Academics
Academic Program

Math

Our philosophy

The ability to work with numbers and to apply mathematics is essential to a solid educational foundation. At Falmouth Academy, students study mathematics every year. The practical application of mathematical theory forms a significant aspect of our approach to math. One application, of course, is the analysis of data students gather for their independent research projects for the Science Fair, co-sponsored by the math and science departments. With every passing year, this analysis becomes more sophisticated and detailed. Other class projects challenge students to design a strategy for their retirement or to describe the enlargement of a drawing using only mathematical formulae. Writing is another facet of the math curriculum as students research historical mathematicians and present their contributions in class.

We offer two series of courses to meet the needs of students with varying math background and skill. All seventh graders take Math 7, which uses group work and projects to challenge the top students and to fill in any gaps in an individual student’s preparation. The seventh-grade year also serves as a placement assessment for eighth grade, where there are two options: Pre-Algebra and Algebra I. For students who begin algebra in eighth grade, the freshman math course is Geometry. The course sequence continues in sophomore year with Algebra II, then Pre-Calculus and Calculus. Alternatively, students may take Algebra I in freshman year, continuing through Statistics and Functions or Pre-Calculus as seniors. At each level, students are taught to take more independent approaches to the solution of problems. Throughout the math curriculum, teachers are coaches rather than lecturers, encouraging students to discover the hows and whys of mathematics.

Course descriptions

List of 10 items.

  • Math 7

    All seventh-graders take math in heterogeneous classes. The curriculum is activity- and project-oriented with a strong basic skills component. The material is organized to emphasize skills and to build upon previously mastered skills. Overlap in the material covered between the units allows for reinforcement of previously taught material. Realizing that students learn and demonstrate their learning in different ways, a variety of approaches and assessment methods are employed.

    The goals of the curriculum are to foster a positive attitude toward math that includes the understanding that math is important and necessary, to enhance students’ abilities to apply the skills they learned to solve practical problems, and to develop their own logic and mental computational skills. To achieve the last goal, we require the students to complete almost all work in this course without the assistance of a calculator. Those students who master foundational concepts and demonstrate a mature work ethic will enter Algebra I at the completion of this course.
  • Math 8

    Math 8/Pre-Algebra is designed to give those students who need reinforcement of their basic math skills the chance to work on these skills as well as develop their algebra skills. These skills include the order of operations, using negative and positive numbers, solving equations, simplifying expressions, percents, ratios, finding perimeter, area, and volume, and analyzing data. Concepts from arithmetic, geometry, and algebra are integrated throughout the course. Most concepts are presented as tools to solve problems or to make mathematical models of real situations. There is an emphasis on communicating mathematics through writing as well as diagrams and computations.
  • Algebra I

    Algebra I is offered to 8th and 9th graders in two levels from the same text. It is taught at different paces and to varying depths depending on student comprehension and the overall ability level of each class. The basic goal of the Algebra I course is to make students proficient in the solution of quadratic equations, systems of equations with two unknowns, and the graphing of linear equations. Students are exposed to various solution methods for both quadratic equations and systems of equations. Word problems are an integral part of this process.
  • Geometry

    Students begin by learning the language and applying basic postulates, definitions, and algebraic principles in the proof of simple theorems. They simultaneously learn the deductive structure, an integral part of the course. The concept of congruency is studied in triangles as students become proficient in logic and proof. The concept of parallel lines is introduced and applied in the study of the properties of special quadrilaterals. After a brief introduction to solid geometry, the proof is de-emphasized as students consider polygons and examine the concept of similarity. They then move to geometry's most elegant theorem, the Pythagorean. This topic provides an introduction to trigonometry and a review of many of the algebraic principles studied in previous years. The year concludes with the study of circles.
  • Algebra II

    The curriculum in Algebra II is an equal balance of theoretical algebra and the application of these concepts. The class is sectioned so that the material may be presented at the appropriate pace for each student. There are three major application projects completed by students. We believe that if students cannot see how a concept is useful, they will not give it the attention it deserves. The class focuses on developing the student's abilities to manipulate equations, graph functions and relations, and solve problems by creating mathematical models.   The major topics include functions, such as linear, quadratic, cubic, and exponential, rational and irrational expressions, logarithms, quadratic relations, trigonometry, and probability.
  • Statistics, Trigonometry, and Functions

    The course consists of three major units: statistics, trigonometry, and functions.

    The statistics unit begins with an analysis of data organization principles and then proceeds to measures of center and measures of dispersion. Students examine real-world systems in the context of confidence intervals and hypothesis testing.  Binomial probability is the final unit, including binomial distributions and the normal distribution.

    The unit on trigonometry begins with angles and their representations in both degrees and radians. The six standard trigonometric functions are then introduced. The concepts of amplitude, phase, period, and vertical displacement are explored in the context of practical as well as theoretical applications. Finally, the unit ends with triangle trigonometry and its practical and theoretical applications.  

    The final unit, functions, examines polynomials, rational expressions, exponential and logarithmic functions, systems of equations, and conics in both theoretical and practical applications.  Graphical analysis and modeling with each type of function are explored in depth. The extensive use of graphing calculators plays a significant role in this course.
  • Pre-Calculus

    This course addresses a combination of topics that are necessary for success in Calculus and offers a glimpse into the deeper world of mathematical beauty.  Functional analysis, especially the manipulation of circular and triangular trigonometric functions, is covered in detail to produce a solid foundation for future work in Calculus.  Astronomical and statistical applications provide opportunities for understanding the power of graphing calculators. The work of the entire course is attentive to nurturing facility with calculations, as well as instilling a love for playing with numbers, taking joy from an elegant proof, and marveling at the interconnectedness of higher mathematics.
  • Math Models and Intro to Calculus

    This course is offered to those seniors who have completed Statistics, Trigonometry, and Functions and those students who have completed Pre-Calculus and are not going on to Calculus in high school. In rare cases, students who have only completed Algebra II may petition to enter the course.

    The course is designed so that students apply the knowledge they learned in previous math courses in long-term projects. The spring trimester includes an introduction to Calculus, including limits and derivatives; consequently, most students are well prepared to take first-semester Calculus.

    There are two major goals to the course. The first is to provide students with the opportunity to apply the mathematical concepts that they have learned in the past three years to a variety of “real world” situations, including an extensive study of financial literacy and investing. The second goal of the course is to provide the students with a strong enough mathematical background so that, at the end of this course, they are prepared for college calculus. There is an emphasis on problem-solving, group work, and the sharing of ideas.
  • Calculus

    This course begins with a brief review of pre-calculus mathematics and quickly moves into differential and then integral calculus.  Students enrolling in this course may choose to take the Advanced Placement AB Calculus exam.

    Upon completion of this course students are able to: work with functions represented in a variety of ways: graphical, numerical analytical, or verbal;  understand the meaning of the derivative in terms of a rate of change and local linear approximation, and use derivatives to solve a variety of problems; understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of a rate of change and to use integrals to solve a variety of problems;  model a written description of a physical situation with a function, a differential equation, or an integral;  use technology to help solve problems, experiment, interpret results and verify calculations; determine the reasonableness of solutions, including size, sign, relative accuracy, and units of measurement; and develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.
  • Calculus II

    The course begins with a brief review of pre-calculus mathematics and quickly moves into differential and integral calculus (Calculus 1).  Students will then do units on parametric equations, polar coordinates, vector-valued functions, and infinite sequences and series.  Students enrolling in this course may choose to take the Advanced Placement BC Calculus exam. 
    Upon completion of this course students are able:
    • To work with functions represented in a variety of ways: graphical, numerical analytical, or verbal.
    • To understand the meaning of the derivative in terms of a rate of change and local linear approximation and to use derivatives to solve a variety of problems.
    • To understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of a rate of change and to use integrals to solve a variety of problems.
    • To model a written description of a physical situation with a function, a differential equation, or an integral.
    • To approximate a function or a number with a polynomial expression.
    • To find derivatives of vector-valued functions and parametric functions and graph those functions.
    • To use derivatives to determine velocity, speed, and acceleration for a particle moving along curves given by parametric or vector-valued functions. 
    • To solve problems involving polar coordinates, their graphs, and calculus work with derivatives, area, arc length, and surface area.
    • Explore a variety of types of sequences and series using a multitude of tests to determine convergence, including infinite, alternating, geometric, and arithmetic sequences.    
    • To use technology to help solve problems, experiment, interpret results, and verify calculations.
    • To determine the reasonableness of solutions, including size, sign, relative accuracy, and units of measurement.
    • To develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.

Meet our Faculty

List of 6 members.

  • Photo of Jon Olson

    Mr. Jon Olson He / Him / His 

    Math Department Chair
  • Photo of Doug Jones

    Mr. Doug Jones 

    Math
  • Photo of Kenneth Kozens

    Mr. Kenneth Kozens 

    Math
  • Photo of Edward Lott

    Mr. Edward Lott 

    Math
  • Photo of Scottie Mobley

    Ms. Scottie Mobley 

    Science/Math
  • Photo of Jill Reves

    Ms. Jill Reves 

    Science/Math
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