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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 I Advanced The Tennessee Mathematics Framework for grades 9 through 12 outlines skills to be taught in Algebra I. |
| 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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Properties: Communicate/Use
The learner will be able to communicate and use algebraic properties in symbolic manipulation.
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Expressions: Operations/Justify
The learner will be able to perform operations on simple expressions, and informally justify 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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Algebraic Concepts: Measure/Approximate
The learner will be able to obtain solutions to problems in measurement and approximation using algebraic thought processes and symbolism.
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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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Linear Equations: Explain Transformation
The learner will be able to explain the transformations of the graph that exist when coefficients and/or constants of the corresponding linear equations are changed.
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Inequality: Interpret
The learner will be able to interpret graphs of inequalities.
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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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Rates: Understand
The learner will be able to illustrate an understanding of rates and various derived and indirect measurements.
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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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Linear System of Equations: Elimination
The learner will be able to apply the elimination method to obtain a solution to a system of two linear equations.
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Linear System of Equations: Graph Method
The learner will be able to apply the graphing method to obtain a solution to a system of two linear equations.
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Properties: Associative/Represent
The learner will be able to model the associative properties of addition and multiplication using manipulatives.
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Properties: Commutative/Represent
The learner will be able to model the commutative properties of addition and multiplication using manipulatives.
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Equation: Describe/Relationship
The learner will be able to write an equation to explain the relationship between data sets.
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Equations: Write/Problem Solving
The learner will be able to symbolically express a problem solving scenario by writing an equation.
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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: Identify
The learner will be able to identify the transformation of the graph that exists when coefficients and/or constants of the corresponding linear equations are changed.
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Linear Equations: Solve/Integers
The learner will be able to apply integers to obtain solutions to one- and two-step linear equations.
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Linear Equations: Solve/Multiple-Step
The learner will be able to obtain solutions to linear equations that involve more than two steps and variables on one side of the equation only.
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Linear Equations: Model/Solution
The learner will be able to apply manipulatives to model the steps for solving basic linear equations.
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Linear Equations: Solve/Multiple-Step
The learner will be able to obtain solutions to linear equations that involve more than two steps and have variables on both sides of the equation.
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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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Inequalities: 1-Variable/Recognize Graph
The learner will be able to recognize the graph of the solution to a one-variable inequality on a number line.
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Absolute Value: Explain/Number Line
The learner will be able to explain the absolute value of a number as distance from the origin by creating a number line.
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Absolute Value: Investigate
The learner will be able to investigate a variety of illustrations of absolute value.
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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: Evaluate/First Degree
The learner will be able to determine an answer for a first degree algebraic expression when given values for one or more variables.
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Expressions: Evaluate/Exponents
The learner will be able to determine an answer for an algebraic expression when given values for one or more variables applying grouping symbols and/or exponents less than four.
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Expressions: Represent/Algebraic
The learner will be able to apply manipulatives to illustrate algebraic expressions and operations.
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Expressions: Translate
The learner will be able to translate word expressions into 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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Monomials: Simplify/Expanded Form
The learner will be able to simplify a monomial expressed in expanded form by applying exponents.
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Binomials: Choose Area Representation
The learner will be able to choose the area illustration for a specific product of two one-variable binomials having positive constants and coefficients.
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Rates: Slope/Real World Scenarios
The learner will be able to use the concept of slope to illustrate rate of change in a real world scenario.
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Algorithms: Explore/Add/Multiply
The learner will be able to explore alternate algorithms that illustrate the relationship of multiplication to addition.
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Algorithms: Explore/Divide/Subtract
The learner will be able to explore alternate algorithms that illustrate the relationship of division to subtraction.
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Systems of Equations: Substitution
The learner will be able to solve a system of two equations with two variables through substitution.
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Systems of Equations: Method/Justify
The learner will be able to justify the choice of a method for obtaining a solution to a system of equations.
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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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Problem Solving: Rate of Change/Apply
The learner will be able to use the concept of rate of change to obtain solutions to real world problems.
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Solution Methods: Justify/Results
The learner will be able to justify correct solutions of algebraic methods.
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Pascal's Triangle: Explore/Patterns
The learner will be able to investigate patterns in Pascal's Triangle.
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Symbols: Choose/Algebraic Notation
The learner will be able to choose the algebraic notation that generalizes the pattern illustrated by data in a table.
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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: Problems/Technology
The learner will be able to apply matrices in real world problem solving using appropriate technology.
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Matrices: Determinant/Describe
The learner will be able to describe the importance of the value of the determinant of a matrix.
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Matrices: Add/Technology
The learner will be able to apply suitable technology to perform addition of matrices.
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Matrices: Subtract/Technology
The learner will be able to apply suitable technology to perform subtraction of matrices.
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Matrices: Multiply Scalar/Technology
The learner will be able to apply suitable technology to perform scalar multiplication of matrices.
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Matrices: Solve/System of Equations
The learner will be able to apply matrices and technology to solve systems of equations.
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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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Circle Graphs: Interpret/Real World
The learner will be able to make interpretations of circle graphs that illustrate real world data.
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Bar Graphs: Interpret/Real World
The learner will be able to make interpretations of bar graphs that illustrate real world data.
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Analyzing Graphs: Judge/Choice
The learner will be able to judge the choice of a graphical illustration which best explains specific 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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