The ESA mathematics department provides courses that are grounded in foundational mathematical content, but emphasize students’ critical thinking skills with respect to logical thinking and data analysis. All of the math courses at ESA focus on creating a classroom of students that can work independently, problem solve persistently, and use patterns they observe to make overarching connections. All courses require students to work in groups, complete homework assignments, and develop a portfolio of projects.

**Algebra 1 – 9/10**

The focus of Algebra is to begin exploring basic algebraic concepts, while reinforcing and building on prior math knowledge. The content of the course will include evaluating and simplifying algebraic expressions, graphing and solving equations, and transformations of functions. Students will enter with varying levels of skills in arithmetic and manipulating algebraic expressions. During the course, they will build these skills, while developing their abilities to create and interpret graphs of linear equations, compare linear equations, make predictions, check work, and justify answers. Students will develop specific language for different algebraic domains (vocabulary for describing graphs vs. for supporting an argument with a table). Students will learn how to become actively engaged mathematical students through collaborating, communicating and cultivating independent thinking. They will build on these math-student skills throughout their math courses culminating in their PBAT.

**Geometry – 9-11**

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By using an investigative approach, this course will introduce students to concepts of geometry while strengthening their algebra skills by integrating the two. Students will become acclimated to the language, symbolism, and importance of Euclidian Geometry. They will explore and conjecture about the properties of triangles, lines, and angles by attempting to defend their logical reasoning with verifiable statements. This course will endeavor to strengthen the student’s’ ability to reason, use visual thinking and models to problem solve, recognize patterns/relationships, and to clearly and effectively communicate their thought processes and solutions.

By using an investigative approach, this course will introduce students to concepts of geometry while strengthening their algebra skills by integrating the two. Students will become acclimated to the language, symbolism, and importance of Euclidian Geometry. They will explore and conjecture about the properties of triangles, lines, and angles by attempting to defend their logical reasoning with verifiable statements. This course will endeavor to strengthen the student’s’ ability to reason, use visual thinking and models to problem solve, recognize patterns/relationships, and to clearly and effectively communicate their thought processes and solutions.

**Trigonometry – 10-12**

“Trigonometry” has its roots in Ancient Greek history, from “trigonon,” meaning “triangle,” and “metron,” meaning “measure.” Demand for this branch of mathematics arose during the birth of astronomy, when Greeks of the 3rd century B.C. were curious about the cyclical nature of orbits. This curiosity gave way to connecting these cyclical relationships to triangles, specifically right triangles and their angle/side relationships. These relationships have found their roots in understanding music, physics, biology, astronomy, and engineering, to name a few. In this course, we will be studying the elements of trigonometry that can be used to solve practical problems and help us understand the natural universe. More specifically, we will dive deep into triangle angle/side relationships, apply these relationships to unearthing relationships that make up the unit circle, and use trigonometric graphs to model natural phenomena. We will collectively build on these understandings, knowledge components, and mathematical skills and demonstrate our learning through regular projects, mini-projects, seminars, and special learning cycles called “formative assessments.” In order to be successful, we must be present and engaged—not just physically present, but mentally, tangibly contributing to our learning community. This type of contribution can only happen if we are all prepared for our time together, completing regular homework and coming to class ready to ask questions.

**Precalculus**

This course is the precursor to understanding Calculus next semester, which focuses on instantaneous rates of change. Precalculus will review and focus on the slope/average rate of change characteristic of different families of functions (linear, quadratic, exponential). Main topics include: arithmetic and geometric sequences, functions and graphs, polynomial functions, inverse functions, exponential and logarithmic functions, and limits. Students will continue to hone their algebraic manipulation skills, ability to represent functions in various ways, and connect these families of functions to real world phenomena and applications.

**Calculus 1A – 11/12**

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This course is designed to teach students the fundamentals of calculus. Students will begin the course by reviewing the concept of a function, then moving on to the ideas of limits and continuity, and finally will formally learn differentiation (they have already been introduced to the general power rule last semester in their final project and the idea of a derivative without being given a name for it) and how to apply it. This will set students up for next semester, when students will learn integration and how to apply it to area and volume problems. We will constantly be reviewing topics from last year’s pre-calculus course as needed to strengthen problem-solving, graphing, and algebra skills, all of which will be helpful in whichever math courses students wind up taking next year (and in college).

This course is designed to teach students the fundamentals of calculus. Students will begin the course by reviewing the concept of a function, then moving on to the ideas of limits and continuity, and finally will formally learn differentiation (they have already been introduced to the general power rule last semester in their final project and the idea of a derivative without being given a name for it) and how to apply it. This will set students up for next semester, when students will learn integration and how to apply it to area and volume problems. We will constantly be reviewing topics from last year’s pre-calculus course as needed to strengthen problem-solving, graphing, and algebra skills, all of which will be helpful in whichever math courses students wind up taking next year (and in college).

**Calculus 1B – 11/12**

This course builds on students’ introduction to differential calculus by going further in depth about the uses and properties of derivatives. Students will compute the derivatives of various kinds of functions using derivative rules, analyze first and second derivatives to do curve sketching, apply derivatives to solve real world problems about speed and acceleration, as well as related rates. In addition to this math content, students will develop their strategic problem solving (as opposed to procedural) and their reasoning and proof, through weekly problem solving tasks both related and unrelated to the calculus content. These skills will then be a focus of the projects.

**Computer Science**

Computer science principles will focus on the iterative development and the logic of writing code, rather than emphasizing a specific language and syntax. Students will use Snap!, an online platform to create programs that will showcase their understanding of building an algorithm, making algorithms more efficient and easy to understand by using abstraction (hiding details), and analyzing and debugging faulty code. Additionally, the course will ask students to explore the implications of technology on our society, culture, and economy by asking them, “Is technology good or bad?”