Morristown-Beard Upper School Curriculum

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Upper School Mathematics Curriculum

Morristown-Beard School's mathematics department strives to produce students fluent in quantitative reasoning who can both do and communicate mathematics. We emphasize connections within and beyond mathematics, while ensuring that students develop the mathematical tools and problem solving skills they will need in the future.




Note: All three levels of Integrated Math employ the Earned Honors model. Click here for a full description of the process.


Integrated Math 1

Instructor: Math Department Staff

Prerequisites:

Required

Open to students in the following grades: 9

Full Year Course

Math 1 initiates the Integrated Math sequence by engaging students in foundational concepts, skills and habits of thought. Pedagogical techniques are eclectic and diverse to allow for different ways of learning math. With a focus on the algebraic, the course also employs geometric, numeric and verbal approaches. Physical manipulatives play a large role in helping students make visual connections to arithmetic and algebraic concepts. Principal topics covered through problem solving and exploration include number sense (large and small numbers, estimation, opposites, reciprocals), data analysis with linear and quadratic equations, and polynomials. Students also begin to learn foundational geometric concepts such as triangle relationships, transformations, and congruence.

Integrated Math 2

Instructor: Math Department Staff

Prerequisites: Integrated Math 1 or equivalent

Required

Open to students in the following grades: 9, 10

Full Year Course

Integrated Math 2 continues the Integrated Math sequence by building on the foundational concepts acquired in Math 1. Students will encounter thought-provoking problems in a variety of contexts that require strong connections between algebra and geometry. Principle topics covered through problem solving and exploration include right triangle trigonometry, quadratic functions, methods of proof, polygons, transformations, and rational expressions. Each topic requires an added level of sophistication and abstraction as students obtain a higher level of mathematical fluency.

Integrated Math 3

Instructor: Math Department Staff

Prerequisites: Integrated Math 2 or Geometry and Algebra 2

Required

Open to students in the following grades: 9, 10, 11

Full Year Course

Integrated Math 3 completes the Integrated Math sequence by building on the foundational concepts acquired in Integrated Math 2. The central theme of learning mathematics through problem solving and exploration continues in Math 3. Principle topics covered include polynomial functions, rational functions, and circles. Exponential and logarithmic functions are also in studied in depth. Many of these topics were already introduced in Math 1 and Math 2, and Math 3 adds another layer of depth and rigor to their study, and focuses on connecting these topics to other mathematical concepts.

Function Analysis and Trigonometry

Instructor: Department Staff

Prerequisites: Integrated Math 3

Open to students in the following grades: 11, 12

Full Year Course

This course acts as a bridge between Integrated Math 3 and Calculus. Over the course of the Integrated math sequence, students are introduced to the major function classes and the fundamental concepts of geometry. In this course students will aggregate their knowledge thus far to analyze these functions at a higher level in preparation for Calculus. The course emphasizes graphing and transformations of each function type. Great attention is paid to trigonometric functions, identities, proofs, and equations.

Mathematical Analysis (Honors)

Instructor: Department Staff

Prerequisites: Completion of Integrated Math 3 with Honors and teacher recommendation

Open to students in the following grades: 10, 11, 12

Full Year Course

This Honors level course begins with a rigorous study of rational functions, at which point the concept of limits is introduced. This fundamental building block of Calculus is incorporated throughout the year as other transcendental function classes are explored, including exponential, logarithmic, and trigonometric functions. Topics emphasized in preparation for AP Calculus include sequences and series, as well as parametric and polar equations. Students wishing to pursue this course have impeccable algebra skills, strong geometric reasoning through proof, and an interest in solving unfamiliar problems.

Calculus

Instructor: Math Department Staff

Prerequisites: Functional Analysis and Trigonometry

Not required

Open to students in the following grades: 12

Full Year Course

Topics covered include mathematical modeling, functions (algebraic and transcendental), continuity, limits, differentiation and integration techniques, and applications of the derivative and integral. This course will cover topics approximately equivalent to a one-semester college course in business Calculus.
Note: This course employs the Earned Honors model. Click here for a full description of the process.

AP Calculus AB

Instructor: Math Department Staff

Prerequisites: Mathematical Analysis (Honors)

Open to students in the following grades: 11, 12

Full Year Course

This course follows the syllabus outlined by the College Board and is equivalent to a one-semester college course in Calculus. Topics covered include graphical, numerical, verbal and modeling approaches to all families of functions (algebraic and transcendental). The course covers limits and continuity, differentiation, and integration, along with their applications and a focus on theory. Students are required to take the Advanced Placement Exam in May.

AP Calculus BC

Instructor: Math Department Staff

Prerequisites: Pre-Calculus Honors, recommendation of Pre-Calculus Honors Teacher

Open to students in the following grades: 12

Full Year Course

The course is equivalent to a full-year college course in Calculus. In addition to the AP Calculus AB topics, the course covers advanced integration techniques, sequences and series, vector calculus, logistic, and curves defined in parametric and polar spaces. Students are required to take the Advanced Placement Exam in May.

AP Statistics

Instructor: Math Department Staff

Prerequisites: Integrated Math 3 and recommendation from current Math and Humanities teachers

Open to students in the following grades: 12

Full Year Course

AP Statistics, equivalent to a college-level statistics course, encompasses four major themes: exploratory analysis, experimental design, probability models and statistical inference techniques. Application of technology, including manipulating statistical software, use of the TI-84 calculator and interpreting advanced computer outputs is integral to the course. Along with more traditional modes of math instruction, the course also integrates reading and analysis of scholarly journals as well as Socratic style seminars. Students are required to take the Advanced Placement exam in May.

Statistics and Probability (H)

Instructor: Math Department staff

Prerequisites: Integrated Math 3 and recommendation from current Math teacher

Open to students in the following grades: 12

Full Year Course

This honors course will introduce students to fundamentals of statistics and probability. Descriptive statistics, including the graphic display and numeric analysis of data, is followed by principles of experimental design, empowering students to think critically about data presented in the popular press. The third major component of the course, probability and combinatorics, serves as both a bridge to inferential statistics and a preparation for topics frequently encountered on college entrance exams. Decision-making, quantitative reasoning, and communication are critical elements of inferential statistics, and this course will emphasize and refine those skills. The use of a Statistical software package will be incorporated. Note: students may not enroll in AP Statistics after taking this course.

Semester Electives

Math and Art

Instructor: Math Department Staff

Prerequisites: Integrated Math 2

Open to students in the following grades: 11, 12

Spring Semester

This course is designed to encourage students to explore the many connections between mathematics and art as well as the potential of mathematics to generate aesthetically pleasing visual art. The mathematics of patterns leads students into architecture and design, while geometry produces additional applications to folk art. In addition, linear and atmospheric perspective allow for the representation of proportional relationships to create the illusion of 3-dimensional space. The imagination soars as students consider alternate realities and ambiguous space/surfaces as a basis for the investigation of fractals, polynomiography, and other modes of digital visual art.

World Making

Instructor: Mr. Fedirko

Prerequisites:

Open to students in the following grades: 10, 11, 12

Fall Semester

How can Math help us appreciate and understand aesthetics and design? In this course, students will work at the intersection of math, philosophy, and art to explore the relationship of a whole and its parts, form and function, and what it means for objects and "worlds" to be complete and sufficient in terms of its design and unity. Some of the questions we ask will be abstract, but we will engage with concrete examples, works of art, and individual and collaborative projects. The work will invite you to approach math, and reality, from new perspectives, often opening up new arenas of mathematical thinking from that you have experienced in other classes. All creative, curious, and open-minded students are encouraged to apply.

Probability Theory

Instructor: Math Department Staff

Prerequisites: Integrated Math 2

Open to students in the following grades: 10, 11, 12

Spring Semester

A lot of events in our life seem random or impossible to predict. However, this course will help us solve interesting problems that range from winning the lottery to diagnosing a medical disease. The course will cover basic principles of probability and more advanced topics, theorems and models. The class will provide the tools necessary to see the world in a different way, one that may not always be intuitive, but is supported by mathematics.

Statistics and Data Analysis

Instructor: Math Department staff

Prerequisites: Integrated Math 2

Open to students in the following grades: 10, 11, 12

Offered in the Fall and in the Spring

This course focuses on the statistical thinking behind data gathering and interpretation. This course teaches students to look closely at surveys, election polls, medical studies, and other intriguing examples to understand what the numbers are really saying. Hands on activities help students interpret and communicate statistical information. Students will also learn the workings of spreadsheets as a data analysis tool.

Quantitative Business Analysis

Instructor: Department Staff

Prerequisites: Integrated Math 3

Open to students in the following grades: 12

Offered in the Fall and in the Spring

This semester course is designed for students interested in the field of business. The course serves as a bridge between a college prep mathematics curriculum and a college level business curriculum. Students will learn mathematical principles in a business context and apply those principles to the study of economics, finance, and modeling. The emphasis is on utilizing mathematical tools and interpreting the results to make sound business decisions. Topics covered will include: supply and demand, pricing, the components of profit and loss, breakeven analysis, optimization, exponential growth and decay, compound and simple interest, bond pricing, loan amortization, and an introduction to the financial markets and investments.