Mathematics

Grade 9
Required
Full Year
Prerequisites: None

Students will build confidence in their ability to recognize patterns, communicate mathematical models and problem-solving techniques. Non-traditional and collaborative assessments will be infused within our curriculum to promote a deeper understanding, mastery, and application of formal algebraic notation and problem-solving. The topics for the course include linear functions, quadratic functions, factoring, radical expressions and equations, and rational expressions. All topics will be studied using a variety of methods including graphing, tabular data analysis, and the application of inverse operations to solve. 

Grades 9-10
Required
Full Year
Prerequisites: Algebra (A and B) or Algebra I

Students develop a logical, deductive system through the establishment of rules of argument, definitions, postulates, and theorems. The formation of a logical argument will be developed through inductive and deductive reasoning. Deductive proof is introduced early in the course and is foundational to many professional settings (including studies in engineering, law, and many others). Methods of proof will continue to be developed and referenced as the course progresses. We will emphasize a variety of shapes in the Euclidean plane as a means to develop modeling critical thinking skills; through scale drawings, construction, comparative analysis, and design.

Grades 9-11
Satisfies the Algebra II Requirement
Full Year
Prerequisites: Geometry

Algebra II as a course expands the basic fundamentals of Algebra I. Much of the course is devoted to the continued study of functions (linear, quadratic, polynomial, exponential, and logarithmic).  As we describe the number of hot dogs eaten by a competitive eater, the profits of your favorite sports drink, or the decreasing value of your new car, students recognize how mathematical functions describe the world all around us.

Grades 9-11
Satisfies the Algebra II Requirement
Full Year
Prerequisites: Geometry

Students dive deeper into Algebra 1 topics (quadratics, radicals, and linear functions). We will use this framework to introduce polynomials, rational, and exponential functions. In addition, we will discuss in-depth trigonometry and its applications. Throughout the course, an emphasis will be placed on pattern recognition and modeling functions both algebraically and graphically. The course also will infuse conversations about practical applications of these mathematical principles. Algebra II with Trigonometry provides all the foundational skills students will need before diverging to specific professional skills development.

Grades 9-11
Satisfies the Algebra II Requirement
Full Year
Prerequisites: Geometry and Algebra I

Students will dive into investigations about Algebra topics (quadratics, radicals, and linear functions) that will blend into polynomials and exponential functions, and finish with a study of trigonometry. Students will prove theorems and relationships for foundational math structures, deepening their understanding. Throughout the course, an emphasis will be placed on obtaining a thorough understanding of functions both algebraically and graphically. This course gives special attention to deriving mathematical principles and expands upon conversations about practical applications of these mathematical principles: car purchases, loan structure, roller coaster design, cyber-encryption, and more.

Grades 11-12
Elective
Full Year
Prerequisites: Algebra II

Mathematics is intertwined in our daily lives. From exploring sunrise and sunset time as sinusoidal functions, population growth as exponential functions, and representation of data from our own lives, this course encourages an appreciation for critical thinking necessary to describe the world around us. As students learn more about advanced functions, statistics, and trigonometry, they will begin to anticipate solutions and reflect on their work as they think analytically, problem solve, and grow as mathematicians.

Grades 9-12
Elective
Full Year
Prerequisites: Algebra II with Trigonometry

This course synthesizes the previous study of algebra, geometry, and mathematical functions to build the foundational skills required for Calculus. From exploring trigonometry, functions, and their applications, this course explains the reasoning behind accepted mathematical practices. Students will become comfortable solving a variety of problems, wrestling with some complicated ideas, and spend time on the questions of why and how concerning the mathematics we process.

Grades 9-11
Elective
Full Year
Prerequisites: Advanced Algebra II with Trigonometry

Precalculus with Differential Calculus (PCDC) as a course prepares students to take AP Calculus BC the following year. Even though the rationale for the course is to prepare for another course, precalculus is a significant discipline in its own right. From closing a chapter on introductory functions to exploring trigonometry and its applications, precalculus is truly a primer course for much of higher mathematics. The latter portion of the course is dedicated to differential calculus and building the early concepts of foundational calculus. From developing the idea of infinity into a formal definition of limits to then using limits to define differentiation and later integration. Beyond the working of many problems (which we will do) and wrestling with some complicated ideas (which we will also do), students will explore applications for what we are learning and spend time on the questions of why and how concerning the mathematics we process.

Grades 9-12
Elective
Full Year
Prerequisites: Precalculus or Functions, Statistics, and Trigonometry

Simply put, calculus is the study of how things change. Lots of things change. We hope to introduce how calculus can describe these changes and systems in this course. While we will explore (and remember) some familiar topics, you’ll also learn more about differentiation and integration. Whether you are launching a mini-catapult, learning about the brain and your memory, or considering the volume of content uploaded to Snapchat daily, your beginning study of calculus can help you enhance your understanding of the world around you.

Grades 10-12
Elective
Full Year
Prerequisites: Functions, Statistics, and Trigonometry or Precalculus

AP Statistics is a non-calculus based introduction to collecting, analyzing, and drawing conclusions from data. Over the course of the year, students will explore four major themes: exploring data, sampling and experimentation, probability and simulation, and statistical inference. Through the lens of data analysis, students will have the knowledge to discuss gender discrimination in the fields of STEM, reflect on a police officer’s use of force, and decide if all Skittles candies actually taste the same. The study of statistics, and this course, are designed to create thoughtful, informed individuals who actively seek to describe the world around them.

Grades 9-12
Elective
Full Year
Prerequisites: Precalculus

AP Calculus I is the study of change - not just from one point to the next, but also what is happening in an instant and how that change may accumulate down the road. After a brief review of intricate algebra-based processes, limits are introduced and this leads to the development of differential and then integral calculus. Students will be challenged to develop techniques for the derivative and integral process, applying their knowledge to a variety of problems. Students will be asked to collaborate and communicate deep understanding through traditional assessments and projects.The indefinite integral and simple integration formulas are studied and applied to problems involving rectilinear motion of a particle. The Fundamental Theorem of Integral Calculus is developed and applied to problems of area and volume. The integration formulas for trigonometric and inverse trigonometric functions, plus differentiation and integration formulas for logarithmic and exponential functions are developed and applied. The course concludes with the study of special methods of integration. The graphing calculator is used throughout the course.

Grades 9-12
Elective
Full Year
Prerequisites: Precalculus/Differential Calculus

College calculus occupies a unique position as the key to the disciplines in science, technology, engineering, and mathematics (STEM). At least one term of calculus is required for almost all STEM majors. Students will prepare for post-secondary mathematics in AP Calculus BC by emphasizing a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. A focus on deep understanding over topics such as hyperbolic functions, differential equations, Taylor’s Series, infinite series, polar graphs, partial differentiation, vector-valued functions, and multiple integrals encourage students to express their views through discussion and small group work. Finally, and perhaps more importantly, challenging, novel, and meaningful problems are the focus of class time, with the goal of fostering positive attitudes towards learning and problem solving in general.

Grades 9-12
Elective
Full Year
Prerequisites: AP Calculus I

College calculus occupies a unique position as the key to the disciplines in science, technology, engineering, and mathematics (STEM). At least one term of calculus is required for almost all STEM majors. Students will explore the concepts of Calculus by emphasizing a multi-representational with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. After a review of the main topics from Calculus I, derivatives and integrals, the course focuses on deep understanding over topics such as hyperbolic functions, differential equations, Taylor’s Series, infinite series, polar graphs, partial differentiation, vector-valued functions, and multiple integrals. The continued study of Calculus is the vessel in which students will continue to deepen their understanding of mathematics, develop their critical thinking skills, and engage with challenging, yet meaningful, problems.

Grades 11-12 only
Elective
Full Year
Prerequisites: Precalculus; Calculus; departmental approval

Math Seminar is a three year rotating continuum of math curriculum generally offered to exceptional math students who have shown a high level of proficiency in either pre-calculus or calculus. Within this framework, students can explore new fields of mathematics throughout their academic career at Park Tudor.

Game Theory is the study of decision making when faced with choosing between two or more strategies. This course will provide an introduction to the formal subject that is Game Theory, both its history and applications. The class will be both highly interactive as well as academically rigorous. From analyzing games and their changing variables to understanding the human element of games, students will likely be experiencing a new field of mathematical study. Student engagement is a key part of the course as the class set outs to "solve" games and apply various strategies of game analysis.