Mathematics

Shannon Lambert, Department Head

The Mathematics Department espouses the standards set forth by the National Council of Teachers of Mathematics. Each course seeks to help the student learn to value mathematics, become confident in her ability to do mathematics, become a mathematical problem solver, and learn to communicate and reason mathematically. The student is expected to be actively involved in doing mathematics through exploration, modeling, conjecture making, researching, decision making, and problem solving.

Algebra 1

Yearlong—Required

Algebraic thinking involves discovering patterns, making generalizations about numbers and using symbols to represent relationships. This course is the foundation of the language of mathematics. Students will study the properties of real numbers, solve equations and inequalities, combine rational expressions, and problem solve. They will practice incorporating real world data into applications of Algebra through the use of iPad applications and TI-84 series graphing calculators.

Prerequisite: none

Algebra 2

Yearlong—Required

This rigorous course thoroughly reviews and extends the concepts of Algebra 1 through the study of quadratic equations and inequalities, complex numbers, roots and radicals, functions, systems of equations, graphing, and advanced problem solving. Students will be expected to use TI-84 series graphing calculators to confirm solutions and support critical thinking skills. The honors level course moves at a faster pace, requires more independent thinking, and expects students to master certain Algebraic topics on a deeper level.

Prerequisite: Algebra 1; recommendation of the department is necessary for honors

Geometry

Yearlong—Required

This course covers geometric construction (via compass and straightedge), the properties of plane and solid figures, perimeter, area, volume, and the Pythagorean Theorem. Concepts are explored using both inductive and deductive reasoning. Students are encouraged to think for themselves about what might be true, explore their ideas through hands-on investigations, and then confirm their results through rigorous proof. The honors level course moves at a faster pace, requires more independent thinking, and expects students to master techniques of proof on a deeper level.

Prerequisite: Algebra 1; recommendation of the department is necessary for honors

College Algebra

Yearlong—Open to Grades 11 and 12

This course focuses on strengthening and expanding intermediate and advanced algebra skills and applications of mathematics. It will familiarize learners with fundamental mathematical concepts such as inequalities, polynomials, linear and quadratic equations, and logarithmic and exponential functions. Upon course completion, students will be able to apply a variety of problem-solving strategies to find solutions to an array of real-life problems. This course also provides the algebraic skills needed to pursue higher level studies in mathematics.

Prerequisite: successful completion of Algebra I, Algebra II, Geometry

Precalculus

Yearlong—Open to Grades 10–12

Our goal for Precalculus is to help students learn the skills and concepts needed to understand Calculus. Precalculus is a combination of elements from Algebra, Trigonometry, and Geometry. This yearlong course includes algebraic, exponential, logarithmic, and trigonometric functions and their graphs as well as an introduction to sequences, summation notation, and analytic geometry. The TI-84 series graphing calculator is required for this course. The honors level course moves at a faster pace, requires more independent thinking, and expects students to master abstract mathematical concepts on a deeper level.

Prerequisite: successful completion of Algebra I, Algebra II, Geometry; recommendation of the department is necessary for honors

Calculus

Yearlong—Open to Grades 11 and 12

This yearlong course begins with a review of polynomial curve sketching and properties of exponents. The concept of limit will be introduced from both an intuitive and formal approach. The definition of and techniques for finding the derivative of polynomial functions will lead to curve sketching and practical applications. The concept of integral along with the techniques for finding the integral and its basic application will also be covered. The TI-84 and TI-84CE calculator is used extensively throughout this course.

Prerequisite: successful completion of Precalculus or Precalculus Honors with a strong background in Algebra.

Advanced Calculus 1

Yearlong—Open to Grades 11 and 12

Calculus allows us to study how some quantities change and accumulate in relation to others. Calculus courses teach students not only how to solve particular problems, but how to think creatively about the skills they are gaining and to express their thinking graphically, analytically, numerically, and verbally. The course covers the concepts of limits, continuity from both and algebraic and graphical point of view for polynomial and trigonometric functions. The concepts of the derivative and the integral, along with their many applications in the real world and in other mathematical topics will be studied. The TI-84CE calculator is used throughout this course.

Prerequisite: successful completion of Precalculus or Precalculus Honors with a strong background in Algebra along with the recommendation of the department based on demonstrated skills and motivation.

Advanced Calculus 2

Yearlong—Open to Grades 11 and 12

Advanced Calculus 2 allows motivated students with strong skills the opportunity to build on work done in Precalculus Honors and learn calculus topics as applied to various types of functions, including trigonometric, logarithmic, and exponential functions. The course begins by taking a new look at graphs of functions with an eye to limits and continuity. The central concept of the derivative, along with its many applications in the real world and in other mathematical topics, is the focus of the middle portion of the year. The Advanced Calculus 2 course wraps up with a study of integration methods and their various applications.

Familiar concepts of differentiation and integration are applied in new graphing situations such as the polar plane, parameterized curves and vector-valued functions. New applications and methods for integration are explored, and the year finishes with a thorough investigation of infinite sequences and series.

Prerequisite: Successful completion of Precalculus Honors and the recommendation of the department based on demonstrated skills and motivation.

Advanced Statistics

Yearlong—Open to Grades 11 and 12

Statistics are everywhere. You don't go a single day without hearing about some study and/or conclusions from a study or an experiment. This course is designed to be an interactive, thought provoking course which will allow you to construct your own understanding of concepts and techniques of statistics. A main goal of the course is to teach you to think carefully about collecting and analyzing data. As such, examples, assignments, and projects will be tied to the real world. As a result, this course will impact your thinking and the way in which you view the world.

Reading and critical thinking are important parts of this course, and answers will often require interpretation rather than simply being taught "right" or "wrong." The skills taught in Statistics are discussed in their real-world applications, and lively debates often erupt on the subject of opinion polling, healthcare, and criminal justice. A TI-84 series graphing calculator will be required for many of the calculations and procedures taught in this course.

Prerequisite: Strong background in Algebra and the recommendation of the department based on demonstrated skills and motivation.

Women in the Global Economy

Fall Semester, Spring Semester—Open to Grade 12

Planning your financial future is one of the most important things you can do in your life. The main objective of this seminar course is to build competence and confidence in the area of personal finance. Tools for making informed decisions concerning personal finance will be introduced and developed. It is the sincere hope that this course will help students to become lifelong skillful managers of their personal finances. Investigations and activities will be created to help them think critically about this subject, to consider appropriate alternatives, and to make appropriate decisions about money matters.

As we introduce students to the basic concepts and vocabulary of personal economics, they will be better equipped to become wise independent consumers, vigilant savers, smart money managers, responsible givers, and an active part of the global economy. Drawing from research written primarily by leading women entrepreneurs, CEOs and market analysts, and articles from business journals, this course is designed to give students a deeper understanding of the global economy and to provide them with a better sense of their role in it and how they can engage in it in the future.

Prerequisite: none

Further Topics in Geometry

Fall Semester–Open to Grades 11 and 12

In this advanced-level Geometry course we will use the skills gained in basic geometry to explore new topics in Euclidean geometry as well as topics related to non-Euclidean geometries. In addition, students will further develop their skills with formal geometric proof through the investigation of challenging problems. Topics covered will partly be determined by student interest and will be drawn from spherical geometry, dissections of squares and cubes, symmetry, Fibonacci numbers and the golden mean, sequences and patterns, knot theory, hyperbolic space, and topology, among others. Most topics will be explored through hands-on activities and assessed through student projects. Students will have the opportunity to independently explore topics that particularly interest them.

Prerequisite: Algebra 2, Geometry, ability to work independently and engage in logical and abstract reasoning.

Introduction to Number Theory

Spring Semester—Open to Grades 11 and 12

“Mathematics is the queen of the sciences and number theory is the queen of mathematics.” –Carl Friedrich Gauss

Number theory is one of the oldest branches of mathematical study, tracing its known roots to the Babylonians and ancient Greeks. This still lively and relevant field involves the study of numbers and why they behave the way they do. In this course we will take an investigative approach, beginning with the inductive search for patterns or relationships within and among integers and confirming (or disproving) our conjectures as we develop and refine our facility with mathematical reasoning and proof. Material covered will partly be determined by student interest and will be drawn from elementary number theory topics including divisibility, prime factorization and the fundamental theorem of arithmetic, congruence, modular arithmetic, quadratic reciprocity, and Diophantine equations, Fibonacci numbers and linear recurrences, and cryptography, among others.

Prerequisite: strong foundation in algebra, and the mathematical maturity and logical precision to engage in abstract arguments. Calculus is not required. Open to juniors and seniors.

Powered by Finalsite