This course introduces geometric concepts through an inductive approach, observing patterns and drawing conclusions. Students build on previous algebraic skills to strengthen their conceptual understanding of mathematics and apply them to geometrical concepts. Students formulate definitions and conjectures involving polygons, circles, three-dimensional figures, parallel and perpendicular lines, congruence and similarity, area and volume, the Pythagorean Theorem, coordinate geometry, and right triangle trigonometry. Students also have the opportunity to explore the deductive structure of mathematics and apply mathematical concepts to the physical world. 

5 periods/cycle   

Full-year course – 4 credits

Prerequisite(s): Algebra I or the equivalent and permission of the department   

This course explores the nature of spatial relationships and the properties of certain geometric figures while helping students understand the nature of an axiomatic deductive system.  Students study the role of postulates, definitions, and theorems, analyze classical proofs, and learn how to write original proofs. Geometric topics studied include: triangles, quadrilaterals, polygons, circles, basic three dimensional shapes, parallel and perpendicular lines, congruence and similarity, area and volume, the Pythagorean Theorem, and an introduction to right triangle trigonometry. Continued algebra review is integrated into various geometric concepts.  Applications to the physical world are included where appropriate.

Full year course – 4 credits
Prerequisite(s): Algebra I or the equivalent and permission of the department                                                                                                              

5 periods/cycle   

Full year course – 4 credits
Prerequisite(s): Algebra II/Trigonometry or the equivalent and permission of the department

The purpose of Precalculus is to prepare students for a rigorous approach to calculus in terms of dexterity with relevant algebraic and trigonometric skills and in terms of mathematical reasoning and problem-solving capabilities. Various functions are introduced, and an exploration of the properties of their graphs is included. Some topics studied in depth are analytic geometry, linear regressions, trigonometric and circular functions, exponential and logarithmic functions, polynomial and rational functions, continuity, and limits. 

5 periods/cycle   

Full-year course – 4 credits 

Prerequisite(s):  Algebra II/Trigonometry or Algebra II/Trigonometry A and permission of the department          

This year-long course will help students build a foundation from which they will be prepared to take an introductory college calculus course.  Course topics include limits, continuity, derivatives, differentiation, and integration; this narrow focus allows students to work at a supportive pace.  May include mathematical applications through the lens of business, physics, and more.  Students will be assessed via traditional assessments as well as self-paced and collaborative projects.  

5 periods/cycle   

Prerequisite(s): Precalculus A, Precalculus or Applied Precalculus and permission of the department

This course will cover all of the main topics included in the first semester of college calculus. Students will be able to dive more deeply into the main concepts learned in a traditional calculus class. Subject matter covered in the first semester of the course will include functions and graphs, limits and continuity, the definition of a derivative, analyzing derivative graphs and differentiating basic functions. Subject matter covered in the second semester will include antiderivatives, evaluating basic integrals, applications of the definite integral limited to particle motion, net change, area and volume. The students will be introduced to differential equations and slope fields. There will be no required time outside of class for students to take tests.

 

5 periods/cycle 

Full year course – 4 credits

Prerequisite(s): Precalculus A or Precalculus and permission of the department

The course begins by revisiting and extending topics from the Advanced Calculus I & II curriculum including numerical integration, techniques of antidifferentiation, differential equations, polar and parametric functions, and Taylor series.  Students learn about vector geometry and cylindrical and spherical coordinates, and the calculus of multivariable functions, including partial derivatives, the gradient, double and triple integrals, line and surface integrals, Green’s Theorem, and Stokes’ Theorem.  The syllabus covers the topics in a standard multivariable course.

 

5 periods/cycle   

Full-year course – 4 credits

Prerequisite(s): Advanced Calculus I & II or the equivalent and permission of the department

This course will develop the statistical skills needed to explore important social problems quantitatively.  Students will learn how to perform exploratory data analysis to detect patterns in data sets. They will learn how sampling distributions work in order to conduct and analyze surveys.  Students will gain an understanding of confidence intervals as they learn ways to reduce the margin of error. Students will research the impact of the Great Migration of Americans from the south to the north during the 20th Century by working with census microdata.  Linear regression models will be utilized to explore numerical relationships that describe social concerns such as racism, healthcare inequity, prison reform, environmental climate change and military spending.  Though we will extend some of the skills learned in Epidemiology, students who haven't taken the first semester Statistics course will be brought up to speed in the first two weeks.

 

5 periods/cycle

One semester course (Spring) – 2 credits                                                             

Prerequisite(s): Algebra II/Trigonometry or permission of the department

This challenging course in statistics follows the curriculum covered in a college level statistics and data science course. The course includes an solid introduction to R programming, data visualization, descriptive statistics and the basics of statistical modeling (e.g. one-way ANOVA and simple regression). The approach to inferential statistics is grounded in simulation, randomization and bootstrapping. Students perform frequent projects that include bivariate and multivariate models. Students will learn to apply statistical methods appropriately while refining their communications skills. 

5 periods/cycle   

Full year course – 4  credits                                                                                                               

Prerequisite(s): Permission of the department 

This course will explore two-dimensional representations of our three-dimensional world. Students will create hand-drafted maps, work with physical maps, and utilize digital maps to create their own maps of New York City. Students will gain an understanding of geographic information systems (GIS) and learn how to create geographic databases used to analyze important issues such as climate change, social inequities, or the future of our city.

Students will build on the mathematical foundations of geometry and trigonometry to learn basic concepts of spherical trigonometry, Non-Euclidean geometries, and graph theory. A review of similarity and an introduction to projections from the spheroid Earth to two-dimensional maps are integral components of the course. 

This class could serve as a senior project class.

5 periods/cycle

One-semester course  – 2 credits                                                             

Prerequisite(s): Algebra II/Trigonometry and permission of the department