|
Data Analysis, Probability, Statistics
|
|
|
PCD.DPS.1
The learner will be able to create tables and charts to display data.
| Strand |
Bloom's |
Scope |
| Tables/Charts |
Application |
Master |
|
PCD.DPS.2
The learner will be able to organize data in charts.
| Strand |
Bloom's |
Scope |
| Tables/Charts |
Application |
Master |
|
PCD.DPS.3
The learner will be able to interpret information presented in graphs.
| Strand |
Bloom's |
Scope |
| Graphs |
Analysis |
Master |
|
PCD.DPS.4
The learner will be able to organize data in graphs.
| Strand |
Bloom's |
Scope |
| Graphs |
Application |
Master |
|
PCD.DPS.5
The learner will be able to interpret information presented in tables and charts.
| Strand |
Bloom's |
Scope |
| Tables/Charts |
Analysis |
Master |
|
PCD.DPS.6
The learner will be able to organize data in tables.
| Strand |
Bloom's |
Scope |
| Tables/Charts |
Application |
Master |
|
PCD.DPS.7
The learner will be able to recognize and/or discern the differences between combinations and permutations, and/or find n things taken r at a time for each.
| Strand |
Bloom's |
Scope |
| Combinations |
Analysis |
Master |
|
PCD.DPS.8
The learner will be able to use the mean, median, mode, variance and standard deviation to analyze data.
| Strand |
Bloom's |
Scope |
| Data Analysis |
Analysis |
Master |
|
PCD.DPS.9
The learner will be able to make a definition of probability that involves the concepts of sample space, outcomes, and/or events.
| Strand |
Bloom's |
Scope |
| Probability |
Application |
Master |
|
PCD.DPS.10
The learner will be able to calculate averages.
| Strand |
Bloom's |
Scope |
| Average/Mean/Median/Mode/Range |
Application |
Master |
|
PCD.DPS.11
The learner will be able to create graphic displays of data.
| Strand |
Bloom's |
Scope |
| Graphical Forms |
Synthesis |
Master |
|
PCD.DPS.12
The learner will be able to analyze data.
| Strand |
Bloom's |
Scope |
| Data Analysis |
Analysis |
Master |
|
PCD.DPS.13
The learner will be able to find the probability of both dependent and independent events.
| Strand |
Bloom's |
Scope |
| Independent/Dependent/Mutually Exclusive |
Application |
Master |
|
PCD.DPS.14
The learner will be able to make predictions from data using curve fitting.
| Strand |
Bloom's |
Scope |
| Prediction |
Analysis |
Master |
|
PCD.DPS.15
The learner will be able to forecast predictions from collected data by applying regression techniques.
| Strand |
Bloom's |
Scope |
| Prediction |
Analysis |
Master |
|
PCD.DPS.16
The learner will be able to recognize typical statistical distributions.
| Strand |
Bloom's |
Scope |
| Probability Distribution |
Knowledge |
Master |
|
PCD.DPS.17
The learner will be able to calculate the probability of a conditional event.
| Strand |
Bloom's |
Scope |
| Independent/Dependent/Mutually Exclusive |
Application |
Master |
|
PCD.DPS.18
The learner will be able to identify the misuses of statistics.
| Strand |
Bloom's |
Scope |
| Statistics |
Knowledge |
Master |
|
PCD.GEO.1
The learner will be able to draw an angle in standard position and/or determine its reference and co terminal angles.
| Strand |
Bloom's |
Scope |
| Angles |
Application |
Master |
|
PCD.GEO.2
The learner will be able to create an equation or graph that is a result of transformations using a parent equation or graph.
| Strand |
Bloom's |
Scope |
| Coordinate Geometry: Graphing |
Synthesis |
Master |
|
PCD.GEO.3
The learner will be able to find equations of parabolas, circles, ellipses, and hyperbolas from given attributes.
| Strand |
Bloom's |
Scope |
| Circles |
Application |
Master |
|
|
Number Sense and Numeration
|
|
|
PCD.NSN.1
The learner will be able to determine terms and write an explicit or recursive formula for a sequence.
| Strand |
Bloom's |
Scope |
| Sequences |
Synthesis |
Master |
|
PCD.NSN.2
The learner will be able to find the sum of finite or infinite series.
| Strand |
Bloom's |
Scope |
| Series |
Application |
Master |
|
PCD.NSN.3
The learner will be able to compute average range of change.
| Strand |
Bloom's |
Scope |
| Change |
Application |
Master |
|
PCD.NSN.4
The learner will be able to determine specific terms in sequences, explain them in terms of recurrence formulas, relate them to linear and exponential functions, and find the first n partial sums of arithmetic and geometric series.
| Strand |
Bloom's |
Scope |
| Series |
Synthesis |
Master |
|
PCD.NSN.5
The learner will be able to define and/or discriminate among arithmetic and geometric series.
| Strand |
Bloom's |
Scope |
| Series |
Analysis |
Master |
|
PCD.NSN.6
The learner will be able to find the limit of an infinite series, make definitions of convergent and divergent series, and/or determine the sum of an infinite series, if possible.
| Strand |
Bloom's |
Scope |
| Series |
Synthesis |
Master |
|
PCD.NSN.7
The learner will be able to find the geometric mean.
| Strand |
Bloom's |
Scope |
| Series |
Application |
Master |
|
PCD.NSN.8
The learner will be able to find the harmonic mean.
| Strand |
Bloom's |
Scope |
| Series |
Application |
Master |
|
PCD.NSN.9
The learner will be able to show a series in correct sigma notation.
| Strand |
Bloom's |
Scope |
| Series |
Application |
Master |
|
|
Patterns, Functions, Algebra
|
|
|
PCD.PFA.1
The learner will be able to solve equations and inequalities algebraically, geometrically, and statistically.
| Strand |
Bloom's |
Scope |
| Linear Equations/Inequations |
Application |
Master |
|
PCD.PFA.2
The learner will be able to solve equations and inequalities by applying a function to each side, using factoring or chunking, or by using properties of various functions.
| Strand |
Bloom's |
Scope |
| Linear Equations/Inequations |
Application |
Master |
|
PCD.PFA.3
The learner will be able to describe, find, and apply the derivative algebraically and geometrically.
| Strand |
Bloom's |
Scope |
| Calculus: Derivatives/Antiderivatives |
Comprehension |
Master |
|
PCD.PFA.4
The learner will be able to locate or approximate zeros of a function by using the Intermediate Value Theorem and the Bisection Method.
| Strand |
Bloom's |
Scope |
| Calculus: Concepts |
Application |
Master |
|
PCD.PFA.5
The learner will be able to use derivatives to find velocity and acceleration of moving objects.
| Strand |
Bloom's |
Scope |
| Calculus: Derivatives/Antiderivatives |
Application |
Master |
|
PCD.PFA.6
The learner will be able to use derivatives to solve optimization problems.
| Strand |
Bloom's |
Scope |
| Calculus: Derivatives/Antiderivatives |
Application |
Master |
|
PCD.PFA.7
The learner will be able to express and graph complex numbers in various forms and perform operations on complex numbers.
| Strand |
Bloom's |
Scope |
| Calculus: Complex Numbers |
Application |
Master |
|
PCD.PFA.8
The learner will be able to perform operations with complex numbers and find powers and roots of complex numbers.
| Strand |
Bloom's |
Scope |
| Calculus: Operations |
Application |
Master |
|
PCD.PFA.9
The learner will be able to graph complex numbers, powers and roots of complex number and polar equations.
| Strand |
Bloom's |
Scope |
| Calculus: Complex Numbers |
Application |
Master |
|
PCD.PFA.10
The learner will be able to use vectors in two and three dimensions.
| Strand |
Bloom's |
Scope |
| Calculus: Vectors |
Application |
Master |
|
PCD.PFA.11
The learner will be able to use vectors to describe forces and motion.
| Strand |
Bloom's |
Scope |
| Calculus: Vectors |
Analysis |
Master |
|
PCD.PFA.12
The learner will be able to use vectors to describe lines and planes algebraically.
| Strand |
Bloom's |
Scope |
| Calculus: Vectors |
Comprehension |
Master |
|
PCD.PFA.13
The learner will be able to use vectors to solve systems.
| Strand |
Bloom's |
Scope |
| Calculus: Vectors |
Application |
Master |
|
PCD.PFA.14
The learner will be able to rewrite vectors in matrix form and perform calculations on the matrices.
| Strand |
Bloom's |
Scope |
| Calculus: Vectors |
Application |
Master |
|
PCD.PFA.15
The learner will be able to convert among geometric, algebraic, and arithmetic descriptions of functions.
| Strand |
Bloom's |
Scope |
| Functions |
Synthesis |
Master |
|
PCD.PFA.16
The learner will be able to analyze a function by determining local extrema, domain and range, local and global behavior.
| Strand |
Bloom's |
Scope |
| Functions |
Application |
Master |
|
PCD.PFA.17
The learner will be able to find the sum, difference, product, quotient, and composite of two given functions.
| Strand |
Bloom's |
Scope |
| Functions: Mapping/Composition |
Application |
Master |
|
PCD.PFA.18
The learner will be able to find inverses and reciprocals of functions.
| Strand |
Bloom's |
Scope |
| Functions: Inverses |
Application |
Master |
|
PCD.PFA.19
The learner will be able to use functions as models to describe phenomena.
| Strand |
Bloom's |
Scope |
| Functions |
Application |
Master |
|
PCD.PFA.20
The learner will be able to use graphs or tables of values to approximate zeros of functions and solve equations and inequalities.
| Strand |
Bloom's |
Scope |
| Functions |
Application |
Master |
|
PCD.PFA.21
The learner will be able to use derivatives to identify properties of functions.
| Strand |
Bloom's |
Scope |
| Calculus: Derivatives/Antiderivatives |
Comprehension |
Master |
|
PCD.PFA.22
The learner will be able to find derivatives and determine properties of derivatives graphically.
| Strand |
Bloom's |
Scope |
| Functions: Graphing |
Analysis |
Master |
|
PCD.PFA.23
The learner will be able to use derivatives to describe properties of parent functions.
| Strand |
Bloom's |
Scope |
| Calculus: Derivatives/Antiderivatives |
Application |
Master |
|
PCD.PFA.24
The learner will be able to effect and describe transformations to functions and relations.
| Strand |
Bloom's |
Scope |
| Functions |
Comprehension |
Master |
|
PCD.PFA.25
The learner will be able to express complex numbers in a+bi, rectangular, polar, and trigonometric form; convert between polar and rectangular coordinate representations.
| Strand |
Bloom's |
Scope |
| Trigonometry:Polar Forms/Equations/Graph |
Synthesis |
Master |
|
PCD.PFA.26
The learner will be able to apply Pascal's Triangle and the Binomial Theorem to find terms of a sequence.
| Strand |
Bloom's |
Scope |
| Binomial Expansion |
Application |
Master |
|
PCD.PFA.27
The learner will be able to apply trigonometric functions to solve problems.
| Strand |
Bloom's |
Scope |
| Functions: Trigonometric |
Application |
Master |
|
PCD.PFA.28
The learner will be able to find values of trigonometric functions on the unit circle.
| Strand |
Bloom's |
Scope |
| Functions: Trigonometric |
Knowledge |
Master |
|
PCD.PFA.29
The learner will be able to find the domain and range of trigonometric functions.
| Strand |
Bloom's |
Scope |
| Functions: Trigonometric |
Analysis |
Master |
|
PCD.PFA.30
The learner will be able to identify properties of trigonometric functions.
| Strand |
Bloom's |
Scope |
| Functions: Trigonometric |
Comprehension |
Master |
|
PCD.PFA.31
The learner will be able to find inverse and reciprocal trigonometric functions.
| Strand |
Bloom's |
Scope |
| Functions: Trigonometric |
Comprehension |
Master |
|
PCD.PFA.32
The learner will be able to graph the circular functions and effect transformations on them.
| Strand |
Bloom's |
Scope |
| Functions: Circular |
Knowledge |
Master |
|
PCD.PFA.33
The learner will be able to determine the goodness-of-fit model.
| Strand |
Bloom's |
Scope |
| Linear Equations/Inequations |
Application |
Master |
|
PCD.PFA.34
The learner will be able to find values of the trigonometric functions in a triangle.
| Strand |
Bloom's |
Scope |
| Trigonometry: Triangles |
Application |
Master |
|
PCD.PFA.35
The learner will be able to use trigonometry to find unknown measures in triangles.
| Strand |
Bloom's |
Scope |
| Trigonometry: Right Triangles |
Application |
Master |
|
PCD.PFA.36
The learner will be able to solve trigonometric equations.
| Strand |
Bloom's |
Scope |
| Trigonometry: Equations |
Application |
Master |
|
PCD.PFA.37
The learner will be able to prove and apply the basic trigonometric identities.
| Strand |
Bloom's |
Scope |
| Trigonometry: Identities |
Evaluation |
Master |
|
PCD.PFA.38
The learner will be able to use trigonometry to solve problems that cannot be solved by direct measurement.
| Strand |
Bloom's |
Scope |
| Trigonometry: Ratios |
Application |
Master |
|
PCD.PFA.39
The learner will be able to represent problem situations using discrete structures such as finite graphs, matrices, sequences, and recurrence relations.
| Strand |
Bloom's |
Scope |
| Calculus: Concepts |
Application |
Master |
|
PCD.PFA.40
The learner will be able to represent and analyze finite graphs and matrices.
| Strand |
Bloom's |
Scope |
| Calculus: Concepts |
Analysis |
Master |
|
PCD.PFA.41
The learner will be able to describe periodic real-world phenomena using the sine and cosine functions.
| Strand |
Bloom's |
Scope |
| Functions: Trigonometric |
Application |
Master |
|
PCD.PFA.42
The learner will be able to obtain solutions to polynomial equations over the field of complex numbers, using the following theorems: Remainder, Factor, Rational Root, and Fundamental Theorem of Algebra.
| Strand |
Bloom's |
Scope |
| Polynomials |
Application |
Master |
|
PCD.PFA.43
The learner will be able to apply the Binomial Theorem to simplify expressions.
| Strand |
Bloom's |
Scope |
| Binomial Expansion |
Application |
Master |
|
PCD.PFA.44
The learner will be able to expand powers of binomial expressions by applying the Binomial Theorem.
| Strand |
Bloom's |
Scope |
| Binomial Expansion |
Application |
Master |
|
PCD.PFA.45
The learner will be able to obtain solutions to exponential equations.
| Strand |
Bloom's |
Scope |
| Exponents |
Application |
Master |
|
PCD.PFA.46
The learner will be able to obtain solutions to logarithmic equations.
| Strand |
Bloom's |
Scope |
| Logarithms |
Application |
Master |
|
PCD.PFA.47
The learner will be able to apply a variety of methods (including technology) to obtain solutions to systems of equations with two and three variables.
| Strand |
Bloom's |
Scope |
| Equations |
Application |
Master |
|
PCD.PFA.48
The learner will be able to define and/or use the elementary operations and properties of complex numbers.
| Strand |
Bloom's |
Scope |
| Calculus: Complex Numbers |
Application |
Master |
|
PCD.PFA.49
The learner will be able to graph and express complex numbers in rectangular and polar form.
| Strand |
Bloom's |
Scope |
| Calculus: Complex Numbers |
Application |
Master |
|
PCD.PFA.50
The learner will be able to apply suitable theorems and/or definitions to determine powers, roots, and/or absolute values of complex numbers.
| Strand |
Bloom's |
Scope |
| Calculus: Complex Numbers |
Application |
Master |
|
PCD.PFA.51
The learner will be able to recognize and/or graph a parabola, circle, ellipse, and/or hyperbola that may or may not be centered at the origin.
| Strand |
Bloom's |
Scope |
| Calculus: Conic Sections |
Application |
Master |
|
PCD.PFA.52
The learner will be able to identify, write, and graph the equations of conic sections, applying properties when appropriate.
| Strand |
Bloom's |
Scope |
| Calculus: Conic Sections |
Application |
Master |
|
PCD.PFA.53
The learner will be able to recognize all of the conic sections (including degenerates) as the intersection of a plane and a conical surface.
| Strand |
Bloom's |
Scope |
| Calculus: Conic Sections |
Knowledge |
Master |
|
PCD.PFA.54
The learner will be able to obtain solutions to systems of equations involving conics and other forms of equations.
| Strand |
Bloom's |
Scope |
| Calculus: Conic Sections |
Application |
Master |
|
PCD.PFA.55
The learner will be able to evaluate the determinant for 2 by 2 and 3 by 3 matrices applying suitable methods.
| Strand |
Bloom's |
Scope |
| Calculus: Matrices |
Application |
Master |
|
PCD.PFA.56
The learner will be able to make evaluations of the results of matrix operations.
| Strand |
Bloom's |
Scope |
| Calculus: Matrices |
Evaluation |
Master |
|
PCD.PFA.57
The learner will be able to determine the inverses of matrices (if possible) for 2x2 and/or 3x3 cases.
| Strand |
Bloom's |
Scope |
| Calculus: Matrices |
Application |
Master |
|
PCD.PFA.58
The learner will be able to use matrices in practical applications.
| Strand |
Bloom's |
Scope |
| Calculus: Matrices |
Application |
Master |
|
PCD.PFA.59
The learner will be able to define and graph the following types of functions: identity, constant, absolute value, step, greatest integer, polynomial, linear, quadratic, square root, and piecewise.
| Strand |
Bloom's |
Scope |
| Functions |
Application |
Master |
|
PCD.PFA.60
The learner will be able to graph relations and/or functions with the aid of concepts including domain, range, rule, symmetry, asymptotes, and/or periodicity.
| Strand |
Bloom's |
Scope |
| Functions: Graphing |
Application |
Master |
|
PCD.PFA.61
The learner will be able to graph polynomial, rational, and algebraic functions using suitable methods and tools.
| Strand |
Bloom's |
Scope |
| Functions: Graphing |
Application |
Master |
|
PCD.PFA.62
The learner will be able to find the inverse of a given function and determine whether that is a function.
| Strand |
Bloom's |
Scope |
| Inverses |
Synthesis |
Master |
|
PCD.PFA.63
The learner will be able to define, graph, and illustrate the inverse relationship that exists between the classes of logarithmic and exponential functions.
| Strand |
Bloom's |
Scope |
| Functions: Exponential/Logarithmic |
Synthesis |
Master |
|
PCD.PFA.64
The learner will be able to define the six trig functions as circular functions as well as right triangle ratios and/or illustrate the relationship that exists among these functions.
| Strand |
Bloom's |
Scope |
| Functions: Trigonometric |
Synthesis |
Master |
|
PCD.PFA.65
The learner will be able to evaluate and graph trigonometric functions by applying the concepts of period, phase shift, vertical shift, and amplitude.
| Strand |
Bloom's |
Scope |
| Functions: Trigonometric |
Evaluation |
Master |
|
PCD.PFA.66
The learner will be able to determine the composite of two functions.
| Strand |
Bloom's |
Scope |
| Functions |
Application |
Master |
|
PCD.PFA.67
The learner will be able to determine the domain and range of the composition of two functions.
| Strand |
Bloom's |
Scope |
| Functions: Mapping/Composition |
Application |
Master |
|
PCD.PFA.68
The learner will be able to solve problems using exponential and logarithmic functions by applying appropriate tools.
| Strand |
Bloom's |
Scope |
| Functions: Exponential/Logarithmic |
Application |
Master |
|
PCD.PFA.69
The learner will be able to graph relations and functions by using their end behavior.
| Strand |
Bloom's |
Scope |
| Functions: Graphing |
Application |
Master |
|
PCD.PFA.70
The learner will be able to determine the domain and range of the inverse of a function.
| Strand |
Bloom's |
Scope |
| Functions: Inverses |
Application |
Master |
|
PCD.PFA.71
The learner will be able to obtain solutions to logarithmic and exponential problems.
| Strand |
Bloom's |
Scope |
| Functions: Exponential/Logarithmic |
Application |
Master |
|
PCD.PFA.72
The learner will be able to solve problems involving exponential and logarithmic functions using suitable methods.
| Strand |
Bloom's |
Scope |
| Functions: Exponential/Logarithmic |
Application |
Master |
|
PCD.PFA.73
The learner will be able to evaluate the inverse of a given trigonometric function.
| Strand |
Bloom's |
Scope |
| Functions: Trigonometric |
Application |
Master |
|
PCD.PFA.74
The learner will be able to graph the inverse of trigonometric functions.
| Strand |
Bloom's |
Scope |
| Functions: Trigonometric |
Application |
Master |
|
PCD.PFA.75
The learner will be able to obtain solutions to equations involving inverse trigonometric functions.
| Strand |
Bloom's |
Scope |
| Functions: Trigonometric |
Application |
Master |
|
PCD.PFA.76
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 |
| Problem Solving |
Application |
Master |
|
PCD.PFA.77
The learner will be able to apply estimation strategies to predict calculated results when solving problems.
| Strand |
Bloom's |
Scope |
| Problem Solving |
Application |
Master |
|
PCD.PFA.78
The learner will be able to evaluate the reasonableness of a given solution.
| Strand |
Bloom's |
Scope |
| Estimation |
Evaluation |
Master |
|
PCD.PFA.79
The learner will be able to choose suitable problem solving strategies.
| Strand |
Bloom's |
Scope |
| Problem Solving |
Application |
Master |
|
PCD.PFA.80
The learner will be able to choose suitable mathematical tools to obtain solutions to problems.
| Strand |
Bloom's |
Scope |
| Problem Solving |
Application |
Master |
|
PCD.PFA.81
The learner will be able to simplify trigonometric expressions and obtain solutions to trigonometric equations by applying trigonometric identities.
| Strand |
Bloom's |
Scope |
| Trigonometry: Equations |
Application |
Master |
|
PCD.PFA.82
The learner will be able to convert angle measures between degrees and radians.
| Strand |
Bloom's |
Scope |
| Trigonometry: Concepts |
Synthesis |
Master |
|
PCD.PFA.83
The learner will be able to use the Law of Sines and Law of Cosines to solve problems.
| Strand |
Bloom's |
Scope |
| Trigonometry: Ratios |
Application |
Master |
|
PCD.PFA.84
The learner will be able to apply right triangle ratios to obtain problem solutions.
| Strand |
Bloom's |
Scope |
| Trigonometry: Right Triangles |
Application |
Master |
|
PCD.PFA.85
The learner will be able to apply a suitable formula to determine the area for any triangle.
| Strand |
Bloom's |
Scope |
| Equations |
Application |
Master |
|
PCD.PFA.86
The learner will be able to identify basic properties of and use logarithms to solve problems.
| Strand |
Bloom's |
Scope |
| Logarithms |
Application |
Master |
|
PCD.PFA.87
The learner will be able to identify and graph parabolas, circles, ellipses, and hyperbolas from their equations.
| Strand |
Bloom's |
Scope |
| Calculus: Conic Sections |
Application |
Master |
|
PCD.PFA.88
The learner will be able to solve trigonometric functions using triangles.
| Strand |
Bloom's |
Scope |
| Functions: Trigonometric |
Application |
Master |
|
PCD.PFA.89
The learner will be able to use the exponential and logarithmic functions.
| Strand |
Bloom's |
Scope |
| Functions: Exponential/Logarithmic |
Analysis |
Master |
|
PCD.PFA.90
The learner will be able to compare exponential and logarithmic functions.
| Strand |
Bloom's |
Scope |
| Functions: Exponential/Logarithmic |
Application |
Master |
|
PCD.PFA.91
The learner will be able to solve simple logarithmic and exponential equations.
| Strand |
Bloom's |
Scope |
| Functions: Exponential/Logarithmic |
Application |
Master |
|
PCD.PFA.92
The learner will be able to apply exponential functions to solve rate of growth problems using the form f(x) = (1 + r) to the x power.
| Strand |
Bloom's |
Scope |
| Functions: Exponential/Logarithmic |
Application |
Master |
|
PCD.PFA.93
The learner will be able to use the form f(x) = a X b to the x power to write an exponential function.
| Strand |
Bloom's |
Scope |
| Functions: Exponential/Logarithmic |
Application |
Master |
|
PCD.PFA.94
The learner will be able to graph an exponential function given in the form f(x) = a X b to the x power.
| Strand |
Bloom's |
Scope |
| Functions: Exponential/Logarithmic |
Application |
Master |
|
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