Mathematics

This course is an in-depth study of trigonometry and advanced algebra topics. The 12-18-week study of trigonometry will include triangle and unit circle trigonometry and trigonometric functions and their applications. Advanced algebra topics will include an extension of previous algebra skills, exponential and logarithmic functions, and rational expressions. Additional topics may include probability, sequences and series, and discrete mathematics. The uses of technology and applications are integral parts of this course.

The Algebra I is a core course that provides a rigorous treatment of mathematics content for all students who are proficient in the Virginia Standards of Learning for Grade 6 and, Grade 7, and who may require additional instruction in core standards from Pre-Algebra for 8th Graders (VDOE Grade 8 Math Standards).

Students in Algebra build understanding within these strands:

1. Expressions and Operations
2. Equations and Inequalities
3. Functions
4. Statistics

In addition, the content of the standards is intended to support the following process goals for learning mathematics: Problem Solving, Communications, Connections, Representations, and Reasoning.

More specific examples of content component of the Virginia Standards of Learning (SOL) for Algebra I include:

• Represent verbal quantitative situations algebraically and evaluate expressions.
• Perform operations on polynomials including applying the laws of exponents, operations, and factoring.
• Simplify square roots and cube roots.
• Algebraically solve multistep equations in one variable including linear, quadratic, and literal with an emphasis on practical problem solving.
• Solve systems of two linear equations in two variables graphically and algebraically.
• Represent the solution of linear inequalities in two variables graphically, including systems of inequalities.
• Determine slope, write equations, and graph linear equations in two variables.
• Investigate and analyze linear and quadratic function families both algebraically and graphically.
• Given a data set or practical situation, determine whether a direct or inverse variation exists and represent these algebraically and graphically.
• Given practical solutions, collect and analyze data, determine the equation of the curve of best fit, and make predictions for linear and quadratic functions.

This course includes properties of the real number system, linear equations and inequalities, systems of equations and inequalities, exponents, radicals, rational expressions and equations, polynomials, factoring, solving, and graphing quadratic equations, functions, statistics, and problem-solving. Students take the Algebra I SOL test at the end of this course. Passing the SOL test and the course earns a verified credit.

The Algebra I, Intensified is a core course that provides a rigorous treatment of mathematics content for all MS students who have demonstrated mastery of the Virginia Standards of Learning for Grade 6, Grade 7, and Grade 8 mathematics and are ready to study additional advanced topics.

Students in Algebra I, Intensified build understanding within these strands:

1. Expressions and Operations
2. Equations and Inequalities
3. Functions
4. Statistics

In addition, the content of the standards is intended to support the following process goals for learning mathematics: Problem Solving, Communications, Connections, Representations, and Reasoning.

More specific examples of content components of the Virginia Standards of Learning (SOL) for Algebra I include:

• Represent verbal quantitative situations algebraically and evaluate expressions.
• Perform operations on polynomials including applying the laws of exponents, operations, and factoring.
• Simplify square roots and cube roots.
• Algebraically solve multistep equations in one variable including linear, quadratic, and literal with an emphasis on practical problem solving.
• Solve systems of two linear equations in two variables graphically and algebraically.
• Represent the solution of linear inequalities in two variables graphically, including systems of inequalities.
• Determine slope, write equations, and graph linear equations in two variables.
• Investigate and analyze linear and quadratic function families both algebraically and graphically.
• Given a data set or practical situation, determine whether a direct or inverse variation exists and represent these algebraically and graphically.
• Given practical solutions, collect and analyze data, determine the equation of the curve of best fit, and make predictions for linear and quadratic functions.

Students in Algebra I, Intensified learn the above topics with greater depth and complexity. In addition, students gain experience with a number of additional topics, including:

• Absolute value equations and inequalities
• Radical expressions and equations
• Rational expressions and equations
• Additional work with quadratics both graphically and algebraically
• Examining additional functions
• Exponential growth and decay
• Pythagorean Theorem
• Distance and Midpoint
• Probability including permutations, combinations, compound events, surveys, and samples.

The content of the standards is intended to support the following process goals for learning mathematics: Problem Solving, Communications, Connections, Representations, and Reasoning.

The Algebra I, Intensified is a core course that provides a rigorous treatment of mathematics content for all MS students who have demonstrated mastery of the Virginia Standards of Learning in mathematics for Grade 6, Grade 7, and Grade 8 and are ready to study additional advanced topics.

Students in Algebra I, Intensified build understanding within these strands:

1. Expressions and Operations
2. Equations and Inequalities
3. Functions
4. Statistics

In addition, the content of the standards is intended to support the following process goals for learning mathematics: Problem Solving, Communications, Connections, Representations, and Reasoning.

More specific examples of content components of the Virginia Standards of Learning (SOL) for Algebra I, Intensified include:

• Represent verbal quantitative situations algebraically and evaluate expressions.
• Perform operations on polynomials including applying the laws of exponents, operations, and factoring.
• Simplify square roots and cube roots.
• Algebraically solve multistep equations in one variable including linear, quadratic, and literal with an emphasis on practical problem solving.
• Solve systems of two linear equations in two variables graphically and algebraically.
• Represent the solution of linear inequalities in two variables graphically, including systems of inequalities.
• Determine slope, write equations, and graph linear equations in two variables.
• Investigate and analyze linear and quadratic function families both algebraically and graphically.
• Given a data set or practical situation, determine whether a direct or inverse variation exists and represent these algebraically and graphically.
• Given practical solutions, collect and analyze data, determine the equation of the curve of best fit, and make predictions for linear and quadratic functions.

Students in Algebra I, Intensified learn the above topics with greater depth and complexity. In addition, student gain experience with a number of additional topics, including:

• Absolute value equations and inequalities
• Radical expressions and equations
• Rational expressions and equations
• Additional work with quadratics both graphically and algebraically
• Examining additional functions
• Exponential growth and decay
• Pythagorean Theorem
• Distance and Midpoint
• Probability including permutations, combinations, compound events, surveys, and samples.

The Algebra I, Intensified is a core course that provides a rigorous treatment of mathematics content for students who have demonstrated mastery of the Virginia Standards of Learning for Pre-Algebra Grade 8 mathematics and are ready to study additional advanced topics.

Students in Algebra I, Intensified build understanding within these strands:

1. Expressions and Operations
2. Equations and Inequalities
3. Functions
4. Statistics

In addition, the content of the standards is intended to support the following process goals for learning mathematics: Problem Solving, Communications, Connections, Representations, and Reasoning.

More specific examples of content components of the Virginia Standards of Learning (SOL) for Algebra I include:

• Represent verbal quantitative situations algebraically and evaluate expressions.
• Perform operations on polynomials including applying the laws of exponents, operations, and factoring.
• Simplify square roots and cube roots.
• Algebraically solve multistep equations in one variable including linear, quadratic, and literal with an emphasis on practical problem solving.
• Solve systems of two linear equations in two variables graphically and algebraically.
• Represent the solution of linear inequalities in two variables graphically, including systems of inequalities.
• Determine slope, write equations, and graph linear equations in two variables.
• Investigate and analyze linear and quadratic function families both algebraically and graphically.
• Given a data set or practical situation, determine whether a direct or inverse variation exists and represent these algebraically and graphically.
• Given practical solutions, collect and analyze data, determine the equation of the curve of best fit, and make predictions for linear and quadratic functions.

Students in Algebra I, Intensified learn the above topics with greater depth and complexity. In addition, students gain experience with a number of additional topics, including:

• Absolute value equations and inequalities
• Radical expressions and equations
• Rational expressions and equations
• Additional work with quadratics both graphically and algebraically
• Examining additional functions
• Exponential growth and decay
• Pythagorean Theorem
• Distance and Midpoint
• Probability including permutations, combinations, compound events, surveys, and samples.

The content of the standards is intended to support the following process goals for learning mathematics: Problem Solving, Communications, Connections, Representations, and Reasoning.

The Algebra Strategies course is an elective course for students who need additional support for success in Algebra I. Students enrolled in the course will build background knowledge, experience more conceptual approaches to the content, and develop the core course content more thoroughly.

A review of those topics needed for the study of calculus; theory of limits, differential calculus, and its applications; integral calculus and its applications, problem solving at the calculus level; and those topics which are contained in the Advanced Placement Calculus AB syllabus as given by the College Entrance Examination Board.

In addition to the topics in Calculus AB, vector functions, polar areas, volumes, sequences, and series are covered. Limits and proofs are given more stress than in Calculus AB. Details may be found in the syllabus for Calculus BC published by the College Entrance Examination Board.

This course is intended to provide students with an understanding of how to visualize and interpret data, identify potential bias in data, and leverage data as a tool to support change and innovation. Students will support problem solving using large data sets through an inquiry-based approach. The analysis of data will be developed through the application of mathematics, statistics, computer science, and information technology. The goal of this course is to prepare students to be data-literate citizens who can navigate a world that is inundated with data.

Differential Equations is offered for those students who have completed Calculus BC prior to their senior year. This course introduces first order differential equations, linear differential equations, numerical methods, and applications. Some of the topics the course will cover are techniques of solving first order differential equations, homogeneous and non-homogeneous linear differential equations with constant coefficients, systems of linear differential equations using eigenvalues, and applied problems.

Geometry involves the student in the study of mathematical structure using deductive reasoning and the application of direct and indirect proof. This course covers the concepts of transformations, congruence, parallelism, similarity, and perpendicularity, as well as the properties of circles, polygons, and solids. Algebra I concepts are reviewed and applied to coordinate geometry. There is a Geometry end-of-course SOL test that students may be required to take to meet Federal requirements and/or earn a verified math credit towards graduation.

Geometry, Intensified is a core course that provides a rigorous treatment of mathematics content for all students who have successfully completed Algebra I, Intensified.

More specific examples of content components of the Virginia Standards of Learning (SOL) for Geometry include:

• Deductive reasoning to construct and judge the validity of a logical argument given a set of premises and a condition.
• Use relationship between angles formed by two lines intersected by a transversal to prove two or more-lines parallel and solve practical problems.
• Solve problems involving symmetry and transformation including applications involving distance, midpoint, slope, and translations using coordinate methods.
• Construct and justify various constructions.
• Given information about lengths of sides and/or angle measures in triangles, solve practical problems.
• Prove two triangles are congruent or similar.
• Solve practical problems involving right triangles including the Pythagorean Theorem, special right triangles, and trigonometric ratios.
• Verify and use properties of quadrilaterals to solve problems.
• Solve practical problems involving angles of convex polygons.
• Apply properties of circles to practical problems.
• Solve problems involving equations of circles.
• Use surface area and volume of three-dimensional geometric figures.

The content of the standards is intended to support the following process goals for leaning mathematics: Problem Solving, Communications, Connections, Representations, and Reasoning.

IB Math: Applications & Interpretation (Part 1) emphasizes the meaning of mathematics in context. This two-year course is for students who are interested in developing their mathematics for describing our world and solving practical problems. Students study and investigate the following mathematical topics: number theory and algebra, geometry and trigonometry, statistics and probability, functions, and introductory differential calculus. Topics are connected using key concepts. Students must complete IB Mathematics: Applications & Interpretation Part I with a C or better to be eligible for part II. As required by IB, each student will complete an internal assessment consisting of an individual exploration. 

Linear Algebra is offered for those students who have completed Calculus BC prior to their senior year. Students will learn about systems of linear equations, vector spaces, linear transformations, and eigenvalues. This course will improve students’ quantitative reasoning and develop deductive logic skills.

Math 6 is a core course that provides a rigorous treatment of mathematics content for sixth grade students.

The Grade 6 standards are a transition from the emphasis placed on whole number arithmetic in the elementary grades to foundations of algebra.

Students will build understanding within these strands:

1. Number and Number Sense
2. Computation and Estimation
3. Measurement and Geometry
4. Probability and Statistics
5. Patterns, Functions, and Algebra

In addition, the content of the standards is intended to support the following process goals for learning mathematics: Problem Solving, Communications, Connections, Representations, and Reasoning.

More specific examples of content components of the Mathematics Virginia Standards of Learning (SOL) for Grade 6 include:

• Operations with fractions, decimals, and percentages, including representational models and practical problems.
• Multistep practical problems involving fractions, mixed numbers, and decimals.
• Integer operations, including integer models and order of operations.
• Discovering and exploring pi, circles, and circle graphs.
• Measures of central tendency, including mean as balance point.
• Proportional relationships, including verbal descriptions, rates, ratio tables, and graphs.
• Equations and inequalities.

Math 7 is a core course that provides a rigorous treatment of mathematics content for seventh grade students.

The Grade 7 standards continue to focus on the prealgebra foundations that are necessary for students’ success in eighth grade and in high school.

Students will build understanding within these strands:

1. Number and Number Sense
2. Computation and Estimation
3. Measurement
4. Probability and Statistics
5. Patterns, Functions, and Algebra

In addition, the content of the standards is intended to support the following process goals for learning mathematics: Problem Solving, Communications, Connections, Representations, and Reasoning.

More specific examples of content components of the Virginia Standard of Learning (SOL) for Grade 7 include:

• Positive and negative exponents, including the order of operations.
• Solving multistep practical problems involving rational numbers, proportional reasoning, and similarity.
• Practical problems involving surface area and volume of a variety of figures.
• Quadrilaterals.
• Transformations.
• Histograms and other graphs.
• Slope as rate of changes.
• Proportional relationships and additive relationships related to graphing a line.
• Connecting proportional relationships using verbal descriptions, tables, equations, and graphs.
• Evaluating algebraic expressions.
• Solving two-step linear equations and inequalities, focused on practical problems.

The Strategies course is an elective course for students who need additional support for success in grade level mathematics. Students in the Strategies course will build background knowledge, experience more conceptual approaches to the content, and develop the core course content more thoroughly.

The Strategies course is an elective course for students who need additional support for success in grade level mathematics. Students in the Strategies course will build background knowledge, experience more conceptual approaches to the content, and develop the core course content more thoroughly.

Multivariable Calculus is offered for those students who have completed the Calculus BC prior to their senior year. Some of the topics the course will cover are graphing three dimensional surfaces, integration and differentiation of vector valued functions, limits, and continuity of functions of two or more variables, partial derivatives, multiple integrals, directional derivatives and gradients, vector fields, Green’s Theorem, and Stoke’s Theorem.

Pre-Algebra for 6th Graders (6/7/8) is a rigorous treatment of all middle school math content found in the Virginia Standards of Learning for Grade 6, Grade 7, and Grade 8. This intensified course includes all pre-algebra content that students need to master prior to studying Algebra I, Intensified and Geometry, Intensified.

Students will build understanding within each pre-algebra strand:

1. Number and Number Sense
2. Computation and Estimation
3. Measurement and Geometry
4. Probability and Statistics
5. Patterns, Functions, and Algebra

In addition, the content of the standards is intended to support the following process goals for learning mathematics: Problem Solving, Communications, Connections, Representations, and Reasoning.

More specific examples of the content of this course includes:

• Operations with fractions, decimals, and percentages, including representational models and practical problems.
• Multistep practical problems involving fractions, mixed numbers, and decimals.
• Integer operations, including integer models and order of operations.
• Discovering and exploring pi, circles, and circle graphs.
• Measures of central tendency, including mean as balance point.
• Proportional relationships, including verbal descriptions, rates, ration tables, and graphs.
• The real number system including computing and classifying with subsets of the system.
• Positive and negative exponents, including the order of operations.
• Solving multiple practical problems involving rational numbers, proportional reasoning, and similarity.
• Slope as rate of change.
• Proportional relationships and additive relationships related to graphing a line and other practical problems.
• Practical problems involving consumer applications.
• Quadrilaterals.
• Determine the measure of unknown angles based on angle relationships.
• Solving practical problems involving volume and surface area of a wide range of figures, including analysis and description of the effects of changing attributes.
• Apply transformations including translations, reflections, and dilatations.
• Constructed three-dimensional models given various views.
• Apply and verify the Pythagorean Theorem.
• Solve practical area and perimeter problems involving composite figures.
• Compare and contrast the probability of independent and dependent events and compute probabilities.
• Represent, make observations and inferences from, and compare and analyze data using a wide variety of graphs including boxplots, scatterplots, and histograms.
• Evaluate and simplify algebraic expressions.
• Domain, range, dependent, and independent variables.
• Identify and interpret slope and intercepts of a function given values, a graph, or an equation and make connections among verbal descriptions, tables, equations, and graphs.
• Solve multistep linear equations and inequalities in one variable on one or both sides, with an emphasis on practical problem application.

Pre-Algebra for 7th Graders is a rigorous treatment of prealgebra topics from the Virginia Standards of Learning for Grade 7 and Grade 8 mathematics. The standards focus on the pre-algebra foundations that students need to master in order to be successful in Algebra I or Algebra I, Intensified in eighth grade and in high school mathematics.

Students will build understanding within these strands:

1. Number and Number Sense
2. Computation and Estimation
3. Measurement
4. Probability and Statistics
5. Patterns, Functions, and Algebra

In addition, the content of the standards is intended to support the following process goals for learning mathematics: Problem Solving, Communications, Connections, Representations, and Reasoning.

More specific examples of content components of the course include:

• The real number system including computing and classifying with subsets of the system.
• Positive and negative exponent, including the order of operations.
• Solving multi-step practical problems involving rational numbers, proportional reasoning, and similarity.
• Slope as rate of change.
• Proportional relationships and additive relationships related to graphing a line.
• Practical problems involving consumer applications.
• Quadrilaterals
• Determine the measure of unknown angles based on angle relationships.
• Solving practical problems involving volume and surface area of a wide range of figures, including analysis and description of the effects of changing attributes.
• Apply transformations including translations, reflections, and dilatations.
• Construct three-dimensional models given top/bottom, side, and front/back views.
• Apply and verify the Pythagorean Theorem.
• Solve practical area and perimeter problems involving composite figures.
• Compare and contrast the probability of independent and dependent events and compute probabilities.
• Represent, make observations and inferences from, and compare and analyze data using a wide variety of graphs including boxplots, scatterplots, and histograms.
• Evaluate and simplify algebraic expressions.
• Determine whether a relation in a function and determine domain and range and dependent and independent variables.
• Identify and interpret slope and intercept of a function given values, a graph, or an equation and make connections among verbal description, tables, equations, and graphs.
• Solve multistep linear equations and inequalities in one variable on one or both sides, with an emphasis on practical problem application.

Pre-Algebra for 8th Graders is a core course that provides a rigorous treatment of content for eighth grade students. The Grade 8 standards refine all pre-algebra foundational understanding that students need to master in order to be successful in Algebra I and beyond. Students will build understanding within these strands:

1. Number and Number Sense
2. Computation and Estimation
3. Measurement
4. Probability and Statistics
5. Patterns, Functions, and Algebra

In addition, the content of the standards is intended to support the following process goals for learning mathematics: Problem Solving, Communications, Connections, Representations, and Reasoning.

More specific examples of content components of the Virginia Standards of Learning (SOL) for Grade 8 include:

• The real number system including computing and classifying with subsets of the system.
• Practical problems involving consumer applications.
• Determine the measure of unknown angles based on angle relationships.
• Computing volume and surface area of wide range of figures, including analysis and description of the effects of changing one attribute.
• Apply transformations including translations, reflections, and dilations.
• Construct three-dimensional models given top/bottom, side, and front/back views.
• Apply and verify the Pythagorean Theorem.
• Solve practical area and perimeter problems involving composite figures.
• Compare and contrast the probability of independent and dependent event and compute probabilities.
• Represent, make observations and inferences from, and compare and analyze boxplots and scatterplots.
• Evaluate and simplify algebraic expressions.
• Determine whether a relation in a function and determine domain and range and dependent and independent variables.
• Identify and interpret slope and intercept of a function given values, a graph, or an equation and make connections among verbal descriptions, tables, equations, and graphs.
• Solve multistep linear equations and inequalities in one variable on one or both sides, with an emphasis on practical problem application.

This dual enrollment course presents topics in proportional reasoning, modeling, financial literacy, and validity studies (logic and set theory). Focuses on the process of taking a real-world situation, identifying the mathematical foundation needed to address the problem, solving the problem, and applying what is learned to the original situation.

Vector Calculus is offered for those students who have completed Calculus BC prior to their senior year. Some of the topics the course will cover are graphing three dimensional surfaces, integration and differentiation of vector valued functions, limits, and continuity of functions of two or more variables, partial derivatives, multiple integrals, directional derivatives and gradients, vector fields, and Green’s Theorem.