Course Search 2022-2023

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Upper School Mathematics Curriculum

Mission Statement: The Mathematics Department produces students fluent in quantitative and abstract reasoning. We emphasize the importance of constructing and evaluating sound arguments while focusing on connections within and beyond mathematics. Within this framework, we aim to cultivate resilience, critical thinking, creativity, and intellectual curiosity.


INTEGRATED MATH PROGRAM
The Integrated Math Program consists of three full year courses: Integrated Math 1, 2 and 3. Combining both traditional and contemporary approaches, this structure represents an evolution in math curriculum design allowing students a much greater opportunity for growth and development in mathematical thinking. In adopting this new program, MBS puts itself squarely in line with state-of-the-art math programs that reflect the professional consensus of the National Council of Teachers of Mathematics Principles and Standards. While the program covers all of the traditional areas (Algebra 1, Geometry, Algebra 2 and Pre-Calculus), Integrated Math blends these different strands of mathematics through each of its three levels and focuses on connections among formerly isolated topics, such as algebra and geometry. This approach reveals a more organic picture of the field of mathematics and fosters deeper insight into its intricacies and beauty. It allows all learners to grasp foundational concepts such as equations, functions and trigonometry through different modes of representation, including graphical, hands-on, geometric, and symbolic. Integrated Math employs the technique of "spiraling" so that each level of the curriculum brings students back through these essential concepts in order to achieve deeper levels of mastery.


Integrated Math 1

Instructor: Math Department Staff

Prerequisites: Intro B or equivalent

Required

Open to students in the following grades: 9

Full Year Course

Integrated Math 1 (IM1) initiates the Upper School math sequence by engaging students in
foundational concepts, skills and habits of thought. The course incorporates both algebraic and geometric elements covering concepts such as logic, algebraic modeling, properties of lines and triangles, systems of equations, and properties of polynomials with factoring. Pedagogical techniques and assessments are diverse to allow for multiple ways of learning and demonstrating mathematical knowledge.

This course employs the Earned Honors model. Click here for a full description of the process.

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 (IM2) continues the Integrated Math sequence by building on the foundational concepts acquired in IM1. Students will encounter thought-provoking problems that require strong connections between algebra and geometry. Topics include applications of systems, behavior of functions, transformations, right triangle trigonometry, and quadratic equations. Each topic requires an added level of sophistication and abstraction as students achieve a higher level of mathematical fluency.

Integrated Math 2 Honors

Instructor: Math Department Staff

Prerequisites: Integrated Math 1H or equivalent

Open to students in the following grades: 9, 10

Full Year Course

Integrated Math 2 Honors (IM2H) continues the Integrated Math sequence by building
on the foundational concepts acquired in IM1. Topics include applications of systems,
behavior of functions, transformations, right triangle trigonometry, and quadratic
functions. These topics will be covered at an increased level of rigor and depth,
requiring students to be independent thinkers who can recognize how to apply existing
skills in unfamiliar contexts. This fast-paced course will require a high level of notational
fluency and a strong foundation of algebraic and geometric concepts.

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 (IM3) completes the Integrated Math sequence by building on the concepts and skills acquired in IM2 while incorporating another layer of depth and rigor. The central theme of learning mathematics through problem solving and exploration continues with topics including a study of polynomial, rational, logarithmic and exponential functions as well as circles and unit circle trigonometry. After successfully completing IM3, students have the background to take a variety of math electives.

Integrated Math 3 Honors

Instructor: Math Department Staff

Prerequisites: Integrated Math 2 Honors or Geometry and Algebra 2

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

Full Year Course

Integrated Math 3 (IM3H) completes the Integrated Math sequence by building on the concepts
and skills acquired in IM2 while incorporating another layer of depth and rigor. The central
theme of learning mathematics through problem solving and exploration continues with topics
including a study of polynomial, rational, logarithmic and exponential functions as well as
circles and unit circle trigonometry. These topics will be covered at an increased level of rigor,
requiring students to be independent thinkers who can recognize how to apply existing skills in
unfamiliar contexts. This fast-paced course will require a high level of notational fluency and a
strong foundation of algebraic and geometric concepts. After

Function Analysis and Trigonometry

Instructor: Department Staff

Prerequisites: Integrated Math 3

Open to students in the following grades: 10, 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 with great attention paid to trigonometric functions, identities, proofs, and equations.

Mathematical Analysis (Honors)

Instructor: Department Staff

Prerequisites: Completion of Integrated Math 3 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 or Mathematical Analysis Honors

Not required

Open to students in the following grades: 11, 12

Full Year Course

Calculus is a continuation of Functions Analysis and Trigonometry or Mathematical Analysis Honors, beginning with a review of precalculus concepts. Topics covered include mathematical modeling, functions (algebraic and transcendental), continuity, limits, differentiation techniques, and applications of the derivative. This course will focus on developing mathematical fluency with an emphasis on application and computation.

Calculus Honors

Instructor: Math Department Staff

Prerequisites: Functional Analysis and Trigonometry or Mathematical Analysis Honors
and teacher recommendation

Open to students in the following grades: 11, 12

Full Year Course

Calculus Honors is a continuation of the Mathematical Analysis Honors course and assumes a strong mathematical background of precalculus concepts. Topics covered include mathematical modeling, functions (algebraic and transcendental), continuity, limits, differentiation techniques, applications of the derivative, integral calculus, and
applications of integration. Students begin the year studying limits and continuity. The focus of the first semester is differential calculus and the second semester is devoted to integral calculus.

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: AP Calculus AB

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 review of 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 Honors 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 graphical 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

Probability Theory (H)

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. We solve interesting problems that range from winning the lottery to the Birthday Paradox. This course will cover basic principles of counting and probability in addition to exploring more advanced topics like using binomial and geometric models used to predict outcomes of random variables. 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 numbers.

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

Statistics focuses on data analysis and interpretation with a focus on real world applications. This course teaches students to be critical thinkers by looking closely at relevant and topical examples to understand what the numbers are really saying, not just what people are telling them the numbers are saying. Hands on activities help students interpret and communicate statistical information both numerically and graphically. Students will also learn how to use technology as a tool for data analysis by using more web based applets. The course starts with foundational statistics including a close look at how statistics can be misleading, then quickly segues to the Normal Model and its applications (such as the Olympics), and finally ends with an introduction to linear regression analysis.

Quantitative Business Analysis

Instructor: Department Staff

Prerequisites: Integrated Math 3

Open to students in the following grades: 12

Fall Semester

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.