The Mathematics department at HSCL is dedicated to helping students develop essential thinking and reasoning skills. Through the exploration of the principles of mathematics, students make real world connections and become confident in their ability to solve difficult mathematical problems, communicate through mathematical discourse, and integrate the use of technology to prepare students for a stronger future. Our students gain competency in Algebra I, Geometry, and Algebra II and Trigonometry. As a result, not only can they complete necessary requirements for the Advanced Regents Diploma, but they will become aware of the importance of understanding mathematics in the world.

# Mathematics

### Algebra I

Algebra I introduces students to the foundational skills needed to succeed in higher level mathematics. The course emphasizes the importance of problem solving, reasoning, and creating mathematical models. Students learn to construct mathematical arguments and use logic to defend them. Algebra I begins with the study of expressions, including how to interpret and write expressions, and continues by developing students’ knowledge of polynomials and rational expressions. The first part of the Algebra I course culminates with a comprehensive exploration of equations in which students learn to create and solve a variety of equations, use graphs to make predictions, apply linear equations to real relationships, and analyze the relationships between variables. During the second part of this course, students build on prior learning to engage in a comprehensive study of functions. Students interpret, analyze, and construct models of a variety of functions. Through their study of Algebra I, students develop a strong mathematical base necessary for taking and passing the New York State Regents Examination in Algebra.

### Geometry

Geometry continues many themes that students explored during Algebra I. An emphasis on problem solving, abstract reasoning, precise work, and clear communication connects geometry directly to earlier coursework. Through the introduction of new material, which includes the examination of statements and the construction of proofs, students develop their logic and reasoning skills as well as improve their ability to identify and evaluate valid arguments. During this course, students frequently visualize in two and three dimensions, thereby gaining a better understanding of measurement and units. The first part of the course focuses heavily on constructing figures and observing geometric relationships. Students also explore properties and theorems involving triangles as they begin to construct proofs. The first half of the course concludes with work on midpoint, distance, and the Pythagorean Theorem. The measurement strand continues in the second half of the course as students explore polygons and solids and create models for finding area, perimeter, surface area, lateral area, and volume in a variety of real-world situations. The course concludes with material involving angles, parallelism, perpendicularity, slope, special quadrilaterals and conic sections. During the course, students have repeated opportunities to connect their algebra skills with the geometric concepts as they work on performance tasks and solve meaningful application problems. Students that complete this course sit for the New York State Regents Examination in Geometry.

### Algebra II and Trigonometry

Algebra II and Trigonometry merge skills learned in Geometry and Algebra I and extends them through an intensive curriculum that develops more advanced topics within both. Exploration, inquiry, discovery, reasoning, and problem solving are at the heart of the course. The first half of the course will expand upon previously learned algebraic techniques including functions and number systems in order to gain a more detailed view of the relationships between variables. At the root of our explorations of functions are rates of change. We will constantly ask: How does one thing change relative to another? The second half of the course will focus on probability, statistics and trigonometry. Probability will allow us to determine the likelihood of an event; it is the foundation of reasoned decision making in those cases where results are not certain. Trigonometry is the field of mathematics devoted to the study of the angles and sides of a triangle. We will explore trigonometry and uncover real world applications of trigonometric formulas. The course culminates in a New York State Regents Exam and is the last of the three Math Regents exams required to obtain a New York State Advanced Regents Diploma.