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. New student placement includes completion of a placement test and is done by Academic Dean and Math Department Co-Chair.
3-block course; Open to grades 9 & 10
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 grades 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: Returning Students - Algebra I. New Students - by placement test.
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: Returning Students - Algebra I with a B or below. New Students - by placement test.
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: Returning Students - Geometry and Algebra I with a B+ or higher or Bridge to Algebra II. New Students - by placement test.
Modules (non-sequential):
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: Returning Students - Geometry with a B+ or higher and department approval. New Students - by placement test and the Academic Dean and Math Department Chair’s approval.
2-block course; Open to grades 9-12
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: Returning Students - Algebra II or Advanced Algebra II. New Students - by placement test and the Academic Dean and Math Department Chair’s approval.
Modules:
Trigonometry -1: Taken in conjunction with PreCalculus or Advanced Algebra II and is a prerequisite for Calculus and AP Calculus AB.
Trigonometry -2: Taken in conjunction with Advanced PreCalculus and is a prerequisite for AP Calculus BC.
2-block course; Open to grades 9-12
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: Returning Students - Algebra II. New Students - by placement test and the Academic Dean and Math Department Chair’s approval.
Modules (non-sequential):
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.
2-block course; Open to grades 9-12
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: Returning Students - Trigonometry -1, Advanced Algebra II with a final grade of B+ or better, and department approval. New Students - by placement test and the Academic Dean and Math Department Chair’s approval.
Modules (non-sequential):
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
3-block course; Open to grades 11 & 12
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: Returning Students - Trigonometry -1, Precalculus, with a final grade of B- or higher, or Advanced Precalculus, and department approval. New Students - by placement test and the Academic Dean and Math Department Chair’s approval.
4-block course; Open to grades 10, 11, and 12
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, completion of Advanced Precalculus with minimum final grade of B or completion of Precalculus with minimum final grade of B+, and department approval. Recommendation: Students have taken, or are concurrently taking, a physics course.
4-block course; open to grades 10, 11, and 12
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, and 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 AB or 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 BC.
1-block course; Open to grades 9-12
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 satisfies 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, Algebra II (or higher), and department approval.
1-2 block course; Open to grades 10, 11, and 12
Prerequisites: Completion of Algebra II.
Modules (non-sequential):
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. This course is the first block of AP Statistics.
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: Algebra II (or higher) and department approval.
1-block course, Open to grades 10, 11, and 12
In the age of data, it is easy to get overwhelmed with the sheer mass of information we have available. Students will learn how to use statistical programming software to synthesize large amount of information in order to present it to a wider audience. Students will need to apply the principles of artistic design to analyze and create interesting and engaging visualization of large amounts of data. Concurrent or
1-block course, Open to grades 10, 11, and 12
Students will be introduced to ideas from number theory, combinatorics, and graph theory. Topics in the course include factorization of numbers, properties of prime numbers, congruencies, Euler's phi function, permutations and combinations, and an introduction to graphs, paths, cycles, and trees. Some discussion of applications and history (from cryptography to "The Traveling Salesman" problem) are worked into the material. Students will learn to solve problems, create and edit basic proofs, and explore and explain the use of these topics outside of the classroom. Pre-requisites: Advanced Algebra II and department permission or Precalculus.
1-block course; Open to grades 10, 11, and 12
In this project-based course, students will bring together math, science, technology, arts and engineering, to design and fabricate a gyroscope. We will build upon the student’s understanding of basic mathematical functions in 2 dimensions, and bring these shapes to life in 3-dimensions. We will discuss the physics of rotational motion, and fabricate a gyroscope using 3D printing technology and other equipment in the Fab Lab. Students will be exposed to engineering concepts, such as critical thinking, CAD (Computer Aided Design), prototyping, testing, and re-evaluating their design. The course will culminate with the students’ presentation of their finished product to the class, including a thorough analysis of their design journey as well as an analysis of their project’s movement. This course will provide students with the opportunity to develop their research, critical thinking, and fabrication skills as they design a functional demonstration of physics in motion.
Class of 2020 and beyond:
Classes of 2019:
New students take placement tests to determine enrollment in the appropriate math course. The Chair of the Math Department and the Academic Dean make all course placements.
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.
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!
Glen Russell is new to the Mathematics Department in 2016. Before landing at Madeira Mr. Russell worked in China for eight years, most recently at the International School of Beijing. In addition to teaching math, Mr. Russell has served as a faculty advisor for a number of clubs and activities including the Duke of Edinburgh International Award, the GSA, Habitat for Humanity, and Student Council. Mr. Russell is originally from Trenton, Ontario and has a B.Sc. from Acadia University, a B.Ed from Nipissing University, and this past spring completed a M.Ed from the University of Toronto.
Josh Singer joins the Madeira Math Department teaching courses across the spectrum in grades 9 through 12. Mr. Singer is a native of the Bethesda/Rockville area, having graduated from Whitman in Montgomery County. He worked at The Charles E. Smith Jewish Day School as well as The McLean School in Potomac where he taught middle and high school math courses in each position. Additionally, Mr. Singer served as Dean of Students at The McLean School in the 2011-2012 school year. Most recently, Mr. Singer worked at The Out-of-Door Academy in Sarasota, FL, continuing to teach math courses in grades 6 through 12. Additionally, he held administrative roles as Dean of Student Life and Dean of Faculty Development. He earned his BA from Skidmore College in Mathematics and continued to earn his MSEd from Johns Hopkins University in the field of School Administration & Supervision. When not at school, Josh loves golfing, running, going to the gym, and skiing!
Dr. Lee Walker joins us as a Math Teacher this year. A graduate of the Darlington School in Rome GA, Lee attended Centre College earning a BS in Physics. After earning a PhD from the University of Florida, Lee researched Electron Magnetic Resonance to study the energetics of photosynthetic organisms. After leaving the lab, he focused on his framebuilding company (Syndrome Cycles) and coaching swimming. He credits his love for working with kids and that for inspiring him to get back into Academia. After subbing in Science at Madeira last year, he’s happy to be a part of the Math team!
Dr. Amanda Curtis has joined us in the math department. Born in Kansas City, Dr. Curtis attended Wellesley College for her undergraduate and received her Master's and PhD degrees from University of California, Santa Barbara. She recently relocated from California to northern Virginia and enjoys running