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Jefferson County Schools Mathematics The Tennessee Mathematics Framework for grades 9 through 12 includes skills for many different High School level courses, and contains the following process standards: Algebra II Advanced The Tennessee Mathematics Framework for grades 9 through 12 outlines skills to be taught in Algebra II. |
| Algebraic Concepts |
| The Algebraic Concepts Unit includes Competencies/Objectives which focus on algebraic equations and operations. Students explore the symbolic nature of algebraic concepts by identifying and extending patterns in algebra, by following algebraic procedures, and by proving theorems with properties. |
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Expressions: Operations/Justification
The learner will be able to perform operations on expressions and give justification of the procedures selected.
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Inverse: Explain/Illustrate
The learner will be able to informally explain and illustrate the concept of inverse.
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Linear System of Equations: Solve
The learner will be able to obtain solutions to linear systems employing a variety of methods including matrices.
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Absolute Value: Connect
The learner will be able to connect concrete, graphical, oral, and symbolic illustrations of absolute value.
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Inverse Operations: Describing
The learner will be able to describe the inverse operations of addition/subtraction and multiplication/division.
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Inverse Operations: Use
The learner will be able to use inverse operations.
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Inverse Operations: Use
The learner will be able to use the concept of inverse.
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Inverse Operations: Model
The learner will be able to model inverse operations.
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Algebraic Concepts: Interpret
The learner will be able to interpret the outcomes of algebraic procedures.
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Variable: Describe
The learner will be able to describe the definition of a variable in an expression, equation, and inequality.
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Variables: Solve Inequalities
The learner will be able to apply the idea of a variable in obtaining solutions to inequalities.
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Variable: Expression/Equation
The learner will be able to use the concept of variable to simplify expressions and obtain solutions to equations.
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Solution Methods: Appropriate Tools
The learner will be able to compute using appropriate tools such as mental math, technology, manipulatives, and pencil-and-paper.
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Linear System of Equations: Solve
The learner will be able to apply a variety of procedures to find the solution to linear systems in two variables.
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Equations: Linear/Three Variables
The learner will be able to find the traces of a linear equation in three variables.
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Equations: Choose/Pattern
The learner will be able to choose the algebraic equation that generalizes the pattern in a given table of data.
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Equations: Translating/Verbal Sentence
The learner will be able to make translations of verbal sentences into algebraic equations.
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Linear Equations: Solve/Parentheses
The learner will be able to obtain solutions to linear equations that involve more than two steps and have one set of parentheses on each side of the equation.
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Linear Equations: Predict Transformation
The learner will be able to predict the transformation of the graph that exists when coefficients and/or constants of the corresponding linear equations are changed.
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Absolute Value: Match/Graph
The learner will be able to match a set of absolute value data to its graph on the coordinate plane.
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Absolute Value: Investigate/Number Line
The learner will be able to investigate a variety of representations of absolute value on a number line.
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Expressions: Operations/Rational
The learner will be able to conduct basic operations on rational expressions.
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Expressions: Add/Algebraic
The learner will be able to add algebraic expressions.
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Expressions: Subtract/Algebraic
The learner will be able to subtract algebraic expressions.
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Expressions: Multiply/Algebraic
The learner will be able to multiply algebraic expressions.
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Polynomials: Multiply/Two/Binomials
The learner will be able to perform multiplication on two polynomials with each polynomial having two terms or less.
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Polynomials: Determine/Roots
The learner will be able to calculate all of the roots of higher order polynomials.
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Binomials: Area Representation
The learner will be able to choose the area illustration for a specific product of two binomials.
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Radicals: Explain/Variable/Restrictions
The learner will be able to describe the restrictions on the variables in radical equations.
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Quadratic Equation: Select/Procedure
The learner will be able to select an appropriate procedure to find the roots of a quadratic equation.
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Exponents: Simplify/Expressions
The learner will be able to simplify expressions containing rational and negative exponents.
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Operations: Justify/Methods
The learner will be able to justify the methods selected when operations on algebraic equations and expressions are conducted.
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Inverse Operations: Describe
The learner will be able to describe inverse operations.
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Inverse Operations: Articulate
The learner will be able to articulate the concept of inverse.
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Inverse Operations: Complex
The learner will be able to find the multiplicative inverse of a complex number.
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Inverse Operations
The learner will be able to choose the inverse notation of powers and roots.
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Inverse Operations: Model
The learner will be able to model the concept of inverse.
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Algebraic Concepts: Real World
The learner will be able to use the results of algebraic processes in real-world situations.
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Logarithms: Simplifying
The learner will be able to use logarithmic properties to simplify expressions.
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Number Sense: LCM/GCF/Algebraic
The learner will be able to compare and differentiate between the least common multiple (LCM) and greatest common factor (GCF) of a set of algebraic expressions.
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Binomial Expansion: Factorial
The learner will be able to apply factorial notation to the coefficients in a binomial expansion.
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Symbols: Delta Notation/Real World
The learner will be able to represent rates of change in real world situations using delta notation.
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Operations: Develop/Proficiency
The learner will be able to develop proficiency in operations with real numbers, vectors, and matrices, by applying mental math or paper and pencil computations for simple problems, and by applying technology for the more complex problems.
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Rates: Estimate/Interpret
The learner will be able to estimate and interpret rates of change using graphical and numerical data.
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Symbols: Manipulation
The learner will be able to assess the meaning, usefulness, and reasonableness of the results of symbol manipulations, including those performed using technology.
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Operations: Relationships
The learner will be able to comprehend the relationships among operations.
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Algebraic Concepts: Symbolism/Apply
The learner will be able to apply algebraic symbolism as a tool to represent mathematical relationships.
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Algebraic Concepts: Apply/Symbolism
The learner will be able to apply algebraic symbolism as a tool to describe mathematical relationships.
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Computation: Fluency
The learner will be able to compute fluently.
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Computations: Assess/Reasonableness
The learner will be able to assess the reasonableness of numerical computations.
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Computations: Assess/Reasonableness
The learner will be able to assess the reasonableness of the results of numerical computations.
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| Calculus and Pre-Calculus |
| The Calculus/Pre-Calculus Unit includes Competencies/Objectives which focus on calculus concepts. Students study limits, matrix algebra, functions, vectors, conic sections, mathematical induction, and sequence and series using graphical calculators, computers, and models. The Calculus/Pre-Calculus Unit includes Competencies/Objectives which focus on calculus concepts. Students study limits, matrix algebra, functions, vectors, conic sections, mathematical induction, and sequence and series using graphical calculators, computers, and models. |
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Matrices: Real World Problem
The learner will be able to apply matrices in real world problem solving.
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Complex Numbers: Conjugate
The learner will be able to determine the conjugate of a given complex number.
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Complex Numbers: Simple Operations
The learner will be able to perform fundamental operations with complex numbers.
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Matrices: Area/Triangle
The learner will be able to apply matrices to find the area of a triangle on a coordinate plane.
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Matrices/Vectors: Comprehension
The learner will be able to build a comprehension of the properties of, and representations for, the addition and multiplication of vectors and matrices.
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Complex Numbers: Comprehend/Solutions
The learner will be able to comprehend complex numbers as solutions to quadratic equations that do not have real solutions.
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Matrices: Comprehend/Real Numbers
The learner will be able to comprehend matrices as systems that have some of the properties of the real number system.
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Vectors: Comprehend/Real Numbers
The learner will be able to comprehend vectors as systems that have some of the properties of the real number system.
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| Data Interpretation |
| The Data Interpretation Unit includes Competencies/Objectives which focus on the study and use of graphical forms. Students collect and classify data, organize and display data, use logical reasoning, and problem solving. The Data Interpretation Unit includes Competencies/Objectives which focus on the study and use of graphical forms. Students collect and classify data, organize and display data, use logical reasoning, and problem solving. |
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Graphs: Draw/Interpret
The learner will be able to draw and/or interpret graphs which model real world phenomena.
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Data Collection: Technology
The learner will be able to gather data using appropriate technology.
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Scatterplots: Equation/Line of Best Fit
The learner will be able to determine the equation for the best fit line for a given scatterplot of real world data.
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Scatterplots: Correlation/Real World
The learner will be able to classify the correlation of a scatterplot that uses real world data.
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Graphs: Model/Real World
The learner will be able to use functions and graphs to model real world events.
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Graphs: Interpret/Real World
The learner will be able to interpret graphs that model real world phenomena.
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Graphs: Connect/Real World
The learner will be able to connect graphs to the real world situations they illustrate.
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Data Collection
The learner will be able to collect data.
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Data Collection: Organize
The learner will be able to organize data.
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Scatterplots: Understand
The learner will be able to understand scatterplots.
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Scatterplots: Create
The learner will be able to create a scatterplot to display data.
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| Functions |
| The Functions Unit includes Competencies/Objectives which focus on exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions. The Functions Unit includes Competencies/Objectives which focus on exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions. |
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Functions: Explain
The learner will be able to explain the domain and range of functions and describe restrictions imposed by either the operations or by the real world scenario which the functions illustrate.
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Functions: Understand Behavior
The learner will be able to illustrate understanding of the behavior of quadratic, exponential, periodic, and logarithmic functions and their graphs.
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Graphing: Analyze/Explain Behavior
The learner will be able to study graphs to explain the behavior of functions.
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Representations: Functions
The learner will be able to represent many different functions.
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Problem Solving: Linear Programming
The learner will be able to solve real world problems using linear programming.
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Functions: Identify
The learner will be able to recognize functions.
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Functions: Recognize
The learner will be able to recognize the attributes of families of functions.
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Functions: Explain
The learner will be able to explain the attributes of families of functions.
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Functions: Describe
The learner will be able to describe the results of changing parameters of a parent function.
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