Mathematics Calculus AP

Jefferson County Schools
Jefferson County Schools

Mathematics - Calculus AP

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 AP

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

The Advanced Placement Program provides objectives for Calculus AB.

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	Advanced Placement Tests (AP), 2000, Calculus AB, II

Connecting: Functions/Geometric/Analytic
The learner will be able to understand the correlation between the geometric and analytic information of a function.

Strand	Bloom's	Scope	Hours	Source
Connecting	Comprehension	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB.; I

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.

Definite Integral: Rate of Change
The learner will be able to determine the definite integral of the rate of change of a quantity over an interval as the change of the quantity over the interval: the integral from a to b of f'(x)dx = f(b) - f(a).

Strand	Bloom's	Scope	Hours	Source
Definite Integral		Master		Advanced Placement Tests (AP), 2000, Calculus AB, III

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		Advanced Placement Tests (AP), 2000, Calculus AB, III

Definite Integral: Riemann Sums
The learner will be able to compute the values of Riemann Sums over equal subdivisions applying left, right, and midpoint evaluation points.

Strand	Bloom's	Scope	Hours	Source
Definite Integral		Master		Advanced Placement Tests (AP), 2000, Calculus AB, III

Definite Integral: Apply
The learner will be able to apply integrals to illustrate concrete, social, or economic scenarios to include determining the area of a region and the distance traveled by a particle along a line.

Strand	Bloom's	Scope	Hours	Source
Definite Integral		Master		Advanced Placement Tests (AP), 2000, Calculus AB, III

Integration: Understanding/Methods
The learner will be able to apply an understanding of integration and methods of integration to obtain applied problem solutions.

Strand	Bloom's	Scope	Hours	Source
Integration		Master		Advanced Placement Tests (AP), 2000, Calculus AB, III

Integration: Use/Model/Solve
The learner will be able to use integration to model and obtain solutions to problems in other areas outside of mathematics applying the integral as a rate of change to give accumulated change and applying the method of setting up and approximating Riemann Sum and illustrating its limit as a definite integral.

Strand	Bloom's	Scope	Hours	Source
Integration		Master		Advanced Placement Tests (AP), 2000, Calculus AB, III

Derivatives: Comprehend
The learner will be able to comprehend the idea of the derivative geometrically, numerically, and analytically.

Strand	Bloom's	Scope	Hours	Source
Derivatives/Antiderivatives		Master		Advanced Placement Tests (AP), 2000, Calculus AB, II

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

Intermediate Value Theorem: Comprehend
The learner will be able to comprehend the Intermediate Value Theorem on a function over a closed interval.

Strand	Bloom's	Scope	Hours	Source
Applying Calculus Concepts	Comprehension	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB.; I

Extreme Value Theorem: Comprehend
The learner will be able to comprehend the Extreme Value Theorem.

Strand	Bloom's	Scope	Hours	Source
Applying Calculus Concepts	Comprehension	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB.; I

Applying: Fundamental Theorem
The learner will be able to illustrate particular antiderivatives both graphically and analytically applying the Fundamental Theorem.

Strand	Bloom's	Scope	Hours	Source
Applying Calculus Concepts	Application	Master	2.0	Advanced Placement Tests (AP), 2000, Calculus AB, III

Curves: Examine/Monotone/Concave
The learner will be able to examine curves as well as the ideas of monotonicity and concavity of the curve.

Strand	Bloom's	Scope	Hours	Source
Curve Sketching	Analysis	Master	1.5	Advanced Placement Tests (AP), 2000, Calculus AB, II

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	Advanced Placement Tests (AP), 2000, Calculus AB, III

Definite Integral: Average Value
The learner will be able to use concepts of the definite integral to calculate the average value of a function.

Strand	Bloom's	Scope	Hours	Source
Definite Integral	Application	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, III

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	Advanced Placement Tests (AP), 2000, Calculus AB, III

Definite Integral: Volume/Known Areas
The learner will be able to use concepts of the definite integral to calculate the volume of a solid of revolution where the cross-sectional area is a known value.

Strand	Bloom's	Scope	Hours	Source
Definite Integral	Application	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, III

Definite Integral: Interpret/Riemann
The learner will be able to interpret the definite integral as the limit of Riemann Sums over subdivision of equal size.

Strand	Bloom's	Scope	Hours	Source
Definite Integral	Analysis	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, III

Differential Equations: Solve
The learner will be able to obtain solutions to separable differential equations.

Strand	Bloom's	Scope	Hours	Source
Differential Equations	Application	Master	1.5	Advanced Placement Tests (AP), 2000, Calculus AB, III

Differential Equation: Solve
The learner will be able to obtain solutions to differential equations of the form y' = ky as applied to growth and decay problems.

Strand	Bloom's	Scope	Hours	Source
Differential Equations	Application	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, III

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	Advanced Placement Tests (AP), 2000, Calculus AB, III

Integration: Substitution/Variables
The learner will be able to integrate by substitution of variables, including substituting for the limits of integration in a definite integral.

Strand	Bloom's	Scope	Hours	Source
Integration	Application	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, III

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	Advanced Placement Tests (AP), 2000, Calculus AB, II

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	Advanced Placement Tests (AP), 2000, Calculus AB, II

Derivatives: Comprehend
The learner will be able to comprehend the relationship of the concavity of functions and the sign of the second order derivative.

Strand	Bloom's	Scope	Hours	Source
Derivatives/Antiderivatives	Comprehension	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, II

Derivatives: Basic Rules
The learner will be able to apply the basic rules for the sum, difference, and product of functions.

Strand	Bloom's	Scope	Hours	Source
Derivatives/Antiderivatives	Application	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, II

Derivatives: Determine/Power Function
The learner will be able to determine the derivative of a power function.

Strand	Bloom's	Scope	Hours	Source
Derivatives/Antiderivatives	Application	Master	0.5	Advanced Placement Tests (AP), 2000, Calculus AB, II

Derivatives: Inverse Trigonometric
The learner will be able to calculate the derivatives of inverse trigonometric functions.

Strand	Bloom's	Scope	Hours	Source
Derivatives/Antiderivatives	Application	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, II

Derivative: Slope of a Curve/Point
The learner will be able to determine the slope of a curve at a point, including points at which there are vertical tangents and no tangents.

Strand	Bloom's	Scope	Hours	Source
Derivatives/Antiderivatives	Application	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, II

Derivatives: Determine/Tangent
The learner will be able to determine tangent lines to a curve at a point and a local linear approximation.

Strand	Bloom's	Scope	Hours	Source
Derivatives/Antiderivatives	Application	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, II

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	Advanced Placement Tests (AP), 2000, Calculus AB, II

Derivatives: Determine
The learner will be able to apply implicit differentiation to determine derivatives of inverse functions.

Strand	Bloom's	Scope	Hours	Source
Derivatives/Antiderivatives	Application	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, II

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	Advanced Placement Tests (AP), 2000, Calculus AB, III

Derivatives: Compare
The learner will be able to make comparisons of the corresponding attributes of the graphs of f, f', and f".

Strand	Bloom's	Scope	Hours	Source
Derivatives/Antiderivatives	Analysis	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, II

Derivatives: Compare/Characteristics
The learner will be able to compare the characteristics of the graphs of the function and the first derivative of the function.

Strand	Bloom's	Scope	Hours	Source
Derivatives/Antiderivatives	Analysis	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, II

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	Advanced Placement Tests (AP), 2000, Calculus AB, II

Derivative: Interpret/Rate of Change
The learner will be able to interpret the derivative as a rate of change in different applied contexts including velocity, speed, and acceleration.

Strand	Bloom's	Scope	Hours	Source
Derivatives/Antiderivatives	Analysis	Master	2.0	Advanced Placement Tests (AP), 2000, Calculus AB, II

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: Describe/Understanding
The learner will be able to describe an understanding of the limiting process.

Strand	Bloom's	Scope	Hours	Source
Limits	Comprehension	Master	2.0	Advanced Placement Tests (AP), 2000, Calculus AB.; I

Limits: Infinity
The learner will be able to explain asymptotic behavior in terms of limits involving infinity.

Strand	Bloom's	Scope	Hours	Source
Limits	Comprehension	Master	2.0	Advanced Placement Tests (AP), 2000, Calculus AB.; I

Limits: Comprehend/Rate of Change
The learner will be able to comprehend instantaneous rate of change as the limit of average rate of change.

Strand	Bloom's	Scope	Hours	Source
Limits	Comprehension	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, II

Limits: Algebraic
The learner will be able to calculate limits applying algebra.

Strand	Bloom's	Scope	Hours	Source
Limits	Application	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB.; I

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	Advanced Placement Tests (AP), 2000, Calculus AB.; I

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: Comprehend
The learner will be able to comprehend the relationship between differentiability and continuity.

Strand	Bloom's	Scope	Hours	Source
Differentiation	Comprehension	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, II

Differentiation: Rate of Change/Point
The learner will be able to estimate the rate of change at a point when presented with the graph of a function or a table of values.

Strand	Bloom's	Scope	Hours	Source
Differentiation	Application	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, II

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	Advanced Placement Tests (AP), 2000, Calculus AB, II

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.

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: 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/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: 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		Advanced Placement Tests (AP), 2000, Calculus AB.; I

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

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

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	Advanced Placement Tests (AP), 2000, Calculus AB.; I

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	Advanced Placement Tests (AP), 2000, Calculus AB.; I

Functions: Comprehend
The learner will be able to comprehend the relationship between the increasing and decreasing behavior of functions and the sign of the first order derivative.

Strand	Bloom's	Scope	Hours	Source
Calculus with Functions	Comprehension	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, II

Functions: Comprehend/Point/Inflection
The learner will be able to comprehend that points of inflection are places where concavity changes.

Strand	Bloom's	Scope	Hours	Source
Calculus with Functions	Comprehension	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, II

Functions: Derivative
The learner will be able to find the derivative of a basic function by using the rules of differentiation.

Strand	Bloom's	Scope	Hours	Source
Calculus with Functions	Application	Master	2.0	Advanced Placement Tests (AP), 2000, Calculus AB, II

Functions: Differentiating
The learner will be able to differentiate the following functions: trigonometric, logarithmic, and exponential.

Strand	Bloom's	Scope	Hours	Source
Calculus with Functions	Application	Master	1.5	Advanced Placement Tests (AP), 2000, Calculus AB, II

Functions: Determine/Maxima/Minima
The learner will be able to determine local and absolute maximum and minimum points.

Strand	Bloom's	Scope	Hours	Source
Calculus with Functions	Application	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, II

Functions: Antiderivative
The learner will be able to find the antiderivative of a basic function.

Strand	Bloom's	Scope	Hours	Source
Calculus with Functions	Application	Master	1.0	Advanced Placement Tests (AP), 2000, Calculus AB, III

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 understand the concept of continuity of a function.

Strand	Bloom's	Scope	Hours	Source
Functions	Comprehension	Master	0.5	Advanced Placement Tests (AP), 2000, Calculus AB.; I

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	Advanced Placement Tests (AP), 2000, Calculus AB.; I

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	Advanced Placement Tests (AP), 2000, Calculus AB.; I

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: 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

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: 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 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

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

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

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

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

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

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

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.

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.

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.

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.).

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: 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

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: 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: 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

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.

Problem Solving: Representations
The learner will be able to choose, use, and translate among mathematical representation 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.

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

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