Mathematics

Year – 6 credits

Prerequisite: Successful completion of Algebra 1

In this course, students will analyze properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. Inductive reasoning is frequently used to discover new conjectures, while deductive reasoning (proofs) is also used to find new geometric relationships. Students will formulate conjectures and solve problems relating to the standard topics of Euclidean geometry. This course also includes the study of right triangle trigonometry. In addition, coordinate geometry methods will be used whenever possible, in order to emphasize the connections between algebra and geometry and to maintain students’ algebra skills. While students will learn traditional geometric constructions with the use of a compass and straight edge, they will also use the dynamic mathematics modeling program GeoGebra to construct and manipulate geometric figures in order to explore their properties and relationships. This course provides students with a balance among activities emphasizing discovery, application, and proof. Students will work individually and frequently work together in small cooperative learning groups. The course assignments include: homework assignments, in class discovery activities, quizzes, tests, and occasional projects. A special unit on tessellations provides students with the opportunity to design, create, and display a set of tessellating ceramic tiles. Students should expect to spend up to an hour each night completing nightly homework exercises.

Year—6 credits

Prerequisite: Geometry

In this course, students will represent and analyze mathematical situations numerically, graphically, and symbolically, building on the concepts and skills developed in Algebra 1. Students will use a variety of symbolic representations to model problem situations, including both explicitly defined and recursively defined functions. In addition, students will begin to investigate and compare the properties of classes of functions and their graphs, including quadratic, higher degree polynomial, exponential, and logarithmic functions. Students will maintain and build on 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. Graphing calculators will be used to look at the table and graphs of explicitly and recursively defined functions. Students will work individually and in small groups. The course assignments include homework assignments, investigations, partial chapter quizzes, and chapter tests. Students should anticipate spending 30-60 minutes per day on homework completion and reviewing content.

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.

Year - 6 credits

Prerequisite: Successful completion of Algebra 2

The central theme of this course is comparing, contrasting, and transforming functions in order to model change. We emphasize that functions can be grouped into families – linear, quadratic, exponential, power, polynomial, rational, and trigonometric – and that these functions can be used as models for real-world behavior. Students will use technology and analytic methods to develop a deeper conceptual understanding of the mathematical underpinnings of functional analysis. The inclusion of non-routine problems is intended to establish the idea that such problems are not only part of mathematics, but in some sense are the point of mathematics. Students taking this course should possess a willingness to work hard and be prepared to spend at least 6 hours weekly on this course outside of class time. Students taking this course should have completed both Algebra 2 and Geometry.

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 AB. 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.

Year - 6 credits

Prerequisite: successful completion of Algebra 2

This course is designed to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. The course will prepare students for life in a world filled with data, as well as for many college majors that require statistics. Students will study the fundamental ideas of statistics in a context that relates to personal experiences and needs of an informed citizen of the 21st century. Statistics helps us to understand our world: Health professionals need to understand statistics to interpret accounts of medical research; businesses use statistical methods (business analytics) to efficiently crunch numbers to support their bottom line; and citizens need to understand statistics to accurately interpret opinion polls and the Consumer Price Index. Because data are omnipresent, everyone will find statistics useful and perhaps even profitable.

In this course, students will study exploratory data analysis, learn the fundamentals of designing a study, use probability models, and use inferential statistics. Students will apply these concepts to such fields as business, biology, engineering, industry, the social sciences and many others. Students will use technology to calculate and display real data. Graphing calculators that can manipulate lists of data and contain statistical applications such as confidence intervals, tests of significance, and probability distributions will be our main technological hardware. In addition, we will be using online apps/programs.

Students will work individually and frequently work together in pairs. Course assignments include: homework assignments, in class practice, computer simulations, hands on activities, quizzes and tests. Students will be invited to join us when we are visited by guest speakers. Students should expect to spend an hour or more each night completing nightly homework exercises. These assignments occasionally include watching videos or taking notes.

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.

Year - 6 credits

Prerequisites: Successful completion of Algebra 2

In this course, students are introduced 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.

Students will work individually and in small groups. The course assignments include class activities, small-scale research, homework assignments, quizzes, and unit tests. Students should anticipate spending 30 minutes per day on homework completion and reviewing content.

Year – 6 credits

Prerequisite: AP Calculus BC

This course is intended for advanced mathematics students who wish to further their studies beyond calculus. In this year's version of the course, students will learn discrete mathematics, which will cover proof techniques, boolean logic, number theory, real-analysis, abstract algebra and combinatorics.

Students will learn how to read and write mathematical proofs, and more deeply understand the fundamentals of mathematics through rigorous in-depth analysis. This course will prepare students for work in a variety of disciplines, including engineering, mathematics, and computer science.

Year – 6 credits

Prerequisites: Statistics, AP Statistics, or permission of instructor

This course extends statistical methods learned in prior statistics classes and introduces new data analysis tools. Students will review sampling and experimental design data collection methods and statistical inference. New statistical methods include analysis of variance (ANOVA), nonparametric methods, and multiple and applied regression. Additional topics could be studied if time allows. This is a project-based course that emphasizes working with authentic data, and data analyses will be carried out using the R programming language. Students will have the opportunity to work with data sets of their choice in areas of interest to them (including, but not limited to, sports analytics, climate change, business/marketing, medicine/epidemiology, politics). Third trimester will be focused on a data analysis project of the student’s choosing which could culminate in a display at the STEM Symposium in May.