Math Department
Philosophy: The Upper School Math Department provides opportunities for all levels of math learners. Most students score extremely well on Advanced Placements tests, while many others achieve success through the Alternative Instruction Program (AIP). The mission of the Math Department is part and parcel of the mission of St. Paul’s Episcopal School - to help every student reach his or her potential by creating classroom environments which are conducive for all learning styles. The Math Department strives to instill mastery of the math fundamentals which students need in order to process abstract problem-solving questions. The math curriculum gives students sufficient experiences with abstractions, enabling them to advance to higher order operations. The department encourages varying levels of achievement to ensure personal success in higher level mathematics. Modern technology is used to encourage independent and group investigations of math concepts.
COURSES OF STUDY
ALGEBRA I
A ninth grade course that covers the basic principles of algebra topics: a brief review of pre-algebra, the language of algebra, integers, polynomial expressions, equations and inequalities of all sorts, factoring, algebraic fractions, graphing linear and quadratic equations, radicals, systems of linear equations, some statistics, basic geometry review, and word problems. Time is devoted to test-taking tips, study skills, and the how/why of homework. The main goal of this class is to provide the students with the math skills and background, critical thinking skills, and confidence needed to succeed in subsequent mathematics courses. Evaluation is based on homework completion, quizzes, tests, graphing calculator/computer mastery, and projects. The technological emphasis of Algebra I are spreadsheets and graphing calculator activities.
GEOMETRY
Algebra I is the prerequisite. This course is designed to enable students to learn to reason inductively in a mathematical system, through formal proof. In addition, students practice problem-solving skills by applying algebra to plane and solid geometry concepts. The basic topics are definitions, theorems, postulates, congruence, similarity, measurement, coordinate geometry, transformations, constructions, trigonometry and space. Graphing calculators with Cabri geometry software and computer software Geometer Sketchpad can be used to enhance visualization. Cooperative learning groups, special class projects, and SAT/ACT preparation are periodically used. Students are evaluated on quizzes, tests, homework completion and group work.
HONORS GEOMETRY
Algebra I is the prerequisite. This accelerated version of the standard geometry course is open to selected students. This course is designed to enable students to learn to reason inductively and deductively in a mathematical system, through formal proof. It includes advanced work in standard geometry topics and additional work in logic, vectors, circular trigonometry, inductive proofs, networks, non-Euclidean geometry, three-dimensional coordinate geometry, analytic geometry, and geometric probability. Instruction is enhanced with computer and graphing calculator activities. SAT/ACT preparation is periodically used. Students are evaluated on tests, quizzes, homework completion and group work.
A-APPLIED MATH
Algebra I (200 or 230) and Geometry (201 or 231) are the prerequisites. This is the second-year course in
algebra, designed for students who need to build a stronger background in the fundamentals of Algebra I and Geometry before entering Algebra II. Concepts from Algebra I and Geometry are reviewed for reinforcement. Algebra II topics covered include: simplifying algebraic expressions; solving word problems; linear equations; determinants; radicals; and solving quadratic systems, and trigonometry. Emphasis is on the mastery and application of basic skills rather than theory. SAT/ACT preparation is periodically used. Students are evaluated on quizzes, tests, graphing calculator proficiency, and homework completion. Algebra II (204 or 233) is required following this course.
ALGEBRA II
This traditional second-year algebra course connects algebra principles to other areas of mathematics as well as to real-life applications. It begins with a review and extension of topics from Algebra I. Emphasis is on simplifying various types of algebraic expressions as well as equation solving and application with word problems. Additional topics include algebraic proofs, linear equations, determinants, complex numbers, logarithms, solving quadratic systems, operations with radicals, solving polynomial functions, rational equations, and statistics. Students are evaluated on tests, quizzes, and homework completion.
HONORS ALGEBRA II/TRIGONOMETRY
This is an accelerated version of the Algebra II course and is open to selected students. This second-year algebra course strives to connect algebra principles to other areas of mathematics as well as to real-life applications. In addition to the areas of study addressed in Algebra II, this course content includes analytical geometry, logarithms, circular and trigonometric functions and their identities, matrices. All topics emphasize both theory and application. Students are evaluated on quizzes, tests and homework completion.
ALGEBRA III/TRIGONOMETRY
The prerequisites for this course are Geometry and Algebra II. Algebra III/Trig is an extension of Algebra II designed to study new and additional topics not covered in Algebra I or Algebra II. This course has been developed in order to bridge the instruction between Algebra II and Pre-Calculus. After working with advanced graphing topics such as polynomial inequalities, polynomial functions and relations, and conics, this course concentrates on extensive study of trigonometric functions from both circular and right triangle perspectives. Topics also include sequences, logarithms, matrices. Students will be evaluated on quizzes, tests, and homework completion.
PRE-CALCULUS
The prerequisite for Pre-Calculus is Algebra II/Trig. In this course topics coinciding with the study of economics cover discrete mathematics, statistics, curve fitting and models, logarithms, probability, combinatorics, matrices and their applications, sequences and series, counting principles and probabilities, limits and an introduction to derivatives. Other topics involve advanced graphing, such as families of functions including trigonometric and discontinuous functions and applications, analytic geometric applications, polar and parametric equations, and vectors. Students are evaluated through tests, quizzes, homework completion, group work and special projects.
HONORS PRE-CALCULUS
This course is an accelerated version of Pre-Calculus with Honors Algebra II/Trigonometry as a prerequisite. This course covers the same topics as Pre-Calculus but at an advanced level, stressing both theory and application. It emphasizes problem-solving skills through additional topics, some of which are mathematical induction , an introduction to calculus with the derivative, limits, continuity, finding maximums and minimums of functions and velocity and accelerations. SAT/ACT preparation is periodically used. Students are evaluated on tests, quizzes, homework completion, graphing calculator mastery, group work, computer activities and special projects.
CALCULUS 211
The prerequisite for this course is Pre-Calculus or Honors Pre-Calculus. This course provides in-depth study of functions, slopes, equalities, inequalities and absolute values. The concept of limit is introduced and developed with applications of the various limit theorems. The concept of limit is also used in the development of the derivative and the integral. Numerous techniques and formulas of differentiation and integration are studied as well as word problem applications and interpretations involving the derivative and integral. Students are evaluated on tests, quizzes and homework completion.
AP CALCULUS AB
The prerequisite for this course is Honors Pre-Calculus. This accelerated version of Calculus is open to selective students. This course provides review of functions, slopes, equations, inequalities, absolute value and limits. The various types of limits and their applications are used in the development of the theory and application of the derivative and the integral. The focus will be both application and theory with preparation geared to the Advanced Placement test. Students in this course have the opportunity to earn college credit through the dual enrollment program with U.S.A.
Additionally, Advanced Placement courses provide the opportunity for students to receive college credit through the advanced placement process. All students enrolled in Advanced Placement courses will be required to take the Advanced Placement exam, for which there is an additional fee.