# Mathematics

We recognize that mathematics is a language shared by all civilizations and all populations regardless of culture, religion, or gender, and our programs are designed to improve every student's quantitative literacy. We aim to foster strong critical thinking and mathematical reasoning in our students, with the goal of teaching them to view the world through a mathematical lens.

Requirements. In Grades 9-12, three years of math, through the 11th grade and including Algebra II, are required for a York diploma. York’s requirement meets University of California admissions requirements, which include a provision that students must complete a geometry course. Any student who wishes to take a credit math course over the summer must receive permission from the Math Department Chair and the Director of Teaching & Learning.
• ## Algebra I

Algebra is the base upon which nearly all of mathematics is built; it is a leap from arithmetic to abstract, defining the rules for the study of mathematical symbols and how to manipulate them. Taken seriously, this is every student's first foray into quantitative thinking. Though Algebra may strike you as a dizzying mix of symbols, definitions, and procedures, it all boils down to just two activities—solving for x and working with formulas.
• ## Algebra II

The goal of this course in advanced algebra is to relate each new idea to the concept of a function. Applications are handled by creating mathematical models of a phenomena in the real world. Students frequently work in small groups learning to select a kind of function (quadratic, exponential, etc) that fits a given situation, and derive an equation that suits the information in the problem. The students then use the equation to make predictions or interpretations about the real world. Although graphing calculators are incorporated to enhance the curriculum, the emphasis remains on the thought process and on understanding mathematical concepts. Computer explorations are utilized throughout the course to assist in the understanding of functions.
• ## AP Calculus AB

Students will master the basic topics of differential and integral calculus, equivalent to one semester of college calculus. Besides learning a variety of differentiation and integration techniques, students will also gain a deep, conceptual understanding of these topics. Clear mathematical statements demonstrating this conceptual knowledge will be required, as students prepare for the AP exam in Calculus AB. All students enrolled in the course are expected to take the AP exam.
• ## AP Calculus BC

Students will continue their understanding of the mathematical contexts and concepts within calculus, namely the three big ideas of limits, derivatives, and integrals, with the addition of a fourth: series. The depth and breadth is equivalent to a second year of college-level calculus. Specifically, this course will focus on drawing connections between verbal, graphical, numerical, and analytic representations of functions. This course is designed to assist students in developing strategies and techniques to solve a diverse set of application problems, and then evaluate the reasonableness of solutions. Students will be required to use proper notation and will be able to communicate effectively with their peers and with the mathematical community. Technology will be used regularly throughout the course, with a special emphasis on graphing calculators, as a way of investigating and analyzing functions to help students draw conclusions that would have been impossible or too time consuming without supporting technology. The course will include all of the concepts and techniques that appear on the AP Calculus BC exam, and all students enrolled in the course will be expected to take this exam in May. Testing throughout the year will be designed to help prepare the students for this exam.
• ## AP Statistics

AP Statistics introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Examples are drawn from applications in the natural and social sciences. Students collaborate with their classmates to learn statistics by doing statistics via in-class activities and simulations, computer labs, and projects. Students will master four broad conceptual themes: (1) Exploring Data (analysis of data through the use of graphical and numerical techniques to study patterns and departures from patterns); (2) Sampling and Experimentation (planning and conducting a study); (3) Anticipating Patterns (exploring random phenomena using probability and simulation for anticipating what the distribution of data should look like under a given model); (4) Statistical Inference (estimating population parameters and testing hypotheses).

Statistics and AP Statistics meet concurrently and cover the same content at the same pace. The main differences between these courses are that AP Statistics students also complete several projects and take the AP Exam.
• ## Calculus

This course meets concurrently with AP Calculus AB and introduces students to the basic concepts of differential and integral calculus, and is roughly equivalent to one semester of college calculus. Although this course is not aimed at preparing students for the AP exam in Calculus AB, the topics covered will be very similar. The pacing of this course will be slower than in Calculus AB, in part because there will be no need to finish the material by the beginning of May.
• ## Geometry

Geometry is the study of shape, and draws on the right side of the brain. The subject appeals to visual thinkers who might otherwise cringe at its logic, though many students love geometry precisely because it is so logical. Students learn important definitions, postulates, and theorems connected with Euclidean geometry and apply them to solve geometrical application problems. A balance is sought between an intuitive understanding of what is true, and the need for a thorough, careful, deductive reasoning about one’s perceptions. Students learn how to order their arguments in clear, precise language when writing their proofs of geometry theorems. Students will also develop spatial skills in two and three dimensions, and review their algebra skills throughout the course. Students work on group projects and utilize computer exploration.
• ## Math Modeling

Offered in alternating years
The overall goal of this course is to enable students to build mathematical models of real-world systems, analyze them, and make predictions about the behavior of these systems. A variety of modeling techniques will be discussed with examples taken from physics, biology, chemistry, economics, social sciences, and other fields. Mathematical modeling uses graphical, numerical, symbolic, and other techniques to describe and explore real-world data and phenomena. Emphasis is on the use of elementary functions to investigate and analyze applied problems and questions, on the use of appropriate supporting technology (e.g., Microsoft Excel or Google Sheets, Python, and other software or programming languages), and on the effective communication of quantitative concepts and results through relevant projects and presentations. This course is not intended to be a prerequisite for Calculus, though it will introduce and help students understand the basic topics of differential and integral calculus through application. Likewise, the class can be a math elective for students seeking an additional math class, for those hoping to solidify math concepts through modeling applications, or both.

• ## Pre-Calculus

This course combines advanced Algebra II skills with trigonometry, data analysis, vectors, and an introduction to Calculus. In addition to strengthening Algebra II skills and problem-solving strategies, students learn to apply concepts to real-world problems through mathematical modeling. While the emphasis is on honing algebraic and graphical analysis skills, the course makes extensive use of the graphing calculator. Many of the same topics will be covered as in the Pre-calculus Honors class, but not as rigorously and at a different pace.
• ## Pre-Calculus Honors

Pre-calculus Honors reinforces and expands upon the concepts encountered in Algebra II in order to prepare students for success in Calculus. Students will learn how to describe both new and already familiar functions verbally, algebraically, graphically, and numerically. Students also will learn how to transform these functions in order to model real-world data. In addition, students become familiar with other coordinate systems and with the use of vectors to model physical quantities. Experience with proofs will strengthen students’ ability to make conjectures, construct logical arguments, and justify their reasoning. Pre-calculus Honors covers Pre-calculus topics in greater depth, and its scope is much broader and includes numerous abstract and challenging enrichment topics. As a result, Pre-calculus Honors is intended for students who have a strong interest and aptitude for math, and who are ready, willing, and able to do the work necessary to tackle demanding problems at an accelerated pace.
• ## Statistics

Statistics introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Examples are drawn from applications in the natural and social sciences. Students collaborate with their classmates to learn statistics by doing statistics via in-class activities and simulations, computer labs, and projects. Students will master four broad conceptual themes: (1) Exploring Data (analysis of data through the use of graphical and numerical techniques to study patterns and departures from patterns); (2) Sampling and Experimentation (planning and conducting a study); (3) Anticipating Patterns (exploring random phenomena using probability and simulation for anticipating what the distribution of data should look like under a given model); (4) Statistical Inference (estimating population parameters and testing hypotheses).

# Faculty

• Jeff Hanna
Math/Science Department Chair
• Grace Baker
Math/Science, ISA
• Pam Durkee
• Scot Johnson
• Kim Kiest
Math/Science, 10th Grade Dean, Discipline Committee Chair, Environmental Sustainability Coordinator
• June Trachsel
Math/Science
• Kande Williston
Math/Science