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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 The Tennessee Mathematics Framework for grades 9 through 12 outlines skills to be taught in Algebra II. |
| Algebraic Concepts |
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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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Quadratic Inequalities: Solving
The learner will be able to solve quadratic inequalities.
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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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| 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: 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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| Data Interpretation |
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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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| 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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Functions: Understand/Variety
The learner will be able to exhibit an understanding of the behavior of a variety of functions and their graphs.
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Logarithmic Functions: Inverse/Graph
The learner will be able to find the inverse of the graph of a logarithmic function.
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Rational Functions: Domain/Range
The learner will be able to find the domain and range of rational functions that have variables in the denominator.
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Representations: Functions
The learner will be able to represent many different functions.
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Functions: Transformations/Parent
The learner will be able to describe the transformation that changes a "parent function" to a related function.
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Functions: Choose/Parent
The learner will be able to choose the "parent function" for a set of related functions (not trigonometric or logarithmic).
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Functions: Rule of Signs
The learner will be able to forecast the zeros of a function using Descartes' Rule of Signs.
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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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Inductive Reasoning: Conjecture
The learner will be able to apply techniques of inductive reasoning to formulate a conjecture.
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Deductive Reasoning: Justify
The learner will be able to use deductive reasoning to justify conclusions.
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Spatial Thinking: Describe Position
The learner will be able to describe position using spatial sense with two-dimensional coordinate systems.
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Spatial Thinking: Describe Position
The learner will be able to describe position using spatial sense with three-dimensional coordinate systems.
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Geometric Concepts: Given/Formulas
The learner will be able to utilize the given formulas when problem solving.
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Geometric Relationships: Investigate
The learner will be able to investigate geometric properties and relationships.
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Geometric Relationships: Properties
The learner will be able to use geometric properties, formulas, and relationships to obtain solutions to real world problems.
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Figures: Square/Dimensions
The learner will be able to calculate the new dimensions of a square when given the original dimensions and the numerical increment of change (all dimensions are one-variable first-degree binomials).
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Pythagorean Theorem: Estimate/Irrational
The learner will be able to make an estimation of the irrational solution of a real world problem that utilizes the Pythagorean Theorem.
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Pythagorean Theorem: Real World
The learner will be able to use the given Pythagorean Theorem in real world problems with no radicals in the answers.
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Deductive Reasoning: Conclusions
The learner will be able to use deductive reasoning to draw valid conclusions.
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Geometric Relationships: Height
The learner will be able to calculate the height of an object by applying properties of similar triangles.
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Geometric Relationships: Model
The learner will be able to model geometric relationships and properties.
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Geometric Relationships: Apply
The learner will be able to apply geometric properties and relationships.
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| Measurement |
| The Measurement Unit includes Competencies/Objectives which focus on measurement concepts, applications, and analysis. Students study length, area, circumference, perimeter, volume, weight, formulas, distance, calendar, money, tools, accuracy, units, constructions, patterns, and problem solving. |
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Problem Solving: Algebraic
The learner will be able to use measurement ideas and relationships in algebraic problem solving scenarios.
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Problem Solving: Geometric
The learner will be able to use measurement ideas and relationships in geometric problem solving situations.
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Measurement Concepts: Rate of Change
The learner will be able to use the concept of rate of change.
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Units: Apply/Appropriate
The learner will be able to apply suitable units of measurement.
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| Number Theory |
| The Number Theory Unit includes Competencies/Objectives which focus on manipulating number forms and classifications. Students make connections between number forms and their real world applications. |
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Number Systems: Comprehend/Complex
The learner will be able to illustrate comprehension of the subsets, elements, properties, and/or operations of the complex number system.
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Number Forms: Apply/Notation
The learner will be able to apply mathematical notations appropriately.
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Scientific Notation: Multiply/Two
The learner will be able to find the product of two numbers written in scientific notation and determine the reasonableness of the result.
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Number Theory: Real Numbers/Operations
The learner will be able to identify, illustrate, represent, and use real numbers and operations verbally, physically, symbolically, and graphically.
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Number Systems: Comprehend
The learner will be able to illustrate comprehension of the properties and operations of the complex number system.
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Equivalent Forms: Exponent/Logarithm
The learner will be able to recognize the exponential forms of logarithmic expressions.
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Ratio/Proportion: Choose/Real World
The learner will be able to choose ratios and proportions to illustrate real world problems.
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| Numeration |
| The Numeration Unit includes Competencies/Objectives which focus on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships. |
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Patterns: Problem Solving/Real World
The learner will be able to study mathematical patterns associated with algebra and geometry in real world problem solving situations.
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Patterns: Generalize/Function Notation
The learner will be able to apply algebraic thought processes to generalize a pattern by expressing the pattern in function notation.
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Estimation Strategies: Predicting
The learner will be able to apply estimation strategies to forecast computational results.
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Patterns/Functions: Real World
The learner will be able to explain, continue, study, and develop a large variety of patterns and functions applying suitable materials and illustrations in real world problem solving.
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Sequences: Function Notation/Arithmetic
The learner will be able to utilize functional notation in order to generalize the pattern of an arithmetic sequence.
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Series: Sigma Notation
The learner will be able to show a series in correct sigma notation.
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Estimation: Determine/Reasonableness
The learner will be able to apply estimation to determine the reasonableness of results.
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Estimation: Unit Conversions
The learner will be able to estimate to find a reasonable solution to a tedious arithmetic computation of a real world situation involving unit conversions.
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Estimation: Predict
The learner will be able to estimate in order to predict.
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Compute/Estimate: Strategies
The learner will be able to create effective estimation and computation strategies.
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Patterns: Explore/Product/Factoring
The learner will be able to explore product and factoring patterns.
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| Probability/Statistics |
| The Probability/Statistics Unit includes Competencies/Objectives which focus on data analysis and probability concepts. Students collect, analyze, and make sense of real world data (including overlapping data, inconclusive data, etc.). |
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Data: Gather/Illustrate/Explain
The learner will be able to gather, illustrate and explain linear and nonlinear data sets formulated from the real world.
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Data: Study/Use/Misuse
The learner will be able to study the validity of statistical conclusions and the use and misuse of data.
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Probability Distribution: Explain/Use
The learner will be able to explain and use the normal distribution and its properties.
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Graphing: Select/Create/Study
The learner will be able to select, create, and study suitable graphical illustrations for a set of data including pie charts, histograms, stem and leaf plots, scatterplots and/or box and whisker plots.
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Probability: Law of Large Numbers
The learner will be able to use the Law of Large Numbers.
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Predictions: Curve Fitting/Technology
The learner will be able to make predictions from data using curve fitting applying appropriate technology.
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Central Tendency: Inferences
The learner will be able to create inferences about a set of information using suitable measures of central tendency and dispersion (including variance and standard deviation).
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Theoretical/Experimental: Analyze
The learner will be able to analyze the likelihood of an event using theoretical and experimental probability.
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Sampling: Apply Randomness
The learner will be able to apply the idea of randomness in sampling.
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Mutually/Non-Mutually Exclusive
The learner will be able to identify events as mutually exclusive and non-mutually exclusive.
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Dependent/Independent: Study
The learner will be able to study the probability of dependent and of independent events.
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Counting: Permutations/Combinations
The learner will be able to use appropriate technology to apply counting principles of permutations and combinations.
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Data Analysis: Technology
The learner will be able to analyze data using appropriate technology.
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Simulations: Approximate Probability
The learner will be able to approximate probability using simulations.
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Outcomes: Permutation/Combination
The learner will be able to calculate the number of possible outcomes for a given experiment using the multiplication counting principle, permutations, or combinations.
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Data Analysis: Present/Evaluate
The learner will be able to make a presentation and an evaluation of arguments that are based on the analysis of data.
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Data Analysis: Inferences
The learner will be able to create and evaluate inferences and predictions from data.
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Statistical Analysis: Use/ Misuse/Abuse
The learner will be able to study the validity of statistical conclusions and the use, abuse, and misuse of data.
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Venn Diagrams: Complex/Number/Relations
The learner will be able to examine the relationships among sets of numbers using a Venn diagram of the complex number system.
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Events: Likelihood/Simple/Theoretical
The learner will be able to determine the likelihood of simple events by using theoretical probability.
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Data: Gather/Real World/Generalize
The learner will be able to gather real world data to make generalizations.
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Data: Represent
The learner will be able to represent data.
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Data: Interpretation
The learner will be able to interpret given data.
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Predictions: Simulations/Probability
The learner will be able to utilize simulations to help predict the probabilities of given situations.
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Central Tendency: Calculate/Real World
The learner will be able to calculate the measures of central tendency for real world data sets.
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Measures of Central Tendency: Select
The learner will be able to select the best measure of central tendency to represent a given real world data set.
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Central Tendency: Inferences
The learner will be able to create inferences about a set of information using suitable measures of central tendency and dispersion.
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Theoretical/Experimental Probability
The learner will be able to select theoretical or experimental probability to determine the likelihood of an event.
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Theoretical Probability: Find
The learner will be able to find the theoretical probability of a compound event.
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Theoretical Probability: Mutually
The learner will be able to find the theoretical probability of events in a given situation that are mutually exclusive.
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Theoretical/Experimental: Model
The learner will be able to model situations to find theoretical and experimental probabilities.
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Theoretical Probability: Estimate
The learner will be able to make an estimation of the theoretical probability of an inclusive event for a certain situation.
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Data Analysis: Student Gathered/Predict
The learner will be able to examine student gathered data to make predictions.
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Distributions: Normal/Mean/Deviation
The learner will be able to recognize the mean and standard deviation of the graph of a normal distribution.
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Simulation: Approximate Probability
The learner will be able to use simulations to approximate probability.
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Graphing: Select
The learner will be able to select suitable graphical illustrations for a set of data.
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Graphing: Study
The learner will be able to study suitable graphical illustrations for a set of data.
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Graphing: Create
The learner will be able to create suitable graphical illustrations for a set of data.
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Graphing: Function/Periodic
The learner will be able to assess the graph of a function in order to decide if it is periodic.
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| Problem Solving |
| The Problem Solving Unit includes Competencies/Objectives which focus on analyzing problems, evaluating solutions, exploring problems, and developing strategies for solving problems. |
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Investigations: Individual/Groups
The learner will be able to explore problems individually or in cooperative groups.
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Solution: Reasonableness
The learner will be able to evaluate the reasonableness of a given solution.
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Problem Solving: Use/Tool/Appropriate
The learner will be able to use appropriate tools.
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| Real Numbers and the Coordinate Plane |
| The Real Numbers and the Coordinate Plane Unit includes Competencies/Objectives which focus on graphing concepts. Students graph equations and make connections between algebraic concepts and their geometric correspondences. |
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Real Numbers: Choose/Use
The learner will be able to choose and use an appropriate strategy for computing with real numbers.
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Real Numbers: Connect/Illustrations
The learner will be able to connect concrete, graphical, verbal, and symbolic illustrations of real numbers.
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Linear Inequalities: Sketch/System
The learner will be able to sketch a system of linear inequalities and calculate the minimum or maximum of the related function.
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Slope: Changes/Non-linear/Real World
The learner will be able to describe in story form the slope changes of a non-linear graph that represents a real world situation.
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Problem Solving: Predict/Graph
The learner will be able to formulate predictions from graphs of real world data sets.
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Coordinate Geometry: Three-Dimensions
The learner will be able to find the coordinate of a point in a three-dimensional coordinate system.
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Ordered Pairs: Match/Linear/Graph
The learner will be able to select the matching linear graph when given a set of ordered pairs.
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Real Numbers: Recognize/Reciprocals
The learner will be able to recognize reciprocals of real numbers.
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Real Numbers: Ordering
The learner will be able to order a set of real numbers.
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Real Numbers: Explore/Relationships
The learner will be able to explore the relationships between a variety of subsets of the real number system.
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Graphs: Inequality/Number Line
The learner will be able to recognize the graph that represents the solution to a one-variable inequality on a number line.
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Graphing: Inequality/Two Variables
The learner will be able to choose the graph of an inequality with two-variables given in standard form.
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Graphing: Linear Function/Choose
The learner will be able to choose the graph that illustrates a linear function expressed in slope-intercept form.
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Distance Formula: Circle Equations
The learner will be able to use the distance formula to derive the equation of a circle for solving real world problems.
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| Technology |
| The Technology Unit includes Competencies/Objectives which focus on studying computer hardware and software, uses for calculators, and applications of technology in problem solving. |
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Problem Solving: Technology
The learner will be able to appropriately use technology to solve problems.
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Algebra: Linear/Quadratic
The learner will be able to examine data from linear and quadratic functions using the appropriate technology.
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| Discrete Mathematics |
| The Discrete Mathematics Unit includes Competencies/Objectives which focus on the concepts of discrete mathematics, matrices, and recursion. |
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Matrices: Create
The learner will be able to create matrices involving real world problem solving.
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| Rational and Irrational Numbers |
| The Rational and Irrational Numbers Unit includes Competencies/Objectives which focus on number concepts. Students manipulate, compare, and perform operations with rational and irrational numbers. |
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Equations: Solve/Linear/Rational
The learner will be able to obtain solutions to one-variable linear equations with rational expressions.
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