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VLA Math Course Descriptions (Grades 9-12)

Listed below are suggested math paths to follow when selecting and/or assigning mathematics courses in the Virtual Learning Academy. The guide is provided to give students the best opportunity for success in mathematics.

Path I

• College Preparatory Algebra I
• College Preparatory Geometry
• College Preparatory Algebra II
• College Preparatory Calculus or AP Calculus AB

Path II

• Basic Algebra I
• Basic Algebra II
• College Preparatory Algebra I
• Integrated Math I
• Intergrated Math II
• Integrated Math III
* Courses marked require additional materials.

2 Semesters: 36 Units
Required Course Materials

In this course, students determine what properties hold for operations with complex numbers. They apply combinations as a method to create coefficients for the Binomial Theorem; solve problems involving derived measurements; use radian measures to solve problems involving angular velocity and acceleration; apply informal concepts of successive approximation, upper and lower bounds, and limits in measurement situations. Students use matrices to represent translations, reflections, rotations, dilations, and their compositions; derive and apply the basic trigonometric identities; relate graphical and algebraic representations of lines, simple curves, and conic sections. Students recognize and compare specific shapes and properties in multiple geometries; analyze the behavior of arithmetic and geometric sequences and series as the number of terms increases; translate between the numeric and symbolic form of a sequence or series. They describe and compare the characteristics of transcendental and periodic functions and represent the inverse of a transcendental function symbolically; solve systems of equations using matrices and graphs, with and without technology. They use mathematical induction and explore the concepts of limit; compare estimates of the area under a curve over a bounded interval by partitioning the region with rectangles; translate freely between polar and Cartesian coordinate systems; use the concept of limit to find instantaneous rate of change for a point on a graph as the slope of a tangent at a point. They use descriptive statistics to analyze and summarize data, including measures of center, dispersion, correlation, and variability; and use theoretical or experimental probability to determine probabilities in real-world situations involving uncertainty.

### AP Calculus AB

2 Semesters: 36 Units
Required Course Materials
AP Course Participation Guidelines

The study of AP Calculus AB in the Virtual Learning Academy (VLA) environment is designed for students who want to extend their knowledge of mathematics and broaden their success in solving problems intuitively.  Students will rigorously explore, discover, and reinforce rich mathematics topics and applications of calculus concepts.  The intent of this course is to give students a "true" understanding and interpretation of calculus concepts and enable them to apply their knowledge in varied problem-solving scenarios, both  real and simulated.  Students will complete many-in-depth investigations and often use the TI-Nspire graphing calculator as a tool to complete their investigations.  Students will have ample opportunities to express and connect problem-solving results graphically, numerically and verbally.  The culminating activity in this course will be the completion of the AP Calculus AB exam successfully. Note: A TI-Nspire graphing calculator is required for this course.

### Basic Algebra I

2 Semesters: 36 Units

In this course, students connect physical, verbal, and symbolic representations of the real number system; investigate properties including closure; demonstrate fluency in computations with real numbers; solve and graph linear equations and inequalities. Students use formulas to solve problems including exponential growth and decay; add, subtract, multiply, and divide monomials and polynomials; and solve quadratic equations with real roots by graphing, formula, and factoring. Students define functions, determine slope, calculate distance, and draw graphs of linear equations using slope, y-intercept, parallel, and perpendicular lines; determine the characteristics of linear, quadratic, and exponential functions; solve systems of linear equations involving two variables graphically and symbolically; simplify and compute with rational and radical expressions; model and solve problem situations involving direct and indirect variation.

In Algebra I, you will begin your journey to learn mathematical and theoretical concepts which lay the foundation to take more advanced math classes, both in high school and beyond. Mathematics knowledge is built in steps and Algebra I is one of its building blocks. With mastery of Algebra I skills, you will have a solid foundation to pursue many different paths and further your knowledge of mathematics.

### Basic Algebra II

2 Semesters: 36 Units

In this course students will begin by reviewing basic algebra and geometry topics. They demonstrate fluency in operations with real numbers, vectors and matrices; represent and compute with complex numbers; use fractional and negative exponents to find solutions for problem situations; describe and compare the characteristics of the families of quadratics with complex roots, polynomials of any degree, logarithms, and rational functions. Students investigate rates of change, intercepts, zeros and asymptotes of polynomial, rational, and trigonometric functions graphically and with technology; identify families of functions with graphs that have rotation symmetry or reflection symmetry about the y-axis, x-axis, or y = x. They solve problems with matrices and vectors, solve equations involving radical expressions and complex roots, solve 3 by 3 systems of linear equations, and solve systems of linear inequalities; solve quadratic expressions, investigate curve fitting, and determine solutions for quadratic inequalities. They investigate exponential growth and decay and use recursive functions to model and solve problems; compute with polynomials and solve polynomial equations using a variety of methods including synthetic division and the rational root theorem; solve inverse, joint, and combined variation problems; solve rational and radical equations and inequalities; and describe the characteristics of the graphs of conic sections. They analyze the behavior of arithmetic and geometric sequences and series. Students use permutations and combinations to calculate the number of possible outcomes recognizing repetition and order; compute the probability of compound events, independent events, and dependent events. They use descriptive statistics to analyze and interpret data, including measures of central tendency and variation.

In some of the units, a graphing calculator will be useful. It is recommended that the graphing calculator be at least a TI-83 model.

### Calculus

2 Semesters: 36 Units

Calculus is a course intended to cover topics similar to the topics explored in an entry-level College Calculus course offered at most colleges or universities. This course is written in accordance with the Ohio Academic Content Standards and includes such topics as Limits, Rates of Change, Differentiation, Functions of Derivatives, Indefinite and Definite Integrals, Areas in a Plane, Volumes of Generated Solids, L’Hôpital’s Rule, and Slope Fields. This course can be demanding at times; however, when explored with an open mind, Calculus can be an enjoyable challenge. Be prepared to be amazed by how math works!A Graphing Calculator is required for this course. Instructions for using the graphing calculator will be based on a TI-84 Plus.

### College Preparatory Algebra I

2 Semesters: 36 Units
Required Course Materials

In this course, students connect physical, verbal, and symbolic representations of the real number system; investigate properties including closure; demonstrate fluency in computations with real numbers; solve and graph linear equations and inequalities. They use formulas to solve problems including exponential growth and decay; add, subtract, multiply, and divide monomials and polynomials; and solve quadratic equations with real roots by graphing, formula, and factoring. Students define functions, determine slope, calculate distance, and draw graphs of linear equations using slope, y-intercept, parallel, and perpendicular lines; determine the characteristics of linear, quadratic, and exponential functions; solve systems of linear equations involving two variables graphically and symbolically; simplify and compute with rational and radical expressions; model and solve problem situations involving direct and indirect variation. They describe and interpret rates of change from graphical and numerical data; find, use, and interpret measures of center and spread to compare and draw conclusions about data; evaluate the appropriateness of data collection and analysis; and identify possible misuses of statistical data. They use counting techniques and the Fundamental Counting Principal to determine possible outcomes, compute probabilities of compound events, independent events, and simple dependent events; and make predictions based on theoretical probabilities and experimental results. Students define basic trigonometric ratios in right triangles and apply proportions to solve problems involving right triangle trigonometry.

### College Preparatory Algebra II

2 Semesters: 36 Units
Required Course Materials

In this course, students will begin by reviewing basic algebra and geometry topics. They demonstrate fluency in operations with real numbers, vectors and matrices; represent and compute with complex numbers; use fractional and negative exponents to find solutions for problem situations; describe and compare the characteristics of the families of quadratics with complex roots, polynomials of any degree, logarithms, and rational functions. They investigate rates of change, intercepts, zeros and asymptotes of polynomial, rational, and trigonometric functions graphically and with technology; identify families of functions with graphs that have rotation symmetry or reflection symmetry about the y-axis, x-axis, or y =x. They solve problems with matrices and vectors, solve equations involving radical expressions and complex roots, solve 3 by 3 systems of linear equations, and solve systems of linear inequalities; solve quadratic expressions, investigate curve fitting, and determine solutions for quadratic inequalities. They investigate exponential growth and decay and use recursive functions to model and solve problems; compute with polynomials and solve polynomial equations using a variety of methods including synthetic division and the rational root theorem; solve inverse, joint, and combined variation problems; solve rational and radical equations and inequalities; and describe the characteristics of the graphs of conic sections. Students use permutations and combinations to calculate the number of possible outcomes recognizing repetition and order; compute the probability of compound events, independent events, and dependent events.

### College Preparatory Geometry

2 Semesters: 36 Units
Required Course Materials

In this course, students formally define geometric figures; describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence. They recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines, and parallel lines; use coordinate geometry to represent and examine the properties of geometric figures including slope, midpoint, distance, parallel, and perpendicular lines; draw and construct representations of two and three dimensional geometric objects using a variety of tools such as straightedge, compass, and technology. Students represent and model transformations in a coordinate plane and describe results; prove or disprove conjectures and establish the validity of conjectures about geometric objects, their properties and relationships by counterexample, inductive and deductive reasoning, and critiquing arguments made by others. Students use right triangle trigonometric relationships to determine lengths and angle measures; use algebraic representations to model and solve problem situations and to describe and generalize geometric properties and relationships; connect physical, verbal, and symbolic representations of irrational numbers; calculate and explain the difference between absolute error and relative error; interpret the relationship between two variables using multiple graphical displays and statistical measures; model problems dealing with uncertainty with area models; differentiate and explain the relationship between the probability of an event and the odds of an event.

### Integrated Math I

2 Semesters: 36 Units
Required Course Materials

In this course, students connect physical, verbal, and symbolic representations of the real number system. They investigate the properties of real numbers and estimate, compute, solve, and judge reasonableness of problems with real numbers including ratio, proportion, percent, integers, rational numbers, numbers expressed in scientific notation, and square roots of perfect and non-perfect squares. Students generalize patterns and sequences and apply formulas to real-world problem situations. Students examine basic geometric properties of two-dimensional and three-dimensional shapes. They graph solutions to equations; use coordinate geometry to analyze properties of two-dimensional figures and perform translations, reflections, rotations, and dilations; define basic trigonometric ratios in right triangles; and apply proportions to solve problems involving right triangle trigonometry. Students apply direct and indirect measurement techniques and tools, and derive formulas to determine perimeter, area, volume, and various attributes of plane and solid geometric figures. They use measures of center and spread to analyze data; evaluate the change of data and display it appropriately in graphs; make predictions based on samples representative of a larger population; use permutations and combinations to calculate the number of possible outcomes recognizing repetition and order; and compute the probability of compound events, independent events, and simple dependent events. Students solve and graph linear equations, absolute value equations, and inequalities; compute with polynomials; define functions; determine slope and intercepts; draw graphs of linear equations and inequalities; solve systems of equations, and explore simple nonlinear equations.

### Integrated Math II

2 Semesters: 36 Units
Required Course Materials

In this course, students study the topics presented in geometry but in a modified format. On occasion, students find that problems and/or explanations have been adapted to a simpler format. Students are given extra guidance with more difficult problems. Students formally define geometric figures; describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence. They recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines, and parallel lines; use coordinate geometry to represent and examine the properties of geometric figures including slope, midpoint, distance, parallel, and perpendicular lines; draw and construct representations of two- and three-dimensional geometric objects using a variety of tools such as straightedge, compass, and technology. Students represent and model transformations in a coordinate plane and describe the results; prove or disprove conjectures and establish the validity of conjectures about geometric objects, their properties and relationships by counterexample, inductive and deductive reasoning, and critiquing arguments made by others. Students use right triangle trigonometric relationships to determine lengths and angle measures; use algebraic representations to model and solve problem situations and to describe and generalize geometric properties and relationships.

### Integrated Math III

2 Semesters: 36 Units
Required Course Materials

In this course, students study the topics presented in algebra but in a modified format. On occasion, students find that problems and/or explanations have been adapted to a simpler format. Students are given extra guidance with more difficult problems. In this course, students review basic algebra and geometry topics. They demonstrate fluency in operations with real numbers, vectors and matrices; represent and compute with complex numbers; use fractional and negative exponents to find solutions for problem situations; describe and compare the characteristics of the families of quadratics with complex roots, polynomials of any degree, logarithms, and rational functions. They investigate rates of change, intercepts, zeros and asymptotes of polynomial, rational, and trigonometric functions graphically and with technology; identify families of functions with graphs that have rotation symmetry or reflection symmetry about the y-axis, x-axis, or y =x. They solve problems with matrices and vectors, solve equations involving radical expressions and complex roots, solve 3 by 3 systems of linear equations, and solve systems of linear inequalities; solve quadratic expressions, investigate curve fitting, and determine solutions for quadratic inequalities; investigate exponential growth and decay and use recursive functions to model and solve problems. They compute with polynomials and solve polynomial equations using a variety of methods including synthetic division and the rational root theorem; solve inverse, joint, and combined variation problems; solve rational and radical equations and inequalities; and describe the characteristics of the graphs of conic sections. Students use permutations and combinations to calculate the number of possible outcomes recognizing repetition and order; and compute the probability of compound events, independent events, and dependent events.

### Intervention Math

2 Semesters: 36 Units

This course is designed to review the student in basic concepts necessary for success in applying mathematics involved in everyday life. The subject matter studied is familiar and motivational, integrating problem solving and focusing on real applications of mathematical skills. This course is designed primarily for the student who seeks to improve his or her knowledge of basic mathematics. Topics studied include computations and applications of whole numbers, decimals, fractions, ratios, and percent; measurement in metric and customary units; geometric figures, finding volume and surface area; statistics, graphs, and probability; and integers, the coordinate plane, and algebraic equations.

### OGT Math

2 Semesters: 36 Units
Required Course Materials

This course is designed to assist students in preparation for the Ohio Graduation Test in mathematics. Students investigate properties and order of operations, evaluate expressions, identify subsets of the real number system, and determine equivalent forms of real numbers; estimate, compute, and solve problems with real numbers including ratio, proportion, percent, integers, rational numbers, scientific notation, and square roots; generalize patterns and sequences and apply formulas to real-world problem situations. Students determine length, area, and volume and the appropriate use of linear, square and cubic unit measurements; generalize patterns and sequences using tables, graphs, and symbolic algebra; define functions; determine slope and intercepts; draw graphs of linear equations and inequalities; and explore simple quadratic and exponential functions. Students solve linear equations, inequalities, systems of equations, quadratic equations, and direct and inverse variation problem situations. They define geometric figures and apply the properties of similar and congruent figures; recognize and apply angle relationships involving intersecting lines, perpendicular lines, and parallel lines; use coordinate geometry to examine the properties of geometric figures including slope, midpoint, distance, parallel, and perpendicular lines. They perform translations, reflections, rotations, and dilations; define basic trigonometric ratios in right triangles and apply proportions to solve problems involving right triangle trigonometry. They use measures of center and spread to analyze data; use permutations and combinations to calculate the number of possible outcomes recognizing repetition and order; and compute the probability of compound events, independent events, and simple dependent events.

### Transition to College Math

1 Semester: 18 Units
Required Course Materials

This course covers traditional topics in college algebra and trigonometry at the freshman level. This course was written in accordance with the Ohio Academic Content Standards for grades 11 and 12 and includes such topics as: Systems of Linear Equations, Complex Numbers, Quadratic Functions, Logarithms, Trigonometry, Matrices, Vectors, and the Conic Sections.

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