# High School Math

Students are required to pass a minimum of three mathematics courses and at least one Regents Exam (or Regents Exam Equivalent) in mathematics to meet State graduation requirements. Many of the courses offer levels (e.g. honors). Assignment to levels is made on the basis of performance in previous courses, student ability, teacher recommendations, and testing. District-wide final examinations are administered in all mathematics courses that do not culminate in a New York State Regents Examination.

**A student may satisfy the mathematics requirement for graduation by completing any one of the paths:**

- Regents Diploma*: Successfully complete three units of math credit and one commencement level Regents Examination in mathematics designated by the commissioner or an approved alternative (e.g., Advanced Placement) pursuant to section 100.2(f) (Part 100.5.b.6.Types of Diplomas.iv.c).
- Regents Diploma with an Advanced Designation*: In addition to the requirements for a Regents diploma, students must successfully complete and pass three commencement level Regents Examinations (i.e., Algebra 1, Geometry, and Algebra 2) (Part 100.5.b.6.Types of Diplomas.v).
- Regents Diploma with an Advanced Designation, with an annotation in mathematics*: Successfully fulfill all of the requirements for a Regents Diploma with an Advanced Designation and earn at least an 85% or better on each of the three Regents Exams in mathematics (Part 100.5.b.6.Types of Diplomas.x).

***A student will be awarded a Regents Diploma with Honors or a Regents Diploma with Advanced Designation with Honors if the student achieves an average of 90 percent in all Regents Examinations required for the diploma (Part 100.5.b.6.Types of Diplomas.ii.a).**

Students planning to further their formal education beyond high school should plan to take four years of mathematics.

**FUNDAMENTALS OF ALGEBRA**

**Final Exam**: District Final Exam

**Course Description**: This is a one-year credit-bearing course that counts towards a student’s mathematical commencement requirements and meets New York State’s mathematics requirements towards earning a Regents Diploma. This course is aligned to the Common Core Learning Standards for Algebra 1, but is intended for students who need additional math preparation by extending Algebra 1 over two years. This course must be followed by Algebra 1R where students will take the Algebra 1 Regents Exam at the end of this second year. This course emphasizes developing skills and processes to successfully solve problems and become more mathematically confident through the study of elementary algebra. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe for students to experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.

**ALGEBRA 1R**

**Final Exam**: Algebra 1 Regents

**Course Description**: This is a one-year credit-bearing course that counts towards a student’s mathematical commencement requirements and meets New York State’s mathematics requirements towards earning a Regents Diploma or Regents Diploma with Advanced Designation. This course is aligned to the Common Core Learning Standards, intended to be the first of a three year sequence. Students will study linear equations and inequalities, linear regression models, quadratic and exponential expressions (including rational exponents), quadratic functions, and formalize and extend the concept of functions (including function notation, domain and range, and exploration of many types of functions). This course is followed by Geometry R.

For more information about Algebra 1, click here.

**ALGEBRA 1A**

**Final Exam**: Algebra 1 Regents

**Required Prerequisite**: Successful completion of "Math 7A" with notable achievement and teacher recommendation.

**Course Description**: This is a one-year credit-bearing course, only available at the middle school level to accelerated students. This course counts towards a student’s mathematical commencement requirements and meets New York State’s mathematics requirements towards earning a Regents Diploma or Regents Diploma with Advanced Designation. Students are expected to maintain a mid-to upper-90 average. This course is aligned to the Common Core Learning Standards, intended to be the first of a three year sequence. Students will study linear equations and inequalities, linear regression models, quadratic and exponential expressions (including rational exponents), quadratic functions, and formalize and extend the concept of functions (including function notation, domain and range, and exploration of many types of functions). This course is typically followed by Geometry A.

For more information about Algebra 1, click here.

**GEOMETRY**

**Final Exam**: District Final Exam

**Required Prerequisite**: Successful completion of "Algebra 1R."

**Course Description:**This is a one-year credit-bearing course that counts towards a student’s mathematical commencement requirements and meets New York State’s mathematics requirements towards earning a Regents Diploma. It is aligned to the Common Core Learning Standards and is intended to be the second year of a three year sequence. This course employs an integrated approach to the study of connecting algebra to geometric relationships and proofs. Properties of triangles, quadrilaterals, and circles will receive particular attention. Congruence and similarity of triangles will be established using appropriate theorems; transformations including rotations, reflections, translations, and glide reflections and coordinate geometry will be used to establish and verify geometric relationships; and topics in trigonometry extending to three-dimensional geometry will be explored.

**GEOMETRY R**

**Final Exam**: Geometry Regents Exam

**Required Prerequisite**: Successful completion of "Algebra 1R."

**Course Description**: This is a one-year credit-bearing course that counts towards a student’s mathematical commencement requirements and meets New York State’s mathematics requirements towards earning a Regents Diploma or a Regents Diploma with Advanced Designation. It is aligned to the Common Core Learning Standards and is intended to be the second year of a three year sequence. This course employs an integrated approach to the study of connecting algebra to geometric relationships and proofs. Properties of triangles, quadrilaterals, and circles will receive particular attention. Congruence and similarity of triangles will be established using appropriate theorems; transformations including rotations, reflections, translations, and glide reflections and coordinate geometry will be used to establish and verify geometric relationships; and topics in trigonometry extending to three-dimensional geometry will be explored.

For more information about Geometry, click here.

**GEOMETRY A**

**Final Exam**: Geometry Regents Exam

**Required Prerequisite**: Successful completion of Algebra 1R is recommended with notable achievement and teacher recommendation; however, successful completion of Algebra 1A Regents exam is strongly recommended.

**Course Description**: This is a one-year credit-bearing course that counts towards a student’s mathematical commencement requirements and meets New York State’s mathematics requirements towards earning a Regents Diploma or a Regents Diploma with Advanced Designation. It is aligned to the Common Core Learning Standards and is intended to be the second year of a three year sequence. This is an advanced course that includes all the topics from Geometry R and explores more complex geometric relationships. Students enrolled in Geometry A move at a faster pace than those in Geometry R and work well beyond the Geometry R curriculum. This course employs an integrated approach to the study of geometric relationships and proofs. Congruence and similarity of triangles will be established using appropriate theorems. Transformations including rotations, reflections, translations, and glide reflections and coordinate geometry will be used to establish and verify geometric relationships. Properties of triangles, quadrilaterals, and circles will receive particular attention. This course also includes topics in three-dimensional geometry.

For more information about Geometry, click here.

**ALGEBRA 2**

**Final Exam**: District Final Exam

**Required Prerequisite**: Successful completion of "Geometry" or "Geometry R."

**Course Description**: This is a one-year credit-bearing course that counts towards a student’s mathematical commencement requirements and meets New York State’s mathematics requirements towards earning a Regents Diploma. It is aligned to the New York State Learning Standards for Mathematics and is intended to be the third year of a three-year sequence. In Algebra 2, students will further develop the concepts learned in Algebra 1 and Geometry and extend those into advanced algebraic applications that require more complex and technical calculations and transformations, but sense-making is still paramount. Topics of study include: the Real and Complex Number systems; seeing structure in expressions; arithmetic with polynomials and rational expressions; creating equations; reasoning with equations and inequalities; building and interpreting functions; linear, quadratic, logarithmic, and exponential models; trigonometric functions; expressing geometric properties with equations; interpreting categorical and quantitative data; making inferences and justifying conclusions; and conditional probability and the rules of probability. This course is typically followed by Pre-Calculus where students will be eligible to take the Algebra 2 Regents Exam.

**ALGEBRA 2R**

**Final Exam**: Algebra 2 Regents Exam

**Required Prerequisite**: Successful completion of "Geometry R" or "Geometry A."

**Course Description**: This is a one-year course intended to be the third course in mathematics for high school. This course meets the requirements for an Advanced Regents Diploma. This course builds on students' work with linear, quadratic, and exponential functions. Students extend their repertoire of functions to include polynomial, rational, and radical functions. Students work closely with the expressions that define the functions and continue to expand and hone their abilities to model situations and to solve equations, including solving quadratic equations over the set of complex numbers and solving exponential equations using the properties of logarithms.

Click here for information on the Algebra 2 course.

**ALGEBRA 2A**

**Final Exam:**Algebra 2 Regents Exam

**Required Prerequisite**: Successful completion of Geometry A with notable achievement and teacher recommendation.

**Course Description**: This is a one-year course intended to be the third course in mathematics for high school. This course moves at a much faster pace than those in Algebra 2 and Algebra 2R, and works well beyond the curriculum for an Advance Regents Diploma in order to prepare students to one day take AP Calculus. This course builds on students' work with linear, quadratic, and exponential functions. Students extend their repertoire of functions to include polynomial, rational, and radical functions. Students work closely with the expressions that define the functions and continue to expand and hone their abilities to model situations and to solve equations, including solving quadratic equations over the set of complex numbers and solving exponential equations using the properties of logarithms.

Click here for information on the Algebra 2 course.

**MATHEMATICAL CONNECTIONS**

**Final Exam:**District Final Exam

**Required Prerequisite**: Successful completion of Geometry.

**Course Description:**This is a one-year credit-bearing elective math course that counts towards a student’s mathematical commencement requirements and meets New York State’s mathematics requirements towards earning a Regents Diploma. It is aligned to the Common Core Learning Standards and is intended to be an alternative third-or fourth-year math course. Mathematical Connections applies, connects, and extends the math skills learned in Algebra 1 and Geometry to real-world applications through the use of technology and hands-on activities. The major area of concentration will be, but not limited to: optimization of time, money, area and volume and analysis of current data (regression) and polls as reported in the news. Topics may also include determination of mortgage and/or car payments and investment return.

**PRE-CALCULUS, PRE-CALCULUS R, PRE-CALCULUS A**

*(District Final Exams)*

Topics of study in all pre-calculus courses include: fundamental concepts of algebra, solving equations and inequalities, functions and graphs, polynomial functions, rational functions and functions involving radicals, exponential and logarithmic functions, trigonometric functions, and conic sections. Additional topics such as mathematical inductions, vectors, and matrices, sequences and series, and polar coordinates may also be included.

Pre-Calculus thoroughly combines algebra and geometry to prepare students to undertake the study of calculus. Since functions are the foundations of calculus, these courses have been specifically developed to give the student a thorough understanding of elementary functions. The use of a graphing utility and the inclusion of realistic applications from the physical world, from the school environment, and from the quantitative world of mathematics, is now an integral part of the fourth year mathematics course.

**PRE-CALCULUS**

**Required Prerequisite:**Successful completion of at least Algebra 2.

**This is a one-year credit-bearing course that counts towards a student’s mathematical commencement requirements and meets New York State’s mathematics requirements towards earning a Regents Diploma. It is aligned to the New York State Learning Standards for Mathematics and is highly recommended preparation for students whose plans include the possibility of formal education beyond high school. In Pre-Calculus, students will further develop the concepts learned in Algebra 2 and extend those into advanced applications that require more complex and technical calculations while sense-making is still paramount. Topics of study include: fundamental concepts of algebra, polynomial equations of higher degrees, complex numbers, solving equations and inequalities, functions and graphs, polynomial functions, rational functions and functions involving radicals, exponential and logarithmic functions, trigonometric functions, sequences and series, conic sections, and advanced probability and stats. The main goal of this course is for students to continue their formal study of functions begun in Algebra 1 and Algebra 2 and develop a deeper understanding of the fundamental concepts and relationships of functions while to reinforcing one’s mathematical skills in preparation for college Calculus 1. Students will investigate and explore mathematical ideas, develop multiple strategies for analyzing complex situations, and use graphing calculators and mathematical software to build understanding, and make connections between representations. Students in pre-calculus will be eligible to take the Algebra 2 Regents Exam.**

Course Description:

Course Description:

PRE-CALCULUS R

PRE-CALCULUS R

**Required Prerequisite**: Successful completion of Algebra 2R or Algebra 2A.

**This is a one-year course that combines trigonometry and advanced algebra. This course is recommended for the motivated, average-to-very good student whose mathematical abilities are at grade level or above, and whose plans include the possibility of post-high school education.**

Course Description:

Course Description:

PRE-CALCULUS A

PRE-CALCULUS A

**Required Prerequisite**: Successful completion of Algebra 2A with notable achievement and teacher recommendation.

**This is a one-year course that combines trigonometry and advanced algebra. This course is designed especially for the student planning to take the Advanced Placement course in Calculus the following year. This course is recommended for the above-average, college-bound student who is highly motivated.**

Course Description:

Course Description:

**MATH 5R (Calculus 5R)**

**Final Exam**: District Final Exam

**Required Prerequisite**: Successful completion of "Pre-Calculus R" or "Pre-Calculus A."

**: It is strongly recommended that college-bound students study mathematics every year that they are in high school. This course is designed for students who have successfully completed Pre-Calculus R or Pre-Calculus A and do not wish to take AP Calculus. Calculus 5R is essentially a first semester college calculus course, stretched over the entire school year, with topics that include: an introduction to calculus and its practical uses, limits, derivatives, rates of change, derivative rules, application of derivatives, curve sketching, asymptotes and symmetry, series and sequences, integration, definite integral, applications of definite integral, transcendental functions, inverse functions, and log and exponential functions.**

Course Description

Course Description

Calculus 5R is a concurrent enrollment course offered through Niagara University (https://www.niagara.edu/nustep/), but is taught at your high school by a certified teacher. As a full year course, students who successfully complete the course will earn one unit of high school credit. However, prior to the course’s completion, students can opt to enroll this course through Niagara University, pay a highly reduced tuition, and to earn 4 college credits. The classroom teacher will provide each student with the necessary paperwork should a student wish to participate in this concurrent enrollment opportunity. Students are responsible for registering themselves prior to the deadlines as stated by Niagara University.

**ADVANCED PLACEMENT CALCULUS (AB)**

**Required Prerequisite:**Successful completion of "Pre-Calculus A."

**Course Description:**This course is equivalent to a one-semester college course in calculus. It includes the fundamentals and development of limits, differential calculus and integral calculus of algebraic and transcendental functions. Strong emphasis is placed on applications and problem solving. This course culminates in the CEEB (College Entrance Examinations Board) examination in Calculus AB. Depending on the student’s performance on this exam and on her/his college’s policies, s/he may receive college credit, advanced placement, or both.

AP Calculus College Board Description

**ADVANCED PLACEMENT CALCULUS (BC)**

**Required Prerequisite:**Successful completion of "Pre-Calculus A."

**Course Description:**This course is equivalent to a two-semester college sequence in Calculus 1 and Calculus 2. Students cultivate their understanding of differential and integral calculus through engaging with real-world problems represented graphically, numerically, analytically, and verbally and using definitions and theorems to build arguments and justify conclusions as they explore concepts like change, limits, and the analysis of functions. This course culminates in the CEEB (College Entrance Examinations Board) examination in Calculus BC. Depending on the student’s performance on this exam and on her/his college’s policies, s/he may receive college credit, advanced placement, or both.

AP Calculus BC College Board Description

**STATISTICS**

**Final Exam**: District Final Exam

**Required Prerequisite:**Successful completion or concurrent enrollment in any level of "Algebra 2 " or higher math course.

**Course Description**: The purpose of this course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students will be exposed to four broad conceptual themes:

- Exploring Data: Observing patterns and departures from patterns.
- Planning a Study: Deciding what and how to measure.
- Anticipating Patterns: Producing models using probability and simulations.
- Statistical Inference: Confirming models.

**AP STATISTICS**

**Required Prerequisite**: Successful completion or concurrent enrollment in any level of "Algebra 2 & Trigonometry" or higher math course.

**Course Description**: This course is equivalent to an introductory statistics course typically required for majors such a social science, health science and business. The course will introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to these conceptual themes: Exploring data, sampling, experimentation, anticipating patterns, probability, simulation, and statistical inference. Students who successfully complete the course and exam may receive college credit for a one-semester introductory college statistics course. Graphing calculators are required.

**Computer Science: The New Literacy**

Whether it’s 3-D animation, engineering, music, app development, medicine, visual design, robotics, or political analysis, computer science is the engine that powers the technology, productivity, and innovation that drive the world. **Computer science experience has become an imperative for today’s students and the workforce of tomorrow.**

**COMPUTER PROGRAMMING**

**Required Prerequisite**: Successful completion of Algebra 1R. No previous computer science course is required.

**This course is designed for college-bound students with an interest in Math, Engineering or Computer Science. During the year, students are exposed to three programming languages. Object-oriented programming is introduced through Visual Basic, C++, and the course concludes with Java. With an emphasis on problem-solving and algorithm development, this course will prepare students for the AP Computer Science A and/or AP Computer Science Principles courses.**

Course Description:

Course Description:

This course is a concurrent enrollment course offered through Niagara University (https://www.niagara.edu/nustep/), but is taught at your high school by a certified teacher. As a full year course, students who successfully complete this course will earn one unit of high school credit. However, prior to the course’s completion, juniors and seniors can opt to enroll this course through Niagara University, pay a highly reduced tuition, and to earn 3 college credits. The classroom teacher will provide each student with the necessary paperwork should a student wish to participate in this concurrent enrollment opportunity. Students are responsible for registering themselves prior to the deadlines as stated by Niagara University.

**EXPLORING COMPUTER SCIENCE**

**Grade 8 Math. No previous computer science course is required.**

**Required Prerequisite**:**Course Description:**The goals of Exploring Computer Science are to develop the computer science skills of algorithm development, problem solving and programming. Students will be introduced to topics such as interface design, limits of computers and societal and ethical issues of software engineering. The course teaches the creative, collaborative, interdisciplinary, and problem-solving nature of computing with instructional materials which feature an inquiry-based approach to learning and teaching. Students will delve into real-world computing problems that are culturally-relevant and address social and ethical issues while delivering foundational computer science knowledge to students. Students will engage in several in-depth projects to demonstrate the real-world applications of computing. This course will prepare students for the AP Computer Science A and/or AP Computer Science Principles courses.

This course is a concurrent enrollment course offered through Niagara University (https://www.niagara.edu/nustep/), but is taught at your high school by a certified teacher. As a full year course, students who successfully complete this course will earn one unit of high school credit. However, prior to the course’s completion, juniors and seniors can opt to enroll this course through Niagara University, pay a highly reduced tuition, and to earn 3 college credits. The classroom teacher will provide each student with the necessary paperwork should a student wish to participate in this concurrent enrollment opportunity. Students are responsible for registering themselves prior to the deadlines as stated by Niagara University.

**AP COMPUTER SCIENCE A**

**Required Prerequisite**

**:**

*Algebra 1R or permission of the teacher.*

**Course Description:**The AP Computer Science A course is a college level introductory course in computer science. Because the design and implementation of computer programs to solve problems involve skills that are fundamental to the study of computer science, a large part of the course is built around the development of computer programs that correctly solve a given problem. These programs should be understandable, adaptable, and, when appropriate, reusable. At the same time, the design and implementation of computer programs is used as a context for introducing other important aspects of computer science, including the development and analysis of algorithms, the development and use of fundamental data structures, the study of standard algorithms and typical applications, and the use of logic and formal methods. In addition, the responsible use of these systems is an integral part of the course.

This course is a concurrent enrollment course offered through Niagara University (https://www.niagara.edu/nustep/), but is taught at your high school by a certified teacher. As a full year course, students who successfully complete this course will earn one unit of high school credit. However, prior to the course’s completion, juniors and seniors can opt to enroll this course through Niagara University, pay a highly reduced tuition, and to earn 3 college credits. The classroom teacher will provide each student with the necessary paperwork should a student wish to participate in this concurrent enrollment opportunity. Students are responsible for registering themselves prior to the deadlines as stated by Niagara University.

For a listing of the topics addressed, see the AP Computer Science A topic outline on pages 8–10 in the AP Computer Science College Board Description link below.

- Click here for additional information on AP Computer Science A

**AP COMPUTER SCIENCE PRINCIPLES**

**Required Prerequisite**: Successful completion of Algebra 1R or permission of the teacher.

**Course Description:**This course is a college level introductory course that requires students to apply creative processes when developing computational artifacts and simulations to explore questions that interest them. Rather than teaching a particular programming language or tool, this course focuses on an iterative process similar to what artists, writers, computer scientists, and engineers use to bring ideas to life. This course emphasizes the vital impact that advances in computing have on people and society. By focusing the course beyond the study of machines and systems, students also have the opportunity to investigate the innovations in other fields that computing has made possible and examine the ethical implications of new computing technologies.

- Click here to access the AP Computer Science Principles Framework
- Click here for additional information on AP Computer Science Principles

**University at Buffalo, Gifted Math Program **

The University at Buffalo’s Gifted Math Program (GMP) offers advanced mathematics courses on UB’s campus twice a week – after the regular school day – throughout the academic year. This program is designed to challenge exceptional math students (i.e., upper 1% in their national peer group) and provide students with the opportunity to earn up to 22 college credit hours. Each year, the GMP admits a class of 60 students who are nominated for entry by parents or teachers from across Western New York. Applicants undergo interviews and a battery of tests, which includes the math section of the Preliminary Scholastic Aptitude Test. Those in grades 7 through 10 study an accelerated curriculum, while 11th and 12th graders take university-level courses in calculus and linear algebra.

While the GMP courses are designed to replace the mathematics courses in the students’ home school, students may elect to take a district math course, in addition to an “aligned” GMP course. The grades for both courses will be factored into a student’s grade point average (GPA), appear on one’s transcript, and each class (beginning in the 2020-21 school year) may earn a NYS seat credit. For example, the GMP program has designated that GMP III is aligned to Geometry. So, if a student takes GMP III and elects to take Geometry in the district, both the GMP course and district’s Geometry course may each receive one NYS seat credit, and both courses will be factored into one’s GPA and appear on one’s transcript.

F.A.Q:

**1. What GMP courses are considered “aligned” to Williamsville’s math courses?**

UB has identified the following Gifted Math courses as “aligned” to Williamsville’s leveled courses:

UB GMP 1 = (no high school association)

UB GMP 2 = Algebra 1

UB GMP 3 = Geometry

UB GMP 4 = Algebra 2

UB GMP 5 = Calc. 1 and Calc. 2

UB GMP 6 = Calc. 3 and Linear Algebra**2. If a student is enrolled in UB GMP and enrolled in an “aligned” math course, which course counts?**

Districts who partner with UB GMP are required to “accept the University coursework in place of the home school mathematics curricula.” In other words, UB’s math courses are designed to supplant the district’s math courses; nevertheless, Williamsville does permit UB GMP students the opportunity to simultaneously enroll in a district math course that is considered to be aligned to UB’s courses. The district, however, does not permit any form of course auditing (see the “Grade Point Average” section in the course catalog); thus, the student will receive grades for both the aligned GMP course(s) and grades from any Williamsville course(s), and all course grades will be averaged into the student’s GPA and appear on one’s transcript. Students will also receive one NYS seat credit for each of the two aligned courses.

For more information, please visit: http://giftedmath.buffalo.edu/