# Math

The mission of the CSS math department is to introduce students to the power, beauty, and joy of mathematics. All students enter an accelerated course sequence that begins in sixth grade and continues through all four years of high school. Middle school culminates in Algebra I, and high school students complete their course of study with AP Calculus or advanced coursework at Columbia University. Throughout their time at CSS, students apply their mathematical knowledge in concurrent science and engineering classes. Successful CSS math students are well-prepared for undergraduate-level work in a variety of quantitative and technical fields.

Course Name | Grade Level | Course Description | Prerequisites and Credit Granted |
---|---|---|---|

6th Grade Math | 6 | This year-long course is the first part of a two year in-depth investigation of the fundamentals of arithmetic and geometry that will lead to a student proficiency level sufficient for entrance to introductory algebra in the eighth grade. | This is a required course in the 6th Grade sequence. All students will take the 6th Grade State Math Exam as an assessment of their proficiency. |

7th Grade Math | 7 | 7th grade math helps students solidify the foundational skills that will help them in the following year’s Algebra I course. Students build on basic concepts used in 6th grade to partake in a more in depth study of topics such as rational numbers, integers, scientific notation, exponents, proportionality, geometric transformations, and statistical analysis. Students also learn some of the basics of algebra, such as solving equations and inequalities, in preparation for the following year. This course is aligned to the Common Core Learning Standards and includes topics from both 7th and 8th grade so that students are prepared to take the high school Algebra I course as 8th graders. |
Prerequisite: 6th Grade Math This is a required course in the 7th Grade sequence. All students will take the 7th Grade State Math Exam as an assessment of their proficiency. |

Algebra I | 8 | Algebra I is a high school level course that is combined with some 8th grade concepts to create an accelerated class that allows students to be one year ahead in the high school math sequence. The majority of the course builds on students’ basic algebra skills to provide an in depth study of linear functions, equations, and inequalities. Students are also introduced to other types of functions in preparation for further study of algebra in high school. |
Prerequisite: 7th Grade Math This is a required course in the 8th Grade sequence. All students will take the Algebra I Regents exam as an assessment of their proficiency. Students who pass the Algebra I Regents will gain two high school credits and will advance to Geometry in the 9th Grade. Students must accumulate 8 credits in math for a CSS diploma. |

Geometry Elective This course is an elective and may or may not be offered, depending on a sufficient number of interested and qualified students and sufficient funding. |
8 | In 8th grade, a select number of students qualify to take Geometry in addition to Algebra I. This elective class is scheduled during the after-school elective period, not during the regular school day. See 9th Grade Geometry course for course description. |
Prerequisite: Teacher recommendation; Math grade point average above 90. Must be concurrently programmed into Algebra I. This is an elective course in the 8th Grade sequence. All students will take the Geometry Regents exam as an assessment of their proficiency. Students who pass both the Geometry Regents and the Algebra Regents will gain four high school credits and will advance to Algebra II in the 9th Grade. Students must accumulate 8 credits in math for a CSS diploma. |

Geometry | 9 | Geometry begins with a minimal number of assumptions and builds up the system of Euclidean geometry through rigorous proof. This process allows students to study mathematics in its purest form. Euclidean geometry will include the study of points, lines, angles, and polygons. Through formal geometric proof and justification, students will be exposed to careful logical reasoning. In addition to Euclidean geometry, students will study topics such as logic, construction, coordinate geometry, three-dimensional figures, transformations, and loci. This course culminates in a New York State Regents Examination. |
Prerequisite: Algebra I course credit This is a required course in the High School sequence. All students will take the Geometry Regents exam as an assessment of their proficiency. Students who pass the course will gain two high school credits and will advance to Algebra II in the 10th Grade. Students must accumulate 8 credits in math for a CSS diploma. |

Algebra 2 and Trigonometry Elective. This course is an elective and may or may not be offered, depending on a sufficient number of interested and qualified students and sufficient funding. |
9-10 | A select number of students may qualify to take Algebra II/Trig as an elective in addition to their Geometry Class. This elective class is scheduled during the after-school elective period, not during the regular school day. See Algebra II/Trig course for course description. |
Prerequisite: Teacher recommendation; Math grade point average above 90. Must be concurrently programmed into Geometry. This is an elective course in the high school sequence. All students will take the Algebra II/Trig Regents exam as an assessment of their proficiency. Students who pass both the Geometry Regents and the Algebra II/Trig Regents will gain four high school credits and will advance to PreCalculus in the 10th Grade. Students must accumulate 8 credits in math for a CSS diploma. |

Algebra 2 and Trigonometry | 9-11 | Algebra 2 and Trigonometry builds on students' knowledge of algebra and linear functions to develop a strong understanding of algebra, as well as functions and relations. Students will delve into polynomial, radical, rational, absolute value, exponential, logarithmic, and trigonometric functions. Introductions to complex numbers, sequences, series, combinatorics, probability, and statistics are also included. This course culminates in a New York State Regents Examination. |
Prerequisite: Algebra I and Geometry course credit. This is a required course in the High School sequence. All students will take the Algebra II/Trigonometry Regents exam as an assessment of their proficiency. Students who pass the course will gain two high school credits and will advance to PreCalculus in the 11th Grade. Students must accumulate 8 credits in math for a CSS diploma. |

Pre-Calculus | 10-12 | Pre-Calculus builds on students' knowledge of algebra, functions, and trigonometry with the goal of giving students a strong foundation for the study of calculus. Students will delve into a variety of advanced mathematical topics, including limits, graphing and analyzing rational functions, synthetic division, conic sections, matrices and systems of equations, mathematical induction, exponential growth, polar coordinates, sequences and series, basic interest theory, and vectors. |
Prerequisite: Algebra I, Geometry and Algebra II/Trig course credit This is a required course in the High School sequence. Students who pass the course will gain two high school credits and will advance to Calculus in the 12th Grade. Students who earn distinction in this course may earn the opportunity to begin the Calculus sequence at Columbia University and earn college credit. Students must accumulate 8 credits in math for a CSS diploma. |

Calculus | 11-12 | Calculus uses limits to study the infinitely small so that we can look at the instantaneous rate of change of and the area underneath a function. In addition to mathematics, calculus is essential for the in-depth analysis of various fields of study such as physics and economics. In Calculus I, after a thorough introduction to limits, students will learn and apply differential and integral calculus in one variable. Calculus I is a full-year course that will prepare students for a standard Calculus II course. This course does not provide college credits. |
Prerequisite: Algebra I, Geometry, Algebra II/Trig and Pre-Calculus course credit This is a required course in the High School math sequence. Students who pass the course will gain two high school credits. Students who earn distinction in this course may earn the opportunity to join the Calculus sequence at Columbia University and earn college credit. Students must accumulate 8 credits in math for a CSS diploma. |

Calculus I CU | 11-12 | See Columbia University Course Catalog |
Prerequisite: Pre-Calculus course credit and qualification based on academic review and criteria for entry to CU courses (see CU Course Catalog for further description). This is an elective course in the High School math sequence. Students will earn both high school and college credit for this class. |

Calculus II CU | 11-12 | See Columbia University Course Catalog |
Prerequisite: Calculus I course grade of B or better and qualification based on academic review and criteria for entry to CU courses (see CU Course Catalog for further description). This is an elective course in the High School math sequence. Students will earn both high school and college credit for this class. |

Calculus III CU | 11-12 | See Columbia University Course Catalog |
Prerequisite: Calculus II course grade of B or better and qualification based on academic review and criteria for entry to CU courses (see CU Course Catalog for further description). This is an elective course in the High School math sequence. Students will earn both high school and college credit for this class. |

Calculus IV CU | 11-12 | See Columbia University Course Catalog |
Prerequisite: Calculus III course grade of B or better and qualification based on academic review and criteria for entry to CU courses (see CU Course Catalog for further description). |

Introduction to Statistical Reasoning CU | 11-12 | See Columbia University Course Catalog |
Prerequisite: Algebra II/Trig course grade of 90 or better and qualification based on academic review and criteria for entry to CU courses (see CU Course Catalog for further description). |

Introduction to Statistics 1111 CU | 11-12 | See Columbia University Course Catalog |
Prerequisite: Precalculus course grade of 90 or better and qualification based on academic review and criteria for entry to CU courses (see CU Course Catalog for further description). |

Introduction to Statistics 1211 CU | 11-12 | See Columbia University Course Catalog |
Prerequisite: Calculus II CU course grade of B or better and qualification based on academic review and criteria for entry to CU courses (see CU Course Catalog for further description). |

Introduction to Higher Mathematics CU | 11-12 | See Columbia University Course Catalog |
Prerequisite: Calculus III CU course grade of B or better and qualification based on academic review and criteria for entry to CU courses (see CU Course Catalog for further description). |

Linear Algebra CU | 11-12 | See Columbia University Course Catalog |
Prerequisite: Calculus III CU course grade of B or better and qualification based on academic review and criteria for entry to CU courses (see CU Course Catalog for further description). |

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