Mathematics

Year – 6 credits

Prerequisite: None

In this course, students will explore relationships between variables and numbers and learn to represent relationships between variables mathematically, graphically, and verbally. To do this, students will work with algebraic expressions, equations, inequalities, and functions. Students will develop the ability to model and solve real-world application problems, demonstrate the appropriate use of graphing calculators, and communicate mathematical ideas clearly. This course helps students to develop the foundation for mathematical literacy that will help them to be successful in subsequent courses across STEM disciplines. Students will be assessed using a variety of methods including, but not limited to homework, quizzes, and tests.

Year—6 credits

Prerequisite: Algebra 1

In this course, properties and relationships between figures in two and three-dimensional space will be discovered with inductive reasoning, manipulatives, and dynamic Geometry software then later proven with deductive reasoning. While simultaneously applying their Algebra skills, students will solve complex problems, develop and present geometric arguments, and explore the possibilities of using geometry to design, create, and share geometric art that integrates concepts such as symmetry and transformation. Students will be assessed using a variety of methods including homework, tests, and projects.

8-week Summer Intensive - 6 credits or Enrichment

Prerequisite: Algebra 1

In this course, properties and relationships between figures in two and three-dimensional space will be discovered with inductive reasoning, manipulatives, and dynamic Geometry software then later proven with deductive reasoning. While simultaneously applying their Algebra skills, students will solve complex problems, develop and present geometric arguments, and explore many applications of geometric thinking. The expectations for students in the Summer Geometry course differ from the year-long course in the following ways: students are expected to be self-motivated and able to focus on math for an extended period of time each day, there is not as much time available in class for extended practice, so students needing extra practice or review will be expected to do additional work at home, and assessments are primarily based on quizzes and tests as opposed to extended projects.  This course is an excellent opportunity for students to reduce summer learning loss, enhance their mathematical skills, build confidence, and prepare for the following school year.  

Year - 6 credits

Prerequisite: Geometry

In Algebra 2, students will build on skills developed in Algebra 1 to investigate and apply more advanced concepts such as systems of linear equations as well as non-linear quadratic, polynomial, radical, rational, exponential, and logarithmic functions. The course focuses on how math can be used to understand and solve critical real-world problems that are important to society today. To do this, the fundamental skills developed through hands-on investigation, discussion, and paper-and-pencil approaches will be applied to projects where students model real-life problems numerically, graphically, and symbolically. Students will practice using technology tools, such as graphing calculators (TI-84) and spreadsheet programs, to facilitate the higher-level computation that they will encounter in upper-level courses, college, and beyond. Students will be assessed using a variety of methods including, but not limited to quizzes, tests, and projects.  

Year - 6 credits

Prerequisite: Algebra 2

In this course, students are introduced to mathematical topics necessary for decision-making in today’s world. Mathematical topics are developed in the context of solving problems from business, science, and daily life. After starting the year with a unit on election theory, students will use the election theory group-ranking methods to determine each new topic of study. Other major units of study may include fair division, game theory, modeling with matrices, graphs and their applications, counting and probability, and personal finance and managing resources. Course assignments include class activities, in-class practice, small-scale research, presentations, homework, simulations, unit projects, and tests.

Year - 6 credits

Prerequisite: Algebra 2

This course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. The course will prepare students for life in a world filled with data, as well as for many college majors that require statistics. Students will study the fundamental ideas of statistics in a context that relates to the personal experiences and needs of an informed citizen of the 21st century. Statistics helps us to understand our world: Health professionals need to understand statistics to interpret medical research studies; businesses use statistical methods (business analytics) to efficiently crunch numbers to support their bottom line; and citizens need to understand statistics to accurately interpret opinion polls and the Consumer Price Index. Because data are omnipresent, everyone will find statistics useful and perhaps even profitable. In this course, students will study exploratory data analysis, learn the fundamentals of designing a study, use probability models, and use inferential statistics. Students will apply these concepts to such fields as business, biology, engineering, industry, the social sciences and many others. Students will use technology to calculate and display real data. Graphing calculators that can manipulate lists of data and contain statistical applications such as confidence intervals, tests of significance, and probability distributions will be our main technological hardware. In addition, we will be using online apps/programs. Students will work individually and frequently work together in groups. Students will be assessed using a variety of methods including, but not limited to, quizzes, tests, and projects.

Year - 6 credits

Prerequisite: Algebra 2

The central theme of this course is comparing, contrasting, and transforming functions to model change. We emphasize that functions can be grouped into families – linear, quadratic, exponential, logarithmic, power, polynomial, rational, and trigonometric – and that these functions can be used as models for real-world behavior. Students will use technology and analytic methods to investigate and apply course material. An introduction to calculus concepts such as sequences, series, limits, and parametric equations will be included as time permits. This course prepares students for Calculus 1.

Year - 6 credits

Prerequisites: Precalculus

Calculus 1 focuses on developing students’ understanding of the concepts, methods, and applications of limits and differential and integral calculus. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The focus of the course is neither manipulation nor memorization of an extensive taxonomy of functions, curves, theorems, or problem types. Thus, while facility with manipulation and computational competence are important outcomes, they are not the core of the course. Graphing calculators and other technology will be used regularly to reinforce the relationships among the multiple representations of functions, to confirm written work, to explore concepts, and to assist in interpreting results. Using the unifying themes of limits, derivatives, integrals, approximation, and applications and modeling, the course becomes a cohesive whole rather than a collection of unrelated topics. This course is comparable to a one-semester calculus course at the college level. While the Calculus 1 skills loosely align with the AP Calculus AB curriculum, our focus is on critical thinking, analysis, and novel application of concepts, not AP-style questions. Students wishing to sit for the AP exam should review Winchester Thurston's AP Testing policy.

6-week Summer Intensive – 4 credits or Enrichment

Prerequisite: A or A- in Precalculus with teacher recommendation and approval of the Department Chair and the Director of the Upper School

This course is an abbreviated version of Calculus 1 intended for strong mathematics students. Just as in the year-long Calculus 1 course, Calculus A emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The focus of the course is neither manipulation nor memorization of an extensive taxonomy of functions, curves, theorems, or problem types. Thus, while facility with manipulation and computational competence are important outcomes, they are not the core of the course. Graphing calculators and other technology will be used regularly to reinforce the relationships among the multiple representations of functions, to confirm written work, to explore concepts, and to assist in interpreting results. 

*Calculus A differs from Calculus 1 with respect to content, pace, and volume of practice. Calculus A covers limits, derivatives, antiderivatives, and a foundational understanding of the concept of integrals.  While Calculus 1 includes an in-depth treatment of integration skills and patterns, Calculus A does not, and because the course is a summer intensive, there is limited time for recursion and practice. Calculus 2 begins with a strong review where students practice basic integration skills before developing more complex ones. Students intending to enter Calculus 2 from Calculus A will learn the foundations of integration during this review period. Those desiring more direct instruction, a more measured pace of learning, and time for practice and reassessment should take the full Calculus 1 course.*

Year – 6 credits

Prerequisites: Calculus 1 or Calculus A (summer)

Calculus 2 is an advanced high school mathematics course designed to deepen students' understanding of calculus concepts and prepare them for higher-level mathematical studies. Building on the foundations of Calculus 1, this course covers a broad range of topics, including advanced integration techniques, sequences and series, parametric equations, polar coordinates, vector coordinates, and differential equations. The differential equations unit is designed to provide students with further study of the topic, which will give them an advantage when they take a more thorough differential equations course. Students will explore these topics through a mix of theoretical concepts and practical applications, enhancing their problem-solving skills and analytical thinking. While the Calculus 2 skills loosely align with the AP Calculus BC curriculum, our focus is on critical thinking, analysis, and novel application of concepts, not AP-style questions. Students wishing to sit for the AP exam should review Winchester Thurston's AP Testing policy.

Year - 6 credits

Open to juniors and seniors 

Prerequisites: Algebra 2

The integration of data, computation, and inferential thinking, or “data science,” is redefining how people and organizations apprehend and solve challenging societal problems. In this course, students learn to extract meaningful insights from data sets to better understand the world in which they live. Organized around the core concepts of statistical modeling and the practice of data analysis, this course introduces the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students will be exposed to three major themes: (1) Exploring Variation, (2) Modeling Variation, and (3) Evaluating Models. Topics include exploratory data analysis, data collection through sampling and experimental design, and inferential methods. In addition to the traditional normal-model inferential methods, students will learn modern computer-intensive methods, including randomization tests and bootstrapping. An integral part of the curriculum is the use of the R statistical programming language to carry out the analyses. Case studies woven throughout the curriculum and an end-of-course project will invite students to apply what they are learning in real-world settings. 

Year - 6 credits

Prerequisites: Calculus 2

This course is intended for advanced mathematics students who wish to further their studies beyond calculus.  In this course, students will learn how to solve differential equations (DEs). Students will cover all of the material covered in a standard college-level differential equations course (ordinary differential equations) including but not limited to solving first order, second order, and higher order DEs, using transforms, solving systems of differential equations, and finding series solutions. In addition, students will have the opportunity to apply this exciting field of mathematics in project work. This course will prepare students for work in a variety of disciplines, including science, engineering, mathematics, and computer science.