# Mathematics

The mathematics curriculum emphasizes an appreciation of the subject through experiences that encourage students to explore ideas, take risks, and think for themselves. We assert the importance of establishing fundamental skills and laying a solid foundation at every level, thereby allowing for subsequent study of mathematics and related fields. When we establish skills, the emphasis is not on rote memory, but on developing and working through logical processes that students understand. As such, daily practice is expected and needed to reinforce and further develop these mathematical skills and abilities. We emphasize that each course is important in and of itself, for its ability to engage and for its ability to enhance mathematical fluency. Applications, connections, and the use of technology make mathematics more relevant and more accessible. The creative and critical thinking, use of logic, and problem-solving skills developed in these courses are not only necessary for successful course completion, but are also applicable to other fields and other situations.

## Mathematics Faculty

## Courses

- Geometry
- Algebra 2
- Precalculus
- AP Calculus AB
- AP Calculus BC
- AP Statistics
- Advanced Topics in Mathematics

## Geometry

## Year – 6 credits

Prerequisite: successful completion of Algebra 1 or equivalent. In this course, students analyze properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. Students formulate conjectures and solve problems relating to the standard topics of Euclidean geometry. The mathematics modeling program GeoGebra is an integral part of the course. With this program, students are able to construct and manipulate geometric figures in order to explore their properties and relationships. Throughout the course, we attempt to maintain a balance among activities emphasizing discovery, application, and proof. A special unit on tessellations provides students with the opportunity to design, create, and display a set of tessellating ceramic tiles. This course also includes the study of right triangle trigonometry and an introduction to trigonometric functions. In addition, coordinate geometry methods are used whenever possible, in order to emphasize the connections between algebra and geometry and to maintain students’ algebra skills.

## Algebra 2

## Year—6 credits

Prerequisite: successful completion of Geometry; may be taken concurrently with Geometry, with permission. In this course, students represent and analyze mathematical situations numerically, graphically, and symbolically, building on the concepts and skills developed in Algebra 1. Students use a variety of symbolic representations to model problem situations, including both explicitly defined and recursively defined functions. In addition, students begin to investigate and compare the properties of classes of functions and their graphs, including polynomial, exponential, logarithmic, and conic functions. The mathematics modeling program GeoGebra is an integral part of the course. With this program, students are able to plot and manipulate algebraic functions in order to explore their properties. Students will maintain proficiencies developed in Algebra 1 as well as learn to solve non-linear equations involving polynomial or exponential expressions. The course emphasizes using mathematical models to represent and understand quantitative relationships and to solve problems.

## Precalculus

## Year - 6 credits

Prerequisite: Successful completion of Algebra 2 or equivalent. This course provides students with an applications-oriented, investigative curriculum in which they analyze complex situations and use technology to solve problems and enhance their understanding of mathematics. Problem contexts provide an introduction to the mathematics used in engineering, the physical and life sciences, business, finance, and computer science. Mathematical topics include mathematical modeling, properties of functions and their graphs, and an in-depth study of classes of functions including exponential, logarithmic, trigonometric, polynomial, and rational functions. Additional topics will be included as time allows. This course lays a foundation to support future coursework in mathematics, including Calculus and Statistics.

## AP Calculus AB

## Year - 6 credits

Prerequisite: successful completion of Precalculus. This is a challenging college-level course, preparing students for the Calculus AB Advanced Placement exam. Applications and mathematical modeling are used to motivate topics and the graphing calculator is used extensively as a tool for investigating and applying the important concepts. Topics from the Calculus AB syllabus of the College Board’s AP curriculum will be covered. These include a review of the properties and graphs of elementary functions; limits of functions; the concept of the derivative, derivatives of elementary functions, applications of derivatives; interpretation and properties of definite integrals; applications of definite integrals; and techniques and applications of anti-differentiation.

## AP Calculus BC

## Year - 6 credits

Prerequisite: successful completion of AP Calculus AB. This course, which prepares students for the Calculus BC Advanced Placement exam, continues the study of calculus from AP Calculus 1. Applications and mathematical modeling are used to motivate topics and the graphing calculator is used extensively as a tool for conducting investigations. Topics from the Calculus BC syllabus of the College Board’s AP curriculum will be covered, along with additional topics from outside the usual BC Calculus curriculum.

## AP Statistics

## Year—6 credits

Prerequisite: successful completion of Algebra 2. This is a challenging college-level course that prepares students for the Advanced Placement Statistics exam. This course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: (1) Exploring Data: Describing patterns and departures from patterns; (2) Sampling and Experimentation: Planning and conducting a study; (3) Anticipating Patterns: Exploring random phenomena using probability and simulation; and (4) Statistical Inference: Estimating population parameters and testing hypotheses. This course emphasizes statistical thinking and decision-making. Technology (TI graphing calculators and statistical software) is used extensively to foster active learning, and to carry out statistical analyses, including making graphs, finding numerical summaries, computing estimates, and testing hypotheses.

## Advanced Topics in Mathematics

## The specific topic rotates across a 3-year cycle

Discrete Mathematics (2021-2022)

Differential Equations (2019-2020)

Multivariable Calculus (2020-2021)

Year – 6 credits

Prerequisite: successful completion of AP Calculus BC. This course is intended for advanced mathematics students who wish to further their studies beyond calculus. Course topics may include linear algebra, multivariable calculus, number theory, probability, and combinatorics.

## Offered on a Rotating Basis

## Statistics

## Year - 6 Credits

Prerequisite: successful completion of the core sequence or equivalent. Open to eleventh and twelfth graders. This course follows the recommendations of the American Statistical Association and the Mathematical Association of America for teaching introductory statistics. The course emphasizes statistical thinking and focuses on data analysis and conceptual understanding with less emphasis on theory and fewer formulas. It takes advantage of the power of technology, such as the TI-84 graphing calculator and statistical software, to foster active learning. The course covers the standard topics of an introductory statistics course including organizing, representing, and describing data; producing data through samples and experiments; using probability theory to understand sampling distributions; and drawing conclusions from data by statistical inference.

## Mathematical Models for Decision Making

## Year - 6 credits

Prerequisite: successful completion of the core sequence or equivalent. Open to eleventh and twelfth graders. This course introduces students to mathematical topics necessary for decision-making in today’s world. Mathematical topics are developed in the context of solving problems from business, science, and daily life. Major units of study include election theory, fair division and game theory, modeling with matrices, graphs and their applications, counting and probability, and personal finance and managing resources.