Upper School

Mathematics

Exploration plays a central role in the acquisition of strong, flexible reasoning abilities. Mathematicians explore ideas, make conjectures, describe patterns, construct rigorous arguments, verify results, and communicate their findings both orally and in writing. The goal of the Ellis mathematics department is to develop these skills in our students. Reading and writing mathematics is also an integral part of doing mathematics. In solving problems, students learn that a lucid explanation is as important as a brilliant insight.   

Our intention is for students to appreciate the place of mathematics in our understanding of the world. Contextual problems allow students to see the power of mathematics in wide-ranging applications. But we also see mathematics as worth doing in its own right. It is a beautiful mode of thought and an unparalleled way to stretch our minds. Doing mathematics empowers girls in every area of life.

Mathematics Curriculum

List of 11 items.

  • Algebra I

    Grade 9

    This course is the foundation of all future mathematical study. Topics include both algebraic and graphical work with linear equations and inequalities, systems of equations, quadratic equations, rational equations, polynomials, radicals, and variation. The application of concepts is emphasized in this course.
  • Geometry

    Grades 9-10

    Using a guided-discovery approach, students in this course use compass and straightedge or dynamic geometry software to explore properties, find connections and relationships, and make and test conjectures. Emphasis is on the process of problem solving rather than simply the solutions to problems. A deep understanding is fostered through the inductive approach and is then strengthened through deductive reasoning and proof writing. Topics include angle relationships, constructions, plane figures, circles, the Pythagorean Theorem, similarity, area, and volume.

    Prerequisite: Algebra I
  • Algebra II

    Grades 9-11

    This course begins with review and extension of topics covered in Algebra I such as systems of equations and quadratic equations with particular attention to the concept of functions. Additional topics include systems of inequalities, polynomial, radical, rational, quadratic, exponential and logarithmic functions.

    Prerequisite: Geometry
  • Algebra II BC

    Grades 9-11

    Algebra II BC
    | 1 credit | grades 9–11| by permission of instructor
    This course is an accelerated study of Algebra II topics with little initial review of Algebra I.  All topics covered in Algebra II are covered, and topics such as polynomial, exponential, logarithmic, and rational functions and conic sections are explored in greater depth than they are in Algebra II.  If time permits, topics in trigonometry are introduced.

    Prerequisite: Geometry
  • Precalculus/Trigonometry

    Grades 9-12

    This course is an in-depth study of various types of functions, with particular attention devoted to polynomial, rational, exponential, logarithmic, and trigonometric functions. The study of trigonometry includes the circular functions, right and oblique triangles, and inverse trigonometric functions. Additional topics may include sequences and series. This course is designed to give students a thorough background for further study of mathematics, especially Calculus.

    Prerequisite: Algebra II or Algebra II BC
  • Precalculus/Introduction to Calculus BC

    Grades 9-12

    During the first part of this course, the study of functions important in calculus––including polynomial, rational, exponential, and logarithmic functions––will be continued. Knowledge of right triangle trigonometry is assumed and is built upon during the study of circular functions and inverse trigonometric functions. Applications of trigonometry include oblique triangles, vectors, and complex numbers. During the third trimester, single-variable differential calculus is introduced. Major topics include limits and the derivative.

    Prerequisite: Algebra II BC
  • Calculus

    Grades 11-12

    This course provides an introduction to the study of calculus, covering single-variable differential and integral calculus. Topics include limits, the derivative, the indefinite and definite integral. Emphasis is placed on the applications of the derivative and the integral. As this is not an AP course, the depth and breadth of coverage is influenced by the needs and interests of the students enrolled. This course is appropriate for students who wish to take a challenging, yet non-AP Calculus course.

    Prerequisite: Precalculus/Trigonometry
  • AP Calculus AB

    Grades 11-12

    This course covers single-variable differential and integral calculus. Topics include limits, the derivative, applications of the derivative, the indefinite and definite integral, the Fundamental Theorem of Calculus, applications of the integral, and separable differential equations. The ability to shift fluidly between analytic, graphical, numerical, and verbal approaches is further developed. Students are required to take the AP Calculus AB examination in May.

    Prerequisite: Precalculus/Trigonometry or Precalculus/Introduction to Calculus BC
  • AP Calculus BC

    Grades 11-12

    This course covers single-variable differential and integral calculus, first order differential equations, series, and the calculus of vector-valued functions. An understanding of limits and the derivative is assumed. Topics include applications of the derivative, the definite integral, the Fundamental Theorem of Calculus, applications of the integral, separable differential equations, parametric and polar equations, and series. The ability to shift fluidly between analytic, graphical, numerical, and verbal approaches is further developed.  Students are required to take the AP Calculus BC examination in May.

    Prerequisite: Precalculus/Introduction to Calculus BC or AP Calculus AB
  • Multivariable Calculus

    Grades 11–12

    Multivariable Calculus builds on students' work in differential and integral calculus in AP Calculus BC and AP Calculus AB. No longer limited to working with just two variables (a dependent and an independent variable), students are provided the opportunity to apply the calculus to functions in three + dimensions. Topics of study include vector-valued functions, partial derivatives, multiple integrals, and various applications of vector calculus. Within this course, students are also introduced to contextualized problem solving via mathematical modeling. In this course, students engage in the process of operationally defining abstract concepts, identifying causal variables, building an interpretive model, and analysis of results.
     
    Prerequisite: AP Calculus AB or AP Calculus BC
  • Statistics

    Grades 10-12

    This course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploratory analysis of data, planning a study in order to collect data, anticipating patterns, and statistical inference. Computer applications are used extensively throughout the course.

    Prerequisite: Algebra II or Algebra II BC