Math (HS)

Overview
Math is the most basic language of science, quantum physics, biology, and economics, even applicable to the behavioral sciences. In our Math Department, we take a tough subject and teach it such that challenges become fun and exciting – and the field’s beauty and precision become evident. Every student can be successful in math if placed in a course that is appropriately challenging. Our approach fosters student motivation, personal responsibility, orderly thinking, and the logical presentation of work.

We offer two pathways in math. Students are able to move from one pathway to the other when their interest in and comfort with math develops. “Advanced” or AP courses are offered to students who are ready for intense challenges and an accelerated pace.

Required Courses

Algebra 1: this course teaches the basic concepts and skills of Algebra. Students solve a range of problems to practice application of key skills and concepts while continuously reviewing earlier ideas and strategies.
Algebra 2 or Advanced Algebra 2: this course emphasizes facility with algebraic expressions and forms, especially linear and quadratic forms, powers and roots, and functions based on those concepts.
Geometry or Advanced Geometry: taken after Algebra 2, this course imparts general and specific knowledge of geometric facts and figures and teaches deductive reasoning as it applies to geometric proofs and problems.

Further Courses

Pre-Calculus or Advanced Pre-Calculus: this course is both a culmination of a sequence of Algebra and a preparation for Calculus. The concept of “function” is fundamental to the course, as well as sharpening algebra skills and refining understanding of algebra and trigonometry.
Calculus AB or AP Calculus AB: this advanced course traditionally follows Pre-Calculus and is roughly equivalent to one semester of college Calculus. It includes the study and application of differentiation and integration, as well as graphical analysis.
AP Calculus BC: AP Calculus BC is a continuation of our AP Calculus AB course, and is available to well-prepared students who have succeeded in AB. The course begins with a review of concepts from AP Calculus AB and is designed to prepare students to take the College Board’s AP exam in May.
Multivariable Calculus: the prerequisite to this course is Calculus BC. Topics include vectors and matrices, parametric curves, partial derivatives, double and triple integrals, and vector calculus in 2- and 3-dimensional space.
Statistics, Algebra & Financial Management: this one-year course provides a general review of mathematical topics relevant in the contemporary world, including an overview of fundamental algebraic concepts, statistical analysis, and financial algebra.
Advanced Statistics: this is a rigorous student-centered, project-based, and social justice-oriented course, covering exploratory data analysis, data collection and experimental design, probability distributions, and statistical inference, including federal statistics and published studies.

Preparation for College

Students conclude our mathematics program with:

problem-solving skills that they may apply to real-world phenomena
positive attitude to approaching difficult tasks
understanding that making mistakes can be an integral part of the learning process
readiness for the next level of math that may be required for their academic goals

Adv. Algebra 2

Advanced Algebra 2 emphasizes facility with algebraic expressions and forms, especially linear and quadratic forms, powers and roots, and functions based on these concepts. In addition to studying exponential, logarithmic, polynomial and other special functions as tools for mathematical modeling, students also explore trigonometry. Emphasis is placed on reasoning, problem solving, note taking and the orderly exposition of ideas. Algebra 2 with Trigonometry proceeds at an ambitious pace and is a pre-requisite to Pre-Calculus.
Adv. Geometry

Advanced Geometry is taken after Algebra 2, and will move at an accelerated pace. The course has two objectives: to impart general and specific knowledge of geometric facts and figures and to teach the logical reasoning skills of deductive reasoning as it applies to geometric proofs and problems. Proofs are an integral component of the class.

The course emphasizes the core ideas of Euclidean Geometry such as right and oblique triangle trigonometry, properties of circles, polygons and solids, and also introduces some key concepts in transformational, coordinate and non-Euclidean geometries.

Students apply this learning to solve real-world mathematical problems.
Adv. Precalculus

Advanced Precalculus is designed to prepare students to take a college level calculus course. It is assumed that students taking this course have mastered both Algebra 2 and Trigonometry and require no remediation and little review. The course focuses on the concept of function and rapidly progresses to a significant level of abstraction in which the mathematical entity and its behavior are emphasized and studied in depth. While many problems reflect the ability of the mathematics to model natural phenomena, the development of strong analytical skills, a conceptual framework and the ability to synthesize mathematical components into a comprehensive whole are critical intellectual elements of the course.
Adv. Statistics

Advanced Statistics is a rigorous, student-centered, project-based and social justice-oriented course. It covers Exploratory Data Analysis (including graphical and numerical techniques), Data Collection and Experimental Design, Probability Distributions, and Statistical Inference. Emphasis is placed on use and analysis of data related to current topics of social relevance, including federal statistics and published studies.

As an advanced math course, Advanced Statistics is designed for students who have taken Precalculus, and who have the approval of the math department chair. It may also serve as a post-Calculus course for students completing Calculus in their junior year, or as a concurrent area of study for motivated students in Calculus in their junior or senior years.

Prerequisites:

Completion of Precalculus

Approval of math department chair
Algebra 1

Of all the math courses students take, none is more important or fundamental to future understanding in mathematics and science than Algebra 1. The goal of the course is to teach the basic concepts and skills of algebra in a manner that allows students to appreciate their utility and power. Students solve a variety of problems to practice application of the skills and concepts they are learning while continuously reviewing earlier ideas and strategies.
Algebra 2

Algebra 2 emphasizes facility with algebraic expressions and forms, especially linear and quadratic forms, powers and roots, and functions based on those concepts. Students study exponential, logarithmic, polynomial and other special functions as tools for mathematical modeling and problem-solving.
AP Calculus AB
This course prepares students for the Calculus AB Advanced Placement examination. It also covers any topics not in the AB syllabus that are typically included in first-semester college calculus. It begins with a brief review of precalculus, which is followed by an exploration of limits, continuity, the derivative and its applications, the fundamental theorem of calculus, indefinite integrals, and definite integrals and their applications.

Prerequisites:
1. B+ or higher in Pre-calculus with Analysis; A average in Pre-calculus
2. Successful completion of summer work
AP Calculus BC
AP Calculus BC is a continuation of our AP Calculus AB course, and is available to well-prepared students who have succeeded in AB. The course begins with a review of concepts from AP Calculus AB, and is designed to prepare students to take the AP Calculus BC exam in May. Topics covered include: antidifferentiation by parts, logistic growth and its differential equation, further applications of definite integrals including curve length and work, sequences, L'Hopital's rule, improper integrals, infinite series, and parametric, vector and polar functions.

Prerequisites:
1. B+ or higher in AP Calculus AB
2. Successful completion of summer work
Calculus AB

Calculus AB is an advanced mathematics course traditionally taken after precalculus and is roughly equivalent to one semester of college calculus. Calculus is the study and application of differentiation and integration, and graphical analysis including limits, asymptotes, and continuity.
Geometry

Geometry is taken after Algebra 2. The course has two objectives: to impart general and specific knowledge of geometric facts and figures and to teach deductive reasoning as it applies to geometric proofs and problems, with an emphasis on using logical reasoning to understand the origin or construction of formulas and theorems. The course explores the core ideas of Euclidean Geometry beginning with a foundation of points, lines and planes and then advancing through triangles, circles, polygons, and solids, and also introduces key concepts in Transformational and Coordinate geometries.

Students will apply their knowledge through a variety of digital and hands-on projects each unit.
Multivariable Calculus

Multivariable calculus is the extension of calculus to more than one variable. The prerequisite to this course is Single Variable Calculus. Functions of two or more independent variables are interesting in their own right, but they are also essential for describing the physical world.

The course covers vector and multi-variable calculus. Topics include vectors and matrices, parametric curves, partial derivatives, double and triple integrals, and vector calculus in 2- and 3- dimensional space.
Precalculus

Precalculus may be thought of as the culmination of a sequence of algebra in high school or as preparation for calculus. The concept of function is fundamental to the course, but considerable emphasis is also placed on sharpening algebra skills and refining understanding of the core concepts of algebra and trigonometry. While the level of abstraction and intellectual demands placed on the student are considerably higher than in Algebra 2, the pace emphasis and depth of the course make it accessible to any student who has satisfactorily completed Algebra 2 and who has exhibited good qualities of studentship. A student who has mastered the concepts of this course and demonstrated the requisite qualities of studentship may next take Calculus with teacher and department head approval.
Statistics, Algebra, & Financial Management

This course provides a general review of mathematical topics relevant in the contemporary world. It enables students to develop their problem-solving skills and their ability to deal with quantitative issues and mathematical ideas that they would encounter in a first year college course in Math. It includes an overview of fundamental algebraic concepts, statistical analysis and financial algebra. Topics may range from Problem-solving and Critical Thinking to Set Theory, Logic, Number Theory, Number Representation and Calculation, Equations and Inequalities, Functions, Graphing, Statistics and Personal Finance.