# Mathematics Course Descriptions

#### Integrated Math I

*(Grade 9, 10) Year-long*

Students will investigate, discuss, formalize, and apply (in that order) concepts across the strands of algebra, geometry, discrete math, probability, and statistics. In this first course, students focus on identifying, extracting, and describing patterns-- patterns of change, patterns in data, patterns in shape, patterns in chance. We will give particular attention to linear, quadratic, and exponential change and associated functions. In addition, we explore vertex-edge graphs as tools to model a number of real-world situations. A focus on authenticity and problem-solving makes for a more more accessible and more meaningful student experience.

#### Integrated Math 2

*(Grade 9, 10)*

*Year-long*

Students continue their study of algebra, geometry, and statistics, using a problem-centered, connected approach. Functions, matrix operations, and algebraic representations of geometric concepts are the principal topics of study. We focus on mathematical modeling as a methodology for approaching the solution to problems. Students will explore operations on algebraic expressions and apply mathematical properties to algebraic equations. They will problem solve using equations, graphs, and tables and investigate linear relationships, including comparing and contrasting options and decision-making using algebraic models. Topics from two-dimensional geometry will be reinforced, including area and perimeter, the Pythagorean Theorem and its applications, and geometric proportion. Finally, students will be introduced to mathematical probability to reinforce use of fractions and numerical modeling. Technology used in this course includes graphing calculators and various software applications.

#### Integrated Math 2 Enriched

*(Grade 9, 10) Year-long*

Students in this course study similar topics to those explored in the regular Integrated Math 2 course; real-world modeling and synthesizing different areas of mathematical study are the major emphases. In this honors-level course, students will be expected to work independently and research mathematical methods to a much greater extent than in the regular level. Because of the faster pace, many of the topics that are reinforced in the regular level Integrated Math 2 course will not be reinforced at the honors level. Students are expected to possess a general mathematical fluency and to have a solid foundation in such basic skills as graphing, simplifying algebraic expressions, two-dimensional geometry, and solving one-step and multi-step equations.

#### Algebra II

*(Grade 10, 11) Year-long*

The emphasis in this course is on applications and problem-solving. Group work on larger projects encourages students to work together and to practice critical thinking. They become very familiar with the graphing calculator, using it as a tool in developing their thinking and problem solving skills. Building on knowledge gained in earlier math courses, students learn to solve realistic and complex equations. The math becomes steadily more abstract as the course advances, enabling students to develop general solutions to a family of problems, as well as solving a specific problem.

#### Algebra II Honors

*(Grade 10, 11) Year-long*

This is a fast-paced course in which students study the topics of Algebra II in greater depth than in the regular course. In addition to proficiency with the various classes of equations and functions covered in regular Algebra II, we will focus extensively on derivation and application. Also, students will explore a handful of supplementary topics and projects. In addition to understanding and solving traditional mathematical problems analytically, students are also challenged to solve problems to which there are no clear solutions. Instead, they are expected to develop the best practical solutions they can.

#### Discrete Math

*(Grade 11, 12) Year-long*

Discrete Math describes the mathematics of real life. Students will discover the way that election results are decided and how the results of an election do or do not reflect the will of the voters. They will also learn the mathematics of money management: the growth of investments and debt and how debts incurring interest get paid off. Business planning mathematics will challenge students to plan an optimal multi-stop trip; they will learn critical path analysis, which will give them the tools to schedule a project in the most cost effective way. The focus of this course is on problem-solving-- deciding what approach is needed to solve a problem, then using the mathematical skills students have acquired throughout their lives to find a solution.

#### Money Talks: An Introduction to Personal Finance

*(Grade 11, 12 )Semester*

This course will introduce students to a variety of real-world personal finance concepts and tools. A guiding principle of the course will be to provide students with knowledge and skills applicable in their own lives that will enable them to set and achieve short-term and long-term goals and help them avoid common financial pitfalls. Topics include, but are not limited to, the basics of budgeting, credit, investing, saving, interest, taxes, home renting and owning, and insurance. Students will engage in the broad discourse of modern economics, via guest speakers, podcasts, and current events discussions, to gain an appreciation and understanding of themselves as agents in complex systems of resource allocation and flow. *Students receive elective credit for this course; it does not fulfill math requirements for colleges.

#### Precalculus

*(Grade 11, 12) Year-long*

The primary emphases of this course is on the fundamentals of problem solving-- the underlying mathematical concepts and the ways in which we can use algebra as a tool for solving real-life problems. Topics are organized into three units of study: general functions, trigonometry, and implicit/parametric/polar functions. These units serve not only to teach students skills necessary for calculus, but also to advance their abilities in problem-solving, algebraic manipulation, use of calculators, visual expressions of solutions, and representation/analysis of mathematical models through graphing.

#### Precalculus Honors

(Grade 11, 12)*Year-long*

Precalculus Honors moves faster and goes into greater depth than Precalculus; students must have strong knowledge of the concepts learned in their prerequisite class. In this course we will concentrate on the ways in which algebra can be used as a tool for solving real-life problems. Topics are organized into five units of study: general functions, trigonometry, implicit/parametric/polar functions, probability, and a brief introduction to calculus. Students will advance their abilities in problem solving, algebraic manipulation, use of calculators, visual expressions of solutions, and representation/analysis of mathematical models through graphing. This course will give students the skills necessary to move on to Calculus 1 or AP Calculus BC.

#### Calculus 1

*(Grade 11, 12) Year-long*This course is equivalent to most first-semester college calculus courses, though it goes into more depth in differential calculus than a standard college course. Units of study include limits, differentiation of several classes of functions, applications of differentiation such as optimization and modelling, the Fundamental Theorem of Calculus, vector/parametric calculus and operations, and additional introductory topics in multivariable calculus, as appropriate. This class is designed for students who either want to get an exposure to calculus and its applications or who want to have a preparatory course before they take calculus in college. It is not intended to be as rigorous or comprehensive as the AP Calculus BC course.

#### AP Calculus BC

*(Grade 11, 12) Year-long*

This course is equivalent to most first-year (two semester) college calculus courses. Students will study a variety of topics, including limits, differentiation of several classes of functions, basic methods of integration, applications of both differentiation and integration, the Fundamental Theorem of Calculus, a variety of integration techniques, the calculus of infinite sequences and series, parametric/polar calculus, and vector calculus. Students who successfully complete the AP Calculus BC exam usually receive college calculus credit. The BC course is recommended for students who have strong mathematical aptitude and want to be exposed to a rigorous, fast-paced calculus curriculum, with the desire to earn college credit.

#### Statistics

*(Grade 11, 12) Year-long*

We encounter data in the media, medicine, politics, and all courses of study. Drawing conclusions from that information and being able to make predictions from it are essential skills, both in everyday life and for future careers. Statistics is the study of patterns and variability in data and the process of analyzing and applying mathematical models in order to draw conclusions and make informed decisions from that analysis. Among the topics studied are univariate data analysis, experimental design, probability, inference, correlation, and regression. Students learn not only to interpret data, but also to communicate analyses and models effectively for others to understand.

#### AP Statistics

*(Grade 11, 12) Year-long*Statistics is about variation and applying models in order to draw conclusions and make predictions from data. AP Statistics consists of data exploration and analysis, experimental design, probability, and statistical inference. Students taking AP Statistics need to have strong quantitative reasoning ability and skill, as well as mathematical maturity. This course emphasizes both analysis and interpretation of predictions and models. After the AP Exam the class will focus on topics beyond those on the AP syllabus, including individual or collaborative projects. The AP Statistics course includes all topics that are on the AP Exam.

#### Advanced Modeling/Multivariable Calculus Honors

*(Grade 11, 12) Year-long*

Students enrolled in this course will spend the year learning concepts of multivariate calculus, including vector calculus, vector operations, multivariable functions, surfaces, differential equations, systems of differential equations, numerical integration, multivariable differentiation/integration, and line integrals. These topics will coincide with students working through a series of focused problems, often involving real-world issues where concepts of multivariable calculus can be applied to solve the problem. This course is ideal for those students who already have at their disposal a wide skill set and who would like to test their merit in authentic and challenging ways. Additionally, students will learn to program/code and utilize Matlab, a very powerful and popular academic and commercially used software package for analysis, plotting, modelling, and creating algorithms to solve problems. The course may be tailored to student interests. *This course may be repeated for Math or Elective credit.