## Mathematics

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.

Integrated Math: In this course, we will be recognizing and developing patterns using tables, graphs and equations. Students will explore operations on algebraic expressions and apply mathematical properties to algebraic equations. They will collaborate to solve problems that investigate linear relationships. Technology will be used to introduce and expand upon the areas of study listed above.

Geometry: 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.

Functions and Applications: This course will focus on the principles of Algebra, problem-solving, and function modeling to explain different patterns and phenomena.  In this course, students will continue learning the skills and procedures that they initially learned in Algebra 1 (such as factoring, graphing, using functions to turn inputs into outputs).  However, we will continue this trajectory by understanding the conceptual backbone to some of these procedures, such as the use of area models to support why factoring works, for example, or how we can use these functions to demonstrate characteristics of functions (such as maxima and minima).   This course will also make more explicit connections between Algebra and Geometry, and will tie in aspects of calculus, such as rates of change, instantaneous rates of change, and slope.