Mathematics

The math department’s goal is to give each student the very best mathematics education possible, taking into

consideration ability, interest, and necessary preparation for success in college and life. Each teacher strives to instill the confidence necessary to extend the student’s horizons into new areas of mathematically related study such as science, coding, or engineering, as well as foster independent study and continued interest in mathematics. Faculty members teach competent use of technology throughout the curriculum. The TI-84 graphing calculator is an integral tool at all levels of instruction. The minimum requirement for graduation is three years of mathematics in the Upper School with four years highly encouraged.

Algebra I Full year, one credit Algebra I introduces the student to the basic structure of algebra and the real number system. Students learn to recognize how the techniques developed are used to formulate a mathematical system. Students will be introduced to the role of deductive reasoning and will appreciate the need for precision of language. Solutions of linear equations and inequalities in one and two variables, graphing of functions, products and factors, fractions and fractional equations, and quadratic equations are a few of the topics stressed.

Geometry Full year, one credit; Prerequisite: Algebra I Geometry is the study of various plane figures, such as points, lines, angles, and circles as well as some simple three-dimensional interrelationships. The course emphasizes proof and deductive reasoning throughout, using a traditional development of geometry as a system of logical thought. Topics from Algebra I are reviewed continuously and applied in a wide variety of geometric settings.

Honors Geometry Full year, one credit; Prerequisites: Algebra I and department approval This course is designed for the student who can move at a faster pace and who desires to go into the subject in greater detail. The content of the course is the same as Geometry; however, many enrichment problems are provided.

Algebra II Full year, one credit; Prerequisites: Algebra I and Geometry The purpose of the second-year algebra course is to offer the student a sound development of the structure of the real number system. Within this development, the skills from the first-year algebra course are reviewed, consolidated, and expanded upon to lay a solid foundation for future work in mathematics. Among the topics considered are linear and quadratic relations and functions, matrices, exponential and logarithmic functions, complex numbers, and an introduction to trigonometric functions.

Honors Algebra II Full year, one credit; Prerequisites: Algebra I, Geometry, and department approval Honors Algebra II is an algebra course designed for students who desire an enriched and rapidly paced second year of algebra. In addition to the topics covered in Algebra II, this class includes sequences and series, as well as an in-depth study of trigonometry. In Honors Algebra II, students frequently make connections to other STEM courses, thus seeing mathematics holistically rather than as a collection of isolated topics.

College Algebra and Trigonometry Full year, one credit; Prerequisites: Algebra II and department approval Designed to provide students with an opportunity to further refine and enhance their algebraic problem-solving skills before college math courses, College Algebra and Trigonometry will focus on functions, including exponential, logarithmic, and trigonometric functions.

Precalculus Full year, one credit; Prerequisite: Algebra II or Honors Algebra II In Precalculus, students extend and deepen mathematics introduced the prior year. Functions form the foundation of the course; functions covered include polynomial, rational, periodic, exponential, and logarithmic. Trigonometry is a major focus, and additional topics include analytic geometry with vectors, matrix algebra, probability and counting, and sequences and series. Concepts are extended through modeling real-world problems. Technology is incorporated, especially graphing calculators. This course prepares a student for Calculus (AP AB or standard Calculus).

Honors Precalculus Full year, one credit; Prerequisites: Honors Algebra II and department approval This course is designed for students who desire an enriched and rapidly paced course. The content is the same as Precalculus with some added topics. Additionally, students will begin the study of Calculus, enabling them to take AP Calculus BC the following year.

Statistics Full year, one credit; Prerequisites: Algebra II and department approval Statistics is the science and art of collecting, analyzing, and drawing conclusions from data. In this course, students analyze and model one- and two-variable data, learn how to collect useful data, learn the basics of probability, and learn how to estimate a parameter. The emphasis is on understanding statistical concepts, not memorizing lots of formulas. We use the TI-84 graphing calculator extensively, as well as online applets. Hands-on projects provide opportunities for experiential learning.

AP Statistics Full year, one credit; Prerequisites: Algebra II and department approval This course is equivalent to the one-semester introductory statistics course offered by most colleges and required for many majors including psychology, sociology, health sciences, and business. The fall semester focuses on descriptive statistics, data collection, probability and simulation; the second half of the course focuses on inferential statistics. Statistical reasoning and clear communication of process and results are emphasized throughout. Students enrolled in this course are required to take the AP Statistics exam in May.

Calculus Full year, one credit; Prerequisites: Precalculus and department approval Calculus covers all the material in a typical first-semester college calculus course, including limits, derivatives and their applications, integrals and their applications, as well as transcendental functions. Students also learn how to use the TI-84 Plus CE graphing calculator to evaluate calculus-related problems. The primary goal of this course is to learn some high-level mathematics in a stress-free environment. Because we do not have to follow the AP Calculus AB curriculum, students set the pace of the class, and there is flexibility in terms of topics covered.

AP Calculus AB Full year, one credit; Prerequisites: Precalculus or Honors Precalculus and department approval Calculus gives methods of solving two large classes of problems: 1) finding the instantaneous rate of change of a variable quantity (differential calculus) and 2) evaluating a product in which one factor varies (integral calculus). This course follows the AP Calculus AB curriculum. Students enrolled in this course are required to take the AP Calculus AB exam in May.

AP Calculus BC Full year, one credit; Prerequisites: Honors Precalculus and department approval This course includes all the material covered in the AP Calculus AB curriculum with the addition of the calculus of variable factor products and the calculus of functions defined by power series. Students enrolled in this course are required to take the AP Calculus BC exam in May.

Honors Multivariable Calculus and Differential Equations Full year, one credit; Prerequisites: AP Calculus BC and department approval This course is offered through One Schoolhouse. Harpeth Hall will cover the tuition for this course. This course will be listed on a student’s Harpeth Hall transcript and the semester grades will factor into her cumulative GPA.

Introduction to Computer Science One semester, one-half credit; Open to 9th, 10th, 11th, and 12th grade students In this course, students will develop critical thinking and problem-solving skills by exploring computer programming. Beginning with TI Calculators and progressing to Python, students will explore the fundamentals of computer science, including variables, logic statements, functions, and loops. Digital literacy is also emphasized, including file systems, career options in computational fields, and the ethical and unethical use of technology in today’s world. A natural progression from this course is a semester of Web Design and Visual Coding, and/or a semester of Game Design and Coding. Juniors and seniors who succeed in the class will also be well positioned for AP Computer Science A.

Web Design and Visual Coding One semester, one-half credit; Open to 9th, 10th, 11th, and 12th grade students In this course, students will plan, design, and implement visual applications. Students will learn proper use of HTML and CSS for aesthetically pleasing design and JavaScript for building interactive web pages. The class will be significantly project-based: students will design their own personal website as a digital resume, then build a website for a topic or nonprofit of interest to them. Students will also explore career options in programming, the power and influence of the internet, and the ethical and unethical uses of technology. Although the class is open to all interested students and has no prerequisites, 9th grade students are recommended to take Introduction to Computer Science first.

Game Design and Coding One semester, one-half credit; Open to 9th, 10th, 11th, and 12th grade students Game Design will teach students how to design, build, and iterate prototypes of their own video games. Students will begin the semester with an exploration of the principles of game design, then advance to coding their own games and interactions, as well as digitally drawing their own characters and backgrounds. Students will create several different types of games during the semester, then choose a genre to explore for their final project. The class will also explore the video game industry and its career opportunities, particularly in entrepreneurship. Students in 9th and 10th grades should take Introduction to Computer Science first, although exceptions may be considered on an individual basis.

AP Computer Science A Full year, one credit; Open to 10th, 11th, and 12th grade students; Prerequisite: Introduction to Computer Science, enrollment in an honors math course, or department approval This course follows the Advanced Placement course description for Computer Science A and is roughly equivalent to a one-semester college programming course. The course emphasizes object-oriented programming methodology with an emphasis on problem solving and algorithm development. It also includes the study of data structures and abstraction. Because the AP exam tests the use of the Java programming language, this course is taught using Java. Students enrolled in this course are required to take the AP Computer Science A exam in May.