The goal of the Math Department is to challenge each student to reach her full potential in mathematics and to foster an ongoing interest in mathematical principles.
Students can choose from a variety of courses. Teachers advise students on appropriate course selection and encourage all students to take mathematics all four years.
3-block course; Open to grade 9
Students apply the basic concepts of arithmetic to the language of algebra and work with the structure and properties of the real number system. They learn to solve first- and second-degree equations, linear systems, and inequalities; they learn techniques of graphing and factoring; they work with polynomials, exponents, and radicals; and they set up and solve word problems. This course or its equivalent is a prerequisite for all subsequent courses in the department. Prerequisites: None
3-block course; Open to grade 9 and 10
Students learn to identify angle relationships, scale, proportion, triangle congruence, and similarity, how perpendicular and parallel relationships unify and extend earlier concepts, and how to apply new knowledge to applications in circles, polygons, and right triangles. Students learn how to compute the area of plane figures and apply trigonometric skills to problem-solving in their work with a variety of 2-D shapes. Students will apply principles of algebra with continued practice and reinforcement throughout the year while also demonstrating increasing flexibility with coordinate geometry, building a strong foundation for success in higher mathematics. Prerequisites: Algebra I. For new students a placement test is required.
1-block course: Open to grades 9, 10, and 11
Students will review Algebra 1 topics. These topics will include: solving linear equations and inequalities, solving absolute value equations and inequalities, direct variation word problems, graphing linear functions, graphing absolute value equations, graphing piecewise functions, solving systems of linear equations. Prerequisites: Algebra I and Geometry.
*Special note: A student has the option to waive this course with a B+ or better grade in Algebra I and with requisite grade on the placement exam.
3-block course; Open to grades 9, 10, and 11
This course expands the algebraic principles learned in Algebra I. Students will learn to solve and graph quadratic functions, polynomial functions; manipulate expressions containing radicals and complex numbers; understand exponential and logarithmic functions. Prerequisites: Algebra 1 and Bridge to Algebra II (or waiver)
Algebraic Functions: Quadratic and Polynomial Functions, Function operations
Transcendental Functions: Exponential and Logarithmic functions, Introductory Trigonometric functions
Elementary Functions: Radical functions, Rational functions
2-block course; Open to grades 9, 10, and 11
The course assumes a strong mastery of the material in Algebra I and an ability to manage material at a faster pace than is offered in Algebra II. The course will broaden a student's understanding of foundation topics while applying these topics to more complex problems. New topics such as polynomial, logarithmic, and rational numbers will be studied. In addition, students will learn skills in abstract reasoning and quantitative thinking with non-traditional problems as well as exploring the full capabilities of the graphing calculator.
Prerequisites: Geometry (final of grade of B+ or higher), teacher recommendation, and placement test. For new students: demonstration of mastery of Algebra I on placement test and completion of a complete Geometry course with a final grade of B+ or better. The Head of the Math Department and the Academic Dean make all math placements.
Trigonometry is a field of mathematics in which the geometric properties of the angles and edges of triangles are used to measure lengths. Real-world problems involving trigonometry are common in engineering, physics, construction and design. Topics include right-triangle relationships, unit circle, sine, cosine, and tangent functions and their applications, inverse trigonometric functions, identities, and trigonometric form of complex numbers. Additional topics such as vectors, polar coordinates, and parametric equations will be included. Prerequisites: Algebra II or Advanced Algebra II.
Trigonometry -1: Taken in conjunction with PreCalculus or Advanced Algebra II and is a prerequisite for Calculus.
Trigonometry -2: Taken in conjunction with Advanced PreCalculus and is a prerequisite for AP Calculus AB & BC.
This course focuses on expanding topics from Algebra II, including quadratic, polynomial, radical, rational, exponential and logarithmic functions. New units, such as conic sections, sequences and series, limits, and the definition of the derivative will be introduced. This course is designed for students who need review and sustained rigor before proceeding to the concepts in Calculus. Prerequisites: Algebra II
Algebraic Functions: Quadratic and Polynomial Functions, Function operations, Conic Sections, Sequences and Series.
Elementary Functions: Radical functions, Rational functions, Exponential and Logarithmic functions, Limits, Definition of the Derivative.
This course provides an introduction to higher mathematics and helps to develop the skills and study habits necessary for a rigorous math program. This course will continue to expand on topics from Advanced Algebra II, including rational, exponential and logarithmic functions. New units, such as probability, conic sections, sequences and series, limits, and derivatives will be introduced. Prerequisites: Trigonometry -1, Advanced Algebra II with a final grade of B+ or better, and department approval.
Elementary Functions, Analytic Geometry, and Probability: Rational Functions, Conic Sections, Sequences, Series, and Probability
Transcendental Functions and Intro to Calculus: Exponential Functions, Logarithmic Functions, Limits, Definition of the Derivative, Rules of Derivatives
This course provides an introduction to first-year college calculus. Topics will include a review of functions, limits, continuity, rates of change, the derivative, and integration. Emphasis is on understanding of concepts and mechanical manipulation. This course is not designed as an AP course leading to the AP exam. Prerequisites: Trigonometry -1, Precalculus, with a final grade of B- or higher, or Advanced Precalculus, and department approval.
This course provides an introduction to higher mathematics and helps to develop the skills and study habits necessary for a rigorous math program. The students explore differential and integral calculus and their applications while learning to approach problems from a variety of perspectives-graphical, analytical, numerical, and verbal. Technology is used to explore the behaviors of functions and to make connections with analytic procedures, all in preparation for the Advanced Placement Calculus AB exam in the spring. Prerequisites: Trigonometry -1, Trigonometry -2, completion of Advanced Precalculus with minimum final grade of B or completion of Precalculus with minimum final grade of B+. Department approval. Recommendation: Students have taken, or are concurrently taking, a physics course.
In this extremely rigorous course, students review the topics covered in Calculus AB, extend the procedures learned to include more sophisticated integration methods, and explore vectors, parametric and polar functions, and techniques in solving differential equations. They also analyze the behavior of sequences and series beyond arithmetic and geometric ones, with particular attention to divergence, convergence, intervals of convergence, and various test methods. Technology is used, particularly the programmable capabilities of the calculator, to simulate real-life applications of the concepts and to enhance understanding. All this is done in preparation for the Advanced Placement Calculus BC exam in the spring. Prerequisites: Trigonometry -1, Trigonometry -2, completion of Advanced Precalculus with a minimum final grade of B+ or completion of Calculus AB with a minimum final grade of B. Department approval.
2-block course; Open to grades 11 and 12
In two modules, this course provides an introduction to multivariable and vector calculus. The course covers vectors and analytic geometry in three dimensions, partial differentiation, multiple integration, and an introduction to line integrals. The primary aims of the course are to help students develop new problem-solving and critical reasoning skills and to prepare them for further study in mathematics, the physical sciences, or engineering. Topics include: surfaces in three-dimensional space; algebraic and geometric properties of vectors and vector functions in two and three dimensions; dot products and cross products; derivatives and integrals of vector functions; partial derivatives of functions of several variables; directional derivatives and gradients of scalar functions; multiple variable maximum and minimum value problems; double and triple integrals; line integrals; Green’s theorem; and Stoke’s theorem. Prerequisites: Completion of AP Calculus BC.
2-block course; Open to grades 11 and 12
In two modules, this course provides a study of computational techniques of matrix algebra and an introduction to vector spaces. Topics covered include: matrix algebra, systems of linear equations, eigen values and eigenvectors, least squares, vector spaces, inner products, and introduction to numerical techniques, and applications of linear algebra. Also covered are linear transformations, matrix representations of a linear transformation, characteristics and minimal polynomials, and diagonalization of a matrix. Prerequisites: Completion of AP Calculus AB or AP Calculus BC.
1-block course; Open to grades 10, 11, and 12
This course is intended to provide students with experiences in using computer programming techniques and skills to solve problems that can be set up as mathematical models. Programming concepts, problem-solving strategies, and mathematical applications are integrated throughout the course. Skills in defining, writing, and running programs on a computer are developed through an individual approach that allows the student to work with both mathematical and non-mathematical problems. Java will be the major programming language. This course does satisfy the math department computer science requirement. Prerequisites: Algebra II
3-block course; Open to grades 10, 11, and 12
The major emphasis in this course is on object-oriented software design and programming methodology, algorithms, and data structures. Java will be the major programming language. This course is equivalent to an introductory college course in Computer Science. Applications of computing provide the context in which these subjects are treated. Applications are used to develop student awareness of the need for particular algorithms and data structures, as well as to provide topics for programming assignments to which students can apply their knowledge. Treatments of computer systems and the social implications of computing are integrated into the course. Prerequisites: Introduction to Computer Science, Precalculus (or higher), and department approval.
1-2 block course; Open to grades 11 and 12
Prerequisites: Completion of Algebra II.
Probability: This course centers on the rules and applications of probability. Students explore many facets of probability from games of chance to simulation to applications in fields as diverse as the internet and medicine. In addition to learning probability rules, permutations and combinations, students will use Venn diagrams, two-way tables and tree diagrams. Students will also learn about conditional probabilities and independence. This hands-on, project-based course will expose students to the real uses of probability.
Data & Display: This course centers on Data and Display. Students examine data on two fronts: how to analyze data using scatterplots and regression calculations, and how to display data to show relationships between variables. These displays will include dot plots, bar charts, stem and leaf diagrams, box plots and histograms. Students further learn when to optimally use each of these displays. This hands-on, project-based course will expose students to real uses of statistics and the role data plays in our fact-hungry culture. In addition to learning how to use tables and display data, students will learn and apply standardization and the normal curve.
3-block course; Open to grades 10, 11, and 12
The AP course in Statistics will introduce students to the major concepts about and tools for collecting and analyzing data. The course begins with a thorough examination of descriptive statistics including graphical and numeric methods for describing data, and observational study vs. experimental design. The next topics include probability, random variables and probability distributions. The course then moves into inferential statistics, covering sampling distributions, confidence intervals and hypothesis testing for single samples and two populations or treatments. Finally, homogeneity, linear regression and inferences about correlation are examined. The course is designed to prepare students to take the AP exam in May. Prerequisites: Option 1- Precalculus and department approval. Option 2- Advanced Algebra II, concurrently taking Precalculus (or higher), and department approval.
1-block course, Open to grades 10, 11, and 12
Think about what it means to know things. For example, I know that the sky is blue, I know how to solve a quadratic equation, and I know that my parents love me. But I know all those things very different degrees of certainty. This class examines those difference. In short, this is a class for thinking about thinking including mathematical thinking and knowing about knowing.
During this course we will examine the nature of our beliefs and how we can justify them, ask questions about our fundamental perceptions of reality, and debate if anything ethical can truly be know.
Incoming juniors and seniors have a slightly modified requirement. Also note that enrollment in AP courses and other higher level courses is with the permission of the department chair. Each course description in the list of available courses (above) ends with a note on prerequisites.
New students take placement tests to determine enrollment in the appropriate math course.
Mr. Hernandez began teaching at Madeira in 2009. He earned a bachelor's degree in Economics from Fordham University and a master's degree in Education from The George Washington University.
Ms. Roshan began teaching at Madeira in 2004. She earned a bachelor's degree in Secondary Education/Math from the University of Maryland and a master's degree in Secondary Education/Math from George Washington University as well.
Ms. Jean Wright joined Madeira in 2013. She earned her bachelor’s degree in mathematics from Ohio University and her master's degree from Duke University. She is certified to teach mathematics as well as computer science. She has previously taught every level of math from Algebra I to AP Calculus.
Nikki Wellington comes to Madeira’s Math Department from Harrisonburg High School. She earned her Bachelor of Science in Mathematics and Anthropology from James Madison University, and her M.Ed. in Secondary Education with Mathematics Concentration at Vanderbilt University. Ms. Wellington has a love of musical theater and volleyball, and is thrilled to be joining the volleyball coaching staff at Madeira this fall.
John Ifft is excited to join Madeira for the 2016-17 school year after teaching at Flint Hill School in Oakton, VA for 18 years. During that time, Mr. Ifft taught the entire spectrum of high school math courses, with a specialty in AP Calculus. A Northern Virginia native, he earned both his B.A. and M.A. from the University of Virginia. He enjoys cheering on his Wahoos in all sports!