The mathematics curriculum has two primary objectives. The first is to provide students with a thorough grounding in the structure and techniques of the subject area, so that they will be well prepared for future work at the secondary or college level as well as motivated to challenge themselves in these venues. The second is to provide students with an understanding of the utility and power of the subject area and of their current competence and abilities as well as their potential for future development and comprehension.
Towards these objectives, the Mathematics Department faculty promote critical thinking and problem solving skills that will enable students to find success in applying their knowledge of mathematics to other fields. In addition, the faculty develop the skills necessary for students to effectively utilize technology as a mathematical tool for exploration and analysis. Finally, the faculty nurture an appreciation for mathematics as an exact science and of the role it plays in the fields of physical science, art, philosophy, engineering, architecture, and industry.
Mathematics Curriculum Overview
In order to graduate from Avon Old Farms School, students must complete at least three mathematics courses: Algebra 1, Geometry, and Algebra 2 with Trigonometry. Upon completion of Algebra 2 with Trigonometry, students are encouraged to enroll in Advanced Mathematics, Precalculus, or Probability and Statistics. After successfully completing Precalculus, students may elect to take Honors Calculus, Advanced Placement Calculus AB, Advanced Placement Calculus BC, or Advanced Placement Probability and Statistics.
Select a course below for a detailed description...
Algebra 1 introduces the student to fundamental operations using signed numbers and their elementary applications. The goal of Algebra 1 is to develop fluency in working with expressions, equations and variables. Students will extend their experiences with tables, graphs, and learn to solve linear equations, inequalities and systems of linear equations. Students will generate equivalent expressions and begin to apply formulas to methodically solve questions involving motion, speed and distance. Students will simplify polynomials and begin to study and apply strategies to solve quadratic relationships.
Students will use technology to learn, investigate, and develop strategies for analyzing complex situations and mathematical relationships. Topics covered in the course include grouping techniques, exponents, algebraic fractions, linear and quadratic equations, radicals, graphing, inequalities, and the solution of verbal problems.
Algebra 1 Honors
This course is designed for students who have demonstrated a strong ability in previous mathematics courses and who wish to pursue upper-level mathematics courses throughout their academic career. In addition to the topics covered in the regular Algebra 1 course, the honors section studies mathematical modeling, trigonometry, and calculator programming.
Algebra 2 with Trigonometry
This course is a more intensive and extensive study of topics introduced in Algebra 1. The primary objective of the Algebra 2 curriculum is to prepare students for Precalculus or Precalculus Honors. The course is designed to prepare students for college level mathematics and is beneficial for those who will pursue further study in mathematics or related fields. Extensive work is included with equalities, inequalities, absolute value, fractional and negative exponents, radicals, systems of quadratics, logarithms and trigonometric properties. The content of the course is organized around families of functions, including linear, quadratic, exponential, logarithmic, radical and rational functions. Students will learn to represent functions in multiple ways, including verbal descriptions, equations, tables, and graphs. Students will also learn to model real-world situations using functions. To help students prepare for standardized tests, this course provides instruction and practice in a variety of formats. Graphing calculator skills will be taught and used extensively in this course. Throughout this course, students will develop learning strategies, critical thinking skills, and problem solving techniques to prepare for future math courses and college entrance exams.
Algebra 2 with Trigonometry Honors
This course is an extensive, fast-moving study of the fundamental principles of algebra, trigonometry, probability, and statistics to prepare students for Precalculus. Students who earn a high “B” range grade or better in this class usually pursue Honors Precalculus the following year. Topics covered include linear equations, functions, polynomials, complex numbers, quadratic equations, and functions. The honors class will also complete chapters on analytic geometry, exponential functions, trigonometry, sequences, series, and probability. Students completing this class in good standing are prepared to study pre-calculus.
Algebra is the language of calculus. Understanding this, there will be special emphasis early in the year on developing a solid working understanding of the algebraic skills and procedures necessary for success in higher level math courses. Students will learn to define the major concepts in a second year algebra course including polynomials, rational expressions, radical expressions, and complex numbers and then learn how to simplify, add, subtract, multiply and divide these expressions. Other major themes include: solving various types of equations and inequalities, factoring, understanding the concept of a function, and graphing functions on the coordinate plane. Linear and quadratic functions are studied in great detail. Later in the year, students will be introduced to higher degree polynomial functions and associated theorems. Students are introduced to conic sections, exponents and logarithms, right triangle and circular trigonometry, and, if time permits, sequences and series.
Geometry’s primary objective is the study of Euclidean Geometry as a formal, logical system. Where possible, excursions are made into three-dimensional figures and elementary analytic geometry. Some review of algebraic materials may be included. This course begins with developing visualization and some drawing skills. Both algebraic and geometric models are introduced and are further enhanced throughout the course. Proofs are developed slowly in the first half of the course. Various proof formats, including paragraph, flow-chart, and two-column proofs are presented. Students are expected to be actively involved in their own learning. The use of manipulatives is integrated into this course.
The Geometry Honors course begins with a strong development of visualization and drawing skills. Both algebraic and geometric models are introduced and are used throughout the course. Proofs are developed slowly in the first half of the year. Various proof formats, including paragraph, flow chart, and two column proofs, are presented. Students are expected to be actively involved in their own learning. Manipulatives, constructions, and the computer program Geometer's Sketchpad are also integrated into this course.
This course consists of a more thorough treatment of Trigonometry and other selected topics in Algebra 2 with Trigonometry to prepare students for further study in mathematics. Algebra 2 with Trigonometry is a prerequisite. The primary objective of the Advanced Math curriculum is to prepare students for Precalculus. Integral to the learning process is the systematic review of earlier concepts learned in Algebra 2 with Trigonometry and procedures in which students use previously learned skills to develop proficiency with more advanced concepts. The Advanced Math course includes organizational skills, communication, mathematical tools, calculators, hands on activities and group work.
The primary objective of the Precalculus curriculum is to prepare students for Calculus. Integral to the learning process is the systematic review of earlier concepts learned in Algebra 2 and/or Advanced Math and procedures in which students use previously learned skills to develop proficiency with more advanced concepts, especially Trigonometry. The Precalculus course includes exploration, communication, mathematical tools, manipulatives, calculators, hands on activities and group work.
Designed to prepare the more advanced student for Advanced Placement Calculus, this course provides students an honors level study of trigonometry, advanced functions, analytic geometry, and data analysis. A faster pace also allows for the introduction of topics from calculus earlier in the second semester. Limits, continuity, the definition of the derivative, techniques of differentiation, and applications of the derivative are all explored. Applications and modeling are included throughout the course. Appropriate technology is used regularly for instruction and assessment.
This advanced course is an introduction to the fundamental topics comprising calculus. Algebraic, trigonometric, and transcendental functions are studied in the context of differentiation and integration. The Calculus curriculum includes exploration, communication, mathematical tools, manipulatives, calculators, hands on activities and group work. At the conclusion of this course, students should be able to use calculus methods in a variety of applications and problem solving situations.
This advanced course is an introduction to the fundamental topics of calculus. Algebraic, trigonometric, and transcendental functions are studied in the context of differentiation and integration. The Honors Calculus curriculum is designed to introduce students to the many application of calculus, learn the fundamental rules of calculus, and develop strong problem solving skills. Students will learn how to use technologies such as the graphing calculator, Mathematica, and Excel to investigate various calculus topics and real world problems. Upon completion of this course, students should be well prepared to move onto a first year college level calculus course.
Probability and Statistics
Less rigorous than Pre-Calculus, the primary objective of Probability and Statistics is to offer students an opportunity to continue their mathematical studies in a new area. This course begins with an overview of statistics and includes an investigation of the fundamental laws of probability. It also includes such topics as distributions, sampling, regression, estimation, and hypothesis testing.
Advanced Placement Calculus AB
This is a rigorous Advanced Placement course designed to prepare students for the AP Calculus AB exam in the spring. The course seeks to develop students’ understanding of the concepts of calculus, while providing experience with its methods and applications. A multi-representational approach to calculus is employed with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The connections between these representations are also explored.
Advanced Placement Calculus BC
This is a rigorous Advanced Placement course that prepares students to take the AP Calculus BC exam in the spring. The course seeks to develop advanced problem solving skills by stressing the application of the concepts covered in the problem solving process. The class requires some vacation assignments that are to reinforce the concepts that have been taught. The class moves quickly and covers all the material outlined by the College Board and is intended for students that have had success in Precalculus or lower levels of Calculus and want to challenge themselves at the highest level.
Advanced Placement Statistics
AP Statistics is the high school equivalent of a one semester, introductory college statistics course. In this rigorous course, students develop strategies for collecting, organizing, analyzing, and drawing conclusions from data. Students design, administer, and tabulate results from surveys and experiments. Probability and simulations aid students in constructing models for chance behavior. Sampling distributions provide the logical structure for confidence intervals and hypothesis tests. Students use a TI-84 graphing calculator, Fathom and Minitab statistical software, and Web-based java applets to investigate statistical concepts. To develop effective statistical communication skills, students are required to prepare frequent written and oral analyses of real data.