Jefferson County Schools
Jefferson County Schools

Mathematics - Calculus

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.

Calculus

The Tennessee Mathematics Framework for grades 9 through 12 outlines skills to be taught in Calculus.

The Principles and Standards for School Mathematics provide standards for students in grades 9-12.


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.

    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
  
    Rate: Change
The learner will be able to illustrate rates of change, including associated rates problems.
Strand Bloom's Scope Hours Source
Rates Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50
  
    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.

    Curves: Study
The learner will be able to study curves applying the notions of monotonicity and concavity; optimization, both absolute and relative extrema.
Strand Bloom's Scope Hours Source
Curve Sketching Master TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50
  
    Definite Integral: Riemann Sum
The learner will be able to apply Riemann sums and the Trapezoidal Rule to estimate definite integrals of functions illustrated algebraically, geometrically, and by tables of values.
Strand Bloom's Scope Hours Source
Definite Integral Master TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 51
  
    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
  
    Calculus Concepts: Differentiability
The learner will be able to describe the relationship between differentiability and continuity.
Strand Bloom's Scope Hours Source
Applying Calculus Concepts Comprehension Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50
  
    Calculus Concepts: Antidifferentiation
The learner will be able to apply strategies of antidifferentiation.
Strand Bloom's Scope Hours Source
Applying Calculus Concepts Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 51
  
    Definite Integral: Riemann Sums
The learner will be able to describe the relationship between a Riemann sum and a definite integral.
Strand Bloom's Scope Hours Source
Definite Integral Comprehension Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50
  
    Definite Integral: Fundamental Theorems
The learner will be able to evaluate definite integrals by applying the Fundamental Theorem of calculus.
Strand Bloom's Scope Hours Source
Definite Integral Application Master 0.5 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50
  
    Definite Integral: Use
The learner will be able to use the basic properties of definite integrals.
Strand Bloom's Scope Hours Source
Definite Integral Application Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50
  
    Differential Equation: Separable
The learner will be able to apply separable differential equations in modeling.
Strand Bloom's Scope Hours Source
Differential Equations Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 51
  
    Derivatives: Define
The learner will be able to give the definition of the derivative as the limit of the difference quotient.
Strand Bloom's Scope Hours Source
Derivatives/Antiderivatives Knowledge Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50
  
    Derivatives: Describe
The learner will be able to describe the relationship of increasing and decreasing behavior of functions and the sign of first order derivatives.
Strand Bloom's Scope Hours Source
Derivatives/Antiderivatives Comprehension Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50
  
    Derivatives: Describe
The learner will be able to describe corresponding attributes of graphs of functions, first order and/or second order derivatives.
Strand Bloom's Scope Hours Source
Derivatives/Antiderivatives Comprehension Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p.50
  
    Derivatives: Mean Value Theorem
The learner will be able to illustrate an understanding of the Mean Value Theorem and its geometric consequence.
Strand Bloom's Scope Hours Source
Derivatives/Antiderivatives Comprehension Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50
  
    Derivatives: Concavity
The learner will be able to describe the relationship of the concavity of functions and the sign of a second order derivative.
Strand Bloom's Scope Hours Source
Derivatives/Antiderivatives Comprehension Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50
  
    Derivatives: Basic Rules
The learner will be able to use basic rules for the derivative of basic functions and their sum, product, and quotient.
Strand Bloom's Scope Hours Source
Derivatives/Antiderivatives Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50
  
    Derivatives: Translate
The learner will be able to make verbal descriptions into equations involving derivatives and vice versa.
Strand Bloom's Scope Hours Source
Derivatives/Antiderivatives Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50
  
    Derivatives: Points of Inflection
The learner will be able to determine points of inflections.
Strand Bloom's Scope Hours Source
Derivatives/Antiderivatives Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50
  
    Derivatives: Implicit Differentiation
The learner will be able to apply the concept of implicit differentiation to determine the derivative of an inverse function.
Strand Bloom's Scope Hours Source
Derivatives/Antiderivatives Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50
  
    Antiderivatives: Determine
The learner will be able to determine specific antiderivatives applying initial conditions including applications to motion along a line.
Strand Bloom's Scope Hours Source
Derivatives/Antiderivatives Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 51
  
    Derivatives: Rate of Change
The learner will be able to make an interpretation of the derivative as an instantaneous rate of change.
Strand Bloom's Scope Hours Source
Derivatives/Antiderivatives Analysis Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 49
  
    Derivatives: Interpret
The learner will be able to interpret the derivative as a rate of change in many different applied contexts.
Strand Bloom's Scope Hours Source
Derivatives/Antiderivatives Analysis Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50
  
    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
  
    Limits: Algebraic
The learner will be able to calculate limits applying algebra.
Strand Bloom's Scope Hours Source
Limits Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 49
  
    Limits: Approximate/Graphs/Tables
The learner will be able to approximate limits from graphs or tables of data.
Strand Bloom's Scope Hours Source
Limits Application Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 49
  
    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
  
    Differentiation: Chain/Implicit
The learner will be able to apply the chain rule and implicit differentiation.
Strand Bloom's Scope Hours Source
Differentiation Application Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50
  

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.

    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
  

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

    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
  

Functions
The Functions Unit includes Competencies/Objectives which focus on exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions.

    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
  
    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
  
    Exploring: Graphs/Technology
The learner will be able to study the graphs of polynomial, rational, radical, and transcendental functions applying suitable technology.
Strand Bloom's Scope Hours Source
Exploring Master TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 49
  
    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: 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
  
    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: Predict/Describe
The learner will be able to predict and describe the observed local and global behavior of a function.
Strand Bloom's Scope Hours Source
Functions Master TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 49
  
    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
  
    Derivatives: Illustrate
The learner will be able to illustrate the idea of the derivative geometrically, numerically, and analytically.
Strand Bloom's Scope Hours Source
Derivatives/Antiderivatives Application Master 2.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 49
  
    Graphing: Understand/Asymptotes
The learner will be able to illustrate an understanding of asymptotes in terms of graphical behavior.
Strand Bloom's Scope Hours Source
Graphing Functions Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 49
  
    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
  
    Limits: Continuity
The learner will be able to illustrate a comprehension of continuity in terms of limits.
Strand Bloom's Scope Hours Source
Limits Comprehension Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 49
  
    Limits: Explain/Asymptotic
The learner will be able to explain asymptotic behavior in terms of infinite limits and limits at infinity.
Strand Bloom's Scope Hours Source
Limits Comprehension Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 49
  
    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
  
    Functions: Continuous
The learner will be able to illustrate a geometric understanding of graphs of continuous functions.
Strand Bloom's Scope Hours Source
Functions Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 49
  
    Functions: Compare
The learner will be able to make a comparison of the relative magnitudes of functions and their rates of change.
Strand Bloom's Scope Hours Source
Functions Analysis Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 49
  

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.

    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: 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
  
    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
  
    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: 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
  
    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
  
    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 mod