Mathematics

Department Head: Britta Milks

Teachers

  • Matt Baron
  • Michelle Gavin
  • Christine Merola
  • David Merola
  • Britta Milks
  • Jennifer Perez
  • Rick Tony

Curriculum

The primary goal of the Mathematics Department is to develop a curriculum sequence that meets the academic needs of all Solebury School students. Above all, students are encouraged to achieve their highest mathematical potential. Many students desire an aggressive math sequence that provides enriching, challenging opportunities, whereas other students look for a program that will build their confidence and comfort level with a discipline that is difficult for them. In developing a curriculum sequence, we recognize that students come from diverse backgrounds and therefore students are placed into courses that will best fit their individual needs. The department offers courses that range from Algebra to Advanced Placement Calculus. Additionally, the department offers electives each year that provide students with an opportunity to explore, analyze, and appreciate mathematics through a nontraditional approach. Three years of mathematics are required for graduation with the typical sequence of courses consisting of Algebra I, Geometry, and Algebra II and Trigonometry. However, with permission of the Mathematics Department Head and the Director of Studies, certain other paths are possible. Students are encouraged to communicate with their math teacher, school adviser, and parents as they determine the appropriate sequence of courses for their high school program. Additionally, it is important for students in their sophomore and junior years to check the mathematics requirements of potential colleges, as many universities recommend (or require) four years of math from applicants.

All students enrolled in high school math courses (Algebra I and higher) are required to obtain a graphing calculator. Today, calculators are an integral component of the learning process and students need to be adept at using this technology. Additionally, a graphing calculator is required by most colleges as well as on standardized math tests such as the SAT, ACT, SAT II subject tests, and the AP Calculus and Statistics exams. The department strongly recommends that students purchase a TI-84 Plus. The school has a small supply of calculators that can be lent to students for the school year if needed and are distributed on a first come, first served basis. Students who are enrolled in AP Calculus BC are required to have a TI-89 graphing calculator as this calculator allows students to explore concepts and functions that were previously difficult or impossible to examine without the use of computer software programs.

If you have any questions about Solebury School’s Mathematics Department, please contact department chair Britta Milks at bmilks@solebury.org.


MATH SUPPORT PROGRAM

Math Support Program (MSP) is a learning enrichment and support program which provides innovative resources and a nurturing environment to support the math curriculum at Solebury School. This program includes three main components:

  • Algebraic Concepts I
  • Algebraic Concepts II
  • Geometry Concepts

This three-year math sequence is for students with math disabilities or significant difficulties with math. For some students, one year with math support is needed followed by mainstreamed classes. For others, support is provided for all three levels of mathematics: Algebraic Concepts I, Geometry Concepts and Algebraic Concepts II. Successful completion of this three year sequence fulfills graduation requirements. We offer Algebraic Concepts I every year and teach the Geometry or Algebraic II course every other year.

  • Students will discover the fundamentals of algebra through a multisensory and multidimensional type of curriculum.
  • By the end of the year of Algebraic Concepts I, students in the program will have a stronger foundation in algebraic concepts. This foundation includes: number sense, operations, analytical analysis, multi-step equations, problem solving, as well as procedural and computational fluency.
  • By the end of the year of Algebraic Concepts II, students in the program will have studied the main topics inherent to an Algebra curriculum. These topics include: linear, quadratic, and polynomial functions, radicals, data analysis, exponential functions, and problem solving skills.
  • By the end of the year in Geometry Concepts, students in the program will have a stronger understanding of two-dimensional plane Geometry as it applies to polygons, stronger critical thinking skills as it applies to conjectures in proofs, and stronger spatial reasoning.
  • Technology will be infused whenever appropriate.
  • Additional information and admission requirements provided on the Algebraic Concepts fact sheet.

If you have any questions about Solebury School’s Math Support Program, please contact the director of the program, Dr. Jen Perez at jperez@solebury.org.

For more information, see our Math Support Program page.


FULL-YEAR COURSES

Algebra I: This course thoroughly examines basic algebraic principles. Topics covered include simplifying expressions using the appropriate order of operations, solving first and second degree equations in one variable with both algebraic and graphical methods, solving absolute value equations and inequalities, and the concept of functions. Additionally, students will simplify and solve rational equations as well as examine the basic principles surrounding radical expressions. Students will explore linear and quadratic functions, as well as systems of equations in two variables. Throughout the course, an emphasis will be placed on solving real-world problems with both algebraic and graphical processes. 6 credits

Honors Algebra I: A faster-paced and more in-depth analysis of the topics covered in Algebra I. Additional topics in this course may include an introduction to right triangle trigonometry as well as basic principles of probability and statistical analysis. Honors, 6 credits

Algebraic Concepts I: Students will discover the fundamentals of algebra within this course. They will be taught through a multisensory and multidimensional type of curriculum. This course is slower-paced with built-in support for reaching and furthering the analysis of topics covered in Algebra I. These fundamentals include number sense, operations, analytical analysis, two-step equations, problem-solving, procedural and computational fluency. Technology will be infused whenever appropriate. Enrollment in this course is predicated on joining the Math Support Program and entails an additional fee. For a description of the broader program, please see the information above in the Math Department section. Prerequisite: Recommendation of math department. 6 credits

Geometry: The purpose of the course is for students to discover the conjectures and definitions of geometry through hands-on investigations. Students will learn to apply deductive and inductive reasoning as they examine geometric proofs. Relationships and properties such as congruence and similarity will be examined in depth. Additionally, students will investigate the properties of circles, right triangle trigonometry, and formulas relating to plane and solid figures. Inherent in the course is the development of critical thinking skills, logic, and geometrical visualization. Time permitting; an exploration of symmetry and/or a review of algebra will be included at the conclusion of the course, as most students will be entering Algebra II the following year. Prerequisite: Algebra I. This course may be taken concurrently with Algebra II. 6 credits

Honors Geometry: A faster-paced and more in-depth analysis of the topics covered in Geometry. This honors version of Geometry is intended for students who plan to follow mathematics through Calculus. There will be greater emphasis on critical thinking skills and proofs. Prerequisite: B or better in Honors Algebra I or with teacher recommendation. This course may be taken concurrently with Algebra II. Honors, 6 credits

Algebra II and Trigonometry: This course is recommended for students who need a moderately paced approach to Algebra II. The subject matter includes a brief review of first-degree polynomials followed by an in-depth study of higher-power polynomials, conic sections, exponential, logarithmic, and trigonometric functions. Attention is given to the relationship between functions and their graphs. This course enables students to move on to the regular Pre-Calculus class, and it fulfills the graduation requirement. Prerequisite: Algebra I. 6 credits

Honors Algebra II and Trigonometry: A faster-paced and more in-depth analysis of the topics covered in Algebra II and Trigonometry. This course is recommended for students who plan to follow mathematics through Calculus. Students in this course will be prepared for Honors Pre-Calculus. Prerequisite: B or better in Honors Algebra I or with teacher recommendation. Honors, 6 credits

Pre-Calculus: The first two trimesters of this course are designed to further the study of trigonometry and its applications. Topics will include the unit circle, the six trig functions, trig identities, the law of sines, the law of cosines, “real world” applications of these functions, and selected applications in physics. The third trimester will introduce functions and relations focusing on conic sections, exponential, logarithmic, and rational functions. This course enables students to move on to the Calculus AB course. Prerequisite: Completion of Alg II and Trig. 6 credits

Honors Pre-Calculus: This honors course is for students who have a very strong background in Algebra II and Trigonometry. The first trimester covers a review of polynomial, exponential and logarithmic functions, as well as other advanced algebraic topics. The second trimester is a study of trigonometry. The third trimester covers linear systems, series and sequences, and an introduction to the Calculus itself. This course enables students to move on to the AP Calculus BC course. Prerequisite: B or better in Honors Algebra II and Trig or with teacher recommendation. Honors, 6 credits

Calculus: This course is designed to give students a strong foundation in the following topics: limits, derivatives, anti-derivatives, integrals and differentials. While much of what is covered in the course parallels the content of AP Calculus AB, the course itself is not bound by the same pace and rigor inherent to the Advanced Placement program. The course is appropriate for students who would benefit from additional review of pre-calculus concepts woven into the course and/or students who want to study calculus but do not want the intensity of an AP course. Students in Calculus will review the following concepts: algebra and functions, mathematical modeling with elementary functions, rates of change, inverse functions, logarithms and exponential functions, trigonometry, and modeling with trigonometry. These concepts will be reviewed in the context of calculus concepts such as the derivative, differential equations, graphical interpretations of the derivative, zeroes of functions, optimization, related rates, anti-differentiation, initial value problems, and the Fundamental Theorem of Calculus. Upon completion of this course, students will be prepared to enroll in AP Calculus AB (or BC with departmental approval) or, in the case of graduating seniors, an appropriate college level calculus course. Prerequisite: Completion of Precalculus. 6 credits

AP Calculus AB (Calculus I): This course is equivalent to a first semester college calculus course, covering differential and integral calculus. Students will study limits of functions, continuity, derivatives and applications of the derivative. As part of integral calculus, students will examine the definite integral as a limit of Riemann sums, the area under a curve, solving differential equations, and various applications to economics, biological, and physical situations. Students are required to take the AB Advanced Placement exam in May. Prerequisite: B or better in Pre-Calc. AP, 6 credits

AP Calculus BC (Calculus I & Calculus II): This course is a full year calculus course that includes all of the topics covered in AP Calculus AB plus topics typically covered in a Calculus II course at the college level. Technology will be an important part of the class to reinforce work and to interpret results of various experiments and data. This course is faster paced than the AB course and students should be prepared to attend occasional class sessions outside of the regularly scheduled times. Students are required to take the BC Advanced Placement exam in May. Prerequisite: B or better in Hon. Pre-Calc. AP, 6 credits

AP Statistics: The Advanced Placement course in Statistics is equivalent to a one-semester introductory, non-calculus-based, college course in statistics. The AP Statistics course covers four broad themes which include: exploring data, planning a study, anticipating patterns, and statistical inference. Students who have successfully completed Algebra II / Trigonometry and who possess sufficient mathematical maturity are eligible for this course. Students are required to take the Advanced Placement exam in May. Prerequisite: B or better in Algebra II and Trigonometry. AP, 6 credits

Financial Mathematics: This yearlong course will use a mixture of arithmetic and algebraic skills to tackle the major concepts involved in the modern world of business and finance. The main topics to be covered include simple & compound interest, consumer credit, and various investment tools, such as annuities and Treasury Bills. Basic business applications will also be included in the course, such as markup, markdown, and inventory methods. While some sophisticated mathematics will be used in this course, (from algebra, pre-calculus, probability & statistics, calculus, and geometry) students need only to have completed a second year course in algebra to be ready for the material here. Lastly, economic concepts will be introduced and studied concurrently for the purpose of applying newfound mathematical skills, as deemed appropriate by the instructor. These concepts include supply & demand, marginal cost, stock market, and FOREX trading. Students should come out of this course with the knowledge of how to use mathematics to make informed decisions as they earn, spend, and save money throughout the rest of their lives. Prerequisite: Completion of Algebra II & Trigonometry. 6 credits

Multivariable Calculus: This yearlong course is similar to a third semester study of calculus at the collegiate level and is a continuation of the topics typically studied in Calculus I and II. While calculus up until this point has focused on the study of scalar-valued functions of one variable, multivariable calculus considers multiple inputs and vector-valued outputs and thus students will learn to analyze functions in a multidimensional setting. Familiar topics such as graphing, differentiation, and integration will be extended as students learn about vector algebra and geometry in space, vector-valued functions, functions of several variables, partial derivatives and chain rules, Lagrange multipliers, multiple integration, iterated integrals, and change of variables. Students may exercise the option to take this course for three college credits in “Advanced Calculus” through Delaware Valley University. Registration and tuition payment of $300 to Del Val will occur during the fall term for interested students. Prerequisite: AP Calculus BC or AP Calculus AB (with approval of Math Department Chair). 6 credits