Mathematics

The aim of the Mathematics department is to nurture each Forest Ridge student to grow in her knowledge of mathematical content and to deepen her mathematical thinking. We lead students through a curriculum that allows every individual to be challenged to realize her highest mathematical potential, as we recognize that students have differing backgrounds and abilities. Thus, we believe it is essential that each student be placed in the level of mathematics that will provide the appropriate level of challenge.

Mathematics is a global language, and to that end our courses guide students through a global awareness of math through a study of current events through a mathematical lens, hands on projects to demonstrate real world applications, and a variety of cultural views and approaches to math.

2021-2022 Course Offerings

Middle School: 5^th-8^th Grade

Foundations of Math (Grade 5)

Foundations of Math (grade 5)

In this course, we focus on three critical areas:

1. Developing fluency with addition and subtraction of fractions and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions).

2. Extending division to 2-digit divisors, integrating decimal fractions into the place value system, developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations.

3. Developing understanding of volume.

Students develop skills to share their process, rationale, and results with others verbally, visually, and in written form. Work and practice are expected daily. We use an open-source curriculum reflecting national standards and research-based teaching practices to develop strong foundations in problem solving, conceptual understanding, and procedural fluency.

Integrated Mathematics Course 1 (Grades 5, 6)

In this course, emphasis is on building a strong number sense and representing or comparing data visually and mathematically. Concepts include operations with decimals and fractions, ratios and unit rate, graphing on the coordinate plane, measures of central tendency, and area of polygons. Students work individually and in groups to continue to develop problem-solving strategies, mathematical vocabulary and critical thinking skills. Students develop skills to share their process, rationale, and results with others verbally, visually, and in written form. Homework is assigned daily, and quizzes and tests are given at frequent and appropriate intervals throughout each unit. The textbook is Math in Focus (Singapore Math) Course 1. Supplementary notes and activities are provided by the instructor.

Integrated Mathematics Course 2 (Grades 5, 6, 7)

The textbook is Math in Focus (Singapore Math) Course 1. Supplementary notes and activities are provided by the instructor.

Prerequisite: Successful completion of IM1 or placement test

Integrated Mathematics Course 3 (Grades 6, 7, 8)

The emphasis in Course 3 is providing students with the foundation needed for success in algebra 1. Major concepts include an understanding of the rules involved in using exponents, including an understanding of negative exponents, work with algebraic linear equations, including systems of equations and functions and relations. Students work individually and in groups to continue developing problem-solving strategies, mathematical vocabulary and critical thinking skills. Standards also include creating and solving two-step equations to represent real world situations, recognizing independent and dependent values, recognizing functions and relations, and calculating compound probability of events. Homework is assigned daily, and quizzes and tests are given at frequent and appropriate intervals throughout each unit.

The textbook is Math in Focus (Singapore Math) Course 3. Supplementary notes and activities are provided by the instructor.

Prerequisite: Successful completion of IM2 or placement test.

Algebra I (Grades 7, 8)

This is a high-school level course.

Placement in this course requires mastery of the concepts that are emphasized in Course 3. The focus of study is on the manipulation of algebraic expressions, equations, and inequalities together with the application of these skills to problem solving. By the end of the course, students will be able to factor polynomials, graph linear equations, solve systems of linear equations, understand functions, use rational and irrational numbers, solve and graph quadratic equations, and use exponential functions.

Prerequisite: Successful completion of IM3 or placement test

Geometry (Grade 7, 8)

This is a high-school level course. Placement in geometry requires mastery of Algebra 1. Geometry introduces students to the logic of mathematics and the development of formal and informal proofs. Students will study topics in Euclidean Geometry including points, lines, angles, polygons, circles, congruence, similarity, area, volume, and right-triangle trigonometry. This course incorporates the use of coordinate geometry and algebra throughout.

Prerequisite: Successful completion of Algebra I or placement test

Algebra II (Grade 8)

Year-long

The focus of study in Algebra II is families of functions. Students will be able to solve systems of equations and inequalities. Students will understand and transform quadratics, conic sections, polynomial, rational, exponential, and logarithmic functions. Students will also explore sequences, series, probability, and statistics. This course prepares students for Precalculus. Students may complete trigonometry lessons over the summer after 8^th grade and take a placement test to enroll in Precalculus with Analysis in 9^th grade.

Prerequisite: Successful completion of Geometry or placement test

High School: 9^th-12^th Grade

Graduation Requirement: 3.0 credits (6 Semesters), and satisfactory completion of Algebra II

Algebra I

Year-long

The focus of this course is on the manipulation of algebraic expressions, equations and inequalities together with the application of these skills to problem solving. By the end of the course, students will be able to factor polynomials, graph linear equations, solve systems of linear equations, understand functions, use rational and irrational numbers, solve and graph quadratic equations and use exponential functions.

Prerequisites: Performance on placement test,

Department recommendation

Grade level: 9

Credit earned: 1.0 Mathematics

Geometry

Year-long

Geometry introduces students to the logic of mathematics and the development of formal and informal proofs. Students study topics in Euclidean geometry including points, lines, angles, polygons, circles, congruence, similarity, area, volume and right-triangle trigonometry. This course incorporates the use of coordinate geometry and algebra throughout.

Prerequisites: Performance on placement test,

successful completion of Algebra I;

Department recommendation

Grade level: 9, 10

Credit earned: 1.0 Mathematics

Algebra II

Year-long
The focus of study in Algebra II is families of functions. Students will be able to solve systems of equations and inequalities. Students will understand and transform quadratics, conic sections, polynomial, rational, exponential, and logarithmic functions. Students will also explore sequences, series, probabilities, and statistics. This course prepares students for Precalculus.

Prerequisites: Performance on placement test, successful completion of Geometry

Grade level: 9, 10, 11

Credit earned: 1.0 Mathematics

Algebra II & Trigonometry

Year-long

The pace of Algebra II & Trigonometry is fast, and students must be an independent math learners. During the first semester, students focus on applying their algebraic skills to evaluate, transform, and solve quadratic, polynomial, rational, logarithmic and exponential functions. Students also learn to use conic sections and explore sequences, series, probability, and statistics.

During the second semester, students focus on trigonometry. Topics include the unit circle, right triangles, graphs of trigonometric functions and trigonometric identities. This course prepares students for Precalculus & Analysis.

Prerequisites: Performance on placement test, two Semesters of Geometry with an A- average or higher

Department recommendation and completion of summer work

Grade level: 9, 10, 11

Credit earned: 1.0 Mathematics

Precalculus

Year-long

The focus of study in Precalculus is advanced applications and techniques for solving and analyzing functions. Students master solving, analyzing and graphing functions including polynomial, rational, logarithmic, exponential, trigonometric and piecewise continuous functions. They also explore sequences, series, vectors, statistics and probability. This course prepares students for Principles of Calculus.

Prerequisites: Successful completion of Algebra II

Grade level: 10, 11, 12

Credit earned: 1.0 Mathematics

Precalculus & Analysis

Year-long

The pace of Precalculus & Analysis is fast, and the student must be an independent math learner. Students explore and apply applications of functions, binomial expansions, factorials, probability and statistics. Students also learn multi-dimensional mathematics including vector and matrix analysis. Students study number theory, induction, limits and begin exploring derivatives. This course will prepare students for Calculus I.

Prerequisites: Two Semesters of Algebra II & Trigonometry with a B average or higher

or Two Semesters of Algebra II with an A- average or higher

Completion of summer homework and fall assessment

Grade level: 10, 11, 12

Credit earned: 1.0 Mathematics

Principles of Calculus

Year-long

Principles of Calculus develops critical thinking through exploration of functions with a calculus lens. Students learn to evaluate limits, explore derivative rules and apply them to optimization, related rates and graphing. They also explore slope fields and be introduced to integrals and their applications. This course prepares students for Calculus I.

Prerequisites: Successful completion of Precalculus & Analysis or two Semesters of Precalculus with a B average or higher;

Department recommendation

Grade level: 11, 12

Credit earned: 1.0 Mathematics

Calculus I: Differential and Integral

Year-long

Calculus I focuses on deepening critical thinking through application in calculus. Course topics include in-depth analysis of and applications of limits, differential and integral calculus. This course prepares students for Calculus II.

Prerequisites: Two semesters of Precalculus & Analysis with a B average or higher;

or two semesters of Precalculus with an A- average or higher,

completion of summer homework and department recommendation

Grade level: 11, 12

Credit earned: 1.0 Mathematics

Calculus I: Differential and Integral

Year-long

Prerequisites: Completion of Precalculus & Analysis with a B average or higher; or completion of Precalculus with an A- average or higher and completion of summer homework

Department recommendation

Grade level: 11, 12

Credit earned: 1.0 Mathematics

Calculus II: Integral and Multivariable (Differential Equations)

Year-long
Calculus II focuses on furthering student understanding of differential and integral calculus through the study of topics of parametric equations with polar coordinates, sequences and series as well as their applications. Other topics may include discrete mathematics, in-depth differential equations, or multi-variable calculus, up to the teacher’s discretion. This course prepares students for a variety of higher-level college math courses.

Prerequisites: Two Semesters of Calculus I with a B average or higher and department recommendation
Grade level: 11, 12
Credit earned: 1.0 Mathematics

Statistics

Year-long

In Statistics, students learn tools for collecting, analyzing, and drawing conclusions from data. Students are introduced to four broad conceptual themes–exploring data, planning a study, anticipating patterns in advance and statistical inferences.

Prerequisites: Successful completion of Algebra II

Department recommendation

Grade level: 11, 12

Credit earned: 1.0 Mathematics

*Course offerings are based on student interest and minimum enrollment requirements; therefore, some classes listed may not be offered every school year.