Upper School Curriculum

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Mathematics

More so than most other disciplines, mathematics is a sequential subject. Each semester builds upon the work of the previous semester, adding new concepts and approaches with a minimum reinforcement of previous knowledge. Therefore, the Mathematics Department believes that students should have a strong problem-solving ability. Tests or homework assignments that require only multiple-choice answers are not an acceptable assessment tool in mathematics. At least half of the test or homework assignment must require students to show work, and the teachers grade the work, not just the answer.
The Mathematics Department recognizes the importance of having students work with data throughout the curriculum. In many courses, students are given the opportunity to learn about the modeling of functions by using data taken from real world situations. The students will learn how to apply “continuous mathematics” to data taken from disciplines including science, politics, and current events.
The Mathematics Department offers a sequence of rigorous courses that cover traditional college preparatory material. At the same time, Benjamin recognizes that all students do not acquire mathematical skills at the same rate or develop the ability for abstract thinking at the same age. There is no 9th grade mathematics course, for instance; rather, our offerings provide a variety of placement options at a given grade level. The goal of placement decisions is to offer all students a course that challenges them and allows them to take risks, but at the same time provides a reasonable opportunity to experience the satisfaction of success.
Students need to have a TI-84 graphing calculator starting with geometry. The aim of the department is to use the calculator as a tool in learning, not merely to get an answer. Teachers place an emphasis on number sense and the ability to solve problems without the calculator. Students must do a problem analytically, then check their work with a calculator, or they can do the problem using a calculator, then show analytically that the answer is correct. The Mathematics Department does not believe in advancing students beyond their ability level. The foundations of algebra and geometry are essential for a good math program. Pushing students too quickly through these basic courses does not make them better mathematicians. Rather it tends to frustrate the student and destroys the love of mathematics and learning. The aim of the Mathematics Department is to produce students with a strong mathematics and problem-solving background. Students must earn four credits in mathematics while in the high school to be eligible for graduation. As part of their math curriculum either in middle school or high school, they must have had Algebra I, Algebra II, and Geometry. See the chart below for guidance.
  • Algebra I

    Algebra I                                                                                                Full Year; 1 Credit
    This course focuses on reinforcement and expansion of real number properties and operations, solutions to linear equations and inequalities, solution and factoring of quadratics, polynomials and irrational numbers. Problem-solving practice is extensive.
    Prerequisite: 8th Grade Pre-Algebra or Eighth Grade Algebra.
  • Geometry

    Geometry                                                                                         Full Year; 1 Credit
    Students in this class investigate logical structures involving the major postulates and theorems of Euclidean Geometry. The class studies coordinate geometry and non-Euclidean geometries. Students apply trigonometric concepts to appropriate facets of geometry. Students are recommended to have a TI-84 graphing calculator. 
    Prerequisite: Algebra I


     
  • Honors Geometry

    Honors Geometry                                                                                  Full Year; 1 Credit
    This rigorous course in geometry integrates coordinates and transformations with a traditional approach to 2-dimensional and 3-dimensional Euclidean geometry.  We will use a variety of methods to prove geometric theorems. We approach and solve problems from different perspectives to gain an appreciation of the interconnectivity among concepts in mathematics. Students will use writing to develop their understanding of geometry by applying concepts to their own experiences and constructing meaning for mathematical symbols, procedures and concepts.  The course will incorporate technology regularly to strengthen and explore geometric properties.  The ability to absorb and master large amounts of material quickly and with little review is essential.  Students are required to have a TI-84 graphing calculator.
    Prerequisite: Algebra I Honors with a grade of at least a B.
  • Algebra II with Data Analysis

    Algebra II with Data Analysis                                                                 Full Year; 1 Credit
    This course includes a study of functions (linear, quadratic, polynomial, and rational), systems of equations in two and three variables, inequalities and complex numbers, variation, conic sections, exponential and logarithmic functions, and trigonometric functions.  The focus is on the representation of problems algebraically, numerically and graphically.  Applications include an introduction to data analysis and modeling through the introduction of regression analysis. Students are required to have a TI-84 graphing calculator.
    Prerequisites:
    Honors Algebra 1 and Honors Geometry with a grade of at least a B or Geometry and Algebra 1 with an A AND departmental approval.

  • Honors Algebra II with Data Analysis

    Honors Algebra II with Data Analysis Honors                                     Full Year; 1 Credit
    This second-year algebra course consists of a thorough and fast-paced study of algebra and an extensive study of trigonometry.  Its emphasis is on the structure of mathematical systems and their underlying concepts.  The focus is on the representation of problems algebraically and graphically.  Topics include a study of functions (linear, quadratic, polynomial, and rational), systems of equations in two and three variables, inequalities and complex numbers, variation, conic sections, exponential and logarithmic functions, and trigonometric functions.  Applications include an introduction to data analysis and modeling through the introduction of regression analysis.  Strong algebraic skills are presumed.  The ability to absorb and master large amounts of material quickly and with little review is essential for success in an honors course.  Students are required to have a TI-84 graphing calculator.
    Prerequisites: Geometry and Algebra 1 with an A or Honors Geometry with a grade of at least a B.
  • College Algebra with Trigonometry

    College Algebra / Trigonometry                                                          Full Year; 1 Credit
    The purpose of this course is to enable students to develop their mathematics knowledge and skills in algebra, trigonometry and using functions as a unifying theme.  Concepts will include the better understanding of graphs, polynomial and rational functions. An introduction of topics will include trigonometric and circular functions, exponential and logarithmic functions.  Students are required to have a TI-84 graphing calculator.
    Prerequisite:  Algebra II
  • Statistical Thinking

    Statistical literacy has become an important part of everyday life. Every time you open the newspaper, turn on the radio or watch television, you are bombarded with data.  This one-semester class is an introduction to the concepts and methods necessary to become a statistical thinker. Topics include graphical and numerical methods for summarizing data; normal probability distributions; point and interval estimates for means and for proportions; one- and two-sample tests for means and for proportions; principles of experimental design. Randomization tests will be introduced as an alternate way to test hypotheses.  The class emphasizes the use of the computer for analysis of data.  This course serves as the first semester of mathematics for those students enrolled in Finite Mathematics but is open anyone who would like to learn about statistics.  Students are required to have a TI-84 graphing calculator.

    Prerequisite:  Algebra II
  • Pre-Calculus

    Pre-Calculus                                                                                          Full Year; 1 Credit
    This rigorous course prepares students for study of calculus. Functions are emphasized, including polynomial and rational, circular (trigonometric), exponential, and logarithmic functions. Other topics may include matrices and determinants, sequences and series, the binomial theorem, and limits. A strong recall and working knowledge of Geometry and Algebra 2 and Trigonometry are essential for success in this class.  The course provides continued development of analytical geometry and a comprehensive review of Algebra II. Students need to have a TI-84 graphing calculator. 
    Prerequisite: Algebra II with a grade of at least a B
  • Statistics

    Statistics                                                                                                 Full Year; 1 Credit
    The purpose of this year-long course in statistics is to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to four broad conceptual themes:
    1. Exploring Data: Describing patterns and departures from patterns
    2. Sampling and Experimentation: Planning and conducting a study
    3. Anticipating Patterns: Exploring random phenomena using probability and simulation
    4. Statistical Inference: Estimating population parameters and testing hypotheses
    Students must have a TI-84 graphing calculator.
    Prerequisite:
    Pre-Calculus or College Algebra.  Can be taken concurrently with Pre-Calculus.  This course is NOT to be used to prepare students for AP Statistics.

  • Honors Pre-Calculus

    Honors Pre-Calculus                                                                           Full Year; 1 Credit
    This course includes an extensive study of trigonometric, exponential, and logarithmic functions. Particular attention is paid to the properties of their graphs. Other topics include polynomials, analytic geometry, matrices and determinants, sequences and series, the binomial theorem, polar coordinates, and probability. During the fourth quarter, students begin their formal study of calculus including limits, continuity, and derivatives. The ability to absorb and master large amounts of material quickly and with little review of Geometry and Algebra 2 and Trigonometry is essential.  Students will continue their study of calculus in Advanced Placement Calculus AB the following year.  Students need to have a TI-84 graphing calculator.
    Prerequisite:  Algebra II Honors with a grade of at least a B.
  • Honors Calculus

    Honors Calculus                                                                                    Full Year; 1 Credit
    This course provides students with an intuitive approach to the fundamentals of differential calculus and integral calculus. The language of calculus will play an important role in developing the definitions of derivatives and integrals.  Focusing on algebraic functions, students explore limits, leading to the definition of derivative. The concepts of average and instantaneous rate of change are investigated. We develop the rules of differentiation, including the chain rule and implicit differentiation, and apply them to problems in optimization, related rates, and curve sketching. We will introduce the concepts of finding area under a curve, the integral regarded as the antiderivative, and the Fundamental Theorem of Calculus. Applications of integration are also included.   Students are required to have a TI-84 graphing calculator.
    Prerequisite: Pre-Calculus with a grade of at least a B or Honors Pre-Calculus.
  • AP Calculus AB

    AP Calculus AB                                                                                       Full Year; 1 Credit
    This course is a study of the basic concepts of differential and integral calculus, including methods and applications. The teacher uses a multi-representational approach with concepts, results, and problems being expressed geometrically, analytically, and verbally. This is a college-level course as determined by the College Board. Topics covered include, but are not limited to differentiation, integration, and volume of solids of revolution. Students may earn one semester of college credit in calculus. Students must have a TI-84 Plus (or better) graphing calculator and must take the College Board AB Calculus exam.
    Prerequisite: Honors Pre-Calculus or Honors Calculus with a grade of at least a B.
     
  • AP Calculus BC

    AP Calculus BC                                                                                    Full Year; 1 Credit
    Students in this course continue their study of calculus begun in AP Calculus AB and complete their preparation for the BC level of the Advanced Placement examination in calculus to be taken in the spring. Coverage includes integration by parts and by partial fractions, improper integrals, first order separable differential equations, infinite series and power series, and parametric and polar coordinates.  Students will then continue their study of mathematics by extending their knowledge to the calculus of three-dimensional space. Students must have a graphing calculator (TI-84 Plus) and must take the College Board BC Calculus exam at the end of the year. 
    Prerequisite: Completion of AB Calculus along with a 3 or higher on the Calculus AB AP exam.  Student course placement might be modified over the summer due to Calculus AB AP exam score.
  • AP Statistics

    AP Statistics                                                                                         Full Year; 1 Credit
    The course follows the syllabus for the Advanced Placement Examination in Statistics. Students study the tools for collecting, organizing, and displaying data. They learn about planning and conducting surveys and experiments and drawing conclusions from their results. The course includes probability, the properties of the normal distribution, and statistical inference. Students must have a TI-84 (or better) graphing calculator and are required to take the College Board AP Statistics exam.
    Prerequisite: Honor Pre-Calculus with a grade of at least a B.
  • AP Pre-Calculus

    AP Pre-Calculus Full Year; 1 Credit
    This course includes an extensive study of trigonometric, exponential, and logarithmic functions. Particular attention is paid to the properties of their graphs. Other topics include polynomials, analytic geometry, matrices and determinants, sequences and series, the binomial theorem, polar coordinates, and probability. During the fourth quarter, students begin their formal study of calculus including limits, continuity, and derivatives. The ability to absorb and master large amounts of material quickly and with little review of Geometry and Algebra 2 and Trigonometry is essential.  Students must have a TI-84 Plus (or better) graphing calculator and must take the College Board AP Pre-Calculus Exam.
    Prerequisite:  Algebra II Honors with a grade of at least a B.
  • Euclidean Geometry

    Students in this class investigate logical structures involving the major postulates and theorems of Euclidean Geometry. The class studies coordinate geometry and non-Euclidean geometries. Students apply trigonometric concepts to appropriate facets of geometry. Students are recommended to have a TI-84 graphing calculator by second semester. 

    Prerequisite: A grade of at least a B+ in Algebra 1 and teacher recommendation.
  • Multivariable Calculus

    Multivariable Calculus                                                 One Semester (Spring); ½ Credit
    This is an honors course in Calculus III.  Students will learn various skills involving functions of several variables, multiple integration and some vector analysis.  Topics include, but are not limited to, limits and continuity, partial derivatives, directional derivatives, gradients and finding extrema of functions of two variables.  Green’s, Stoke’s, and Gauss’ theorems will be discussed and learned. There is no AP test for this course. 
    Prerequisite: Completion or currently taking AP Calculus BC with a grade of at least a B.

Department Faculty

A premier PK3 - Grade 12 independent, coeducational day school with campuses in North Palm Beach and Palm Beach Gardens. Since 1960, The Benjamin School has provided a challenging college preparatory education to a diverse student body in a structured, nurturing community environment.
 
After hours emergency contact:
Leslie Downs/Chief Operating Officer
Ph:  561.657.0075 or 561.747.0585