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mvsd |
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Math Curriculum 01/12/03 |
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Mathematics - Calculus |
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Functions/Relations: Recognize
The learner will be able to
recognize the characteristics of functions and relations according to domain, range, intercepts, symmetry, odd, even, asymptotes, and zeros, as well as graph them according to these characteristics and recognize these characteristics according to the graphs.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Functions/Relations |
Comprehension |
Master |
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ID: State Achievement Standards, 2001, Grades 9-12, 353.03.a/353.01 |
Classroom
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Functions: Properties
The learner will be able to
recognize and apply the properties of algebraic, trigonometric, exponential, and logarithmic functions, including polynomials, absolute value, and functions with bounded/unbounded behavior.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Functions |
Application |
Master |
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ID: State Achievement Standards, 2001, Grades 9-12, 353.03.a |
Classroom
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Operations: Functions/Algebra
The learner will be able to
apply the algebra of functions in determining the sum, product, quotient, composition, and inverse if they exist.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Operations |
Comprehension |
Master |
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District Expectation |
Classroom
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Calculus and Pre-Calculus
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Limits: Approximate/Graphs/Tables
The learner will be able to
approximate limits from graphs or tables of data.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Limits |
Application |
Master |
1.5 |
District Expectation |
Classroom
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Limits: Infinity
The learner will be able to
explain asymptotic behavior in terms of limits involving infinity.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Limits |
Comprehension |
Master |
2.0 |
District Expectation |
Classroom
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Limits: Evaluate
The learner will be able to
evaluate the limit of a function and apply the properties of limits, including one-sided limits.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Limits |
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Master |
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District Expectation |
Classroom
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Apply Calculus Concepts: Fundamental
The learner will be able to
recognize the Fundamental Theorem of Calculus.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Applying Calculus Concepts |
Knowledge |
Master |
1.0 |
District Expectation |
Classroom
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Applying Calculus Concepts: Continuity
The learner will be able to
apply the definition of continuity of a function at a point & over an interval.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Applying Calculus Concepts |
Application |
Master |
1.0 |
District Expectation |
Classroom
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Applying Calculus Concepts: Extreme
The learner will be able to
use the Extreme Value Theorem in problem scenarios.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Applying Calculus Concepts |
Application |
Master |
1.0 |
District Expectation |
Classroom
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Applying Calculus Concepts: L'Hopital
The learner will be able to
appropriately apply L'Hopital's Rule.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Applying Calculus Concepts |
Application |
Master |
1.0 |
District Expectation |
Classroom
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Applying Calculus Concepts: Theorems
The learner will be able to
apply the Mean Value and Rolle's Theorem.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Applying Calculus Concepts |
Application |
Master |
1.0 |
District Expectation |
Classroom
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Apply Calculus Concepts: Sums
The learner will be able to
compute area values through the evaluation of sums and application of sigma notation.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Applying Calculus Concepts |
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Master |
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District Expectation |
Classroom
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Derivatives: Slope of a Tangent/Define
The learner will be able to
define a derivative as the slope of a line tangent to a curve at a given point.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Derivatives/Antiderivatives |
Knowledge |
Master |
0.5 |
District Expectation |
Classroom
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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.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Derivatives/Antiderivatives |
Knowledge |
Master |
1.0 |
District Expectation |
Classroom
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Differentiation: Define/Instant/Limit
The learner will be able to
define the derivative of a function as the instantaneous rate of change and as the limit of the average rate of change.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Differentiation |
Knowledge |
Master |
0.5 |
District Expectation |
Classroom
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Differentiation: Function/Over Interval
The learner will be able to
determine whether a function is differentiable over an interval.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Differentiation |
Application |
Master |
1.0 |
District Expectation |
Classroom
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Differentiation: Function/Point
The learner will be able to
find points where a function's derivative does not exist.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Differentiation |
Application |
Master |
1.0 |
District Expectation |
Classroom
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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.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Differentiation |
Application |
Master |
1.0 |
District Expectation |
Classroom
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Differentiation: Apply
The learner will be able to
apply the derivative to find the slope of a curve at a given point, the equation of a tangent line to a point on the curve, and the equation of the normal line to a point on the curve.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Differentiation |
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Master |
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District Expectation |
Classroom
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Differentiation: Apply/Relationships
The learner will be able to
apply the relationships between f(x), f'(x), and f''(x) to find the increasing and decreasing behavior of f(x), the critical points of f(x), the concavity of f(x) over an interval, the points of inflection of f(x), to sketch the graphs of f'(x) and f''(x) when given f(x), and sketch the graph of f(x) when given f'(x).
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Differentiation |
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Master |
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District Expectation |
Classroom
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Differentiation: Find/Apply
The learner will be able to
find and apply the successive derivatives of a function.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Differentiation |
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Master |
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District Expectation |
Classroom
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Derivatives: Composite/Chain Rule
The learner will be able to
calculate the derivative of composite functions using the chain rule.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Derivatives/Antiderivatives |
Application |
Master |
1.0 |
District Expectation |
Classroom
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Differentiation: Chain Rule/Implicit
The learner will be able to
apply the chain rule to functions defined implicitly and related rates of change situations.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Differentiation |
Application |
Master |
1.0 |
District Expectation |
Classroom
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Derivatives: Inverse Functions
The learner will be able to
calculate the derivative of the inverses of functions, including trigonometric inverses.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Derivatives/Antiderivatives |
Application |
Master |
1.0 |
District Expectation |
Classroom
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Differentiation: Use/Rules
The learner will be able to
use the rules of differentiation with algebraic and transcendental functions.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Differentiation |
Application |
Master |
1.0 |
District Expectation |
Classroom
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Integration: Define/Apply
The learner will be able to
make definitions of and/or use properties of the definite integral.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Integration |
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Master |
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District Expectation |
Classroom
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Integration: Define/Use/Properties
The learner will be able to
state the definition of the antiderivative and use its properties in problems.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Integration |
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Master |
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District Expectation |
Classroom
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Definite Integral: Relate/Area
The learner will be able to
relate the definite integral to the idea of the area under a curve.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Definite Integral |
Analysis |
Master |
1.0 |
District Expectation |
Classroom
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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 |
Activities |
| Definite Integral |
Application |
Master |
0.5 |
District Expectation |
Classroom
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Integration: Apply/Mean Value
The learner will be able to
apply the integral to the mean value of a function over an interval.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Integration |
Application |
Master |
1.0 |
District Expectation |
Classroom
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Integration: Apply/Identities
The learner will be able to
perform integration by applying identities.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Integration |
Application |
Master |
2.0 |
District Expectation |
Classroom
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Integration: Parts
The learner will be able to
perform integration by parts.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Integration |
Application |
Master |
1.0 |
District Expectation |
Classroom
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Integration: Substitution
The learner will be able to
integrate using substitution.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Integration |
Application |
Master |
1.0 |
District Expectation |
Classroom
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Integration: Changing Variables
The learner will be able to
integrate by changing variables.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Integration |
Application |
Master |
2.0 |
District Expectation |
Classroom
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Integration: Natural Log
The learner will be able to
interpret the natural log ( ln x ) as the area under the curve of the function f(x) = 1/x.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Integration |
Analysis |
Master |
1.5 |
District Expectation |
Classroom
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Integration: Estimate/Areas
The learner will be able to
estimate areas through the application of inscribed rectangles, circumscribed rectangles, trapezoids, and other suitable techniques.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Integration |
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Master |
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District Expectation |
Classroom
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Integration: Find/Area/Curves
The learner will be able to
find the area between curves through the use of integration formulas.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Integration |
Application |
Master |
1.0 |
District Expectation |
Classroom
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Integration: Find/Volume/Solid
The learner will be able to
find the volume of a solid of revolution through the use of several different techniques.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Integration |
Application |
Master |
2.0 |
District Expectation |
Classroom
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Optimization Problems
The learner will be able to
solve optimization problems.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Correlation/Deviation/Variance |
Application |
Master |
0.5 |
ID: State Achievement Standards, 2001, Grades 9-12, 352.05.a |
Classroom
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Problem Solving: Relate
The learner will be able to
obtain solutions to problems that relate ideas to practical applications as well as to other ideas utilizing suitable instruments.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Problem Solving |
Application |
Master |
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ID: State Achievement Standards, 2001, Grades 9-12, 353.03.a; 352.05.a |
Classroom
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Problem Solving: Estimate/Predict
The learner will be able to
apply estimation strategies to predict calculated results when solving problems.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Problem Solving |
Application |
Master |
1.0 |
District Expectation |
Classroom
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Solution: Reasonableness
The learner will be able to
evaluate the reasonableness of a given solution.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Solution |
Evaluation |
Master |
1.5 |
District Expectation |
Classroom
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Strategies: Choose/Suitable
The learner will be able to
choose suitable problem solving strategies.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Strategies |
Application |
Master |
1.0 |
District Expectation |
Classroom
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Strategies: Choose/Tools/Suitable
The learner will be able to
choose suitable mathematical tools to obtain solutions to problems.
| Strand |
Bloom's |
Scope |
Hours |
Source |
Activities |
| Strategies |
Application |
Master |
1.0 |
District Expectation |
Classroom
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