MATHEMATICS

The Mathematics Department seeks to incorporate some of the best mathematical pedagogy from around the world. Also, taking a page from some of Asia’s most successful systems, students build new knowledge from previously learned skills and become comfortable with multi-step problems. Our mission is to expand each student's quantitative reasoning skills in order to ensure success in their higher mathematical endeavors and in their post-secondary education. Students learn to face mathematical problems with confidence while becoming equipped with the necessary skills and strategies to be successful. Students are taught how to solve problems both with and without technology. Math courses are yearlong and, except for courses such as Statistics, are designed to be sequential. Due to the diverse backgrounds of entering students, all new students are placed in appropriate courses by the department chair. Enrollment in Honors, Advanced Placement and post-Advanced Placement courses requires departmental permission. Typical course progression options are listed below. Please see complete descriptions for more information. Sample course progression:

Grade 9 Options Grade 10 Options

Algebra 1 Honors Algebra 1 Geometry Honors Geometry Algebra 2 Honors Algebra 2 Geometry Honors Geometry Algebra 2 Honors Algebra 2 Precalculus Honors Precalculus Algebra 2 Honors Algebra 2 College Preparatory Math Precalculus Honors Precalculus Calculus AP Calculus AB AP Calculus BC College Preparatory Math Precalculus/Honors Precalculus Statistics & Probability AP Statistics Calculus AP Calculus AB AP Calculus BC Multivariable & Vector Calculus Linear Algebra

Grade 11 Options Grade 12 & PG Options

ALGEBRA I

Level: Introductory Prerequisite: Pre-Algebra Overview: Topics in this course include linear equations and inequalities, graphing linear equations and inequalities, exponents, factoring, absolute value expressions and functions, and an introduction to quadratic equations. Students will develop foundational algebra skills and prepare for Geometry.

HONORS ALGEBRA I

Level: Accelerated Introductory Prerequisite: Pre-Algebra and departmental permission Overview: Topics studied in-depth in this accelerated course include: linear equations and inequalities; graphing linear equations and inequalities; exponents; factoring; and absolute value expressions and functions. In addition, students are introduced to quadratic equations and right-angle trigonometry. Students will develop foundational algebra skills and prepare for Geometry.

GEOMETRY

Level: Introductory Prerequisite: Algebra I Overview: This course is an introduction to: the basic elements of Euclidean geometry; measurement, proof development, congruency and similarity in two- and threedimensional settings; and area, volume and other applications of geometry. Students will develop geometric reasoning skills, reinforce algebra skills and prepare for Algebra II. ALGEBRA II

Level: Intermediate Prerequisite: Algebra I and Geometry Overview: This course focuses on manipulation of algebraic quantities and solving equations and inequalities. Students will gain skills in the topic areas of linear, quadratic, higherdegree polynomial, and exponential functions. Students will be introduced to logarithms. ALGEBRA II Essentials

Level: Intermediate Prerequisite: Algebra 1, Geometry. Department recommendation Overview: This course focuses on building basic skills with the essential topics in Algebra II. Students will study linear and quadratic equations in depth with a focus on applications. There will also be a thorough introduction to higher-degree polynomials and exponential equations along with a brief introduction to logarithms.

HONORS GEOMETRY

Level: Accelerated Introductory Prerequisite: Algebra I and departmental permission Overview: Students in this accelerated program are introduced to the basic elements of Euclidean geometry; measurement, proof development, congruency and similarity in two- and three-dimensional settings; and area, volume and other applications of geometry. Students will develop geometric reasoning skills, reinforce algebra skills and prepare for Algebra II.

Level: Accelerated Intermediate Prerequisite: Algebra I, Geometry and departmental permission Overview: In this course, students will experience an in-depth study of the manipulation of algebraic quantities and solving equations and inequalities. Students study linear, quadratic, higher-degree polynomial, exponential, rational, and logarithmic functions. There is a thorough introduction to trigonometry including right-angle trigonometry, basic identities and some basic graphs.

COLLEGE PREPARATORY MATH

Level: Intermediate Prerequisite: Algebra I, Algebra II and Geometry, teacher recommendation Overview: This course serves to reinforce algebra skills and prepare students for the next level through in-depth coverage of linear and quadratic equations, exponential and radical number concepts and trigonometric topics. Students gain confidence and improved readiness for college math. This course is not approved for NCAA credit.

PRECALCULUS

Level: Advanced Prerequisite: Algebra I, Algebra II and Geometry Overview: Emphasis in this course is on functions – linear, piece-wise, quadratic, higher-degree, rational, exponential, logarithmic and trigonometric. Students will participate in an in-depth study of trigonometric identities.

HONORS PRECALCULUS

Level: Accelerated advanced Prerequisite: Algebra I, Algebra II, Geometry and departmental permission Overview: The emphasis in this accelerated course is on functions – linear, piece-wise, quadratic, higher-degree, rational, exponential, logarithmic and trigonometric. In addition, students will participate in an in-depth study of trigonometric identities, polar equations, conic sections and limits.

STATISTICS & PROBABILITY

Level: Intermediate, Grade 12 and postgraduate Prerequisite: Algebra I, Algebra II and Geometry Overview: Students will embark on the study of group data applied to a variety of real-world problems. Graphic, numeric and algebraic analysis (with and without technology), and group projects will allow students to examine statistical and probability concepts from a broad perspective. 12

Level: Advanced Placement. The AP exam in May is mandatory. Exam fee is charged. Prerequisite: Algebra I, Geometry, Algebra II, recommendation Overview: Students are exposed to four broad conceptual themes: exploring data – describing patterns and departures from patterns; sampling and experimentation – planning and conducting a study; anticipating patterns – exploring random phenomena using probability and simulation; and statistical inference – estimating population parameters and testing hypotheses. In addition to preparing students for the AP Statistics exam, this course prepares them to use their statistical knowledge to determine the validity of surveys and reports, analyze scientific data and design experiments in future college-level work. CALCULUS: Calculus with Applications

Level: Advanced, Grade 11 or above Prerequisite: Algebra I, Algebra II, Geometry, Precalculus and departmental permission Overview: This course is the study of differentiation and integration and how both functions relate to the business world. Students use graphic, numeric and algebraic analysis with and without technology to develop foundational calculus skills with business applications. AP CALCULUS AB: Calculus I

Level: Advanced Placement, Grade 11 or above. The AP exam in May is mandatory. Exam fee is charged. Prerequisite: Precalculus and departmental permission Overview: This college-level course is intended for students who wish to develop a strong base understanding of the concepts of calculus. Topics include limits, calculating derivatives and integrals (polynomial, rational, logarithmic, trigonometric, and inverse trigonometric functions), maxima and minima, slope fields, exponential growth and volumes of solids. Students will perform graphic, numeric and algebraic analysis (with and without technology) and prepare for the AP Calculus AB exam.

CALCULUS BC Plus: Calculus II

Level: Advanced Placement, Grade 12. The AP exam in May is mandatory. Exam fee is charged. Prerequisite: AP Calculus AB and department permission Overview: This college-level course builds on topics learned in Calculus I. This course goes beyond the curriculum for AP Calculus BC in depth and breadth. Topics include integration by parts, integration by trigonometric substitutions, Euler's Method, differential equations, logistics growth, sequence, series, polynomial approximations using series, Maclaurin and Taylor Series, and parametric, polar and vector functions. Students will perform graphic, numeric and algebraic analysis with and without technology and prepare for the AP Calculus BC exam.

MULTIVARIABLE CALCULUS & DIFFERENTIAL EQUATIONS

Online*** Level: Post-Advanced Placement Prerequisite: AP Calculus BC (Calculus II); department permission Overview: This year-long course covers a typical collegelevel Calculus III curriculum, including vectors and vectorvalued functions, curves and surfaces in space, partial derivatives and gradients, multiple integration, and line and surface integrals. In the course’s final unit, students learn how to identify and solve various kinds of differential equations, including exact first-order equations, second-order homogeneous and nonhomogeneous linear equations, and partial differential equations, and they practice using such equations to model systems from science and engineering. Built on a foundation of sophisticated problem solving, the course also features 3D visualization and model-building activities that help students develop their geometric intuitions about doing calculus in higher dimensions. Offered Online

through One Schoolhouse. Fees apply.

Online*** Level: Post-Advanced Placement Prerequisite: AP Calculus AB (Calculus I); department permission Overview: Through a wide variety of practical problems, conceptual questions, and visualizations, students learn how to think about vectors, the spaces in which vectors live, and linear mappings between those spaces. They develop powerful new ways of thinking mathematically and apply their new skills to solve a wide variety of problems from other fields, including computer graphics, economics, and population biology. This year-long course covers a typical one-semester college linear algebra curriculum, including matrix algebra, vector spaces, eigenvalues and eigenvectors, and applications to differential equations. Linear algebra is a required and very useful subject in college for many science and engineering majors, and it can be studied either before or after multivariable calculus. It’s a great fit for the student who has completed AP® Calculus AB or BC, who is passionate about a challenge to think in new ways, and who wants to see math applied to the real world. Offered Online

through One Schoolhouse. Fees apply. *** Students will need to adhere to the One Schoolhouse academic schedule for these online courses. Work will be expected during WMA vacation periods. Failure to do so could result in course failure.

An understanding of computational thinking and the fundamental principles of computer science are becoming more and more valued across all disciplines. Colleges, universities and the industries they feed note the necessity of being conversant with these practices in all fields. WMA is committed to the design and implementation of a program that provides grounding in these skills for all students, and is also a gateway for those who wish to pursue computer science in more depth. The Exploring CS series of electives develops the computational thinking skills that are applicable in any discipline. Mobile Computer Science Principles deepens the understanding of these skills and is also accessible to students who don’t think of themselves as traditional computer science students. This suite of courses encompasses a comprehensive set of inquiry-based lessons, which use a variety of tools and platforms. A major aim of these courses is to attract students who might not think of themselves as “typical” candidates for computer science and allow them to explore project-based lessons that emphasize writing, communication, collaboration, and creativity.

Grade 9 Options

CS: Exploring Web Design CS: Exploring/Using Big Data CS: Exploring Robotics

Grade 10 Options

CS Term Electives Java Programming- online Mobile CSP

Grade 11 Options

Java Programming - online Mobile CSP AP Computer Science A- online

Grade 12 & PG Options

Mobile CSP AP Computer Science A- online

CS: EXPLORING WEB DESIGN Term

Level: Introductory, open to Grades 9 through PG. Overview: Students take the role of developer as they design a web page while exploring issues of social responsibility. They plan and code their web pages using a variety of tools and collaborate with their peers to ensure usability and relevance. Students will also explore programming as they design, code, test and execute a program that corresponds to a set of expectations. They will use the Scratch (MIT Media Lab) visual programming tool to develop understanding of the logical processes of programming which are applicable across computer languages. As the student designers work through all concepts, they will apply the fundamental notions of Human Computer Interactions and algorithmic problemsolving techniques. CS: EXPLORING & USING BIG DATA

Term Level: Introductory, open to Grades 9 through PG. Overview: Students explore how computing has facilitated new methods of managing and interpreting data. Students will review the connections between mathematics and computer science. They will use computers to translate, process and visualize data in order to find patterns and test hypotheses; discuss appropriate methods for data collection and aggregation of data necessary to support making a case or facilitating a discovery; examine what constitutes a good survey and create one for a personalized study. Students will work with a variety of large data sets that illustrate how widespread access to data and information facilitates identification of problems. Students will use popular tools for organization and analysis of datasets.