Math

Math Mission Statement

Mathematics is a common language that can help students unlock complex problems and provide a lens of understanding by which to make applied and important connections to other fields, professions and disciplines. Mathematics offers its own unique set of knowledge, skills and processes enabling students to discover ways to solve old problems and develop new ways of thinking about the world around them – a skill that is essential to tackling the biggest challenges in our interconnected, global world. The Mathematics Department's mission is to produce students who are flexible and critical thinkers, able to independently problem solve and effectively communicate both reasoning and results. We strive to create a consistent learning experience for all students while honoring the individual talents of our faculty. In order to value the uniqueness of each student we offer a wide array of courses and appropriately place students based on ability.

Math Curriculum Trajectory

New incoming students take a math placement test to determine their initial math course selection. This placement can change over time based on academic performance. Students may move between honors and regular levels on a year-by-year basis and, under certain conditions, students may use summer work to accelerate their pace through the curriculum. Please see this document for more details. A number of electives exist at the upper school level, giving students choices to match their interests and desired level of academic rigor.

Department Policy on Honors and Placement/Acceleration
Please find the document here.

Algebra I

Course Length: Year
Open to Grades: 9
Prerequisites: C- or above in previous math course

Estimated hours of homework per class period: 45 minutes
Graduation Requirement: Each student must complete three years of math through Algebra II

Algebra I continues the transition from working with numbers to manipulating algebraic expressions. All operations are performed on these expressions, stressing the interplay of multiplication/ division with addition/ subtraction. Students are challenged to understand the reasoning behind their computations. Developing the ability to problem solve using multi step processes is a major theme. Topics include linear equations/ inequalities, graphing, factoring, rational expressions, radicals, quadratics and systems of equations.
AP Statistics

Course Length: Year
Open to Grades: 11, 12
Prerequisite: C or above in Algebra II

Estimated hours of homework per class period: 45 minutes
Graduation Requirement: Each student must complete three years of math through Algebra II

In AP Statistics, students are introduced to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Important components of the course will include students conducting classroom experiments, carrying out individual and group projects, performing simulations involving probabilistic concepts, and analyzing data with appropriate technology. The AP Statistics course not only accommodates students with a wide variety of interests, but also serves those with a relatively wide range of math proficiency. The course is equivalent to a one-semester, introductory, non-calculus-based, college course in statistics.
Geometry

Course Length: Year
Open to Grades: 9, 10, 11, 12
Prerequisites: C- or above in Algebra I
Estimated hours of homework per class period: 1-2 hours
Graduation Requirement: Each student must complete three years of math through at least Algebra II

The study of Geometry develops visual-spatial, logical and conceptual thinking skills in a context that uses the rules of geometry, algebra and problem solving. Hands on activities, learning by discovery, applications to real world situations and creative thinking are important strategies in this course. The topics that will be covered are angles and parallel lines, triangles, quadrilaterals, polygons, circles and three-dimensional figures. Within those topics, the ideas of congruence, similarity, area, perimeter, volume and trigonometry are explored. Writing formal and informal proofs are a major component of the course.
Geometry H

Course Length: Year
Open to Grades: 9, 10, 11, 12
Prerequisites: A in Algebra I

Estimated hours of homework per class period: 1 hour
Graduation Requirement: Each student must complete three years of math through at least Algebra II

The study of Geometry develops visual-spatial, logical and conceptual thinking skills in a context that uses the rules of geometry, algebra and problem solving. Hands on activities, learning by discovery, applications to real world situations and creative thinking are important strategies in this course. The topics that will be covered are angles and parallel lines, triangles, quadrilaterals, polygons, circles and three-dimensional figures. Within those topics, the ideas of congruence, similarity, area, perimeter, volume and trigonometry are explored. Writing formal and informal proofs are a major component of the course. Compared to Geometry, the Honors course covers additional material, is more conceptual in nature, and has less review of past topics and homework.
Algebra II

Course Length: Year
Open to Grades: 9, 10, 11, 12
Prerequisites: C- or above in Geometry
Estimated hours of homework per class period: 1 hour
Graduation Requirement: Each student must complete three years of math through Algebra II

Building off Algebra I, this class introduces students to new topics and explores old ideas at a greater level of complexity. Emphasis is placed on critical thinking and conceptual comprehension. Graphing calculators are used as tools to handle complex calculations as well explore new concepts. Students learn to simplify, solve, graph and model a variety of formats including absolute value, quadratics, polynomials, logarithms, exponentials and trigonometry. Function notation is used extensively and transformations are stressed as a unifying theme. Lecture, discussion and group projects are all part of the learning experience.
Algebra II H

Course Length: Year
Open to Grades: 9, 10, 11
Prerequisites: B+ in Geometry Honors or A in Geometry

Estimated hours of homework per class period: 1-2 hours
Graduation Requirement: Each student must complete three years of math through Algebra II

Building off Algebra I, this class introduces students to new topics and explores old ideas at a greater level of complexity. Emphasis is placed on critical thinking and conceptual comprehension. Graphing calculators are used as tools to handle complex calculations as well explore new concepts. Students learn to simplify, solve, graph and model a variety of formats including absolute value, quadratics, polynomials, logarithms, exponentials and trigonometry. Function notation is used extensively and transformations are stressed as a unifying theme. Lecture, discussion and group projects are all part of the learning experience. Compared to Algebra II, the Honors course covers additional material, is more conceptual in nature, and has less review of past topics and homework.
Precalculus Principles

Course Length: Year
Open to Grades: 10, 11, 12
Prerequisite: C- or above in Algebra II
Estimated hours of homework per class period: 30 minutes
Graduation Requirement: Each student must complete three years of math through Algebra II

This course is designed for students looking for a reliable math preparation for college but do not intend to pursue college mathematics. The first semester will review and further develop their understanding of algebra topics such as polynomial, rational, exponential, and logarithmic functions. The second semester covers trigonometric concepts such as trig ratios, inverse trig, trig identities, and the law of sine and cosine. Additional units will focus on analytic geometry and descriptive statistics with a graphical calculator. Students will engage in problem-based lessons structured around a core idea and build problem-solving strategies, analyze critically, and justify their thinking through the course. Completion of this course does not qualify students to take AP Calculus at Priory.
Precalculus

Course Length: Year
Open to Grades: 9, 10, 11, 12
Prerequisite: B- or above in Algebra II
Estimated hours of homework per class period: 1 hour
Graduation Requirement: Each student must complete three years of math through Algebra II

This course prepares students for college-level calculus by continuing to build upon the topics presented in earlier studies. Students experience a thorough analysis of all functions such as polynomial, exponential, logarithmic, and rational functions, and curve-sketching both by hand and by a TI-84 graphical calculator. Trigonometric functions, inverse trigonometry, and trigonometric applications, including trig identities and the law of sine and cosine, are part of the topics in the second semester. Additional units will focus on analytic geometry and limits. Throughout the course, emphasis will be placed on critical thinking and conceptual comprehension as well as presentation of work.
Precalculus H

Course Length: Year

Open to Grades: 9, 10, 11, 12

Prerequisite: A in Algebra II or B+ in Algebra II Honors

Estimated hours of homework per class period: 2-3 hrs

Graduation Requirement: Each student must complete three years of math through Algebra II

This course prepares students for college level calculus by continuing to build upon the topics presented in earlier courses. Functions, in a wide variety of forms, will play a key role. Additionally, analytic trigonometry and geometry (conics), polar equations and graphs, sequences & binomial theorem, and systems of equations and inequalities will be studied. The course will wrap up with a preview of calculus including limits, derivatives and integrals. Throughout the course, emphasis will be placed on critical thinking and conceptual comprehension as well as presentation of work. Compared to Precalculus, the Honors course covers additional material, moves at a faster face, and is more conceptual in nature. This course is designed to prepare students for BC Calculus.
AP Calculus AB

Course Length: Year
Open to Grades: 9, 10, 11, 12
Prerequisite: A- in Precalculus, B in Precalculus Honors, or B+ in Applied Calculus.
Estimated hours of homework per class period: 1 hr
Graduation Requirement: Each student must complete three years of math through Algebra II

AB Calculus is an AP class that is equivalent to roughly 70% of a first year college Calculus course. The class focuses on applying concepts in new contexts and not just mimicking homework problems. Most students find the total workload somewhat heavier than Precalculus but the concepts more difficult. It is not “easier” than BC Calculus but covers less material and therefore moves at a slower pace and goes more in-depth. The class has a different feel than previous math classes, using AP-style questions extensively and therefore graded on a curve to mimic the AP grading standards. Topics covered include limits, differentiation, integration and their applications.
AP Calculus BC

Course Length: Year
Open to Grades: 9, 10, 11, 12
Prerequisites: B+ in Precalculus Honors or B in AP Calculus AB

Estimated hours of homework per class period: 1 hour
Graduation Requirement: Each student must complete three years of math through Algebra II

BC Calculus is an AP class that is equivalent to a first year college Calculus course. The class focuses on applying concepts in new contexts and not just mimicking homework problems. Most students find the total workload somewhat heavier than Precalculus but the concepts more difficult. It is not “harder” than AB Calculus but covers more material and therefore moves at a faster pace. It is appropriate for students who have a deep conceptual understanding of math as well as computational proficiency. The class has a different feel than previous math classes, using old AP questions extensively and therefore graded on a curve to mimic the AP grading standards. The class covers all of the AB curriculum as well as additional topics including polar coordinates, parametric equations, sequences and series.
Advanced Topics: Differential Equations

Course Length: Year
Open to Grades: 10, 11, 12
Prerequisite: A in AP Calculus BC or B in current post-AP math course
Estimated hours of homework per class period: 1 hour
Graduation Requirement: Each student must complete three years of math

Perhaps the most important of all applications of calculus is differential equations. When physical scientists or social scientists use calculus, more often than not it is to analyze a differential equation that has arisen in the process of modeling some phenomenon that they are studying. Although it is often impossible to find an explicit formula for the solution of a differential equation, we will learn analytical, graphical, and numerical approaches to provide us with a direction. We will start with a study of first-order ordinary differential equations then move on to higher-order differential equations. We will also see how infinite series can be used to solve differential equations. Additional topics include systems of differential equations and Laplace Transforms. This course is part of the four-year rotating post-calculus sequence: Multivariable Calculus, Discrete Mathematics, Differential Equations and Linear Algebra.
Advanced Topics: Linear Algebra

Course Length: Year
Open to Grades: 11, 12
Prerequisites: Calculus BC
Estimated hours of homework per class period: 30-60 minutes
Graduation Requirement: Each student must complete three years of math through Algebra II

Linear Algebra is offered once every four years as part of Priory's post-calculus sequence. The other classes in this sequence are Multivariable Calculus, Discrete Math, and Differential Equations which are offered (in this order) on a rotating basis. These extremely challenging classes are appropriate only for talented students who have earned an A in AP Calculus BC and are traditionally offered only in college. For most students, this will be their first true course in higher mathematics - one in which theory and rigor are explored much more than computational skills typically mastered in a high school mathematics course. Applications of linear algebra abound in science and engineering, so the theory is complemented with a set of hands-on practical lab to give students some understanding of the utility of Linear Algebra in the real world. Topics covered include those taught in a college level Linear Algebra course: vectors, systems of (linear) equations, matrix operations, linear combinations and linear independence, bases and dimensionality, LU decomposition, determinants, eigenvalues and eigenvectors, similarity, diagonalization, orthogonality and Gram-Schmidt orthogonalization, QR factorization, vector spaces, norms and inner product spaces.
Applied Calculus for Finance and Social Sciences

Course Length: Year
Open to Grades: 11, 12
Prerequisite: Algebra II
Estimated hours of homework per class period: 30 minutesGraduation Requirement: Each student must complete three years of math through Algebra II

Applied Calculus for Finance and Social Sciences focuses on calculus concepts applied in economics, business, and the social sciences. Topics covered include linear programming, matrices, business and personal finance, and differential and integrated calculus. Semester one will focus on finance with long-term investigations into business decisions (linear programming) and personal finance. Semester two will focus on calculus topics such as the derivative (calculating, graphing and applications) and integration (techniques and applications).