# Mathematics

Mathematics is the language of creative problem solvers and deep thinkers. At Forest Ridge, mathematics is brought to life using current events and real-world examples.

Students in middle school are offered three levels of integrated mathematics courses. As students are ready to move up to high school and collegiate-level math, they are encouraged to take risks and believe in their potential. We offer multiple classes in Algebra, Geometry, Precalculus and three levels of Calculus to challenge students at every level.

## Middle School: 5^{th}-8^{th} Grade

- Integrated Mathematics Course 1 (Grades 5, 6)
- Integrated Mathematics Course 2 (Grades 5, 6, 7)
- Integrated Mathematics Course 3 (Grades 6, 7)
- Algebra I (Grades 7, 8)
- Geometry (Grade 8)

## Integrated Mathematics Course 1 (Grades 5, 6)

Emphasis in the course 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)

In this course, emphasis is on solidifying math facts and furthering the understanding of number theory. Algebraic concepts, sequences and series, and number patterns are introduced. Students work individually and in groups to continue to develop problem-solving strategies, mathematical vocabulary and critical thinking skills. Measurement, graphing on a coordinate plane, one and two-step equations are some of the topics the students get exposure to in this class.

Standards include the use of proportions to solve problems, converting and comparing positive and negative fractions, decimals and percentages, and analyzing slope as a rate of change when given graphs or tables. 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 2*. Supplementary notes and activities are provided by the instructor.

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

The emphasis in Course 3 is providing students with the foundation needed for success in Algebra 1. Students will develop an understanding of the rules involved in using exponents, including negative exponents, work with algebraic linear equations, 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.

## 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. Emphasis is on applying algebraic skills to a variety of concepts in algebra, including expressions and functions, linear equations, linear and nonlinear functions, equations of linear functions, linear inequalities, systems of linear equations and inequalities, exponents and exponential functions, polynomials, quadratic functions and equations. Students are immersed in problem-solving that requires the use of new skills. Homework is assigned daily, and quizzes and tests are given at frequent and appropriate intervals throughout each unit.

The textbook is *Glencoe Algebra 1,* published by McGraw-Hill^{®}. Supplementary notes and activities are provided by the instructor.

## Geometry (Grade 8)

*This is a high school level course. *

Placement in geometry requires mastery of Algebra 1. In this course, students begin to synthesize their geometry experiences from previous grades to develop and apply precise definitions and precise proofs. Students explore the concepts of congruence, similarity and symmetry from the perspective of geometric transformations.

Students identify triangle congruence criteria to prove theorems about triangles, quadrilaterals and other geometric figures. Students will also work with right triangles and trigonometric ratios, as these are fundamental in many real-world and theoretical situations. Finally, students explore characteristics of circles and extend their understanding of measurements of three-dimensional shapes. Homework is assigned daily, and quizzes and tests are given at frequent and appropriate intervals throughout each unit.

The textbook for this course is *Glencoe Geometry*, published by McGraw-Hill.

## High School: 9^{th}-12^{th} Grade

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

- Algebra I
- Geometry
- Algebra II
- Algebra II & Trigonometry
- Precalculus
- Precalculus & Analysis
- Statistics
- Principles of Calculus
- Calculus I: Differential and Integral
- Calculus II: Integral and Multivariable (Differential Equations)

## 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;**

**Department recommendation**

**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,**

**successful completion of Geometry;**

**Department recommendation**

**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*

*Department recommendation*

*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;*

*Department recommendation*

*Grade level: 10, 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**## 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 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 equation or multi-variable calculus. 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;**

**Department recommendation**

**Grade level: 11, 12**

**Credit earned: 1.0 Mathematics**