## Mathematics Course Descriptions

“From the Virginia Department of Education”

While learning mathematics, students will be actively engaged, using concrete materials and appropriate technologies to facilitate problem solving. However, facility in the use of technology shall not be regarded as a substitute for a student’s understanding of quantitative and algebraic concepts or for proficiency in basic computations. The acquisition of specialized mathematical vocabulary and language is crucial to a student’s understanding and appreciation of the subject and fosters confidence in mathematics communication and problem solving. Problem solving is integrated throughout the content strands. The development of problem-solving skills is a major goal of the mathematics program at every grade level. The development of skills and problem-solving strategies must be integrated early and continuously into each student’s mathematics education. The use of appropriate technology and the interpretation of the results from applying technology tools will be an integral part of teaching, learning, and assessment.

Grade 6(02036)

The sixth-grade standards provide a transition from the emphasis placed on whole number arithmetic in the elementary grades to foundations of algebra. The standards include a focus on rational numbers and operations involving rational numbers. Students will use ratios to compare data sets; recognize decimals, fractions, and percents as ratios; solve single-step and multistep problems, using positive rational numbers; and gain a foundation in the understanding of and operations with integers. Students will solve problems involving area and perimeter and begin to graph in a coordinate plane. In addition, students will build on the concept of graphical representation of data developed in the elementary grades and develop concepts regarding measures of center. Students will solve linear equations and inequalities in one variable and use algebraic terminology. Students will represent proportional relationships using two variables as a precursor to the development of the concept of linear functions.

Math 6 – Designed for students who have demonstrated proficiency in prior math classes or may need additional intervention to help close gaps in mathematical understanding.

Advanced Math 6 – Designed for students who have demonstrated excellence in prior math classes as referenced by growth measures, previous SOL assessments, and problem-solving abilities as well as work ethic. Students in this course will receive instruction on all Math 6 Standards of Learning as well as the correlated Standards from Math 7.

Students in either course will take the Math 6 SOL assessment in the Spring.

Grade 7(02037)

The seventh-grade standards continue to emphasize the foundations of algebra. The standards address the concept of and operations with rational numbers by continuing their study from grade six. Students will build on the concept of ratios to solve problems involving proportional reasoning. Students will solve problems involving volume and surface area and focus on the relationships among the properties of quadrilaterals. Probability is investigated through comparing experimental results to theoretical expectations. Students continue to develop their understanding of solving linear equations and inequalities in one variable by applying the properties of real numbers. Students discern between proportional and non-proportional relationships and begin to develop a concept of slope as rate of change.

Math 7 – Designed for students who have demonstrated proficiency in prior math classes or may need additional intervention to help close gaps in mathematical understanding.

Advanced Math 7 – Designed for students who have demonstrated excellence in prior math classes as referenced by growth measures, previous SOL assessments, and problem-solving abilities as well as work ethic. Students in this course will receive instruction on a correlated set of Math 7 and Math 8 Standards of Learning .

Students in either course will take the Math 7 SOL assessment in the Spring.

Grade 8-(PreAlgebra)(02038)

The eighth-grade standards continue to build on the concepts needed for success in high school level algebra, geometry, and statistics. Students will explore real numbers and the subsets of the real number system. Proportional reasoning is expounded upon as students solve a variety of problems. Students find the volume and surface area of more complex three-dimensional figures and apply transformations to geometric shapes in the coordinate plane. Students will verify and apply the Pythagorean Theorem creating a foundation for further study of triangular relationships in geometry. Students will represent data, both univariate and bivariate data, and make predictions by observing data patterns. Students build upon the algebraic concepts developed in the standards for grades six and seven mathematics, which include simplifying algebraic expressions, solving multistep equations and inequalities, and graphing linear functions. The grade eight standards are vital to providing a solid foundation in Algebra I for students in middle school mathematics. Students in this course will take the Math 8/Pre-Algebra SOL assessment in the Spring.

Algebra I (02052)

Prerequisite: Pre-Algebra

Credit: 1

This course provides a study of the basic principles of algebra, including using the rational number system; performing operations with polynomials; solving linear equations and inequalities; solving quadratic equations; organizing and manipulating data; and graphing linear and quadratic equations. The course requires students to use algebra as a tool for representing and solving a variety of practical problems. Included in the progression of algebraic content is patterning, generalization of arithmetic concepts, proportional reasoning, and representing mathematical relationships using tables, symbols, and graphs. All students are expected to achieve the Algebra I standards via problem-solving, making connections, reasoning, and communicating mathematical ideas and strategies. The study of Algebra I assists students in generalizing patterns or modeling relevant, practical situations with algebraic models. Students will use graphing calculators, computers, and other appropriate technology. Students taking this course will take an end-of-course SOL test in Algebra I.

Algebra, Functions and Data Analysis (02902)

Prerequisites: Algebra I

Credit: 1

This course is designed for students who have successfully completed the standards for Algebra I and may benefit from additional support in their transition to Algebra II. Within the context of mathematical modeling and data analysis, students will study functions and their behaviors, systems of equations and inequalities, probability, and analysis of data. Data will be generated through practical applications arising from science, business, and finance. Students will solve problems that require the formulation of linear, quadratic, or exponential equations. Through the investigation of mathematical models and interpretation/analysis of data from relevant, applied contexts and situations, students will strengthen conceptual understandings in mathematics and further develop connections between algebra and statistics. Students should use the language and symbols of mathematics in representations and communication, both orally and in writing, throughout the course.

These standards include a transformational approach to graphing functions and writing equations when given the graph of the equation. Graphing utilities (calculators, computers, and other technology tools) will be used to assist in teaching and learning. Note:

If Algebra Functions and Data Analysis (AFDA) is scheduled any time after Algebra 2, it will count as an elective credit only.

This course does not apply toward an Advanced Studies Diploma for CCPS.

Geometry (02072)

Prerequisites: Algebra I

Credit: 1

This course provides a study of lines, angles, triangles, logic, polygons, circles, three-dimensional figures, coordinate relations, and transformations. All students are expected to achieve the Geometry standards. The course includes an emphasis on developing reasoning skills through the exploration of geometric relationships including properties of geometric figures, trigonometric relationships, and mathematical proofs. In this course, deductive reasoning and logic are used in direct proofs. Direct proofs are presented in different formats (typically two-column or paragraph) and employ definitions, postulates, theorems, and algebraic justifications including coordinate methods. Emphasis is placed on two- and three-dimensional reasoning skills, coordinate and transformational geometry, and the use of geometric models to solve problems. A variety of applications and some general problem-solving techniques, including algebraic skills, will be used to implement the standards. Graphing utilities (calculators, computers, and other technology tools) and dynamic geometry applications will be used to assist in teaching and learning. Students taking this course will take an end-of-course SOL test in Geometry.

Pre-AP Geometry/Trigonometry (02072H)

Prerequisite: Algebra I

Credit: 1 (weighted)

In addition to the content and process goals outlined in Geometry (3143), this course adds trigonometry content including the study of trigonometric definitions and applications. Emphasis placed on using connections between right triangle ratios, trigonometric functions, and circular functions. In addition, applications and modeling will be included throughout the course of study. Oral and written communication concerning the language of mathematics, logic of procedure, and interpretation of results will also permeate the course.

Algebra II (02056)

Prerequisite: Algebra I

Credit: 1

This course includes a thorough treatment of advanced algebraic concepts will be provided through the study of functions, equations, inequalities, systems of equations, polynomials, rational and radical equations, complex numbers, and sequences and series. Emphasis will be placed on practical applications and modeling throughout the course of study. Oral and written communication concerning the language of algebra, logic of procedures, and interpretation of results will also permeate the course. A transformational approach to graphing functions will be employed using translation, reflection, dilation, and rotation to generate a “family of functions” from a given “parent” function. Graphing utilities (calculators, computers, and other technology tools) will be used to assist in teaching and learning. Graphing utilities facilitate visualizing, analyzing, and understanding algebraic and statistical behaviors and provide a powerful tool for solving and verifying solutions.

Pre-AP Algebra II/Trig (02056H)

Prerequisites: Algebra I and Geometry

Credit: 1 (weighted)

This course is designed for a more accelerated pace of study. The course covers the concepts listed in the Algebra II (3135) description and includes additional trigonometry content that includes the study of trigonometric definitions, applications, graphing, and solving trigonometric equations and inequalities. Oral and written communication concerning the language of mathematics, logic of procedure, and interpretation of results will also permeate the course. Graphing utilities (calculators, computers, and other technology tools) will be used to assist in teaching and learning. Graphing utilities facilitate visualizing, analyzing, and understanding algebraic and statistical behaviors and provide a powerful tool for solving and verifying solutions. Students taking this course will take an end- of-course SOL test in Algebra II.

Pre-AP Calculus (02104H)

Prerequisite: Pre-AP Algebra II/ Trigonometry OR Elementary Math Functions

Credit: 1 (weighted)

This is a rigorous course that includes the advanced study of algebra, theory of equations, analytic geometry, and trigonometry, and an introduction to calculus concepts. It is recommended that students demonstrate a sound understanding of the principles of Algebra I, Algebra II, and Geometry before enrolling in this course. Students will use graphing calculators, computers, and other appropriate technology. There is no SOL test given for this course.

Elementary Math Functions (02019)

Prerequisites: Algebra II and Geometry OR Pre-AP Algebra II

Credit: 1

This course is an extension of the concepts learned in Algebra II and an introduction to pre-calculus concepts. The course is comprised of the following three units of study: algebra, trigonometry, and statistics. The algebra unit will include a study of linear relations and functions, systems of equations and inequalities, polynomial and rational functions, exponential and logarithmic functions, and the nature of graphs. The trigonometric unit will include a study of trigonometric functions, graphs and inverses of trigonometric functions, and trigonometric identities and equations. Real-world applications will be incorporated when appropriate. Graphing utilities (calculators, computers, and other technology tools) will be used to assist in teaching and learning. Graphing utilities facilitate visualizing, analyzing, and understanding algebraic and statistical behaviors and provide a powerful tool for solving and verifying solutions. There is no SOL test given for this course.

*This class is an option in certain schools. Choose Probability and Statistics or Pre-AP Calculus as an alternative.

Probability and Statistics (02021)

Prerequisites: Algebra II and Geometry OR Pre-AP Algebra II

Credit: 1

Probability and Statistics introduces the study of likely events and the analysis, interpretation, and presentation of quantitative data. Course topics generally include basic probability and statistics: discrete probability theory, odds, and probabilities, probability trees, populations and samples, frequency tables, measures of central tendency and variation, and presentation of data (including graphs). Course topics may also include normal distribution and measures of variability. This course provides a foundational understanding of statistical concepts and techniques. Students will learn how to collect, analyze, and interpret data, enabling them to draw meaningful conclusions and make predictions. Emphasis will be placed on practical applications using graphing utilities (such as calculators and computers) to enhance visualization and problem-solving.

AP Calculus AB (02124)

Pre-requisite: Pre-AP Calculus or Elementary Math Functions

Credit: 1 (weighted)

Advanced Placement Calculus AB is a course designed to provide advanced mathematics students an opportunity to earn college credit while simultaneously earning credit toward high school graduation. The course is intended for students who have a thorough knowledge of analytic geometry and elementary functions in addition to college preparatory algebra, geometry, and trigonometry. The purpose of the course is to prepare students for advanced placement in college calculus. The course standards incorporate The College Board Advanced Placement Course Description Syllabus. As mandated by The College Board, graphing calculators are required for this course. Instructional activities that engage students in solving application problems of varying complexities will be used. There is no SOL test given for this course.

AP Calculus BC (02125)

Pre-requisite: AP Calculus AB

Credit: 1 (weighted)

Advanced Placement Calculus BC is a course designed to provide advanced mathematics students an opportunity to earn college credit while simultaneously earning credit toward high school graduation. Calculus BC is a full-year course in the calculus of functions of a single variable. It includes all topics taught in Calculus AB plus additional topics: Analysis of parametric, polar, and vector functions, applications of derivatives, integrals, and antidifferentiation. The course standards incorporate The College Board Advanced Placement Course Description Syllabus. As mandated by The College Board, graphing calculators are required for this course. Instructional activities that engage students in solving application problems of varying complexities will be used. There is no SOL test given for this course.

AP Statistics (02203)

Pre-requisite: Algebra II

Credit: 1 (weighted)

Advanced Placement Statistics is a course designed to introduce students to the tools for collecting, analyzing, and drawing conclusions from data. The course incorporates The College Board Advanced Placement Course that exposes students to the following four themes:

Looking for patterns in data

Planning and conducting studies

Exploring data using probability and simulation

Estimating population parameters and testing hypotheses

Graphing calculators will be used in the course. There is no SOL test given for this course.