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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 a comprehensive course that includes topics such as recognizing and using patterns, operations in the real number system, solving equations and inequalities, proportional reasoning and statistics, linear functions, absolute value functions, solving system of equations, laws of exponents and exponential equations, polynomials and factoring, quadratic functions, rational functions, square-root functions, trigonometry, probability and set theory, and transformations of functions. 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
This course 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
This course 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
This course follows the mathematics curriculum delineated by the National Council of Teachers of Mathematics. Increased emphasis is placed on reading comprehension, problem solving, and the use of functions as tools for modeling real-world situations. Some of the topics in this course include: linear and quadratic functions, polynomial equations, exponential and logarithmic functions, trigonometric functions, matrices, and systems of equations.

Algebra II Trigonometry Honors (1.0)

1.0 credits
This course 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, rations 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
This course provides 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
This course 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
This course 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
This course 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 (with at least a B average for the year) and teacher recommendation.

AP Calculus BC

1.0 credits
This course 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 Honors 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. 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).

Introduction to Programming

0.5 Credits

This course introduces students to the core concepts of programming while simultaneously teaching students how to program. It covers fundamental programming ideas like functions, control structure, variables and assignments, etc as well as basic abstract data structures like vectors, queues, stacks, etc. It will also touches on the topics of data abstraction, recursion and algorithms. The prerequisite for this course is Algebra I.

Introduction to Statistics

0.5 credits
This course 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.

AP Statistics

1.0 credits
This course, which follows the College Board AP Statistics Course requirements, 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 an 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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