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Jefferson County Schools Mathematics The Tennessee Mathematics Framework for grades 9 through 12 includes skills for many different High School level courses, and contains the following process standards: Calculus AP 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. |
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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.
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Rates: Estimate/Interpret
The learner will be able to estimate and interpret rates of change using graphical and numerical data.
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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.
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Operations: Relationships
The learner will be able to comprehend the relationships among operations.
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Algebraic Concepts: Symbolism/Apply
The learner will be able to apply algebraic symbolism as a tool to represent mathematical relationships.
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Algebraic Concepts: Apply/Symbolism
The learner will be able to apply algebraic symbolism as a tool to describe mathematical relationships.
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Rate: Change
The learner will be able to illustrate rates of change, including associated rates problems.
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Connecting: Functions/Geometric/Analytic
The learner will be able to understand the correlation between the geometric and analytic information of a function.
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Computation: Fluency
The learner will be able to compute fluently.
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Computations: Assess/Reasonableness
The learner will be able to assess the reasonableness of numerical computations.
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Computations: Assess/Reasonableness
The learner will be able to assess the reasonableness of the results of numerical computations.
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| Calculus and Pre-Calculus |
| The Calculus/Pre-Calculus Unit includes Competencies/Objectives which focus on calculus concepts. Students study limits, matrix algebra, functions, vectors, conic sections, mathematical induction, and sequence and series using graphical calculators, computers, and models. |
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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).
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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.
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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.
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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.
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Integration: Understanding/Methods
The learner will be able to apply an understanding of integration and methods of integration to obtain applied problem solutions.
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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.
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Derivatives: Comprehend
The learner will be able to comprehend the idea of the derivative geometrically, numerically, and analytically.
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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.
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Intermediate Value Theorem: Comprehend
The learner will be able to comprehend the Intermediate Value Theorem on a function over a closed interval.
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Extreme Value Theorem: Comprehend
The learner will be able to comprehend the Extreme Value Theorem.
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Applying: Fundamental Theorem
The learner will be able to illustrate particular antiderivatives both graphically and analytically applying the Fundamental Theorem.
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Curves: Examine/Monotone/Concave
The learner will be able to examine curves as well as the ideas of monotonicity and concavity of the curve.
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Definite Integral: Fundamental Theorems
The learner will be able to evaluate definite integrals by applying the Fundamental Theorem of calculus.
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Definite Integral: Average Value
The learner will be able to use concepts of the definite integral to calculate the average value of a function.
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Definite Integral: Use
The learner will be able to use the basic properties of definite integrals.
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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.
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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.
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Differential Equations: Solve
The learner will be able to obtain solutions to separable differential equations.
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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.
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Differential Equation: Separable
The learner will be able to apply separable differential equations in modeling.
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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.
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Derivatives: Define
The learner will be able to give the definition of the derivative as the limit of the difference quotient.
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Derivatives: Mean Value Theorem
The learner will be able to illustrate an understanding of the Mean Value Theorem and its geometric consequence.
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Derivatives: Comprehend
The learner will be able to comprehend the relationship of the concavity of functions and the sign of the second order derivative.
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Derivatives: Basic Rules
The learner will be able to apply the basic rules for the sum, difference, and product of functions.
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Derivatives: Determine/Power Function
The learner will be able to determine the derivative of a power function.
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Derivatives: Inverse Trigonometric
The learner will be able to calculate the derivatives of inverse trigonometric functions.
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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.
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Derivatives: Determine/Tangent
The learner will be able to determine tangent lines to a curve at a point and a local linear approximation.
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Derivatives: Translate
The learner will be able to make verbal descriptions into equations involving derivatives and vice versa.
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Derivatives: Determine
The learner will be able to apply implicit differentiation to determine derivatives of inverse functions.
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Antiderivatives: Determine
The learner will be able to determine specific antiderivatives applying initial conditions including applications to motion along a line.
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Derivatives: Compare
The learner will be able to make comparisons of the corresponding attributes of the graphs of f, f', and f".
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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.
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Derivatives: Rate of Change
The learner will be able to make an interpretation of the derivative as an instantaneous rate of change.
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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.
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Complex Numbers: Comprehend/Solutions
The learner will be able to comprehend complex numbers as solutions to quadratic equations that do not have real solutions.
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Limits: Describe/Understanding
The learner will be able to describe an understanding of the limiting process.
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Limits: Infinity
The learner will be able to explain asymptotic behavior in terms of limits involving infinity.
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Limits: Comprehend/Rate of Change
The learner will be able to comprehend instantaneous rate of change as the limit of average rate of change.
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Limits: Algebraic
The learner will be able to calculate limits applying algebra.
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Limits: Approximate/Graphs/Tables
The learner will be able to approximate limits from graphs or tables of data.
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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.
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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.
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Differentiation: Comprehend
The learner will be able to comprehend the relationship between differentiability and continuity.
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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.
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Differentiation: Chain/Implicit
The learner will be able to apply the chain rule and implicit differentiation.
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| Data Interpretation |
| The Data Interpretation Unit includes Competencies/Objectives which focus on the study and use of graphical forms. Students collect and classify data, organize and display data, use logical reasoning, and problem solving. |
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Scatterplots: Understand
The learner will be able to understand scatterplots.
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Scatterplots: Create
The learner will be able to create a scatterplot to display data.
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| Discrete Mathematics |
| The Discrete Mathematics Unit includes Competencies/Objectives which focus on the concepts of discrete mathematics, matrices, and recursion. |
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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.
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| Functions |
| The Functions Unit includes Competencies/Objectives which focus on exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions. |
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Function/Relation: Apply/Representation
The learner will be able to apply many different symbolic representations, including recursive and parametric equations, for functions and relations.
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Functions/Relations: Comprehend
The learner will be able to comprehend relations and functions and choose, proficiently perform conversions, and use different representations of them.
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Functions: Apply/Explicit and Recursive
The learner will be able to apply explicitly and recursively defined functions in order to generalize patterns.
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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.
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Functions: Predict/Describe
The learner will be able to predict and describe the observed local and global behavior of a function.
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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.
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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.
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Graphing: Understand/Asymptotes
The learner will be able to illustrate an understanding of asymptotes in terms of graphical behavior.
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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.
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Representations: Interpret
The learner will be able to make interpretations of representations of functions of two variables.
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Limits: Continuity
The learner will be able to illustrate a comprehension of continuity in terms of limits.
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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.
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Functions: Comprehend/Point/Inflection
The learner will be able to comprehend that points of inflection are places where concavity changes.
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Functions: Derivative
The learner will be able to find the derivative of a basic function by using the rules of differentiation.
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Functions: Differentiating
The learner will be able to differentiate the following functions: trigonometric, logarithmic, and exponential.
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Functions: Determine/Maxima/Minima
The learner will be able to determine local and absolute maximum and minimum points.
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Functions: Antiderivative
The learner will be able to find the antiderivative of a basic function.
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