Jefferson County Schools
Jefferson County Schools

Mathematics - Algebra II Advanced

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:

MATHEMATICS AS PROBLEM SOLVING

The study of mathematics must emphasize Problem Solving opportunities which require various approaches to investigate, understand, and apply mathematical concepts.
The development of each learner’s ability to solve problems is essential if he or she is to be a productive citizen. We strongly endorse the first recommendation of An Agenda for Action (NCTM, 1980): "Problem solving must be the focus of school mathematics." To develop such abilities, students need to work on problems that may take hours, days, and even weeks to solve. Some may be relatively simple exercises to be accomplished independently; some should involve small groups or an entire class working cooperatively; and some problems should also be open-ended with no single right answer.
"Mathematics as Problem Solving" emphasizes the learners’ use of a broad base of strategies to:
Investigate and understand mathematical content
Recognize and formulate problems from within and outside of mathematics
Use mathematical modeling and appropriate technology to solve a wide variety of problems, including real-world problems.
Generalize solutions and strategies, applying them to new problems
Increase confidence in their ability to use mathematics meaningfully and to become independent problem solvers.

MATHEMATICS AS COMMUNICATION

The study of mathematics must emphasize Communication by requiring opportunities to explain, conjecture, summarize, and defend one’s ideas orally, in writing, and through the use of technology.
The development of a learner’s power to think mathematically involves learning the signs, symbols, and terms of mathematics. This is best accomplished in problem situations in which students have an opportunity to read, write, and discuss ideas in which the use of the language of mathematics becomes natural. As students communicate their ideas, they learn to clarify, refine, and consolidate their answers.
"Mathematics as Communication" focuses on the learners’ development of using language and symbols to:
Reflect and clarify thinking about mathematical ideas and situations
Express mathematical ideas and relationships, orally, in writing, and with physical material, pictures, and diagrams
Understand and value the role of mathematical notation
Realize that representing, discussing, listening, writing, and reading mathematics are vital aspect of mathematics study and use
Use mathematical notation to formulate generalizations.

MATHEMATICS AS REASONING

The study of mathematics must emphasize Reasoning which requires critical thinking, logical argument, and justification of solutions, of thought processes, and of conjectures.
Making conjectures, gathering evidence, and building an argument to support such notions are fundamental to doing mathematics. In fact, a demonstration of good reasoning should be rewarded even more than the learner’s ability to find correct answers.
"Mathematics as Reasoning" concentrates on leading the learners to:
Make and test mathematical conjectures
Make, follow, and judge the value of mathematical arguments
Draw logical conclusions
Justify solution-finding processes and answers.

MATHEMATICAL CONNECTIONS

The study of mathematics must emphasize making Connections among the various topics within mathematics, between mathematics and other disciplines, and between mathematics and "real world" situations.
The mathematics curriculum is often viewed as consisting of several discrete stands; so topics tend to be taught in isolation. Unless the learners connect ideas both among and between areas of mathematics, they learn isolated skills rather than develop the ability to recognize general principles and procedures relevant to several areas. Connecting conceptual understanding to procedures will enable learners to apply, recreate, and invent new procedures when needed. Failure to connect conceptual understanding to procedures results in a view of mathematics as an arbitrary set of rules. Learners should have many opportunities to observe and work with the interaction of mathematics with other subjects and with everyday society. Problems become meaningful when they relate to the learners’ experiences. Mathematics must be integrated into contexts that give its symbols and processes practical meaning. The school environment is rich with opportunities to use mathematics in other subject areas as well as other subject area content in mathematics.
"Mathematical Connections" concentrate on enabling the learners to:
Appreciate mathematics as an integrated whole, linking conceptual and procedural knowledge within the discipline and relating multiple representations of concepts or procedures to one another.
Apply mathematical thinking and modeling to solve substantial problems that arise in other disciplines and curriculum areas, such as art, business, music, psychology, industrial arts, computer technology, social studies, and sciences, such as biology, chemistry, and physics.
Use, recognize, and value the varied roles of mathematics in their lives, cultures, and society.

The Principles and Standards for School Mathematics describe the mathematical understanding, knowledge, and skills that students should acquire from prekindergarten through grade 12.

Algebra I is the Tennessee End-of-course test that must be passed before graduation to earn a high school diploma.

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.

    Expressions: Operations/Justification
The learner will be able to perform operations on expressions and give justification of the procedures selected.
Strand Bloom's Scope Hours Source
Expressions Master TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 29
  
    Inverse: Explain/Illustrate
The learner will be able to informally explain and illustrate the concept of inverse.
Strand Bloom's Scope Hours Source
Inverse Operations Master TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 29
  
    Linear System of Equations: Solve
The learner will be able to obtain solutions to linear systems employing a variety of methods including matrices.
Strand Bloom's Scope Hours Source
Linear Systems of Inequalities Application Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Absolute Value: Connect
The learner will be able to connect concrete, graphical, oral, and symbolic illustrations of absolute value.
Strand Bloom's Scope Hours Source
Absolute Value Analysis Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 29
  
    Inverse Operations: Describing
The learner will be able to describe the inverse operations of addition/subtraction and multiplication/division.
Strand Bloom's Scope Hours Source
Inverse Operations Comprehension Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 29
  
    Inverse Operations: Use
The learner will be able to use inverse operations.
Strand Bloom's Scope Hours Source
Inverse Operations Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 29
  
    Inverse Operations: Use
The learner will be able to use the concept of inverse.
Strand Bloom's Scope Hours Source
Inverse Operations Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 29
  
    Inverse Operations: Model
The learner will be able to model inverse operations.
Strand Bloom's Scope Hours Source
Inverse Operations Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 29
  
    Algebraic Concepts: Interpret
The learner will be able to interpret the outcomes of algebraic procedures.
Strand Bloom's Scope Hours Source
Algebraic Concepts Analysis Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Variable: Describe
The learner will be able to describe the definition of a variable in an expression, equation, and inequality.
Strand Bloom's Scope Hours Source
Variable Comprehension Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Variables: Solve Inequalities
The learner will be able to apply the idea of a variable in obtaining solutions to inequalities.
Strand Bloom's Scope Hours Source
Variable Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Variable: Expression/Equation
The learner will be able to use the concept of variable to simplify expressions and obtain solutions to equations.
Strand Bloom's Scope Hours Source
Variable Application Master 2.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Solution Methods: Appropriate Tools
The learner will be able to compute using appropriate tools such as mental math, technology, manipulatives, and pencil-and-paper.
Strand Bloom's Scope Hours Source
Solution Methods Master TN: End-of-Course tests, 2001, Algebra II, 2.0 week tested: 16.
  
    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.
Strand Bloom's Scope Hours Source
Linear Systems of Inequalities Application Master 1.5 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIT Level 2 week tested: 16.
  
    Equations: Linear/Three Variables
The learner will be able to find the traces of a linear equation in three variables.
Strand Bloom's Scope Hours Source
Equations Comprehension Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 5.0 PIT Level 3 week tested: 16.
  
    Equations: Choose/Pattern
The learner will be able to choose the algebraic equation that generalizes the pattern in a given table of data.
Strand Bloom's Scope Hours Source
Equations Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIS Level 1 week tested: 16.
  
    Equations: Translating/Verbal Sentence
The learner will be able to make translations of verbal sentences into algebraic equations.
Strand Bloom's Scope Hours Source
Equations Synthesis Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIS Level 1 week tested: 16.
  
    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.
Strand Bloom's Scope Hours Source
Linear Equations Application Master 0.5 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIS Level 1 week tested: 16.
  
    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.
Strand Bloom's Scope Hours Source
Linear Equations Analysis Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIS Level 2 week tested: 16.
  
    Absolute Value: Match/Graph
The learner will be able to match a set of absolute value data to its graph on the coordinate plane.
Strand Bloom's Scope Hours Source
Absolute Value Knowledge Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 1.0 PIS Level 2 week tested: 16.
  
    Absolute Value: Investigate/Number Line
The learner will be able to investigate a variety of representations of absolute value on a number line.
Strand Bloom's Scope Hours Source
Absolute Value Analysis Master 0.5 TN: End-of-Course tests, 2001, Algebra II, 1.0 PIT Level 1 week tested: 16.
  
    Expressions: Operations/Rational
The learner will be able to conduct basic operations on rational expressions.
Strand Bloom's Scope Hours Source
Expressions Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 2.0 PIT Level 2 week tested: 16.
  
    Expressions: Add/Algebraic
The learner will be able to add algebraic expressions.
Strand Bloom's Scope Hours Source
Expressions Application Master 0.5 TN: End-of-Course tests, 2001, Algebra II, 2.0 PIS Level 2 week tested: 16.
  
    Expressions: Subtract/Algebraic
The learner will be able to subtract algebraic expressions.
Strand Bloom's Scope Hours Source
Expressions Application Master 0.5 TN: End-of-Course tests, 2001, Algebra II, 2.0 PIS Level 2 week tested: 16.
  
    Expressions: Multiply/Algebraic
The learner will be able to multiply algebraic expressions.
Strand Bloom's Scope Hours Source
Expressions Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 2.0 PIS Level 2 week tested: 16.
  
    Polynomials: Multiply/Two/Binomials
The learner will be able to perform multiplication on two polynomials with each polynomial having two terms or less.
Strand Bloom's Scope Hours Source
Polynomials Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 2.0 PIS Level 1 week tested: 16.
  
    Polynomials: Determine/Roots
The learner will be able to calculate all of the roots of higher order polynomials.
Strand Bloom's Scope Hours Source
Polynomials Application Master 1.5 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIT Level 2 week tested: 16.
  
    Binomials: Area Representation
The learner will be able to choose the area illustration for a specific product of two binomials.
Strand Bloom's Scope Hours Source
Polynomials Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 2.0 PIS Level 3 week tested: 16.
  
    Radicals: Explain/Variable/Restrictions
The learner will be able to describe the restrictions on the variables in radical equations.
Strand Bloom's Scope Hours Source
Radicals Comprehension Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIT Level 2 week tested: 16.
  
    Quadratic Equation: Select/Procedure
The learner will be able to select an appropriate procedure to find the roots of a quadratic equation.
Strand Bloom's Scope Hours Source
Quadratic Equations/Formula Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIT Level 2 week tested: 16.
  
    Exponents: Simplify/Expressions
The learner will be able to simplify expressions containing rational and negative exponents.
Strand Bloom's Scope Hours Source
Exponents Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 1.0 PIS Level 2 week tested: 16.
  
    Operations: Justify/Methods
The learner will be able to justify the methods selected when operations on algebraic equations and expressions are conducted.
Strand Bloom's Scope Hours Source
Operations Evaluation Master 1.5 TN: End-of-Course tests, 2001, Algebra II, 2.0 PIT Level 3 week tested: 16.
  
    Inverse Operations: Describe
The learner will be able to describe inverse operations.
Strand Bloom's Scope Hours Source
Inverse Operations Comprehension Master 0.5 TN: End-of-Course tests, 2001, Algebra II, 1.4 week tested: 16.
  
    Inverse Operations: Articulate
The learner will be able to articulate the concept of inverse.
Strand Bloom's Scope Hours Source
Inverse Operations Comprehension Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 1.3 week tested: 16.
  
    Inverse Operations: Complex
The learner will be able to find the multiplicative inverse of a complex number.
Strand Bloom's Scope Hours Source
Inverse Operations Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 1.0 PIT Level 3 week tested: 16.
  
    Inverse Operations
The learner will be able to choose the inverse notation of powers and roots.
Strand Bloom's Scope Hours Source
Inverse Operations Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 1.0 PIT Level 2 week tested: 16.
  
    Inverse Operations: Model
The learner will be able to model the concept of inverse.
Strand Bloom's Scope Hours Source
Inverse Operations Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 1.3 week tested: 16.
  
    Algebraic Concepts: Real World
The learner will be able to use the results of algebraic processes in real-world situations.
Strand Bloom's Scope Hours Source
Algebraic Concepts Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIT Level 2 week tested: 16.
  
    Logarithms: Simplifying
The learner will be able to use logarithmic properties to simplify expressions.
Strand Bloom's Scope Hours Source
Logarithms Application Master 1.5 TN: End-of-Course tests, 2001, Algebra II, 2.0 PIT Level 2 week tested: 16.
  
    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.
Strand Bloom's Scope Hours Source
Number Sense Analysis Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 2.0 PIT Level 1 week tested: 16.
  
    Binomial Expansion: Factorial
The learner will be able to apply factorial notation to the coefficients in a binomial expansion.
Strand Bloom's Scope Hours Source
Binomial Expansion Application Master 0.5 TN: End-of-Course tests, 2001, Algebra II, 1.0 PIT Level 3 week tested: 16.
  
    Symbols: Delta Notation/Real World
The learner will be able to represent rates of change in real world situations using delta notation.
Strand Bloom's Scope Hours Source
Symbols Application Master 0.5 TN: End-of-Course tests, 2001, Algebra II, 1.0 PIT Level 2 week tested: 16.
  
    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.
Strand Bloom's Scope Hours Source
Operations Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  
    Rates: Estimate/Interpret
The learner will be able to estimate and interpret rates of change using graphical and numerical data.
Strand Bloom's Scope Hours Source
Rates Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    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.
Strand Bloom's Scope Hours Source
Symbols Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Operations: Relationships
The learner will be able to comprehend the relationships among operations.
Strand Bloom's Scope Hours Source
Operations Comprehension Master 2.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  
    Algebraic Concepts: Symbolism/Apply
The learner will be able to apply algebraic symbolism as a tool to represent mathematical relationships.
Strand Bloom's Scope Hours Source
Algebraic Concepts Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Algebraic Concepts: Apply/Symbolism
The learner will be able to apply algebraic symbolism as a tool to describe mathematical relationships.
Strand Bloom's Scope Hours Source
Algebraic Concepts Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Computation: Fluency
The learner will be able to compute fluently.
Strand Bloom's Scope Hours Source
Computation Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  
    Computations: Assess/Reasonableness
The learner will be able to assess the reasonableness of numerical computations.
Strand Bloom's Scope Hours Source
Computation Evaluation Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  
    Computations: Assess/Reasonableness
The learner will be able to assess the reasonableness of the results of numerical computations.
Strand Bloom's Scope Hours Source
Computation Evaluation Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  

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.

    Matrices: Real World Problem
The learner will be able to apply matrices in real world problem solving.
Strand Bloom's Scope Hours Source
Matrices Application Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 29
  
    Complex Numbers: Conjugate
The learner will be able to determine the conjugate of a given complex number.
Strand Bloom's Scope Hours Source
Complex Numbers Application Master 0.5 TN: End-of-Course tests, 2001, Algebra II, 1.0 PIS Level 3 week tested: 16.
  
    Complex Numbers: Simple Operations
The learner will be able to perform fundamental operations with complex numbers.
Strand Bloom's Scope Hours Source
Complex Numbers Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 1.0 PIS Level 2 week tested: 16.
  
    Matrices: Area/Triangle
The learner will be able to apply matrices to find the area of a triangle on a coordinate plane.
Strand Bloom's Scope Hours Source
Matrices Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 5.0 PIS Level 3 week tested: 16.
  
    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.
Strand Bloom's Scope Hours Source
Matrices Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  
    Complex Numbers: Comprehend/Solutions
The learner will be able to comprehend complex numbers as solutions to quadratic equations that do not have real solutions.
Strand Bloom's Scope Hours Source
Complex Numbers Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  
    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.
Strand Bloom's Scope Hours Source
Matrices Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  
    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.
Strand Bloom's Scope Hours Source
Vectors Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  

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.

    Graphs: Draw/Interpret
The learner will be able to draw and/or interpret graphs which model real world phenomena.
Strand Bloom's Scope Hours Source
Graphing Master TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Data Collection: Technology
The learner will be able to gather data using appropriate technology.
Strand Bloom's Scope Hours Source
Data Collection and Classification Comprehension Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    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.
Strand Bloom's Scope Hours Source
Scatterplots Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 4.0 PIS Level 2 week tested: 16.
  
    Scatterplots: Correlation/Real World
The learner will be able to classify the correlation of a scatterplot that uses real world data.
Strand Bloom's Scope Hours Source
Scatterplots Analysis Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 4.0 PIS Level 2 week tested: 16.
  
    Graphs: Model/Real World
The learner will be able to use functions and graphs to model real world events.
Strand Bloom's Scope Hours Source
Graphing Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.14 week tested: 16.
  
    Graphs: Interpret/Real World
The learner will be able to interpret graphs that model real world phenomena.
Strand Bloom's Scope Hours Source
Graphing Analysis Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.13 week tested: 16.
  
    Graphs: Connect/Real World
The learner will be able to connect graphs to the real world situations they illustrate.
Strand Bloom's Scope Hours Source
Graphing Synthesis Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIS Level 1 week tested: 16.
  
    Data Collection
The learner will be able to collect data.
Strand Bloom's Scope Hours Source
Data Collection and Classification Comprehension Master 0.5 TN: End-of-Course tests, 2001, Algebra II, 4.0 week tested: 16.
  
    Data Collection: Organize
The learner will be able to organize data.
Strand Bloom's Scope Hours Source
Data Collection and Classification Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 4.0 week tested: 16.
  
    Scatterplots: Understand
The learner will be able to understand scatterplots.
Strand Bloom's Scope Hours Source
Scatterplots Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Scatterplots: Create
The learner will be able to create a scatterplot to display data.
Strand Bloom's Scope Hours Source
Scatterplots Synthesis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  

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.

    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.
Strand Bloom's Scope Hours Source
Functions Master TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Functions: Understand Behavior
The learner will be able to illustrate understanding of the behavior of quadratic, exponential, periodic, and logarithmic functions and their graphs.
Strand Bloom's Scope Hours Source
Functions Master TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Graphing: Analyze/Explain Behavior
The learner will be able to study graphs to explain the behavior of functions.
Strand Bloom's Scope Hours Source
Graphing Functions Analysis Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Representations: Functions
The learner will be able to represent many different functions.
Strand Bloom's Scope Hours Source
Representations of Functions Application Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Problem Solving: Linear Programming
The learner will be able to solve real world problems using linear programming.
Strand Bloom's Scope Hours Source
Problem Solving Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Functions: Identify
The learner will be able to recognize functions.
Strand Bloom's Scope Hours Source
Functions Knowledge Master 0.5 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Functions: Recognize
The learner will be able to recognize the attributes of families of functions.
Strand Bloom's Scope Hours Source
Functions Comprehension Master 0.5 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Functions: Explain
The learner will be able to explain the attributes of families of functions.
Strand Bloom's Scope Hours Source
Functions Comprehension Master 0.5 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Functions: Describe
The learner will be able to describe the results of changing parameters of a parent function.
Strand Bloom's Scope Hours Source
Functions Comprehension Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Functions: Understand/Variety
The learner will be able to exhibit an understanding of the behavior of a variety of functions and their graphs.
Strand Bloom's Scope Hours Source
Functions Master TN: End-of-Course tests, 2001, Algebra II, 3.0 week tested: 16.
  
    Logarithmic Functions: Inverse/Graph
The learner will be able to find the inverse of the graph of a logarithmic function.
Strand Bloom's Scope Hours Source
Logarithmic Functions Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIS Level 3 week tested: 16.
  
    Rational Functions: Domain/Range
The learner will be able to find the domain and range of rational functions that have variables in the denominator.
Strand Bloom's Scope Hours Source
Rational Functions Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIS Level 2 week tested: 16.
  
    Representations: Functions
The learner will be able to represent many different functions.
Strand Bloom's Scope Hours Source
Representations of Functions Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.6 week tested: 16.
  
    Functions: Transformations/Parent
The learner will be able to describe the transformation that changes a "parent function" to a related function.
Strand Bloom's Scope Hours Source
Functions Comprehension Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIS Level 2 week tested: 16.
  
    Functions: Choose/Parent
The learner will be able to choose the "parent function" for a set of related functions (not trigonometric or logarithmic).
Strand Bloom's Scope Hours Source
Functions Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIS Level 2 week tested: 16.
  
    Functions: Rule of Signs
The learner will be able to forecast the zeros of a function using Descartes' Rule of Signs.
Strand Bloom's Scope Hours Source
Functions Analysis Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 1.0 PIT Level 3 week tested: 16.
  
    Function/Relation: Apply/Representation
The learner will be able to apply many different symbolic representations, including recursive and parametric equations, for functions and relations.
Strand Bloom's Scope Hours Source
Functions/Relations Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Functions/Relations: Comprehend
The learner will be able to comprehend relations and functions and choose, proficiently perform conversions, and use different representations of them.
Strand Bloom's Scope Hours Source
Functions/Relations Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Functions: Comprehend/Compare
The learner will be able to comprehend and make comparisons of the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions.
Strand Bloom's Scope Hours Source
Functions Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Functions: Comprehend/Apply
The learner will be able to comprehend and apply transformations (such as arithmetically combining, composing, and inverting commonly used functions) by applying technology to perform such operations on more complex symbolic expressions.
Strand Bloom's Scope Hours Source
Functions Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Functions: Apply/Explicit and Recursive
The learner will be able to apply explicitly and recursively defined functions in order to generalize patterns.
Strand Bloom's Scope Hours Source
Functions Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Functional Relationships: Recognize
The learner will be able to recognize essential quantitative relationships in a scenario and find the class or classes of functions that might model the relationships.
Strand Bloom's Scope Hours Source
Functional Relationships Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Exploring: Study/1 Variable Functions
The learner will be able to study functions of one variable by exploring rates of change, intercepts, zeros, asymptotes, and local and global behavior.
Strand Bloom's Scope Hours Source
Exploring Analysis Master 2.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Representations: Interpret
The learner will be able to make interpretations of representations of functions of two variables.
Strand Bloom's Scope Hours Source
Representations of Functions Analysis Master 2.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Relations: Comprehend
The learner will be able to comprehend relations.
Strand Bloom's Scope Hours Source
Relations Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Functions: Understand
The learner will be able to understand functions.
Strand Bloom's Scope Hours Source
Functions Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  

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. 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.

    Problem Solving: Properties/Formulas
The learner will be able to use geometric relationships, properties, and formulas to obtain solutions to real world problems.
Strand Bloom's Scope Hours Source
Problem Solving Master TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 31
  
    Inductive Reasoning: Conjecture
The learner will be able to apply techniques of inductive reasoning to formulate a conjecture.
Strand Bloom's Scope Hours Source
Reasoning Synthesis Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 31
  
    Deductive Reasoning: Justify
The learner will be able to use deductive reasoning to justify conclusions.
Strand Bloom's Scope Hours Source
Reasoning Synthesis Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 31
  
    Spatial Thinking: Describe Position
The learner will be able to describe position using spatial sense with two-dimensional coordinate systems.
Strand Bloom's Scope Hours Source
Spatial Thinking Comprehension Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 31
  
    Spatial Thinking: Describe Position
The learner will be able to describe position using spatial sense with three-dimensional coordinate systems.
Strand Bloom's Scope Hours Source
Spatial Thinking Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 31
  
    Geometric Concepts: Given/Formulas
The learner will be able to utilize the given formulas when problem solving.
Strand Bloom's Scope Hours Source
Geometric Concepts Master TN: End-of-Course tests, 2001, Algebra II, 5.0 PIS Level 1 week tested: 16.
  
    Geometric Relationships: Investigate
The learner will be able to investigate geometric properties and relationships.
Strand Bloom's Scope Hours Source
Geometric Relationships Master TN: End-of-Course tests, 2001, Algebra II, 5.0 week tested: 16.
  
    Geometric Relationships: Properties
The learner will be able to use geometric properties, formulas, and relationships to obtain solutions to real world problems.
Strand Bloom's Scope Hours Source
Geometric Relationships Master TN: End-of-Course tests, 2001, Algebra II, 5.1 week tested: 16.
  
    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).
Strand Bloom's Scope Hours Source
Figures Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 2.0 PIS Level 2 week tested: 16.
  
    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.
Strand Bloom's Scope Hours Source
Pythagorean Theorem Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 5.0 PIT Level 1 week tested: 16.
  
    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.
Strand Bloom's Scope Hours Source
Pythagorean Theorem Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 5.0 PIS Level 1 week tested: 16.
  
    Deductive Reasoning: Conclusions
The learner will be able to use deductive reasoning to draw valid conclusions.
Strand Bloom's Scope Hours Source
Reasoning Synthesis Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 5.0 PIT Level 2 week tested: 16.
  
    Geometric Relationships: Height
The learner will be able to calculate the height of an object by applying properties of similar triangles.
Strand Bloom's Scope Hours Source
Geometric Relationships Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 5.0 PIS Level 2 week tested: 16.
  
    Geometric Relationships: Model
The learner will be able to model geometric relationships and properties.
Strand Bloom's Scope Hours Source
Geometric Relationships Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 5.0 week tested: 16.
  
    Geometric Relationships: Apply
The learner will be able to apply geometric properties and relationships.
Strand Bloom's Scope Hours Source
Geometric Relationships Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 5.0 week tested: 16.
  
    Two-/Three-Dimensional: Study
The learner will be able to study properties and identify the characteristics of two- and three-dimensional objects.
Strand Bloom's Scope Hours Source
Figures: Two-/Three-Dimensional Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Two-/Three-Dimensional: Investigate
The learner will be able to investigate relationships, including congruence and similarity, among classes of two- and three-dimensional objects, formulate and test conjectures about them, and obtain solutions to problems involving them.
Strand Bloom's Scope Hours Source
Figures: Two-/Three-Dimensional Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Two-/Three-Dimensional: Draw/Create
The learner will be able to draw and create representations of two- and three-dimensional geometric objects using many different tools.
Strand Bloom's Scope Hours Source
Figures: Two-/Three-Dimensional Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Three-Dimensional: Visualize
The learner will be able to visualize three-dimensional objects from various perspectives and study their cross sections.
Strand Bloom's Scope Hours Source
Three-Dimensional Solids Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Transformations: Apply/Representations
The learner will be able to apply different representations to aide in the understanding of the effects of simple transformations and their compositions.
Strand Bloom's Scope Hours Source
Transformations Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Transformations: Comprehend/Illustrate
The learner will be able to comprehend and illustrate translations, reflections, rotations, and dilations of objects in the plane by applying sketches, coordinates, vectors, function notation, and matrices.
Strand Bloom's Scope Hours Source
Transformations Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Geometric Concepts: Apply
The learner will be able to apply geometric concepts to obtain solutions to problems in, and gain insights into, other content areas and other areas of interest.
Strand Bloom's Scope Hours Source
Geometric Concepts Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Proofs/Theorems: Establish/Validity
The learner will be able to establish the validity of geometric conjectures by applying deduction, prove theorems, and judge arguments made by others.
Strand Bloom's Scope Hours Source
Geometric Proofs/Theorems Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Spatial Relationships: Location
The learner will be able to specify locations and explain spatial relationships by applying coordinate geometry and various other representational systems.
Strand Bloom's Scope Hours Source
Spatial Relationships Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Geometric Models: Apply
The learner will be able to apply geometric models in order to gain insights into, and answer questions in, other topics in mathematics.
Strand Bloom's Scope Hours Source
Geometric Models Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Solids: Study/Characteristics
The learner will be able to study the characteristics of three-dimensional solids.
Strand Bloom's Scope Hours Source
Three-Dimensional Solids Analysis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Solids: Study/Properties
The learner will be able to study the properties of three-dimensional solids.
Strand Bloom's Scope Hours Source
Three-Dimensional Solids Analysis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Shapes: Study/Characteristics
The learner will be able to study the characteristics of two-dimensional shapes.
Strand Bloom's Scope Hours Source
Two-Dimensional Shapes Analysis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Shapes: Study/Properties
The learner will be able to study the properties of two-dimensional shapes.
Strand Bloom's Scope Hours Source
Two-Dimensional Shapes Analysis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Transformations: Apply
The learner will be able to apply transformations to study mathematical situations.
Strand Bloom's Scope Hours Source
Transformations Analysis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Reasoning: Spatial
The learner will be able to use spatial reasoning to solve problems.
Strand Bloom's Scope Hours Source
Reasoning Synthesis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Proofs: Choose
The learner will be able to choose from many different methods of proofs.
Strand Bloom's Scope Hours Source
Proofs Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Reasoning and Proof Standard
  
    Proofs: Apply
The learner will be able to apply many different methods of proofs.
Strand Bloom's Scope Hours Source
Proofs Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Reasoning and Proof Standard
  
    Symmetry: Apply
The learner will be able to apply symmetry to study mathematical scenarios.
Strand Bloom's Scope Hours Source
Symmetry Analysis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Problem Solving: Geometric Models
The learner will be able to obtain solutions to problem situations with geometric models.
Strand Bloom's Scope Hours Source
Problem Solving Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Problem Solving: Apply
The learner will be able to apply vertex-edge graphs in order to model problems.
Strand Bloom's Scope Hours Source
Problem Solving Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Problem Solving: Apply
The learner will be able to apply vertex-edge graphs in order to obtain solutions to problems.
Strand Bloom's Scope Hours Source
Problem Solving Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Spatial Thinking: Problem Solving
The learner will be able to obtain solutions to problems using spatial visualization.
Strand Bloom's Scope Hours Source
Spatial Thinking Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Geometric Relationships: Create/Argument
The learner will be able to create mathematical arguments about geometric relationships.
Strand Bloom's Scope Hours Source
Geometric Relationships Synthesis Master 2.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  

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. 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.

    Problem Solving: Algebraic
The learner will be able to use measurement ideas and relationships in algebraic problem solving scenarios.
Strand Bloom's Scope Hours Source
Problem Solving Master TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 29
  
    Problem Solving: Geometric
The learner will be able to use measurement ideas and relationships in geometric problem solving situations.
Strand Bloom's Scope Hours Source
Problem Solving Master TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 29
  
    Measurement Concepts: Rate of Change
The learner will be able to use the concept of rate of change.
Strand Bloom's Scope Hours Source
Measurement Concepts Application Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Units: Apply/Appropriate
The learner will be able to apply suitable units of measurement.
Strand Bloom's Scope Hours Source
Units Application Master 1.5 TN: End-of-Course tests, 2001, Algebra II, 2.0 week tested: 16.
  
    Measurement Processes: Comprehend
The learner will be able to comprehend the measurable characteristics of objects and the units, systems, and processes of measurement.
Strand Bloom's Scope Hours Source
Measurement Processes Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Measurement Standard
  
    Measurement: Apply/Ideas
The learner will be able to use informal ideas of successive approximation, upper and lower bounds, and limit in measurement scenarios.
Strand Bloom's Scope Hours Source
Measurement: Application Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Measurement Standard
  
    Formulas: Comprehend/Apply
The learner will be able to comprehend and apply formulas for the area, surface area, and volume of figures, including cylinders, spheres, and cones.
Strand Bloom's Scope Hours Source
Formulas Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Measurement Standard
  
    Measurement Processes: Use
The learner will be able to use various methods to determine measurements.
Strand Bloom's Scope Hours Source
Measurement Processes Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Measurement Standard
  
    Units: Decide/Appropriate
The learner will be able to make decisions about appropriate units for measurement problem scenarios.
Strand Bloom's Scope Hours Source
Units Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Measurement Standard
  
    Measurement Analysis: Apply/Units
The learner will be able to apply unit analysis to check computations in measurement.
Strand Bloom's Scope Hours Source
Measurement: Analysis Analysis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Measurement Standard
  
    Scales: Decide/Appropriate
The learner will be able to make decisions about appropriate scales for measurement problem scenarios.
Strand Bloom's Scope Hours Source
Scale Drawings Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Measurement Standard
  
    Accuracy: Study
The learner will be able to study accuracy in measurement scenarios.
Strand Bloom's Scope Hours Source
Accuracy Analysis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Measurement Standard
  
    Accuracy: Study/Precision
The learner will be able to study precision in measurement scenarios.
Strand Bloom's Scope Hours Source
Accuracy Analysis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Measurement Standard
  
    Accuracy: Study/Error
The learner will be able to study approximate error in measurement scenarios.
Strand Bloom's Scope Hours Source
Accuracy Analysis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Measurement Standard
  
    Formulas: Use/Determine Measures
The learner will be able to use various formulas to determine measurements.
Strand Bloom's Scope Hours Source
Formulas Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Measurement Standard
  
    Tools: Use/Determine Measures
The learner will be able to use various tools for determining measurements.
Strand Bloom's Scope Hours Source
Tools/Instruments Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Measurement Standard
  

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. 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.

    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.
Strand Bloom's Scope Hours Source
Number Systems Master TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 29
  
    Number Forms: Apply/Notation
The learner will be able to apply mathematical notations appropriately.
Strand Bloom's Scope Hours Source
Number Forms Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 29
  
    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.
Strand Bloom's Scope Hours Source
Scientific Notation Master TN: End-of-Course tests, 2001, Algebra II, 2.0 PIT Level 2 week tested: 16.
  
    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.
Strand Bloom's Scope Hours Source
Number Theory Master TN: End-of-Course tests, 2001, Algebra II, 1.0 week tested: 16.
  
    Number Systems: Comprehend
The learner will be able to illustrate comprehension of the properties and operations of the complex number system.
Strand Bloom's Scope Hours Source
Number Systems Master TN: End-of-Course tests, 2001, Algebra II, 1.0 week tested: 16.
  
    Equivalent Forms: Exponent/Logarithm
The learner will be able to recognize the exponential forms of logarithmic expressions.
Strand Bloom's Scope Hours Source
Equivalent Forms Knowledge Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 1.0 PIS Level 2 week tested: 16.
  
    Ratio/Proportion: Choose/Real World
The learner will be able to choose ratios and proportions to illustrate real world problems.
Strand Bloom's Scope Hours Source
Ratio/Proportion Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 1.0 PIT Level 1 week tested: 16.
  
    Equivalent Forms: Write
The learner will be able to write equivalent forms of equations, inequalities, and systems of equations and obtain solutions for them with fluency by applying mental math or paper and pencil in simple scenarios and by applying technology in all scenarios.
Strand Bloom's Scope Hours Source
Equivalent Forms Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Number Size: Comprehend/Large/Small
The learner will be able to build a deeper comprehension of very large and very small numbers and the different representations of them.
Strand Bloom's Scope Hours Source
Number Size Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  
    Math Structures: Illustrate/Analyze
The learner will be able to illustrate and analyze mathematical situations and structures by applying algebraic symbols.
Strand Bloom's Scope Hours Source
Math Structures Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Equivalent Forms: Comprehend
The learner will be able to comprehend the meaning of equivalent forms of expressions, equations, inequalities, and relations.
Strand Bloom's Scope Hours Source
Equivalent Forms Comprehension Master 2.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Number Theory: Apply/Arguments
The learner will be able to apply number theory arguments in order to justify relationships involving whole numbers.
Strand Bloom's Scope Hours Source
Number Theory Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  
    Number Forms: Understand/Relationships
The learner will be able to understand number relationships.
Strand Bloom's Scope Hours Source
Number Forms: Relationships Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  
    Number Forms: Represent/Understand
The learner will be able to understand the various ways of representing numbers.
Strand Bloom's Scope Hours Source
Number Forms: Representing Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  
    Number Systems: Understand
The learner will be able to comprehend number systems.
Strand Bloom's Scope Hours Source
Number Systems Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  

Numeration
The Numeration Unit includes Competencies/Objectives which focus on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships. The Numeration Unit includes Competencies/Objectives which focus on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships.

    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.
Strand Bloom's Scope Hours Source
Patterns: Problem Solving Master TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    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.
Strand Bloom's Scope Hours Source
Patterns: Generalize Synthesis Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Estimation Strategies: Predicting
The learner will be able to apply estimation strategies to forecast computational results.
Strand Bloom's Scope Hours Source
Estimation Strategies Application Master 2.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 29
  
    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.
Strand Bloom's Scope Hours Source
Patterns: Relationships Master TN: End-of-Course tests, 2001, Algebra II, 3.0 week tested: 16.
  
    Sequences: Function Notation/Arithmetic
The learner will be able to utilize functional notation in order to generalize the pattern of an arithmetic sequence.
Strand Bloom's Scope Hours Source
Sequences Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIS Level 2 week tested: 16.
  
    Series: Sigma Notation
The learner will be able to show a series in correct sigma notation.
Strand Bloom's Scope Hours Source
Series Application Master 0.5 TN: End-of-Course tests, 2001, Algebra II, 1.0 PIS Level 3 week tested: 16.
  
    Estimation: Determine/Reasonableness
The learner will be able to apply estimation to determine the reasonableness of results.
Strand Bloom's Scope Hours Source
Estimation Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 2.1 week tested: 16.
  
    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.
Strand Bloom's Scope Hours Source
Estimation Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 2.0 PIT Level 1 week tested: 16.
  
    Estimation: Predict
The learner will be able to estimate in order to predict.
Strand Bloom's Scope Hours Source
Estimation Analysis Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 2.1 week tested: 16.
  
    Compute/Estimate: Strategies
The learner will be able to create effective estimation and computation strategies.
Strand Bloom's Scope Hours Source
Computing/Estimating Synthesis Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 2.0 week tested: 16.
  
    Patterns: Explore/Product/Factoring
The learner will be able to explore product and factoring patterns.
Strand Bloom's Scope Hours Source
Patterns: Exploring Analysis Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 2.0 PIT Level 1 week tested: 16.
  
    Number Properties/Systems: Compare
The learner will be able to make comparisons and contrast the properties of numbers and number systems, including the rational and real numbers.
Strand Bloom's Scope Hours Source
Number Properties/Systems Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  
    Quantity: Comprehend/Models
The learner will be able to comprehend quantitative relationships using mathematical models.
Strand Bloom's Scope Hours Source
Quantity Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Quantity: Illustrate/Models
The learner will be able to illustrate quantitative relationships using mathematical models.
Strand Bloom's Scope Hours Source
Quantity Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Patterns: Comprehend
The learner will be able to comprehend patterns.
Strand Bloom's Scope Hours Source
Patterns Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Change: Analyze/Contexts
The learner will be able to analyze change in many different contexts.
Strand Bloom's Scope Hours Source
Change Analysis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Estimation Strategies: Reasonableness
The learner will be able to apply estimation to obtain reasonable approximations.
Strand Bloom's Scope Hours Source
Estimation Strategies Application Master 0.5 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  
    Magnitude: Assess/Operations
The learner will be able to assess the effects of operations on the magnitudes of quantities.
Strand Bloom's Scope Hours Source
Magnitude Evaluation Master 2.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  
    Numeration: Numbers/Comprehend
The learner will be able to comprehend numbers.
Strand Bloom's Scope Hours Source
Numeration Comprehension Master 0.5 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  

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.). 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.).

    Data: Gather/Illustrate/Explain
The learner will be able to gather, illustrate and explain linear and nonlinear data sets formulated from the real world.
Strand Bloom's Scope Hours Source
Data Master TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Data: Study/Use/Misuse
The learner will be able to study the validity of statistical conclusions and the use and misuse of data.
Strand Bloom's Scope Hours Source
Data Master TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 31
  
    Probability Distribution: Explain/Use
The learner will be able to explain and use the normal distribution and its properties.
Strand Bloom's Scope Hours Source
Probability Distribution Master TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    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.
Strand Bloom's Scope Hours Source
Graphing Master TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 31
  
    Probability: Law of Large Numbers
The learner will be able to use the Law of Large Numbers.
Strand Bloom's Scope Hours Source
Probability Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Predictions: Curve Fitting/Technology
The learner will be able to make predictions from data using curve fitting applying appropriate technology.
Strand Bloom's Scope Hours Source
Predictions Analysis Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    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).
Strand Bloom's Scope Hours Source
Measures of Central Tendency Synthesis Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Theoretical/Experimental: Analyze
The learner will be able to analyze the likelihood of an event using theoretical and experimental probability.
Strand Bloom's Scope Hours Source
Theoretical Probability Analysis Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Sampling: Apply Randomness
The learner will be able to apply the idea of randomness in sampling.
Strand Bloom's Scope Hours Source
Sampling Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Mutually/Non-Mutually Exclusive
The learner will be able to identify events as mutually exclusive and non-mutually exclusive.
Strand Bloom's Scope Hours Source
Independent/Dependent/Mutually Exclusive Knowledge Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Dependent/Independent: Study
The learner will be able to study the probability of dependent and of independent events.
Strand Bloom's Scope Hours Source
Independent/Dependent/Mutually Exclusive Analysis Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Counting: Permutations/Combinations
The learner will be able to use appropriate technology to apply counting principles of permutations and combinations.
Strand Bloom's Scope Hours Source
Counting Methods Application Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Data Analysis: Technology
The learner will be able to analyze data using appropriate technology.
Strand Bloom's Scope Hours Source
Data Analysis Analysis Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    Simulations: Approximate Probability
The learner will be able to approximate probability using simulations.
Strand Bloom's Scope Hours Source
Event Simulation Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 30
  
    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.
Strand Bloom's Scope Hours Source
Outcomes Master TN: End-of-Course tests, 2001, Algebra II, 4.0 PIS Level 2 week tested: 16.
  
    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.
Strand Bloom's Scope Hours Source
Data Analysis Master TN: End-of-Course tests, 2001, Algebra II, 4.0 week tested: 16.
  
    Data Analysis: Inferences
The learner will be able to create and evaluate inferences and predictions from data.
Strand Bloom's Scope Hours Source
Data Analysis Master TN: End-of-Course tests, 2001, Algebra II, 4.0 week tested: 16.
  
    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.
Strand Bloom's Scope Hours Source
Statistical Analysis Master TN: End-of-Course tests, 2001, Algebra II, 4.13, 4.0 PIT Level 2 week tested: 16.
  
    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.
Strand Bloom's Scope Hours Source
Venn Diagram Analysis Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 1.0 PIT Level 2 week tested: 16.
  
    Events: Likelihood/Simple/Theoretical
The learner will be able to determine the likelihood of simple events by using theoretical probability.
Strand Bloom's Scope Hours Source
Probability Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 4.0 PIS Level 2 week tested: 16.
  
    Data: Gather/Real World/Generalize
The learner will be able to gather real world data to make generalizations.
Strand Bloom's Scope Hours Source
Data Comprehension Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIT Level 2 week tested: 16.
  
    Data: Represent
The learner will be able to represent data.
Strand Bloom's Scope Hours Source
Data Application Master 0.5 TN: End-of-Course tests, 2001, Algebra II, 4.0 week tested: 16.
  
    Data: Interpretation
The learner will be able to interpret given data.
Strand Bloom's Scope Hours Source
Data Analysis Master 0.5 TN: End-of-Course tests, 2001, Algebra II, 4.0 week tested: 16.
  
    Predictions: Simulations/Probability
The learner will be able to utilize simulations to help predict the probabilities of given situations.
Strand Bloom's Scope Hours Source
Predictions Analysis Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 4.0 PIT Level 2 week tested: 16.
  
    Central Tendency: Calculate/Real World
The learner will be able to calculate the measures of central tendency for real world data sets.
Strand Bloom's Scope Hours Source
Measures of Central Tendency Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 4.0 PIS Level 1 week tested: 16.
  
    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.
Strand Bloom's Scope Hours Source
Measures of Central Tendency Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 4.0 PIS Level 3 week tested: 16.
  
    Central Tendency: Inferences
The learner will be able to create inferences about a set of information using suitable measures of central tendency and dispersion.
Strand Bloom's Scope Hours Source
Measures of Central Tendency Synthesis Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 4.7 week tested: 16.
  
    Theoretical/Experimental Probability
The learner will be able to select theoretical or experimental probability to determine the likelihood of an event.
Strand Bloom's Scope Hours Source
Theoretical Probability Application Master 1.5 TN: End-of-Course tests, 2001, Algebra II, 4.0 PIT Level 2 week tested: 16.
  
    Theoretical Probability: Find
The learner will be able to find the theoretical probability of a compound event.
Strand Bloom's Scope Hours Source
Theoretical Probability Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 4.0 PIS Level 2 week tested: 16.
  
    Theoretical Probability: Mutually
The learner will be able to find the theoretical probability of events in a given situation that are mutually exclusive.
Strand Bloom's Scope Hours Source
Theoretical Probability Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 4.0 PIT Level 2 week tested: 16.
  
    Theoretical/Experimental: Model
The learner will be able to model situations to find theoretical and experimental probabilities.
Strand Bloom's Scope Hours Source
Theoretical Probability Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 4.0 week tested: 16.
  
    Theoretical Probability: Estimate
The learner will be able to make an estimation of the theoretical probability of an inclusive event for a certain situation.
Strand Bloom's Scope Hours Source
Theoretical Probability Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 4.0 PIT Level 3 week tested: 16.
  
    Data Analysis: Student Gathered/Predict
The learner will be able to examine student gathered data to make predictions.
Strand Bloom's Scope Hours Source
Data Analysis Analysis Master 2.0 TN: End-of-Course tests, 2001, Algebra II, 4.0 PIT Level 1 week tested: 16.
  
    Distributions: Normal/Mean/Deviation
The learner will be able to recognize the mean and standard deviation of the graph of a normal distribution.
Strand Bloom's Scope Hours Source
Probability Distribution Knowledge Master 1.5 TN: End-of-Course tests, 2001, Algebra II, 4.0 PIS Level 2 week tested: 16.
  
    Simulation: Approximate Probability
The learner will be able to use simulations to approximate probability.
Strand Bloom's Scope Hours Source
Event Simulation Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 4.11 week tested: 16.
  
    Graphing: Select
The learner will be able to select suitable graphical illustrations for a set of data.
Strand Bloom's Scope Hours Source
Graphing Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 4.12 week tested: 16.
  
    Graphing: Study
The learner will be able to study suitable graphical illustrations for a set of data.
Strand Bloom's Scope Hours Source
Graphing Analysis Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 4.12 week tested: 16.
  
    Graphing: Create
The learner will be able to create suitable graphical illustrations for a set of data.
Strand Bloom's Scope Hours Source
Graphing Synthesis Master 1.5 TN: End-of-Course tests, 2001, Algebra II, 4.12 week tested: 16.
  
    Graphing: Function/Periodic
The learner will be able to assess the graph of a function in order to decide if it is periodic.
Strand Bloom's Scope Hours Source
Graphing Evaluation Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIT Level 3 week tested: 16.
  
    Data: Display/Bivariate
The learner will be able to display a scatterplot for bivariate data, explain its shape, and identify regression coefficients, regressions equations, and correlation coefficients by applying technological tools.
Strand Bloom's Scope Hours Source
Data Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Data: Questions/Answer
The learner will be able to create questions and gather, organize, and illustrate data to answer those questions.
Strand Bloom's Scope Hours Source
Data Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Data: Comprehend/Meaning
The learner will be able to comprehend the meaning of measurement data and categorical data, univariate and bivariate data, as well as the term variable.
Strand Bloom's Scope Hours Source
Data Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Data: Display/Univariate
The learner will be able to display the distribution for univariate measurement data, explain its shape, and choose and compute summary statistics.
Strand Bloom's Scope Hours Source
Data Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Data: Recognize/Bivariate
The learner will be able to recognize trends in bivariate data and determine functions that model the data or transform the data so they can be modeled.
Strand Bloom's Scope Hours Source
Data Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Sampling: Comprehend/Statistics
The learner will be able to comprehend the way in which sample statistics reflect the values of population parameters and apply sampling distributions as the basis for informal inference.
Strand Bloom's Scope Hours Source
Sampling Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Experiments: Comprehend/Differences
The learner will be able to comprehend the differences among different types of studies and which kinds of legitimate inferences can be drawn from each.
Strand Bloom's Scope Hours Source
Experiments Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Experiments: Understand/Attributes
The learner will be able to understand the attributes of a well-designed study, including the part that randomization in surveys and experiments plays.
Strand Bloom's Scope Hours Source
Experiments Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Simulations: Apply/Variability
The learner will be able to apply simulations to investigate the variability of sample statistics from a known population and to create sampling distributions.
Strand Bloom's Scope Hours Source
Event Simulation Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Published Data: Evaluate
The learner will be able to evaluate published reports of data by examining the design of the study, the suitability of the analysis of the data, and the validity of conclusions drawn.
Strand Bloom's Scope Hours Source
Published Data/Experiments Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Probability: Comprehend/Concept
The learner will be able to comprehend the basic concept of probability.
Strand Bloom's Scope Hours Source
Probability Comprehension Master 0.5 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Probability: Calculate/Compound Events
The learner will be able to comprehend how to calculate the probability of a compound event.
Strand Bloom's Scope Hours Source
Probability Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Probability: Comprehend/Conditional
The learner will be able to comprehend the ideas of conditional probabilities.
Strand Bloom's Scope Hours Source
Probability Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Probability: Use/Basic/Concepts
The learner will be able to use the basic concepts of probability.
Strand Bloom's Scope Hours Source
Probability Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Data: Identify/Linear Transformations
The learner will be able to identify how linear transformations of univariate data affect shape, center, and spread.
Strand Bloom's Scope Hours Source
Data Knowledge Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Data: Describe/Bivariate
The learner will be able to describe bivariate data when one or more variables are categorical.
Strand Bloom's Scope Hours Source
Data Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Predictions: Formulate
The learner will be able to make predictions based on a given set of data.
Strand Bloom's Scope Hours Source
Predictions Analysis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Independent Events: Comprehend/Idea
The learner will be able to comprehend the ideas of independent events.
Strand Bloom's Scope Hours Source
Independent/Dependent/Mutually Exclusive Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Statistics: Comprehend/Difference
The learner will be able to comprehend the difference between a statistic and a parameter.
Strand Bloom's Scope Hours Source
Statistics Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Statistical Methods: Comprehend
The learner will be able to comprehend how basic statistical methods are utilized in order to monitor process characteristics in the workplace.
Strand Bloom's Scope Hours Source
Statistics Comprehension Master 2.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Statistical Methods: Choose
The learner will be able to choose suitable statistical methods to analyze data.
Strand Bloom's Scope Hours Source
Statistics Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Statistics: Calculate
The learner will be able to calculate basic statistics.
Strand Bloom's Scope Hours Source
Statistics Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Statistical Methods: Apply
The learner will be able to apply suitable statistical methods to analyze data.
Strand Bloom's Scope Hours Source
Statistics Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Permutations: Understand/Counting Method
The learner will be able to develop an understanding of permutations as a method of counting.
Strand Bloom's Scope Hours Source
Permutations Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  
    Combinations: Understand/Counting Method
The learner will be able to develop an understanding of combinations as a method of counting.
Strand Bloom's Scope Hours Source
Combinations Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  
    Data Analysis: Inferences/Predictions
The learner will be able to formulate inferences and/or predictions for data.
Strand Bloom's Scope Hours Source
Data Analysis Analysis Master 2.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Data Analysis: Evaluate/Inferences
The learner will be able to evaluate inferences from data.
Strand Bloom's Scope Hours Source
Data Analysis Evaluation Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Probability Distribution: Comprehend
The learner will be able to comprehend the concepts of probability distribution.
Strand Bloom's Scope Hours Source
Probability Distribution Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Probability Distribution: Create
The learner will be able to create probability distributions in simple cases.
Strand Bloom's Scope Hours Source
Probability Distribution Synthesis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Probability Distribution: Create
The learner will be able to create empirical probability distributions using simulations.
Strand Bloom's Scope Hours Source
Probability Distribution Synthesis Master 2.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Random Variable: Calculate
The learner will be able to calculate the expected value of random variables in simple contexts.
Strand Bloom's Scope Hours Source
Randomness Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Random Variable: Interpret
The learner will be able to interpret the expected value of random variables in simple contexts.
Strand Bloom's Scope Hours Source
Randomness Analysis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Sample Space: Comprehend
The learner will be able to comprehend the concepts of a sample space.
Strand Bloom's Scope Hours Source
Sample Space Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Sample Space: Create
The learner will be able to create sample spaces in simple cases.
Strand Bloom's Scope Hours Source
Sample Space Synthesis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Data Display: Comprehend/Histogram
The learner will be able to comprehend histograms.
Strand Bloom's Scope Hours Source
Data Display Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Data Display: Comprehend/Box Plot
The learner will be able to comprehend parallel box plots.
Strand Bloom's Scope Hours Source
Data Display Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Data Display: Histogram
The learner will be able to display data in a histogram.
Strand Bloom's Scope Hours Source
Data Display Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Data: Display/Bivariate
The learner will be able to display bivariate data when one or more variables are categorical.
Strand Bloom's Scope Hours Source
Data Display Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  
    Data Display: Parallel Box Plot
The learner will be able to display data using parallel box plots.
Strand Bloom's Scope Hours Source
Data Display Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard
  

Problem Solving
The Problem Solving Unit includes Competencies/Objectives which focus on analyzing problems, evaluating solutions, exploring problems, and developing strategies for solving problems. The Problem Solving Unit includes Competencies/Objectives which focus on analyzing problems, evaluating solutions, exploring problems, and developing strategies for solving problems.

    Investigations: Individual/Groups
The learner will be able to explore problems individually or in cooperative groups.
Strand Bloom's Scope Hours Source
Investigations Master TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 29
  
    Solution: Reasonableness
The learner will be able to evaluate the reasonableness of a given solution.
Strand Bloom's Scope Hours Source
Solution Evaluation Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 29, p. 29
  
    Problem Solving: Use/Tool/Appropriate
The learner will be able to use appropriate tools.
Strand Bloom's Scope Hours Source
Problem Solving Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 2.0 week tested: 16.
  
    Problem Solving: Representations
The learner will be able to choose, use, and translate among mathematical representations to obtain solutions to problems.
Strand Bloom's Scope Hours Source
Problem Solving Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Representation Standard
  
    Strategies: Adapt/Strategies
The learner will be able to adapt many different appropriate strategies in order to obtain problem solutions.
Strand Bloom's Scope Hours Source
Strategies Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Problem Solving Standard
  
    Strategies: Applying Variety
The learner will be able to apply a variety of strategies to obtain problem solutions.
Strand Bloom's Scope Hours Source
Strategies Application Master 2.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Problem Solving Standard
  
    Problem Solving: Mathematics
The learner will be able to solve mathematical problems.
Strand Bloom's Scope Hours Source
Problem Solving Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Problem Solving Standard
  
    Problem Solving: Outside Math
The learner will be able to obtain solutions to problems that arise in contexts outside of mathematics.
Strand Bloom's Scope Hours Source
Problem Solving Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Problem Solving Standard
  
    Problem Solving Effort: Reflect/Process
The learner will be able to reflect on the processes applied to solve a problem.
Strand Bloom's Scope Hours Source
Problem Solving Effort Analysis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Problem Solving Standard
  
    Problem Solving Effort: Monitor/Process
The learner will be able to monitor the processes applied to obtain solutions to mathematical problems.
Strand Bloom's Scope Hours Source
Problem Solving Effort Analysis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Problem Solving Standard
  

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. 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.

    Real Numbers: Choose/Use
The learner will be able to choose and use an appropriate strategy for computing with real numbers.
Strand Bloom's Scope Hours Source
Real Numbers Master TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 29
  
    Real Numbers: Connect/Illustrations
The learner will be able to connect concrete, graphical, verbal, and symbolic illustrations of real numbers.
Strand Bloom's Scope Hours Source
Real Numbers Analysis Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 29
  
    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.
Strand Bloom's Scope Hours Source
Linear Inequalities Master TN: End-of-Course tests, 2001, Algebra II, 3.0 PIT Level 3 week tested: 16.
  
    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.
Strand Bloom's Scope Hours Source
Slope Comprehension Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIT Level 1 week tested: 16.
  
    Problem Solving: Predict/Graph
The learner will be able to formulate predictions from graphs of real world data sets.
Strand Bloom's Scope Hours Source
Problem Solving Analysis Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 4.0 PIS Level 1 week tested: 16.
  
    Coordinate Geometry: Three-Dimensions
The learner will be able to find the coordinate of a point in a three-dimensional coordinate system.
Strand Bloom's Scope Hours Source
Coordinate Geometry Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 5.0 PIS Level 2 week tested: 16.
  
    Ordered Pairs: Match/Linear/Graph
The learner will be able to select the matching linear graph when given a set of ordered pairs.
Strand Bloom's Scope Hours Source
Coordinate Geometry Application Master 0.5 TN: End-of-Course tests, 2001, Algebra II, 4.0 PIS Level 1 week tested: 16.
  
    Real Numbers: Recognize/Reciprocals
The learner will be able to recognize reciprocals of real numbers.
Strand Bloom's Scope Hours Source
Real Numbers Knowledge Master 0.5 TN: End-of-Course tests, 2001, Algebra II, 1.0 PIS Level 1 week tested: 16.
  
    Real Numbers: Ordering
The learner will be able to order a set of real numbers.
Strand Bloom's Scope Hours Source
Real Numbers Analysis Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 1.0 PIS Level 1 week tested: 16.
  
    Real Numbers: Explore/Relationships
The learner will be able to explore the relationships between a variety of subsets of the real number system.
Strand Bloom's Scope Hours Source
Real Numbers Analysis Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 1.0 PIT Level 1 week tested: 16.
  
    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.
Strand Bloom's Scope Hours Source
Graphing Knowledge Master 0.5 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIS Level 1 week tested: 16.
  
    Graphing: Inequality/Two Variables
The learner will be able to choose the graph of an inequality with two-variables given in standard form.
Strand Bloom's Scope Hours Source
Graphing Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIS Level 2 week tested: 16.
  
    Graphing: Linear Function/Choose
The learner will be able to choose the graph that illustrates a linear function expressed in slope-intercept form.
Strand Bloom's Scope Hours Source
Graphing Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIS Level 1 week tested: 16.
  
    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.
Strand Bloom's Scope Hours Source
Distance Formula Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 5.0 PIT Level 2 week tested: 16.
  
    Coordinate Geometry: Apply/Cartesian
The learner will be able to apply Cartesian coordinates and other coordinate systems to study geometric scenarios.
Strand Bloom's Scope Hours Source
Coordinate Geometry Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Coordinate Geometry: Explore/Cartesian
The learner will be able to explore conjectures and obtain solutions to problems involving two- and three-dimensional objects illustrated with Cartesian coordinates.
Strand Bloom's Scope Hours Source
Coordinate Geometry Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  

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.

    Problem Solving: Technology
The learner will be able to appropriately use technology to solve problems.
Strand Bloom's Scope Hours Source
Problem Solving Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Algebra II, p. 29
  
    Algebra: Linear/Quadratic
The learner will be able to examine data from linear and quadratic functions using the appropriate technology.
Strand Bloom's Scope Hours Source
Algebra Analysis Master 1.5 TN: End-of-Course tests, 2001, Algebra II, 4.0 PIT Level 2 week tested: 16.
  

Discrete Mathematics
The Discrete Mathematics Unit includes Competencies/Objectives which focus on the concepts of discrete mathematics, matrices, and recursion. The Discrete Mathematics Unit includes Competencies/Objectives which focus on the concepts of discrete mathematics, matrices, and recursion.

    Matrices: Create
The learner will be able to create matrices involving real world problem solving.
Strand Bloom's Scope Hours Source
Matrices Synthesis Master 1.5 TN: End-of-Course tests, 2001, Algebra II, 2.0 PIT Level 2 week tested: 16.
  
    Recursion/Iteration: Apply/Relationships
The learner will be able to apply symbolic expressions, including iterative and recursive forms, to illustrate relationships that come from various scenarios.
Strand Bloom's Scope Hours Source
Recursion Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  

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.

    Equations: Solve/Linear/Rational
The learner will be able to obtain solutions to one-variable linear equations with rational expressions.
Strand Bloom's Scope Hours Source
Equations Application Master 1.0 TN: End-of-Course tests, 2001, Algebra II, 3.0 PIS Level 2 week tested: 16.
  

Mathematics Processes
The Mathematics Processes Unit includes Competencies/Objectives which focus on mathematical connections. Students communicate and model concepts and procedures.

    Mathematical Concepts: Comprehend
The learner will be able to comprehend how mathematical concepts interconnect and build on one another to create a coherent whole.
Strand Bloom's Scope Hours Source
Mathematical Concepts Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Connections Standard
  
    Math Concepts: Organize/Thought
The learner will be able to integrate their mathematical thought processes through communication.
Strand Bloom's Scope Hours Source
Mathematical Concepts Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Communication Standard
  
    Math Concepts: Study/Evaluate
The learner will be able to study and evaluate the mathematical thought processes and strategies of others.
Strand Bloom's Scope Hours Source
Mathematical Concepts Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Communication Standard
  
    Mathematical Concepts: Express
The learner will be able to express mathematical thought processes in an understandable and precise way to peers, teachers, and others.
Strand Bloom's Scope Hours Source
Mathematical Concepts Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Communication Standard
  
    Math as Reasoning: Create/Evaluate
The learner will be able to create and evaluate mathematical arguments and proofs.
Strand Bloom's Scope Hours Source
Reasoning Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Reasoning and Proof Standard
  
    Reasoning: Identify/Proof
The learner will be able to identify reasoning and proof as fundamental aspects of mathematics.
Strand Bloom's Scope Hours Source
Reasoning Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Reasoning and Proof Standard
  
    Learning: Create/Knowledge
The learner will be able to create new mathematical knowledge through the problem solving process.
Strand Bloom's Scope Hours Source
Learning Mathematics Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Problem Solving Standard
  
    Modeling: Make
The learner will be able to make mathematical representations for organizing, recording, and explaining mathematical concepts.
Strand Bloom's Scope Hours Source
Mathematical Modeling Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Representation Standard
  
    Models: Apply/Illustrate/Interpret
The learner will be able to apply representations to illustrate and interpret physical, social and mathematical scenarios.
Strand Bloom's Scope Hours Source
Mathematical Modeling Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Representation Standard
  
    Modeling: Apply/Variety
The learner will be able to apply a variety of mathematical representations for organizing, recording, and explaining mathematical concepts.
Strand Bloom's Scope Hours Source
Mathematical Modeling Master National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Representation Standard
  
    Mathematical Concepts: Identify
The learner will be able to identify mathematics in contexts outside of mathematics.
Strand Bloom's Scope Hours Source
Mathematical Concepts Knowledge Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Connections Standard
  
    Math Concepts: Organize/Thought
The learner will be able to organize their mathematical thought processes through communication.
Strand Bloom's Scope Hours Source
Mathematical Concepts Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Communication Standard
  
    Mathematical Concepts: Use
The learner will be able to use mathematics in contexts outside of mathematics.
Strand Bloom's Scope Hours Source
Mathematical Concepts Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Connections Standard
  
    Reasoning: Choose/Strategies
The learner will be able to choose various types of reasoning strategies.
Strand Bloom's Scope Hours Source
Reasoning Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Reasoning and Proof Standard
  
    Reasoning: Use/Strategies
The learner will be able to use many different reasoning strategies.
Strand Bloom's Scope Hours Source
Reasoning Synthesis Master 2.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Reasoning and Proof Standard
  
    Communicate: State/Ideas/Mathematical
The learner will be able to state mathematical ideas clearly using mathematical language.
Strand Bloom's Scope Hours Source
Communication Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Communication Standard
  
    Mathematical Connections: Identify
The learner will be able to identify connections among mathematical concepts.
Strand Bloom's Scope Hours Source
Connections Knowledge Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Connections Standard
  
    Mathematical Connections: Apply
The learner will be able to apply connections among mathematical concepts.
Strand Bloom's Scope Hours Source
Connections Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Connections Standard
  
    Modeling: Reasonable Conclusions
The learner will be able to come to reasonable conclusions about a scenario being modeled.
Strand Bloom's Scope Hours Source
Mathematical Modeling Analysis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard
  
    Conjecture: Explore
The learner will be able to explore mathematical conjectures.
Strand Bloom's Scope Hours Source
Conjecture/Argument Analysis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Reasoning and Proof Standard
  
    Conjecture: Formulate
The learner will be able to formulate conjectures.
Strand Bloom's Scope Hours Source
Conjecture/Argument Synthesis Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Reasoning and Proof Standard
  

Trigonometry
The Trigonometry Unit includes Competencies/Objectives which focus on trigonometric concepts. Students study triangles, trigonometric ratios, and triangle measurements; apply triangle properties; and solve right triangle problems.

    Trigonometric Concepts: Find/Lengths
The learner will be able to apply trigonometric relationships to find lengths.
Strand Bloom's Scope Hours Source
Trigonometric Concepts Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  
    Trigonometric Concepts: Find/Angle
The learner will be able to apply trigonometric relationships to find angle measures.
Strand Bloom's Scope Hours Source
Trigonometric Concepts Application Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Geometry Standard
  

Whole Numbers
The Whole Numbers Unit includes Competencies/Objectives which focus on whole number concepts. Students perform operations with whole numbers, use manipulatives to demonstrate whole number concepts, and solve problems with whole numbers in real world contexts.

    Operations: Meaning
The learner will be able to understand the meaning of operations.
Strand Bloom's Scope Hours Source
Operations Comprehension Master 1.0 National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard
  

© 2003 by Jefferson County Schools and EdVISION Corporation.  All Rights Reserved. Made with Curriculum Designer by EdVISION Corporation.