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Mathematics

The Mathematics Department believes successful students actively engage in learning. We design courses and select textbooks to maximize student learning through explorations, discussions, student presentations, and a wide variety of assessments. We teach students to communicate ideas effectively and to use fundamental skills, mathematical models, and technology to solve a variety of problems. We support students in developing confidence, academic resilience, and an appreciation for mathematics.

In addition to traditional core mathematics courses ranging from Algebra 1 through Calculus, a broad set of Advanced Math electives encourage students to pursue individual interests ranging from Probability to Surveying. A minimum of three years of math is required, and honors sections challenge highly motivated students in Geometry, Algebra 2, and Precalculus.
  • Advanced Math: Design Theory I

    DESIGNATION: Level I elective (Winter & Spring)
     
    GOALS: To offer students an opportunity to explore mathematics from a viewpoint different from that of their earlier courses.
     
    MATERIAL COVERED: This course blends mathematics with design theory and fundamentals of art. Color theory is also introduced, as some of this course is project oriented. Students are tested on the mathematics and history behind these concepts. Topics covered include Golden Ratio, Fibonacci sequence, constructions to derive geometry axioms, quadratic formula, rational expressions, proofs, perspective, and translational, rotational, and reflectional symmetry.
     
    TEXT: Malleable Matter/Stretchable Space and Universal Patterns, Pythagorean Press
     
    PREREQUISITE: Algebra 2; this class can satisfy the Level I Art requirement.
  • Advanced Math: Discrete Math

    Designation: Level 1 elective winter term
     
    Goals: This course introduces the study of discrete math in which numbers used are only integers or countable sets, as opposed to the study of algebra in which numbers are continuous. Students will gain an understanding of the various topics covered in this class that are not found in the traditional college prep sequence but are used widely in such fields as programming, cryptology and logic. A graphing calculator is required for this course.
     
    Material Covered: The topics covered in this course include election theory, fair division, the four color problem, Euler paths  Euler circuits and probability.
     
    Text: Discrete Mathematics Through Applications Third Edition
     
    Prerequisite: Algebra 2
  • Advanced Math: Engineering I

    DESIGNATION: Level I Elective

    GOALS: The purpose of this course is to teach
    mathematics and science through a project-based
    curriculum and to understand how it can be used to make
    informed engineering decisions. While building 
    problem solving skills, students will be exposed to
    sound engineering practices.

    MATERIAL COVERED:  In the fall term robotics will be used as a platform to teach programing, machine design, and engineering processes.  The winter term will focus on Individual design projects that reinforce sound engineering practices and the use of CAD 3D modeling software.  In the spring students will learn to use spreadsheets as a way to simplify complex rate of change formulae and to calculate position, velocity, and acceleration of a rocket based on thrust, gravitation, and drag force profiles. Students will use mathematical modeling to make predictions about rocket performance and to make rocket design decisions. A numeric approach to the mathematics will allow for the analysis of intricate design problems.
     
    TEXTS: may include: Physics, McGraw Hill; Algebra 2,
    Pearson; Online Resources
  • Advanced Math: Field Based Math

    DESIGNATION: Level I elective (Spring)
     
    Goal: To explore the myriad applications of Mathematics in possible career paths through visiting speakers, field trips and projects.
     
    MATERIAL COVERED: Students will explore career fields which have unique applications of Mathematics such as medicine, landscape design, the food industry and graphic design. Through field trips, visiting speakers, application exercises, activities and introductory research projects students will study individual subtopics more deeply.  
     
    TEXT: Various articles and readings relevant to each unit
     
    PREREQUISITE: Algebra 2
  • Advanced Math: Finance

    DESIGNATION: Level I elective (Spring)

    GOALS: The objective of this course is for students to develop the skills necessary to become fiscally and financially responsible in today’s global economy.

    MATERIAL COVERED: Using a personal paycheck as a guide, students learn how to calculate FICA, income tax, Medicare, and a variety of other payroll deductions.
    Students then focus on financial planning, both for present day expenses, including purchasing a car and financing a mortgage, and future investments, including retirement accounts and stock market investments. Covered topics are mathematical modeling, compound
    and continuous interest rates, exponential growth/decay, Excel spreadsheets, stock market investments, and retirement accounts. A calculator is required.

    TEXT: Financial Algebra by Robert Gerver and Richard Sgroi

    PREREQUISITE: Algebra 2
  • Advanced Math: Problem Solving

    DESIGNATION: Level I elective (Fall)
     
    GOALS: There are two main objectives of this course: first, to master the vocabulary of mathematics and second, to learn to analyze written problems and translate them into accurate diagrams and formulas. By confronting tough and interesting problems, students also learn to communicate ideas, work with others, and persist.
     
    MATERIAL COVERED: Diagrams, lists, patterns, sub-problems, working backwards, matrix logic, functions, linear equations, and sequences.
     
    TEXT: Problem Solving Strategies: Crossing the River With Dogs, Key Curriculum Press, and other supplementary materials.
     
    PREREQUISITE: Algebra 2
  • Advanced Math: Statistics

    DESIGNATION: Level I elective (Fall)
     
    GOALS: This course introduces students to elements of statistical thinking through data, concepts, case studies, activities, and investigations. Rather than memorize formulas and their derivation, students read about concepts and apply them to the rich selection of examples provided by the text. Students gain a strong understanding of the statistical principles that abound in fields such as politics, medicine, business, sports, entertainment, and education. A TI-Nspire graphing calculator is required.
     
    MATERIAL COVERED: Collecting data (measurement, sample, surveys, experiments), analyzing one-variable data with graphs and numbers, normal distribution, analyzing two-variable data with scatter-plots, regression, correlation, predication, and causation.
     
    TEXT: Statistics Through Applications, W.H. Freeman & Co.
     
    PREREQUISITE: Algebra 2
  • Advanced Math: Surveying

    DESIGNATION: Level I elective (Spring)
     
    GOALS: This course teaches students how to use a variety of surveying instruments, and to apply basic mathematical principles of geometry and trigonometry to create an accurate topographic map.
     
    MATERIAL COVERED: In the first half of the term, students work on a variety of field labs that are designed to develop knowledge and expertise with the surveying equipment. Once the students have acquired the basic skills necessary to work with relative independence by working in pairs, they are set to the task of creating an accurately rendered site plan. This is accomplished by field data collection that is then used to construct mathematically balanced and scaled topographic maps. Each student creates a map that is presented in class as the final examination.
     
    TEXT: Selected passages from the following sources: Elementary Surveying, Charles D. Ghilani & Paul R. Wolf, Surveying Your Land, Charles E. Lawson, and Schaum’s Outline of Introductory Surveying, James Wirshing & Roy Wirshing
     
    PREREQUISITE: Algebra 2 with a solid understanding of trigonometry.
  • Algebra 1 (1)

     
    DESIGNATION: Level I requirement
     
    GOALS: Algebra 1 is the foundation of high school mathematics courses. The goal of this course is to introduce students to the vocabulary, grammar, and basic skills of algebra. Throughout the course, we emphasize student responsibility and participation in group work, as well as in communicating mathematics clearly, both verbally and in writing.
     
    MATERIAL COVERED: Course content includes a study of the real number system, basic operations of variable expressions including factoring, solving, and graphing linear equations and inequalities in the context of real life situations, exponent properties and scientific notation, radicals, and rational expressions and equations. Students are also instructed in the use of the TI-NSPIRE as it applies to the concepts covered in Algebra 1.
     
    TEXT: Big Ideas Math Algebra 1 A Bridge to Success, Houghton Mifflin Harcourt
  • Algebra 2 (1)

    DESIGNATION: Level I requirement
     
    GOALS: This course builds upon skills learned in Algebra 1 and Geometry. The goal is not only to enable students to solve familiar problems, but to also instill a rational approach to new material and to analyze data using new concepts. This course requires extensive use of the TI-Nspire graphing calculator to enhance the visual/graphical understanding of mathematics and allow study of topics in greater depth.
     
    MATERIAL COVERED: The first term covers a review of linear equations and inequalities. The students then solve systems of linear equations and inequalities by several methods, including matrices. The second term offers an in-depth study of quadratic and polynomial functions and the graphs of these functions. The third term refreshes students’ understanding of exponents and radicals. Students are introduced to logarithmic functions and their properties, and investigate the relationship between exponential and logarithmic functions. The term finishes with focus on trigonometry through the Law of Sines and Cosines.
     
    TEXT: Big Ideas Math Algebra 2 A Bridge to Success, Houghton Mifflin Harcourt
     
    PREREQUISITE: Algebra 1 and Geometry
     
  • Algebra 2 (1) (Hon)

    DESIGNATION: Level I requirement
     
    GOALS: This course builds upon skills learned in Algebra 1 and Geometry. The goal is not only to enable students to solve familiar problems, but to also instill a rational approach to new material and to analyze data using new concepts. This course requires extensive use of the TI-Nspire graphing calculator to enhance the visual/graphical understanding of mathematics and allow study of topics in greater depth.
     
    MATERIAL COVERED: The first trimester covers a fast-paced review of linear equations and inequalities. The students solve systems of linear equations and inequalities by several methods, including matrices, and end the term with an in-depth study of quadratic functions, transformations of quadratic functions, and the graphs of these functions. The second trimester refreshes students’ understanding of exponents and radicals, and covers an in-depth study of polynomials and the graphs of polynomial functions. The students review exponential functions, are introduced to logarithmic functions and their properties, and investigate the relationship between the exponential and logarithmic functions. The final term of the year has students working with rational functions and equations, quadratic relations, and conic sections. We end the year with an introduction to trigonometric ratios and functions.
     
    TEXT: Big Ideas Math Algebra 2 A Bridge to Success, Houghton Mifflin Harcourt
     
    PREREQUISITES: Geometry, a grade of 90 or above in Algebra 1, and departmental approval.
  • AP Calculus AB (1)

    DESIGNATION: Level I elective
     
    GOALS: To use and apply derivatives and integration, to develop the ability to communicate mathematics clearly, both verbally and in writing, to develop problem solving techniques, and to develop an understanding of how calculus can be applied to a wide variety of real life problems. The ability to work in collaboration with others is essential to success in this course. A TI-Nspire graphing calculator is required.
     
    MATERIAL COVERED: The first trimester begins with an overview of the four topics of Calculus: limits, derivatives, integrals, and definite integrals. This is followed by a detailed study of limits: left hand limits and right hand limits. Limits are then used to define the derivative. The term concludes with an in depth study of derivatives, the power rule, the chain rule, the product rule, the quotient rule, implicit differentiation, and applications of the derivative. The second term begins with applications of the derivative including extrema and related rates. This is followed by a study of the integral, the definite integral, and applications of integrals, such as the area between curves, volumes of rotation through plane slicing, and cylindrical shells. The third term begins with differential equations, slope fields, and exponentials, followed by a review of the entire year in preparation of the AP exam. Also, interwoven throughout each term is the study of graphs and interpreting and analyzing derivatives and anti derivatives from the graphs.
     
    TEXT: Calculus: Early Transcendentals/Single Variable Text, 10th edition, Wiley
     
    PREREQUISITE: Successful completion of Honors Precalculus and departmental approval.
  • AP Statistics (1)

    DESIGNATION: Level I elective
     
    GOALS: AP Statistics is the high school equivalent of a one semester, introductory college statistics course, typically required for business, social science, and health science majors. This course introduces students to the major concepts and tools for collecting, organizing, analyzing, and drawing conclusions from data. Science, engineering, and mathematics majors usually take an upper-level calculus-based course in statistics, for which the AP Statistics course is effective preparation.
     
    MATERIAL COVERED: The topics of AP Statistics are divided into four major themes: exploratory analysis, planning and conducting a study, probability, and statistical inference. Probability and simulations aid students in constructing models for chance phenomena. Sampling distributions provide the logical structure for confidence intervals and hypothesis tests. Students use a TI-Nspire graphing calculator, and Web-based java applets to investigate statistical concepts. To develop effective statistical communication skills, students are required to prepare frequent written and oral analysis of real data. Several individual and group projects are assigned throughout the year to provide an opportunity to apply the statistical techniques studied.
     
    TEXT: The Practice of Statistics, 4th edition, Starnes, Yates, and Moore
     
    PREREQUISITE: Successful completion of Calculus, or (a grade of 80 or better) in Precalculus with departmental approval, or (a grade 80 or better) in Algebra 2 or Honors Algebra 2 with departmental approval.
  • Calculus (1)

    DESIGNATION: Level I elective
     
    GOALS: This course provides an opportunity to gain an understanding of the basic concepts of the mathematics of change.
     
    MATERIAL COVERED: This class takes an application-based approach to the discovery of calculus. This approach allows students to simultaneously gain a conceptual understanding of the topics and to also become familiar with the steps necessary for successful completion of a wide variety of calculus exercises. The first term focuses on the strengthening of fundamental algebraic and precalculus topics, followed by the introduction to the concept of the derivative. The second term focuses on the application of the derivative, and the fundamental theorem of calculus. The last term looks into applications of integration, differential equations, and basic multidimensional calculus.
     
    TEXT:  Brief Applied Calculus 7 E - Cengage Learning publishers
     
    PREREQUISITE: A grade of 85 or above in Precalculus and departmental approval.
  • Geometry (1)

    DESIGNATION: Level I requirement
     
    GOALS: The goals of this course are to develop independence and confidence while becoming familiar with techniques of deductive reasoning through numerous activities of discovery. These investigations often take place in a cooperative setting and are set in the context of topics such as plane and solid geometry, triangle congruence and similarity, circles and their properties, and trigonometry. The focus of this course is to “learn by doing”. Students continue to develop study skills through homework, collaborative exercises, a variety of testing methods, and numerous projects. A TI-NSPIRE calculator is required.
     
    MATERIAL COVERED: The first trimester covers inductive reasoning, number patterns, compass, straightedge, and patty-paper constructions, as well as line and angle properties. Second-term material includes triangle congruence, polygon properties, circles, and area. The third term investigates the topics of right triangles, volume, similarity, and trigonometry.
     
    TEXT: Big Ideas Math Geometry A Bridge to Success, Houghton Mifflin Harcourt
     
    PREREQUISITE: Algebra 1
  • Geometry (1) (Hon)

    DESIGNATION: Level I requirement
     
    GOALS: To place the responsibility for learning on the student by emphasizing an inductive approach, collaboration, and presentations. Students develop their ability to write detailed descriptions of their solutions as they complete challenge problems and problem sets.
     
    MATERIAL COVERED: Same as Geometry listing but also including deductive reasoning and formal proof.
     
    TEXT: Big Ideas Math Geometry A Bridge to Success, Houghton Mifflin Harcourt
     
    PREREQUISITE: Successful completion of Algebra 1 and departmental approval.
  • PreCalculus (1)

    DESIGNATION: Level I elective
     
    GOALS: To study a variety of functions, to use functions to model and study real life applications, to recognize functions based on a core “family” with common features, and to develop an understanding that mathematics is an essential component of a wide variety of studies.
     
    MATERIAL COVERED: The first trimester begins with a review of linear relations and functions, and is followed by coverage of systems of linear equations and inequalities.  The course then investigates graphs and polynomial and rational functions. The second trimester begins by covering exponential and logarithmic functions, and then moves to a study of trigonometric functions and their graphs.  The term concludes with an investigation of trigonometric identities. In the third term, we study conic sections, combinatorial optimization, probability, sequences, series, the binomial theorem, and basic statistics. A TI-Nspire graphing calculator is required.
     
    TEXT: Precalculus 9th Edition by Ron Larson, Cengage Learning; 9th edition
     
    PREREQUISITE: A grade of 85 or above in Algebra 2 and departmental approval.
  • PreCalculus (1) (Hon)

    DESIGNATION: Level I elective
     
    GOALS: To improve each student’s ability to communicate about mathematics in both written and spoken form, to develop problem solving techniques, to enhance abstract reasoning and generalization processes, and to understand the appropriate use of technology in the exploration of mathematical questions.
     
    MATERIAL COVERED: The first trimester begins with a review of functions in general, followed by a detailed study of linear, polynomial, and rational functions. During the second trimester we explore trigonometry, vectors, and parametric functions. In the third term we study conic sections, combinatorics, probability, sequences, series, the binomial theorem, and limits.
     
    TEXT: Precalculus with Limits 3rd Edition by Ron Larson, Houghton Mifflin; 3rd edition (2001)
     
    PREREQUISITE: A grade of 85 or above in Algebra 2 Honors (or equivalent) and departmental approval.

Faculty

  • Lindsay Brown

    Mathematics Department Faculty
    603-735-6630
    Bio
  • Starr Fair

    Mathematics Department Faculty
    603-735-6630
  • Christopher Farrell

    Mathematics Department
    603-735-6630
    Bio
  • Kristen Farrell

    Mathematics Department
    603-735-6630
    Bio
  • Douglas Houston

    Mathematics Department Faculty
    603-735-6630
    Bio
  • Matthew MacKenzie

    Mathematics Department
    603-735-6630
    Bio
  • Joshua Norris

    Mathematics and Science Departments/Mountain Biking
    603-735-6000
    Bio
  • Patricia Pond

    Mathematics Department, Mountain Classroom Director
    603-731-6800
    Bio
  • Susan Rochon

    Math Department Chair
    603-735-6629
    Bio
  • Sarah Whitehead

    Mathematics Department
    603-735-6630
    Bio
  • Richelle Winkler

    Costa Rica Math Educator
Located in  Andover, NH,  Proctor Academy is a private coeducational day and boarding school for grades 912. Students benefit from a rigorous academic program, experiential off-campus programs, fine and performing arts, competitive athletics, and a wide selection of extracurricular activities.
204 Main Street  .  PO Box 500  .  Andover, NH 03216
p. (603) 735-6000   f. (603) 735-6300   webmaster@proctoracademy.org