Upper School Mathematics

Department:  Upper School

The goal of our Upper School math program is to offer a wide range of courses that will challenge each of our students at the appropriate level for their age, ability and needs.  Students gain critical mathematical thinking skills including algebraic thinking and problem solving using technology when appropriate. After completing foundational courses, students have options to pursue further studies in advanced mathematics and applied mathematics.  A student's mathematical power increases as the student is required to explore, to conjecture, to reason, to solve non-routine problems, to communicate mathematically and to make mathematical connections between concepts and among disciplines.

Math: US Algebra
Algebra is the first course in the core curriculum at Waterford.  It is a course that generalizes the arithmetic of early years into a formal, symbolic language.  Each student is introduced to the various aspects related to understanding algebra: its skills, its properties, its uses, and its representations.  During the year, a student develops mathematical power meaning the ability to explore, to conjecture, to reason logically, to solve non-routine problems, to communicate about mathematics, and to connect mathematical ideas.  Students in the Algebra curriculum study the use of variables and operations involving algebraic symbols. They learn how to solve different types algebraic sentences, including linear and quadratic equations and inequalities.  They work with exponents, radicals, and rational expressions and they learn how to solve and graph linear and quadratic equations.

Math: US Geometry
Geometry connects the physical and visual world with the students' previous knowledge of algebra. Upper School Geometry is taught in three distinct terms.  In Fall Term, the curriculum is organized around a traditional Euclidean geometry. Students explore relationships among lengths, angles and triangles. The focus this term is on providing a first look and exploration with an axiomatic mathematical system and students begin to learn how to justify and prove their own thinking using both informal and formal methods.  In Winter Term, the course focuses on developing geometric formulas and exploring properties of other geometric shapes, including three-dimensional shapes. During this term, students are also introduced to right triangle trigonometry and learn to use the trigonometric ratios to solve real-world problems. In Spring Term, the geometry curriculum shifts to coordinate geometry.  Students review and expand their algebraic skills in order to study some of the geometric concepts on a coordinate plane. Students learn the algebra that is connected with the geometric concepts such as slope, parallel and perpendicular lines, circles, and intersection points. Students use hand-held and other technology to explore and answer questions they previously could not using only analytic techniques.  Upon completion of this course students are prepared for Algebra 2.

Math: Algebra 2
Algebra 2 is a continuation of the study of Algebra, tackling concepts and skills beyond linear and quadratic equations.  It introduces the student to the skills, properties, uses and representations of the more complex aspects of algebra. A student's mathematical power increases as the student is required to explore, to conjecture, to reason, to solve non-routine problems, to communicate mathematically and to make mathematical connections between concepts and among disciplines.  The course covers the specific topics of functions including polynomial, power, rational, exponential and logarithmic; sequences and series. Students learn to connect the analytic representation with numerical and graphical representations. Students learn to use technology as a tool to explore and solve problems previously inaccessible using basic skills of analysis.  

Math: Algebra 2 Honors
Algebra 2 Honors is an enriched Algebra 2 course where students continue their study of Algebra, tackling concepts and skills beyond linear and quadratic equations.  This course introduces the student to the skills, properties, uses and representations of the more complex aspects of algebra and requires students to understand, prove and extend the theorems and properties presented in the Algebra 2 curriculum.  The student's mathematical power increases as the student is required to explore, to conjecture, to reason, to solve non-routine problems, to communicate mathematically and to make mathematical connections between concepts and among disciplines. The course covers the specific topics of functions including polynomial, power, rational, exponential and logarithmic; sequences and series and matrices.  Students learn to connect analytic representations with numerical and graphical representations and do so in many applied settings. Students learn to use technology as a tool to explore and solve problems previously inaccessible using basic skills of analysis. The Algebra 2 Honors course builds on the theoretical foundation established in a formal Geometry course and prepares students to continue in the accelerated Honors Precalculus course.  Students are placed in this course by teacher recommendation or by test.

Math: Precalculus 1
Precalculus 1 is a course designed to formalize and intensify a student's understanding of functions.  Students learn to work both analytically and graphically with functions. They review polynomial, rational, exponential and logarithmic functions and are introduced to trigonometric functions. Students study trigonometry (both right triangle and functions) in depth, learning how to solve equations as well and provide identities and formulas involving the trigonometric ratios.  Throughout the entire course, students learn how to model real world problems using their library of functions. Students use handheld and other technology to explore and answer questions they previously could not using only analytic techniques.

Math: Precalculus 2
PreCalculus 2 is a continuation of the Precalculus 1 curriculum.  It introduces and focuses on both infinte (continuous) and finite (discrete) processes.  Its topics include functions of many kinds, polar coordinates, complex numbers, advanced trigonometry and vectors, and introductions to the basic concepts of calculus:  derivatives and integrals. In addition, in this course students delve into some topics of discrete mathematics, looking at the finite and iterative processes. Its topics include logic, sequences, algorithms, recursion and induction, combinatorics, graphs, and networks.  The focus of this course is developing students' mathematical thinking in the context of these new and somewhat unfamiliar math topics. Students use handheld and other technology to explore and answer questions they previously could not using only analytic techniques. After completing this course, students are prepared for advanced study in Calculus or Statistics.

Math: Precalculus Honors
Precalculus Honors is an accelerated course that covers the two courses Precalculus 1 and Precalculus 2 in one year. Students learn to work with functions both analytically and graphically.  They review polynomial, rational, exponential and logarithmic functions and are introduced to trigonometric functions. Students study trigonometry (both right triangle and functions) in depth, learning how to solve equations as well and prove identities and formulas involving the trigonometric ratios.  In addition, students learn polar coordinates, complex numbers, advanced trigonometry and vectors, and are introduced limits. Also, students become familiar with the discrete mathematics including logic, sequences, algorithms, recursion and induction, combinatorics, graphs, and networks. Throughout the entire course, students learn how to model real world problems using their library of functions.  Students use handheld and other technology to explore and answer questions they previously could not using only analytic techniques. This course moves quickly and upon completion, students are prepared for the AP Calculus AB course. Students are placed in this course by teacher recommendation or test.

Math: Calculus
The course is rigorous and thorough study of Calculus, but is a step back from the demands of the AP Calculus curriculum.  It is designed for students who are prepared and interested in calculus but lack the time required for a thorough preparation for the AP Exam.  This course will include a review of Precalculus topics and functions and then introduces students to limits, differential calculus, integral calculus and applications of calculus. After taking this course, students are very well prepared for AP Calculus or any other college level calculus course.  

Math: AP Calculus AB
The curriculum of the Advanced Placement Calculus AB course follows the specifications required by the College Board.  Specific topics include an extensive study of the common functions including exponential, logarithmic, rational, and trigonometric; limits and continuity; derivatives and differentials; techniques of differentiation; applications of differentiation; antiderivatives, integration, differential equations and applications of integration.  Students learn to connect the analytic representations with numerical and graphical representations and do so in many applied settings. This approach allows formal definitions and proofs to evolve from extended exposure to common sense investigation, rather than memorizing abstract algorithms. In addition, students focus on gaining advanced skills in communicating mathematical thoughts and reasoning.  Finally, students are taught appropriate uses of hand-held and other technology that will allow them to explore and solve problems previously inaccessible using basic skills of analysis. Students are expected to take the AP Calculus AB exam at the completion of the course.

Math: AP Calculus BC
The curriculum of the Advanced Placement Calculus BC course follows the specifications required by the College Board.  This course is designed to be a continuation of the Advanced Placement Calculus AB curriculum. While continually reviewing the basic calculus topics covered in the AP Calculus AB curriculum, students learn the new topics of infinite series (including power, geometry and Taylor polynomials); the calculus of conic sections and polar coordinate; three-dimensional analytic geometry, vector functions and curvilinear motion, vector integral calculus, differential equations, vectors and vector fields, parametric equations.  A prerequisite for this course is successful completion of AP Calculus AB. Students are expected to take the AP Calculus BC exam.

Math: Introduction to Statistics
This term-long course focuses on introducing students to the use of statistics from a practical standpoint.  Students will learn the language and symbols of statistics and will learn how statistics are appropriately and inappropriately used in the world around us.  Students will also be introduced to techniques for gathering data as well as making decisions based on those statistics. This course is open to any student who is not currently enrolled or who has not completed the AP Statistics curriculum.  

Math: AP Statistics
The curriculum of the Advanced Placement Statistics course follows the specification required by the College Board.  The purpose of this course is to provide a practical introduction to statistics. As such, the focus is primarily on the statistical thinking behind data gathering and interpretation with less emphasis on computation and theory.  General topics taught in this course are producing data, organizing data and statistical inference. Producing data will include learning the ideas behind what constitutes "good" data, how to select samples and design studies and experiments.  Organizing data includes learning the methods and strategies for exploring, organizing and describing data using graphs and numerical summaries. Students learn techniques of decision-making using probability including statistical tests of inference (z-tests, t-tests and Chi-squared tests) as well as confidence intervals. Students learn to use hand-held and other technology to help them tackle statistical problems from real-world data.

Math: Advanced Topics
This course is designed for advanced math students who have already completed the full breadth of our other math courses, including all Advanced Placement courses.  This course is taught as three separate term courses. Content for each term is determined by teacher and by interest of students, and has included topics such as linear algebra, number theory, multivariate calculus, the history of mathematics and advanced proof and reasoning.  Students may enroll in Advanced Topics multiple years or after completing this course one year, may design an independent study course with a math faculty member.

Math: College Prepatory Mathematics
This term-long course focuses on making sure students are prepared for the rigor and content of an entry level college math course.  Topics will vary from term to term and may include a review of previous math curriculum, quantitative reasoning, number theory, formal logic, set theory, and probability.  This is not designed for students who have completed an AP level math course at Waterford. Rather, this will help make sure students have a familiarity with the mathematics that they will be expected to master before graduation from college.

Math: Introduction to Statistics
The term-long Introduction to Statistics Course is a one-term course designed to introduce students to the language and decision making process used in a world full of data.  Students will learn to see the world around them through the eyes of a statistician, from data gathering, experimental and observational design. The course reviews basic probability in order to understand the decision making process used to draw conclusions from data. This course is not open to students how are currently enrollled in or who had already taken AP Statistics.

Math: Introduction to Financial Math
This term-long course introduces students to basics of financial mathematics.  Students will learn various applications of mathematics in the real world including loans, mortgages, taxes, annuities and the like.  The course will also focus on applications of personal finances including savings, credit and investments. In addition, students will learn to use spreadsheets to analyze real life budgets and track investments.  This course is open to students of any mathematical background.