Where limits don't exist.

Constructing understanding through a problem based learning (PBL) curriculum, inspires curiosity, challenges students, and rewards them with the a-ha moments of deep learning.

One student reflected, “While it was difficult [at first], PBL never failed to be the class I looked forward to the most. I have grown to love the creativity and I am always looking forward to showing my cool solutions to the class. [Guided] discussions have taught me a lot about how flexible math thinking is which has translated into SO many unexpected areas of my life.”

Frequently Asked Questions about Cate PBL

Full year – .33 credits/trimester
PBL 1 is a problem-solving course where the ultimate goal is for students to gain confidence in their ability to make sense of a problem, and once a problem is understood, to apply mathematical knowledge and tools strategically during the problem-solving process, and to persist in solving the problem. As a result of this course, students learn to express these patterns in the abstract language of algebra, and to apply properties of numbers to these algebraic expressions in order to manipulate them. Students engage with contextual problems that deepen their understanding of proportional relationships, linear and absolute value functions, inverse relationships, and shared work and mixture problems. At the heart of all these problems is the power of mathematics to model the world around us. Students are expected to be at the very center of a cooperative process, discussing, writing about, and presenting well-reasoned explanations. The course uses a variety of materials, primarily problems from the Math 1 text written by the math department at Phillips Exeter Academy and Desmos graphing technology. This course is best suited for students who have had a full year of Algebra 1 but seek to deepen their mastery of this foundation material. For students who excel and find the curriculum rewarding, the class can also serve as an entry point to our Honors Problem Based Learning strand. Prerequisite: Algebra 1 or equivalent.

Full year – .33 credits/trimester
PBL 2 is a problem-solving course where the ultimate goal is for students to gain confidence in their ability to make sense of a problem, and once a problem is understood, to apply mathematical knowledge and tools strategically during the problem-solving process, and to persist in solving the problem. At this level, the course provides students with a rigorous, integrated, and in-depth study of algebra processes and geometric principles. Topically, there is a major emphasis on quadratic functions: factoring, graphing, moving between forms, the inverse (the square root function), using quadratics to model scenarios, and using quadratics for the purpose of optimization. Absolute value functions and new forms of linear functions are also explored. In addition to investigating exponent rules, algebraic fractions, and imaginary numbers, students are asked to connect their understanding of algebra to topics in geometry, such as linking equations of quadratics to the geometric definition of a parabola and solving polygon problems on the Cartesian coordinate plane. Other classic types of algebra problems include advanced distance-rate-time questions, shared work, mixture problems, and systems of equations. This class will also cover topics in Euclidean Geometry including polygons (with an emphasis on triangles), their properties and proofs, parallel lines and angle relationships, and circles. We use a variety of materials, including iPad technology, graphing software like Desmos, and problems from “Math 1” and “Math 2” written by the math department at Phillips Exeter Academy to use pattern-building in the service of eventually developing mathematical generalizations. In this course, the math topics are valuable, but equal importance is given to the style in which students take on responsibility for thinking critically, creatively, and collaboratively. This course may serve as a transition into Math 30: Algebra 2 and Trigonometry or, for those who excel and find the curriculum rewarding, it can also serve as an entry point to our Honors Problem Based Learning strand. Prerequisite: an Algebra 1 course, PBL 1, or the equivalent and consent of the department.

Full year – .33 credits/trimester
PBL 2H is a problem-solving course that provides students with a more rigorous, integrated, and in-depth study of algebra processes. In addition to investigating exponent rules and imaginary numbers, students are asked to transfer their understanding of algebra to topics in geometry such as lines, vectors, parabolas, and trigonometry. Through the exploration of linear motion via parametric equations, students are introduced to optimization and transformations. We use a variety of materials, including iPad technology, graphing software like Desmos, and problems from “Math 1” and “Math 2” written by the math department at Phillips Exeter Academy, which focus on pattern building through the integration of algebra and geometry. In this course, students take on the responsibility of thinking critically, creatively, and collaboratively to solve meaningful problems on their own, learning content and making connections through the problem-solving context. This course may serve as a transition into Algebra 2 and Trigonometry or, for those who excel and find the curriculum rewarding, it can also serve as an entry point to our Honors Problem Based Learning strand. Prerequisite: PBL 1 or the equivalent and consent of the department.

Full year – .33 credits/trimester
Algebra 2 and Trigonometry builds a strong foundation of algebraic skills and understanding by reviewing and extending the topics from previous courses. Students work extensively with the “toolkit functions.” Linear, absolute value, quadratic, cubic, roots, rational, exponential, logarithmic, and trig functions are spiraled throughout the course, ensuring that students are able to connect their graphs, tables, and equations. Students learn to create new functions from their toolkit functions through transformations and explore how these new functions model real life situations. In all cases, the relationship between multiple representations (graphical, symbolic, numeric, and applied) is heavily emphasized. The mechanics of manipulating symbolic notation is traditionally the most challenging part of an Algebra 2 course, and we continually practice these cumulative skills throughout the year, connecting the symbolic representation of these functions to their more accessible graphical representations at every opportunity. The result is stronger algebraic, graphical, and problem-solving skills, all of which are essential to future studies in mathematics. Prerequisite: PBL 2 or the equivalent.

Full year – .33 credits/trimester
PBL 3H is a problem-based learning course that expands on the algebra and geometry content in PBL 2H (or Algebra 2) to include nonlinear motion and nonlinear functions. Students investigate circular motion by using trigonometric functions, model various scenarios using exponential functions, straighten nonlinear data using logarithms, and describe geometric transformations using matrices. In preparation for the study of calculus, students are introduced to instantaneous rates of change through the exploration of slopes on nonlinear graphs. We use a variety of materials, including iPad technology and problems that focus on pattern-building through the integration of precalculus and trigonometry from the “Math 3” text written by members of the Math Department at Phillips Exeter Academy. As is the case in all our PBL courses, in this class students take on the responsibility of thinking critically, creatively, and collaboratively to solve meaningful problems on their own, learning content and making connections through the problem-solving context. Prerequisite: PBL 2H and consent of department.

Full year – .33 credits/trimester
Pre-Calculus: Functions builds on the foundation laid in Algebra 2 and Trigonometry. Students delve more deeply into transformations, inverse functions, and composition of functions while continuing to strengthen their graphical reasoning and symbolic manipulation skills. Writing equations, solving or evaluating them, and interpreting results are emphasized as students work with problems in context. Students write equations to model physical situations (tides, population growth, projectile motion, etc) and to set up and solve optimization problems, and they continue to use Desmos in problem solving. This course provides a thorough study of functions as a preparation for calculus. Entering students should have a strong background in Algebra, usually meaning B or better in Algebra 2 and Trigonometry. Prerequisite: Algebra 2 and Trigonometry

Full year – .33 credits/trimester
Advanced PBL 4 begins with a foray into complex numbers, polar coordinates, recursion, functional notation, slope, velocity, asymptotes, the fundamental constant e and applications of the preceding before officially delving into differential and integral calculus. Through a carefully crafted sequence of problems, students become fluent in the conceptual and notational language of differential equations. Students also discover, explore, and apply the Fundamental Theorem of Calculus, which connects differential (rate problems) and integral (accumulation problems) calculus. Throughout the curriculum, students encounter problems in context (physics, economics, environmental studies) to emphasize the application power of calculus. They also continue to work with multiple representations of functions (graphical, numerical, symbolic) and are empowered to make strategic decisions about what tools they want to employ when solving problems. Prerequisite: Honors PBL 3 and consent of department.

Full year – .33 credits/trimester
Probability, Statistics, and Calculus is an introductory statistics elective taught through real world data and applications designed for seniors who do not choose to pursue one of the advanced options. In the fall and winter trimesters, the course provides an introduction to the discrete math topics of probability and statistics, including the analysis of data, the conducting of surveys, sampling, experiments, and inference. In the spring the major themes of calculus (the limit, derivative, and integral) are introduced in a conceptual approach using applications, with extensive use of graphing tools such as Desmos or the TI-84. Prerequisite: Algebra 2 and Trigonometry

Full year – .33 credits/trimester
Advanced Calculus 1 is a college-level mathematics course designed as an introduction to a variety of topics relating to integral and differential calculus including functions, graphs, limits, the conception and application of derivatives, the interpretation and application of integrals, and the fundamental theorem of calculus. The course outline focuses on the tools of calculus for problem solving. Prerequisite: Pre-Calculus: Functions and consent of department.

Full year – .33 credits/trimester
Advanced Calculus 2 seeks to challenge our most advanced student by providing a rigorous course in college calculus with relevant applications and elegant connections. Emphasis is on problem solving skills, preparation for college math, and using proof to understand why methods work. The course continues with the PBL approach as students learn calculus through problem solving and includes a high level of theory, proof of methods, practical applications, and connections between Algebra, Geometry, Functions, and Trigonometry. Topics include limits, derivatives, integrals, series, parametric functions, polar curves, and vectors. Students are encouraged to discover ideas and connections through challenging problems, labs, and inquiry activities. Pre-requisite: PBL 4H or Advanced Calculus 1 and consent of the department.

Full year – .33 credits/trimester
Advanced Statistics is equivalent to a college level, one-semester, introductory course in statistics. The purpose of Advanced Statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring data (observing patterns and departures from patterns), planning a study (deciding what and how to measure), anticipating patterns in advance (producing models using probability and simulation), and statistical inference (confirming models). Prerequisite: PreCalculus: Functions and consent of department. * This course is not offered every year, depending on student enrollment.

Full year – .33 credits/trimester
Advanced Statistics, Multivariable Calculus, and Linear (Math 61H) is intended for students who have completed Advanced Calculus 2 and have a strong interest in higher mathematics. The fall and winter terms of this course comprise an equivalent to a college level, one-semester, introductory course in statistics. The purpose of the Advanced Statistics section of this course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring data (observing patterns and departures from patterns), planning a study (deciding what and how to measure), anticipating patterns in advance (producing models using probability and simulation), and statistical inference (confirming models). The spring term is designed to expose our most advanced students to areas of higher collegiate mathematics beyond Calculus and Statistics. We specifically introduce Linear Algebra and Multivariable Calculus through a series of questions and problems, emphasizing graphs, visuals, and technology. In the Linear Algebra portion, we connect matrices and vectors through applications in economics and science. The Multivariable unit includes gradient, partial derivatives, double and triple integrals with applications to Physics. We use Mathematica software to provide 3- D visuals and expose students to powerful computing tools used in college mathematics. Each student is provided a license for the term. Emphasis will also be placed on proof, a required component of theoretical mathematics. Prerequisite: Advanced Calculus 2 and consent of the department.

Full year – .33 credits/trimester
Advanced Computer Science equips students with the programming skills to solve a diverse set of complex computational problems. The course covers Object-Oriented Programming principles, data structures and algorithms, and data science and visualization. Each trimester-long unit culminates in a major project in which students are given considerable leeway to pursue specific interests (e.g. video games, arts, economics, physics, and more). Open to juniors and seniors. Prerequisite: Introduction to Computational Thinking or permission of the department

INTERDISCIPLINARY ELECTIVES: Math and Science
Full year – .17 credits/trimester
This full-year course will equip students with the necessary skills to begin writing computer programs and provide an overview of the ways computational tools and approaches can be used to solve problems in many disciplines. Working in a hands-on, collaborative format, students will learn core computer programming concepts of variables, loops, functions, conditionals, arrays, and objects. Students will spend the last trimester applying these skills in the development of software projects. This class meets twice each week and carries no homework load. Open to sophomores, juniors, and seniors. Prerequisites: None