra II is a fast-paced second course in algebra. The main objective of this course is to develop in students a sophisticated understanding of the concept of mathematical function, which is central to higher math courses such as Pre-Calculus and beyond. During the course we look in depth at linear, polynomial, exponential, logarithmic, radical and rational functions. We analyze the behavior of these functions and develop the tools to solve a variety of equations involving them. The course concludes with an introduction to probability and statistics and basic trigonometry. Problem solving skills are developed through emphasis on many real-life examples. Honors Algebra II is a rigorous course intended for students who have demonstrated the ability to think flexibly and creatively, and who have the desire and capacity to learn and work independently.

This course is designed for students who have completed a second year algebra course and are planning on taking Math Analysis their senior year. This course continues the work begun in Algebra II. The main objective is to continue developing in students an understanding of the concept of mathematical function and to ready students for the rigors of higher level math courses. This course covers radical, rational, and exponential functions, logarithms, series and sequences, probability, and trigonometric functions. **Open to students who have completed Algebra II or the equivalent.**

This course continues the work begun in Advanced Algebra II but at a much more sophisticated level. The topics of study include the theory and graphs of functions and their inverses, exponentials, logarithms, trigonometric functions, analytic trigonometry, and rational functions. Well into the second semester, the course introduces basic topics of differential calculus such as limits, continuity, the definition of the derivative, and techniques of differentiation. **This course is a prerequisite for students planning to take Calculus. Open to students who have earned an 83 or higher in Advanced Algebra II or scored exceptionally well on the placement test, with permission of the department, and who have completed a full year of algebra and geometry**.

This course is designed for students who have completed Pre-Calculus and wish to continue preparing for mathematics in college. The main objective of this course is to continue the work begun in Precalculus. Students revisit some of the same topics they saw in Precalculus, but with more rigor and with more emphasis on the problem-solving process. This course covers probability, trigonometric and inverse trigonometric functions, and statistics. In the spring, students study basic topics in differential calculus, such as limits, continuity, the definition of the derivative, and techniques of differentiation. **Prerequisite: Pre-Calculus**.

This course follows the development of ideas started in Honors Pre-Calculus, which is a prerequisite. The main objective of this course is to ready students for the continued study of Calculus in college. The first half of the year focuses on the theory behind and the application of the derivative. The course covers how to differentiate various types of functions, including polynomial functions, rational functions, exponential and logarithmic functions, and trigonometric functions. Applications include optimization and related rates, and the course explores connections with physics in the fall. The second half of the year introduces students to integral calculus, again with a mix of theory and application. **Open to students who have earned an 85 or higher in Advanced Pre-Calculus or the equivalent**.