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Mathematics

The Mathematics Department aims to help students simultaneously develop specific mathematical competencies and sharpen their general analytical reasoning skills. We believe that mathematics is worthy of study both because of its direct applications and due to its cultivation of mathematical modes of thinking, which provide powerful tools, useful across many fields.

Our standard course sequence is: Algebra I; Geometry; Algebra II/Trigonometry; Precalculus; Calculus. Our honors sequence is: Geometry Honors; Algebra II/Trigonometry Honors; Precalculus Honors; Calculus AB or BC. While we encourage students to challenge themselves, we appreciate that many factors contribute to a student’s selected path.

We appreciate the role of technology in teaching and learning, and we attempt to promote intentional uses of technology coupled with an understanding of the mathematics underlying the tool. Skills in mental arithmetic and approximation, for example, prevent a calculator from becoming an oracle.

As the learning of mathematics often happens at its own pace, we work closely with students both inside and outside of class hours. Our doors are open early and our classrooms are often full during the lunch time study period.

Available Courses

Algebra 1

1.0 credits
Algebra I is organized around families of functions, with special emphasis on linear and quadratic functions. As students learn about each family of function, they will learn to represent them in multiple ways – as verbal descriptions, equations, tables, and graphs. They will also learn to model real-world situations using functions in order to solve problems arising from those situations. In addition to its algebra content, lessons on probability and data analysis are also included. Algebraic thinking skills are developed through a variety of classroom activities, including group and individual investigations, hands-on manipulatives, real-world problem solving, projects, class discussions, note taking, and utilizing technology. The prerequisite for this course is Pre-Algebra.

Geometry

1.0 credits

Geometry builds students' understanding of the principles of Geometry. Students develop geometric reasoning skills such as, analyzing rigid motions, completing formal constructions, and writing proofs. Some of the topics in this course include: reasoning in geometry, using tools of geometry, discovering and proving triangle properties, discovering and proving polygon properties, discovering and proving circle properties, transformations and tessellations, area, the Pythagorean Theorem, volume, similarity, and trigonometry. The prerequisite for this course is Algebra I.

Geometry Honors

1.0 credits

Geometry Honors presents the topics of geometry and provides students with a solid preparation and firm foundation of concepts, techniques, and applications for more advanced mathematics. Students actively engage in a process of self-discovery, constructing meaning, and making connections to geometric concepts with greater depth of understanding and retention. Some of the topics in this course include: constructions, deductive and inductive reasoning, congruence, parallel lines, quadrilaterals, area, volume, circles, trigonometry, and non-Euclidean geometries. Accelerated mathematical thinking skills are developed through a variety of classroom activities, including group and individual investigations, class discussions, note taking, and proofs. The prerequisite for this course is Algebra I (with at least an A- average for the year) and teacher recommendation.

Algebra II Trigonometry

1.0 credits

Algebra II Trigonometry is organized around families of functions, including linear, quadratic, exponential, logarithmic, radical, and rational functions. As students study each family of functions, they learn to represent them in multiple ways — as verbal descriptions, equations, tables, and graphs. Students also learn to model situations using functions in order to solve problems arising from those situations. Other math topics in this course include: polynomial equations, sequence and series of numbers, conic sections, system of equations, trigonometric rations, graphs, identities, and equations. The prerequisite for this course is geometry.

Algebra II Trigonometry Honors

1.0 credits

Algebra II Trigonometry Honors presents the topics of a college freshman course covering Algebra and Trigonometry and provides students with a solid preparation and firm foundation of concepts, techniques, and applications for more advanced college-level mathematics. Topics presented include: equations, inequalities, mathematical modeling, functions and their graphs, polynomial functions, ratios, functions with conics, logarithmic functions, basic trigonometry, analytic trigonometry, systems of equations, and matrices. Accelerated algebraic thinking skills are developed through a variety of classroom activities, including group and individual investigations, real-world problem solving, class discussions, note taking, and utilizing technology. The prerequisite for this course is Geometry Honors (with at least a B average for the year) or Geometry (with at least an A average for the year) and teacher recommendation.

Precalculus

1.0 credits

Precalculus helps students to solidify and develop their understanding of concepts and techniques from algebra, geometry and trigonometry, thereby preparing students for future math courses including calculus and statistics. Topics covered include: trigonometric functions, complex trigonometry, polynomial, rational, exponential and logarithmic functions, combinatorics, recursion, analytic geometry, probability and statistics, and an introduction to the ideas of calculus. The prerequisite for this course is Algebra II Trigonometry.

Precalculus honors

1.0 credits

Precalculus Honors continues to provide students with a solid preparation and firm foundation of concepts, techniques, and applications for more advanced college-level mathematics. It additionally prepares them for AP Calculus BC. Topics include polynomial, rational, exponential and logarithmic functions, trigonometric functions, applications of trigonometry, vectors, matrices, sequences, series, probability, analytic geometry (including 3-D), conics, polar and parametric functions, and limits. Accelerated algebraic thinking skills are developed through a variety of classroom activities, including group and individual investigations, real-world problem solving, class discussions, note taking, and utilizing technology. The prerequisite for this course is Algebra II Trigonometry Honors (with at least a B average for the year) and teacher recommendation.

Calculus

1.0 credits

Calculus begins by extending the study of functions and introduces students to functions, limits and derivatives. In the second semester, this course is devoted to extending these topics to include more complex families of functions and to introducing the integral calculus. The goals of this course are to: (a) support and strengthen the students’ understanding of the fundamental concepts underlying calculus (b) develop the students’ problem-solving skills (c) provide students with a solid conceptual introduction to calculus. This course is primarily designed to prepare students for an introductory college-level calculus course. The prerequisite for this course is Precalculus.

AP Calculus AB

1.0 credits

AP Calculus AB follows the Advanced Placement Calculus AB syllabus. It presents the topics of a college freshman course in differential and integral calculus that include: limits and continuity, derivatives, applications of derivatives, the definite integral, differential equations and mathematical modeling, applications of definite integrals. Upper School students who complete the course and earn satisfactory grades on the AP exam (given in May) may be awarded credit at the college they will attend. The prerequisite for this course is Precalculus Honors or Calculus (with at least a B average for the year) and teacher recommendation.

AP Calculus BC

1.0 credits

AP Calculus BC follows the Advanced Placement Calculus BC syllabus. It presents the topics of a college freshman course in differential and integral calculus that include: limits and continuity, derivatives, applications of derivatives, the definite integral, differential equations and mathematical modeling, applications of definite integrals. Additionally, it presents parametric, polar and vector functions, and polynomial approximations and series. Upper School students who complete the course and earn satisfactory grades on the AP exam (given in May) may be awarded credit at the college they will attend. The prerequisite for this course is Precalculus Honors (with at least a B average for the year) and teacher recommendation.

Multivariable Calculus Honors

1.0 credits

Multivariable Calculus is a second year calculus course, which involves the extension of calculus to two or more variables. This course will be run in a seminar style with participants expected to contribute to the discussion and presentation of the material. This course will also involve a number of self-directed projects and a strong modeling component. The prerequisite for the course is the completion of AP Calculus AB (with a 4 or higher on the AP exam) or AP Calculus BC (with a 3 or higher on the AP exam).

Statistics

0.5 credits

Statistics provides students with an understanding of the basics of statistics to help them both in other areas of study and in every-day life. The three main topics of the course are analyzing data, producing data and chance. This course focuses on developing an understanding of statistics through examining its applications, and activities play a large role in this class on a daily basis. The prerequisite for this course is Algebra I.

Programming

0.5 Credits

Programming introduces students to the world of computer science and software by building up fundamental programming skills in Python, a modern scripting language that is used in web-programming and other fields. The course makes use of CodeHS, an online learning platform designed to help high school students learn the basics of computer science and programming in a hands-on and interactive fashion. The CodeHS system is designed to be flexible, allowing students to progress at their own pace through the units, and encourages self-directed learning by providing easy access to documentation. By the end of the course, students will have a solid foundation in designing and writing Python programs, from which they can branch out to learn other languages concepts in future courses or on their own. Students will be charged a one-time software fee in lieu of a textbook.

AP Statistics

1.0 credits

AP Statistics follows the Advanced Placement Statistics syllabus. It introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students learn to conduct statistical analyses, reflect on what these concepts and techniques mean, and identify how they were derived. Students are challenged to develop their critical thinking and general analytical skills. The prerequisite for this course is Precalculus or Algebra II Trigonometry (with at least a B+ average for the year) and teacher recommendation (which may take into account ACT scores as well as reading and writing proficiency).

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