Curriculum Guide

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The Woodberry Forest mathematics program teaches students to draw conclusions using both contemporary and traditional approaches and to justify and prove conjectures through examples, counterexamples or formal proofs. The courses offered include traditional college preparatory offerings for secondary school: Geometry, Algebra 1, Algebra 2, Precalculus, Calculus, Statistics, and a Seminar in Advanced Mathematics. Independent study opportunities are also available for the most advanced students. Honors classes are available in courses beyond Algebra 1, and students are placed in these courses based on their aptitude and performance in mathematics. Initial placement is made based on prior studies of mathematics, teacher recommendations, and proficiency demonstrated on standardized tests. A Foundational course is available as a bridge for incoming students to ensure readiness for Algebra. Students are required to successfully complete one course beyond the level of Geometry and Algebra 2 OR one course in each year enrolled (culminating with Algebra 2) in order to satisfy the school’s graduation requirement. Promotion to the next level of study in a sequential course requires a final grade of C- or better. Unless otherwise specified, all courses are year-long.

Common course progressions in order from most common to least common (over four years): (Regular/Honors designations not shown)

3rd Form
4th Form
5th Form
6th Form
Algebra 1
Algebra 2
FST or Precalculus  and/or Statistics
Algebra 2
Calculus and/or
Algebra 2
Calculus and/or
SAM and/or
Foundations of Algebra
Algebra 1
Algebra 2
(and Statistics, if desired)
  • Mathematics_Algebra 1

    (Prerequisite: solid pre-algebra foundation)

    The first four weeks of Algebra 1 overlap with the Foundations of Algebra curriculum and require students to demonstrate their readiness for the remainder of the course. Students deemed by the instructor to need additional support may be asked to move to Foundations of Algebra.

    Algebra 1 is required for entering students who lack Algebra 1 credit. The emphasis is on mathematical literacy and problem solving to build a strong mathematical foundation for future studies. Students will study how to recognize, classify, and use numbers and their properties; recognize, create, extend, and apply patterns, relations, and functions; simplify algebraic expressions including polynomials and rational expressions; solve and graph relations, inequalities, and systems in both one and two variables; and communicate using the language of algebra. We expect students to develop proficiency in reading and writing good mathematical expressions; factoring and divisibility of numbers and expressions; manipulating rational expressions; solving linear and quadratic equations and inequalities; solving linear problems with absolute value; and graphing in both one and two dimensions. Student work is evaluated frequently. Calculators are not permitted in Algebra 1.  Upon completion of this course, a student will be prepared and recommended for the most appropriate level of Geometry or Algebra 2 (or both with the support of their teacher and approval of the department chair and advisor).
  • Mathematics_Geometry

    (No prerequisite, although it is recommended that Geometry follow Algebra 1 and precede (or be taken concurrently with) Algebra 2.)

    Geometry is a required course that normally follows Algebra 1. Geometry encourages students to value mathematics as a means of interpreting and understanding their world. Emphasis is on problem-solving and developing logical, sequential arguments. Through reading, writing, and discussions, students develop inductive, deductive, and indirect reasoning skills. Major topics include similarity, congruence, constructions, proof, and an introduction to trigonometry. An Honors section is available for advanced students. Students study how to communicate using the prescriptive language of plane Euclidean geometry; identify, explore, discuss, and apply properties, theorems, axioms, and definitions related to plane figures; and develop problem-solving skills utilizing multiple heuristic methods as outlined in George Polya’s, How to Solve It. We expect students to develop proficiency in defining and recognizing terms and symbols of geometry and using them to communicate mathematical ideas; write organized deductive proofs and clear definitions; apply skills learned in algebra and use proportions and other equations to solve geometric problems; and develop elementary constructions with a compass and a straightedge.

    Generally, a students understanding is assessed every few days with a quiz in preparation for a full-period unit test given once every two weeks. A cumulative exam is given at the end of each trimester. Students may also be asked to perform constructions using software such as Geometer’s Sketchpad or Geogebra. 
  • Mathematics_Algebra 2

    (Prerequisite: C- or better in Algebra 1) 

    Second-year algebra builds on the understanding and the skills developed in Algebra 1. Students are taught to use mathematical thinking in problem solving; emphasis is placed on developing student communication skills, both written and oral. We expect students to develop the skills necessary to solve many types of equations, develop an organized methodology for solving certain types of word problems and use mathematical functions to describe real-world phenomena. Additional topics may include linear programming, sequences and series, and an introduction to statistics. Students will study how to write mathematics in a clear and logically consistent manner, using appropriate mathematical notation. The goal of this course is to teach students in depth about parent functions (linear, quadratic, exponential, logarithmic, rational, and polynomial) - how to graph , identify, transform, translate, add, and multiply them. There are three levels of Algebra 2 offered - Honors, Regular, and Foundations. Placement will be based on the student’s mastery of algebraic concepts and computational accuracy.
  • Mathematics_Functions, Statistics, Trigonometry, and Finance

    (Prerequisite: C- or better in Algebra 2 or equivalent) 

    Functions, Statistics, and Trigonometry (FST) is for students seeking math credit beyond the Algebra 2 level. The course contains many topics of traditional pre calculus courses, extending the concepts developed in Algebra with a focus on the use of functions and inverse functions. In addition to the algebraic functions introduced in previous courses, we explore transcendental and trigonometric functions. We expect students to read mathematics to develop understanding, to develop skill in carrying out various algorithms, use properties and relationships found in mathematics, represent and picture mathematical concepts with graphs, tables, and charts, and bolster the confidence of those students for whom success in mathematics has been elusive. Students should develop the ability to use the graphing calculator appropriately; read and write good mathematics and study mathematics individually so that he will be able to deal with the mathematics he sees in newspapers, magazines, television, on the job and in school.
  • Mathematics_Pre-Calculus

    (Prerequisite: B- or better in Algebra 2 and a recommendation from the teacher.) 

    Precalculus generally follows Algebra 2 and is designed to build a strong foundation in mathematics leading to calculus. Students develop a firm grasp of the underlying mathematical concepts, while using algebra as a tool for solving problems. Topics include elementary functions, their properties, and transformations on these functions, trigonometric functions, systems of equations, matrices, and analytic geometry. The goals of precalculus are to provide the student with an understanding of the major functions used in the study of calculus with emphasis on both a graphical and analytic perspective using both technology and traditional methods; develop the critical analytical techniques to effectively model, interpret and analyze data within its appropriate context. Precalculus provides students with the opportunity to further develop critical thinking skills and become more effective problem solvers through the application of mathematical knowledge; provide an environment to use appropriate technology and communicate knowledge and understanding more effectively. Students are expected to develop the ability to analyze algebraic functions with an emphasis on end behavior, zeros, and asymptotes, analysis of transcendental functions and their inverses; use of vectors to gain insight into trigonometry, and know how to analyze and use logarithmic and exponential functions.
  • Mathematics_Honors Introduction to Calculus

    (Prerequisite: B or higher in Honors Algebra 2 or an A in Algebra 2 and a recommendation from the teacher.) 

    The honors precalculus course is known as Honors Introduction to Calculus. Students are expected to solve more complex problems than the regular section of precalculus. Calculus concepts of the limit and continuity are integrated throughout the year. This course starts the Calculus curriculum in the spring and formalizes the idea of the limit as well as how the limit is used to define the derivative. Students are also expected to learn how to take the derivative of all algebraic and trigonometric functions. 
  • Mathematics_Calculus

    (Prerequisites: C- or better in Precalculus)
    Honors Calculus A (Prerequisites: B or better in Precalculus and a recommendation from teacher.)
    Honors Calculus B (Prerequisites: B or better in Honors Intro to Calculus or Honors Calculus A and a recommendation from the teacher.) 

    Calculus consists of a full academic year of work in calculus comparable to courses in colleges and universities. There are three levels of Calculus at Woodberry: Calculus, Honors Calculus A, and Honors Calculus B. All levels address the development of a student’s understanding of the concepts of calculus and provide experience with its methods and applications. Honors Calculus A and Honors Calculus B are specifically targeted to the Advanced Placement courses Calculus AB and Calculus BC, respectively, as described by the College Board. Calculus mirrors Honors Calculus A with the omission of a few topics and greater emphasis on applying calculus to other disciplines. Honors Calculus B is an extension of Honors Calculus A rather than an enhancement; thus, common topics are addressed with similar depth. The goals of the class are to help students understand the concept of the limit and its use to analyze the behavior of functions; understand the derivative and integral and their use to analyze the behavior of functions and to solve problems with rates of change and accumulation; develop analytical thinking and problem-solving skills and the ability to clearly communicate ideas both orally and in writing; incorporate the use of technology as an aid to understanding concepts. Honors Calculus A & B prepare students to succeed on the Advanced Placement Calculus examination. Students are encouraged, but not required to register for the Advanced Placement exams.  In all the Calculus courses, students learn how to use the limit process to both predict and explain observed local and global behavior of a function; evaluate derivatives of basic functions both explicitly and implicitly, and to apply the derivative to problems involving graphical analysis, projectile motion, related rates, and optimization; evaluate the integral of basic functions and apply to problems of area, volume, average value, projectile motion, and differential equations. In Honors Calculus B, students learn how to use parametric, vector-valued, and polar functions to solve problems as well as how to analyze power series and use them to approximate functions.
  • Mathematics_Statistics

    (Prerequisite: minimum of a C or higher Algebra 2, Completion of Precalculus is recommended) 

    Statistics introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring data, planning a study, anticipating patterns and statistical inference. Exploratory analysis of data makes use of graphical and numerical techniques to study patterns, and departures from patterns. The year begins with an exploration of some familiar statistical measures such as mean and median. Familiar measures such as these are used as a springboard to introduce statistical tools of increasingly complexity, such as standard deviation and then standardized scores, including z-scores and t-score. An emphasis is placed on learning to represent data and sets of data with an appropriate graphic model. Students will learn to choose the appropriate model and then construct the model. Students will then explore linear relationships between quantitative variables and the notions of association, correlation, and residual. Moving forward, the students will explore probability and methods of simulation, including settings that are binomial and geometric in nature. Students will be required to develop an appropriate method to simulate a randomly occurring event and implement that simulation. The year concludes with a broad exploration of significance tests where the students will learn the formal definition of “significant”, the different levels of significance, and the methods by which we can measure significance. All students will be required to explore data in a wide variety of “hands-on” settings and to apply appropriate statistical means of measurement to those “hand-on” events. A graphing calculator is used to not only compute descriptive statistics but also assist in performing significance tests. An Honors option to Statistics is also available.
  • Mathematics_Honors Statistics

    (Prerequisite: minimum of a B or higher Algebra 2. Completion of Precalculus is recommended) 

    Honors Statistics introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring data, planning a study, anticipating patterns and statistical inference. Exploratory analysis of data makes use of graphical and numerical techniques to study patterns, and departures from patterns. Data must be collected according to a well-developed plan if valid information on a conjecture is to be obtained. Probability is the tool used for anticipating what the distribution of data should look like under a given model, and statistical inference guides the selection of appropriate models. We expect students to develop the ability to find data descriptors (mean, variance, median) and determine expected shapes of graphs based upon these descriptors; to reason probabilities from given physical models, such as dice, coins, cards, etc. and for students to be able to use inferential statistics and perform significance tests and find confidence intervals. To accomplish these goals a student will need to learn how to determine the median, IQR, and outliers of a data set and how to use the normal distribution to find similar results of a continuous distribution. Students will learn how to use scatter plots, histograms, and other types of graphs to analyze data. The transformation of non-linear data sets to achieve linearity will be required to successfully model some sets of data. Students will be required to assess the validity of a variety of tests in given situation and utilize the correct test. Application of learned techniques for “hands-on” analysis of data will be required to successfully complete the course. A graphing calculator is used to not only compute descriptive statistics but also assist in performing significance tests. 

    Entry into Honors Statistics is available to those with a history of excellence in previous mathematics classes, recommendation from the math teacher from the previous year, and approval of the teacher of the Honor-level section(s). Honors Statistics will include all topics taught in the traditional Statistics course, but will also explore non-linear relationships and transforming to achieve linearity, non-Normal distributions, determining Power of and error probability in tests, determining appropriate tests to assess data, and topics to be determined at the discretion of the instructor as the needs of the class dictates. Students enrolled in Honors Statistics should show a well-developed ability to work independently and in small groups. Students enrolled in Honors Statistics will be required to take the AP Statistics exam that is given by the College Board every year in May. 
  • Mathematics_Seminar in Advanced Mathematics (SAM)

    (Prerequisite: Calculus and a recommendation from the calculus teacher.) 

    Seminar in Advanced Mathematics (SAM) is an adventure in the study of mathematics unlike that of any other academic or extracurricular offering in secondary mathematics. The students retrace the steps, suffer the frustrations, enjoy the excitement, and bask in the accomplishments of many legendary mathematicians. The primary goal is to give each student superior proving and problem-solving skills, making the method more important than the content. Content varies according to the instructors and students. Topics have included group theory, abstract algebra, symbolic logic, multivariable calculus, analysis (advanced calculus), number theory, RSA cryptography, linear algebra and game theory.

Our Faculty

  • Photo of Matthew Keating
    Matthew Keating
    (540) 672-3900 Ext. 8636
    University of Connecticut - BS
    Teachers College, Columbia University - MA
  • Justin Cook
    (540) 672-3900 Ext. 8653
    University of Pretoria - BA
  • Photo of Joe Fischer
    Joe Fischer
    (540) 672-3900 Ext. 8634
    United States Naval Academy - BS
    University of Rhode Island - MBA
  • Photo of Courtney Hamilton
    Courtney Hamilton
    (540) 672-3900 Ext. 8650
    University of Southern California
    University of the Pacific
  • Photo of Chris Holmes
    Chris Holmes
    Head Varsity Baseball Coach
    (540) 672-3900 Ext. 8637
    Auburn University - BS
  • Photo of SaraGrace Kimball
    SaraGrace Kimball
    Kenan-Lewis Fellow in the Mathematics Department
    (540) 672-3900 ext. 8610
    Penn State University - BS
  • Photo of David McRae
    Dr. David McRae
    Samford University - BS
    University of Alabama at Birmingham - MS, PhD
  • Photo of Beth  Menzie
    Beth Menzie
    (540) 672-3900 Ext. 8647
    Williams College - BA
    Wesleyan University - MA
    Bank Street College of Education - MA
  • Photo of Mark O'Donnell
    Mark O'Donnell
    Colby College - BA
    University of Virginia - MEd
  • Photo of Zachary Scarano
    Zachary Scarano
    (540) 672-3900 ext. 8619
    Wabash College - BA
Woodberry Forest admits students of any race, color, sexual orientation, disability, religious belief, and national or ethnic origin to all of the rights, privileges, programs, and activities generally accorded or made available to students at the school. It does not discriminate on the basis of race, color, sexual orientation, disability, religious belief, or national or ethnic origin in the administration of its educational policies, admissions policies, scholarship and loan programs, and athletic or other school-administered programs. The school is authorized under federal law to enroll nonimmigrant students.