###### Academics

# Mathematics

Four groups have been proposed to give all students 4-years of a solid math education:

### GROUP 1

For the students who begin their freshman year having already taken and demonstrated proficiency in Algebra. advanced students in mathematics. By the end of their four years, students would have a received 3 math regents and 2 advanced mathematics classes (PreCalculus and AP Calculus).

### GROUP 2

For the advanced students in mathematics. By the end of their four years, students would have a received 3 math regents and 2 advanced mathematics classes (PreCalculus and AP Calculus).

### GROUP 3

For most students in mathematics. By the end of their four years, students in this group would have received 2-3 mathematics regents and a thorough exposure to all major disciplines in mathematics (Algebra I, Geometry, and Algebra II), as well as an introduction to PreCalculus to prepare them for an introductory-level college math course.

### GROUP 4

For the most struggling students in mathematics. By the end of their four years, students in this group would have received 2 math regents and exposure to all three major disciplines in mathematics, with an emphasis on the study of Algebra to prepare them for College Algebra.

**To enter Honors Algebra II, students must pass a placement exam (either at the beginning of freshman year or at the end of Algebra I).*

*Placement into a specific track will be determined by a cut score which is comprised of their internal exit exam score for each math course (50%), their score on their course’s Regents examination (30%), and their course grade (20%, average of two semesters). The cut score will be determined by the following formula: cut score=0.5x+0.3y+0.2z. Teacher recommendation will be considered for students entering/switching tracks in addition to the formula. Cut scores will be split into upper 1/3, middle 1/3, and bottom 1/3. Actual cut scores are subject to change pending department approval.*

### Algebra I (Terms 1 and 2)

CCLS Algebra I is the first mathematics course in high school. The focal point of this course is the algebra content strand aligned to Common Core Learning Standards. Algebra provides tools and ways of thinking that are necessary for solving problems in a wide variety of disciplines, such as science, business, social sciences, fine arts, and technology. This course will assist students in developing skills and processes to be applied using a variety of techniques to successfully solve problems in a variety of settings. Problem situations may result in all types of linear equations in one variable, quadratic functions with integral coefficients and roots as well as absolute value and exponential functions. Students will be exposed to basics statistics in one and two variables and use difference statistical metrics to analyze data. The course culminates with a Regents exam in June.

**Requirements:** CCLS-Aligned Regents exam in June.**Pre-Requisites:** 65% mastery on the FHSA Mathematics Diagnostic Exam.**Credits: **2

### Pre-Algebra II (Algebra I Term 3/Algebra II Term 1)

Pre-Algebra II is an extension of the first-year Algebra curriculum in the fall semester (coded Algebra I term 3). This course is designed to support students who may have entered high school with major deficits and would benefit from an additional semester exploring the topics of Algebra I. In this course, students will engage in lab-based activities to explore the real-world applications of the content. Topics will include linear, exponential and quadratic functions, mathematical modeling, and statistics in one and two variables. After the Algebra I Common Core Regents in January, students will begin an introduction to the Algebra II curriculum in the spring semester (coded Algebra II term 1). Students will explore exponential functions and logarithmic functions, an intro to probability and statistics, and an introduction into Algebraic Trigonometry. Students will continue into Algebra II in the subsequent school year.

**Requirements:** CCLS-Aligned Regents exam in January.**Pre-Requisites:** N/A**Credits: **2

### Honors Algebra II (Terms 1 and 2)

Advanced Algebra II is a yearlong course aligned to the Regents Algebra II & Trigonometry and Common Core Learning Standards. This course represents the second mathematics course in the NYS math sequence and is intended for the mathematically talented student who desires an extensive and comprehensive treatment of Algebra II topics and who intends to take the maximum units of high school math. Students will be expected to develop an in-depth understanding of the topics including functional analysis, and will be expected to draw relationships among the concepts studied. The course involves a continuation of the study of the properties of real numbers begun in Algebra I. A study of operations with polynomials and rational expressions leads to an extension of the real number system to the complex number system. Linear, quadratic, and other polynomial functions are studied, followed by the exponential and logarithmic functions. Systems of linear equations and inequalities are carefully discussed, as are quadratic relations and systems. An introduction to trigonometry is included. Statistics and probability are studied through their applications to real data and simulations. The above concepts are reinforced and applied through verbal problem solving and applications to the real world through mathematical modeling, lab reports, and performance tasks. Additionally, the use of a graphing calculator will occur though the course and a good balance of activities, practice, and re-teaching will be included in lessons to assure that the material is covered and that the students demonstrate learning. Lessons will contain a variety of experiences in order to address the range of learning styles in order to prepare students to take the Algebra II Regents Exam to obtain an Advanced Regents Diploma upon graduation.

**Requirements:** Successful completion of both terms to sit for Algebra II/Trigonometry Regents in June.**Pre-Requisites: **Successful completion of the Regents Algebra exam with a 70 or higher.**Co-requisite: **Regents Physics or Chemistry.**Credits: **2

### Algebra II (Terms 1 – 3)

Algebra II & Trigonometry is a three-semester course aligned to the Regents Algebra II & Trigonometry and Common Core Learning Standards. This course represents the second mathematics course in the NYS math sequence and is intended for the student who desires an extensive and comprehensive treatment of Algebra II & Trigonometry topics and who intends to take the maximum units of high school math, but may benefit from covering material at a slower pace to deepen understanding. Students will be expected to develop an in-depth understanding of the topics including functional analysis, and will be expected to draw relationships among the concepts studied. The course involves a continuation of the study of the properties of real numbers begun in Integrated Algebra. A study of operations with polynomials and rational expressions leads to an extension of the real number system to the complex number system. Linear, quadratic, and other polynomial functions are studied, followed by the exponential and logarithmic functions. Systems of linear equations, matrices, and inequalities are carefully discussed, as are quadratic relations and systems. An introduction to trigonometry is included. The above concepts are reinforced and applied through verbal problem solving and applications to the real world through mathematical modeling, lab reports, and performance tasks. Additionally, the use of a graphing calculator will occur though the course and a good balance of activities, practice, and re-teaching will be included in lessons to assure that the material is covered and that the students demonstrate learning. Lessons will contain a variety of experiences in order to address the range of learning styles in order to prepare students to take the Advanced Algebra II & Trigonometry Regents Exam to obtain an Advanced Regents Diploma upon graduation. Students may sit for the Algebra II Regents Exam following the 2^{nd} or 3^{rd} term of the course depending on mastery of content.

**Requirements:** Successful completion of 3 terms to sit for Algebra II/Trigonometry Regents exam in June of year II of the course.**Pre-Requisites:** A 65 or higher on the Regents Algebra I exam.**Credits: **3

### Honors Geometry (Terms 1 and 2)

Honors Geometry is intended to be the third course in mathematics for high school students. Within this course, students will have the opportunity to make conjectures about geometric situations and prove in a variety of ways, both formal and informal, that their conclusion follows logically from their hypothesis. This course is meant to employ an integrated approach to the study of geometric relationships. Integrating synthetic, transformational, and coordinate approaches to geometry, students will justify geometric relationships and properties of geometric figures. Congruence and similarity of triangles will be established using appropriate theorems. Transformations including rotations, reflections, translations, glide reflections and coordinate geometry will be used to establish and verify geometric relationships. A major emphasis of this course is to allow students to investigate geometric situations. Properties of triangles, quadrilaterals, and circles should receive particular attention. It is intended that students will use the traditional tools of compass and straightedge as well as dynamic geometry software that models these tools more efficiently and accurately, to assist in these investigations. Geometry is meant to lead students to an understanding that reasoning and proof are fundamental aspects of mathematics and something that sets it apart from the other sciences.

**Requirements:** Successful completion of both terms to sit for Geometry Regents exam in June.**Pre-Requisites:** Successful completion of both Algebra I and Algebra II, and a score of at least a 65 on the Algebra I Regents.**Credits: 2 **

## Advanced Mathematics Courses

### Pre-Calculus (Terms 1 and 2)

Pre-Calculus, as its name indicates, is designed to prepare students for Calculus, either in high school or college. Topics include understanding functions from symbolic, tabular, and graphical perspectives, transformations and function composition, polynomial functions, rational polynomial functions, trigonometry, and conic sections. In addition to content mastery, the course goals are to further develop students’ problem solving and critical thinking skills. Pre-Calculus is a fast-paced course. The difficulty level of the material increases significantly throughout the year. Students should be prepared to be challenged and work hard. Students are encouraged to form study groups with peers, practicing beyond daily assignments in an effort to master skills.

**Requirements:** Students must re-sit for the Algebra II Regents exam at the end of the course if they have not scored a 70 or higher.**Pre-Requisites: **Successful completion of Algebra II and Geometry, having passed at least one of the corresponding regents exams.**Co-requisite: **Regents Physics or a higher-level science.**Credits:** 2

### Advanced Placement Calculus AB (Terms 1 and 2)

The curriculum for AP Calculus AB is equivalent to that of a first-semester college calculus course. In order for students to be able to apply their knowledge of Calculus, they need to be able to understand why the equations and patterns used result in solving problems. Understanding of Calculus topics will be done through algebra, graphs, and a calculator. Students also will be asked to explain in words, how to solve a problem and why they solve a problem a specific way. Outside resources and examples from life applications (such as design, architecture, and physics) will be used to help deepen students’ understanding of Calculus. The first three weeks of Calculus will review Pre-Calculus material then move into Limits and Continuity. After this, Derivatives and finally the Application of Derivatives will be studied. Second Semester will start with Integrals, move into Applications of Integrals, and will finish with AP Practice Tests and AP Test strategies. This rigorous course is designed to prepare students for college, and to complete and take the AP Calculus Exam.

**Requirements:** Students must pass both semesters of AP Calculus AB in order to sit for the Advanced Placement exam in May of the course year.**Pre-Requisites: **Successful completion of Algebra, Algebra II, Geometry, and Pre-Calculus and passing of the three required Math Regents (Algebra, Algebra II, and Geometry) with at least one of the Regents with an 70 or higher. Successful completion of Physics preferred.**Co-requisite: **Regents Physics or a higher-level science.**Credits:** 2