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 IA 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 Euclidean 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 Euclidean 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.

**Algebra 2 and Statistics– 10-12**

This course is a survey of Algebra and Statistics, through the lens of content from other classes. Students are exploring content from other classes through a statistical lens. This means that students are engaging with that data (for example, experimental data in a Biology class) , but also learning a set of skills that will help them be more critical when analyzing statistics. Students will learn how to approach all data sets consistently with a refined eye, and will also learn to make reasonable claims that will support the way in which they examine data in all of their other classes.

**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.

**Math and Physics**

Physics is the science of how things move and that forces that cause motion. In this interdisciplinary course, students will explore physics topics around Newtonian Motion and the mathematical concepts that support these models, namely vectors, trigonometry, exponential functions, and calculus. Students will practice modeling physical systems to solve problems, such as

*How fast does a boat need to move to rescue an overboard passenger?*and*What initial angle and velocity does a projectile need to hit a target?*The written components of students’ projects will be a Model Report, in which they will 1) describe the context, 2) connect to math and physics background, 3) model the system with given constraints, 4) make a prediction about how the system would change if a constant varied, 5) confirm how accurately their model predicted system behavior against real data, and 6) conclude with an answer to the initial problem.