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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 AB The Algebra I End-of-course test is given after completion of 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: 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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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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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: 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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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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Inequality: Interpret
The learner will be able to interpret graphs of inequalities.
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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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Absolute Value: Connect
The learner will be able to connect concrete, graphical, oral, and symbolic 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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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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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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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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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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| 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. |
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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: Problems/Technology
The learner will be able to apply matrices in real world problem solving using appropriate technology.
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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. |
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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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| 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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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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Representations: Real World Phenomena
The learner will be able to use functions (such as tables, graphs, and expressions) to model real world phenomena.
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Functions: Relationships/Illustrate
The learner will be able to identify relationships which can and cannot be illustrated by a function.
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Functions: Identify
The learner will be able to identify many different functions.
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Functions: Patterns/Real World
The learner will be able to explain in writing the pattern for real world information entered in a function table.
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Functions: Domain/Range/Find
The learner will be able to find the domain and/or range of a function illustrated by the graph of a real world scenario.
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Functions: Distinguish
The learner will be able to differentiate between a function and other relationships.
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Functions: Families/Investigate
The learner will be able to apply technology to investigate function families.
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| Geometry |
| The Geometry Unit includes Competencies/Objectives which focus on exploring geometric concepts from multiple perspectives. Students study properties and construction of figures, proofs and theorems, history of geometry, transformations, logic, and problem solving. |
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Problem Solving: Properties/Formulas
The learner will be able to use geometric relationships, properties, and formulas to obtain solutions to real world problems.
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Problem Solving: Applying Concepts
The learner will be able to apply learned geometry concepts in solving problems.
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Geometric Relationships: Height
The learner will be able to find the height of an item that is hard to measure by applying the properties of similar triangles or the angle of elevation.
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Geometric Relationships: Properties
The learner will be able to study, represent, and use geometric properties and relationships.
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Geometric Relationships: Explain
The learner will be able to explain real world applications of geometric formulas and relationships.
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Triangles: Similar/Proportion
The learner will be able to determine the length of an unknown side of a triangle using proportion and the concepts of similar triangles.
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Pythagorean Theorem: Show
The learner will be able to show the Pythagorean theorem by measuring the length, width, and diagonals of rectangles.
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