The goal of the Math Department is to build mathematical thinking skills, 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 paths as they complete their twelve required blocks of math over a four-year period. Teachers and deans advise returning students on appropriate course selection; new students take math placement tests.
3-block course; Open to grades 9 and 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 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 including 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 - Geometry B or below. New Students - by placement test.
3-block course; Open to grades 9, 10, and 11
This course extends the algebraic principles learned in Algebra I, including an exploration of different number systems such as radical and complex numbers. Students will study the algebraic and graphical properties of a wide variety of functions including quadratic, polynomial functions, radical, rational, trigonometric, exponential and logarithmic. Prerequisites: Returning Students - Bridge to Algebra II or Geometry B+ or higher. New Students - by placement test.
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 - by placement test. New Students - by placement test and the Academic Dean and Math Department Chair’s approval.
1-block course; Open to grades 9-12
Trigonometry is a field of mathematics in which the geometric properties of the angles and side-lengths of triangles are used in both theory and real-world applications. Foundational geometry concepts will be extended in order to address right-triangle relationships, the unit circle, equations with and graphs of all six trigonometric functions, sinusoidal motions, inverse trigonometric functions, identities, double angle formulas, and half angle formulas. This course is taken in conjunction with Precalculus or Advanced Algebra II and is a prerequisite for Calculus and AP Calculus AB. Prerequisites: Returning Students - Advanced Algebra II or PreCalculus -1. New Students - by placement test and the Academic Dean and Math Department Chair’s approval.
2-block course; Open to grades 10, 11, and 12
This course reviews and extends topics from Algebra II, including quadratic, polynomial, exponential and logarithmic functions, while introducing the concepts of data collection and analysis. Students will work on projects that require the analysis of real-world data. This course emphasizes problem solving and modeling and is designed to be taken in conjunction with Applied Mathematics: Math in Motion. Prerequisites: Algebra II Offered in alternate years. Not offered in 2021-2022.
2-block course; Open to grades 9-12
This course focuses on extending 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 will proceed to the concepts in Calculus. Prerequisites: Returning Students - Algebra II with a B- or higher or Applied Mathematics (3 blocks). New Students - by placement test and the Academic Dean and Math Department Chair’s approval.
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, trigonometric exponential and logarithmic functions. New units, such as conic sections, sequences and series, limits, vectors, parametric and polar equations and derivatives will be introduced. This course is designed to prepare students for AP Calculus. Prerequisites: Returning Students - Advanced Algebra II with a A- or higher; by placement test and department approval. New Students - by placement test and the Academic Dean and Math Department Chair’s approval.
3-block course; Open to grades 11 and 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. Prerequisites: Returning Students - Trigonometry-1, Precalculus with a B- or higher, or Advanced Precalculus. New Students - by placement test and the Academic Dean and Math Department Chair’s approval.
3-block course; Open to grades 10, 11, and 12
This course continues the path to higher mathematics and helps to develop the skills and study habits necessary for a rigorous math program. 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. Students are required to sit for the Advanced Placement Calculus AB exam in the spring. Prerequisites: Trigonometry -1, Advanced Precalculus with a B or higher, Precalculus with an A or higher, or Calculus, and department approval.
3 or 4-block course; open to grades 10, 11, and 12
In this 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. Students 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. Students are required to sit for the Advanced Placement Calculus BC exam in the spring. Students who complete AP Calculus AB prior to taking this course may elect not to take the first block of BC. Prerequisites: Trigonometry -1, Trigonometry -2, Advanced Precalculus with a A- or higher, AP Calculus AB with a B or higher, or Calculus with an A or higher, and department approval.
3-block course; Open to grades 11 and 12
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 ends with vector calculus topics that build up to Green's, Stokes', and the Divergence Theorem. 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. This course will be offered on a rotating basis with Linear Algebra and will be offered in '21-'22. Prerequisites: AP Calculus BC or AP Calculus AB with an A or higher.
3-block course; Open to grades 11 and 12
This course provides a study of computational and proof techniques of matrix algebra and an introduction to vector spaces. It pushes students to ask questions and communicate mathematical thinking. Topics covered include matrix algebra, systems of linear equations, eigenvalues and eigenvectors, least squares, vector spaces, inner products, and introduction to numerical techniques, and applications of linear algebra. Students also explore linear transformations, matrix representations of a linear transformation, characteristics and minimal polynomials, and diagonalization of a matrix. This course will be offered on a rotating basis with Multivariable Calculus and will be offered in '22-'23. Prerequisites: AP Calculus BC or AP Calculus AB with an A or higher.
1-block course; Open to grades 9-12
A first look at computer programming in Python. This course will take a project-based approach to developing essential programming skills. Students will be exposed to functions, variables, APIs, external libraries and other topics in modern Python programming. With this strong foundation, “Advanced Programming” courses are open to interested students following completion. Prerequisite: Algebra I
*Special note: This course satisfies the coding requirement.
3-block course; Open to grades 10, 11, and 12
This course provides students with a strong foundation in a wide array of computing topics such as programming, algorithms and networking. As an AP course, the rigor matches that of a college course. While programming is not strictly the focus, a foundation in both programming & logical systems is a necessary prerequisite for success. As is typical in an introductory college course, programming Both “Applied Mathematics: Logic and Proofs” and “Introduction to Programming: Python” are recommended, but not required for this course. Prerequisite: Algebra II
1-3 block course; Open to grades 9, 10, 11, and 12
Some say that we live in the age of data. These statistics electives allow students to explore different ways to understand and communicate about the data all around us. In addition to studying statistics, students will be able to explore some of their own interests through the study of statistics.
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 use each of these displays optimally. 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. Prerequisites: Algebra II
Probability: This course centers on the rules and applications of probability. Students will 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 learn about conditional probabilities and independence. This hands-on, project-based course will expose students to the real uses of probability. Prerequisites: Algebra II
Research and Analysis: Why are some schools more successful than others? Is the water in Flint safe to drink? Are there biases in the hiring process? These are very important questions whose answers lie in the numbers. Students will look at the data for real-life problems and pose questions and provide answers using statistical analysis with the help of technology. Prerequisites: Algebra II AND AP Statistics or Statistics: Data and Display
3-block course; Open to grades 10, 11, and 12
This course introduces 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. Students are required to sit for the AP Statistics exam in May. Students who complete Statistics: Data and Display prior to taking this course may elect not to take the first block of AP Statistics. Prerequisites: Advanced Algebra II, or Pre-Calculus, (or higher), or Applied Mathematics (3 blocks) and department approval.
1-3 block course; Open to Grades 9, 10, 11, 12
Mathematics is all around us, but where is it exactly? In these elective courses, students will explore the mathematics of different parts of our world. Students taking these courses will learn not only the process of how to “do” mathematics but will focus on the context of the problem and see the connection between the abstract world of mathematics and our own concrete world. Students may take each course as an elective or as three blocks to create the equivalent of a full-year math class.
Financial Mathematics: In this course students will look at the mathematics of personal finance including budgeting, the stock market, credit cards, mortgages, and student loans. In learning the mathematics of personal finance students will explore mathematical concepts such as exponential functions, sequences and series, and statistics. Prerequisites: Algebra II
Logic and Proofs: An exploration of logic, proofs and algorithms. This course will provide students with a strong basis in Boolean logic, construction and analysis of proofs, and algorithm development. This course is recommended for students who wish to study computer programming. Prerequisites: None
Math in Motion: In this project-based course, students will bring together math, science, technology, arts and engineering, to design and fabricate a gyroscope. Students will develop an understanding of basic mathematical functions in 2 dimensions and how to bring these shapes to life in 3-dimensions. Students will discuss the physics of rotational motion and will 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’ presentations of their finished products to the class, including a thorough analysis of their design journey and the product’s movement. This course will provide students with opportunities to develop their research, critical thinking, and fabrication skills as they design a functional demonstration of physics in motion. Prerequisites: Algebra II
1-2 block course; Open to Grades 9, 10, 11, and 12
Advanced Programming electives will allow students to pursue their interests in different applications of computer programming through project-based courses. These courses built upon the concepts explored in Introduction to Programming and take them further. Some will use the Python language, and some will introduce students to different computing languages. There will be different sets of electives offered each year depending on student interest. Prerequisites: Introduction to Programming: Python OR Introduction to Computer Science OR Coding Projects D Block
Web Development: This course builds upon the foundation developed in “Introduction to Programming: Python”. With a strong foundation in the Python language, students will be asked to apply their existing skills to build modern web applications. Drawing on current trends in serverless cloud computing, and single page applications, this course runs the gamut from design to non-relational databases.
Business Systems Development: This is a project-oriented course designed to provide essential knowledge and skills required to develop desktop software particularly business systems using Java as the programming language. Topics will include user interface design, relational database management, report generation, and data security. Students are expected to work on a project that produces a professional-quality business system.
12 credits (including one of coding)
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.
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!
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!