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© 2002 by School City of Hobart and EdVISION Corporation.
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Curriculum Designer by
EdVISION Corporation

School City of Hobart
School City of Hobart Mathematics
Mathematics - IN: Precalculus

Algebraic Concepts

Equations: Comprehend/Logic
The learner will be able to comprehend that the logic of finding the solutions to equations begins with the assumption that the variable is a number that satisfies the equation, and that the process used when solving equations generates new equations that usually have the same solution set as the original, and understand that similar logic applies to obtaining solutions to systems of equations simultaneously.
Strand Bloom's Scope Source Activities
Equations   Master IN: Academic Standards, 2000, Precalculus, PC.9.5 Classroom
  
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Calculus and Pre-Calculus

Conic Sections: Write/Graphs
The learner will be able to write the equations of conic sections in standard form to determine the type of conic sections and to determine its geometric properties.
Strand Bloom's Scope Source Activities
Conic Sections   Master IN: Academic Standards, 2000, Precalculus, PC.1.10 Classroom
  
Conic Sections: Study/Graph
The learner will be able to study and create graphs of circles, ellipses, parabolas, and hyperbolas.
Strand Bloom's Scope Source Activities
Conic Sections   Master IN: Academic Standards, 2000, Precalculus, Standard 1 Classroom
  
Complex Numbers: Define
The learner will be able to express a definition of complex numbers.
Strand Bloom's Scope Source Activities
Complex Numbers Knowledge Master IN: Academic Standards, 2000, Precalculus, PC.6.4 Classroom
  
Complex Numbers: DeMoivre's/Explain
The learner will be able to explain DeMoivre's theorem.
Strand Bloom's Scope Source Activities
Complex Numbers Comprehension Master IN: Academic Standards, 2000, Precalculus, PC.6.5 Classroom
  
Complex Numbers in Trigonometric Form
The learner will be able to show complex numbers in trigonometric form.
Strand Bloom's Scope Source Activities
Complex Numbers Application Master IN: Academic Standards, 2000, Precalculus, PC.6.4 Classroom
  
Complex Numbers in Trigonometric Form
The learner will be able to perform the multiplication of complex numbers in trigonometric form.
Strand Bloom's Scope Source Activities
Complex Numbers Application Master IN: Academic Standards, 2000, Precalculus, PC.6.4 Classroom
  
DeMoivre's Theorem: Apply
The learner will be able to use DeMoivre's Theorem.
Strand Bloom's Scope Source Activities
Complex Numbers Application Master IN: Academic Standards, 2000, Precalculus, PC.6.5 Classroom
  
Complex Numbers: DeMoivre's/Prove
The learner will be able to prove DeMoivre's theorem.
Strand Bloom's Scope Source Activities
Complex Numbers Synthesis Master IN: Academic Standards, 2000, Precalculus, PC.6.5 Classroom
  
Limits: Limit Concept
The learner will be able to understand the concept of a limit.
Strand Bloom's Scope Source Activities
Limits Comprehension Master IN: Academic Standards, 2000, Precalculus, Standard 7 Classroom
  
Problem Solving: Mathematical Induction
The learner will be able to apply the concept of Mathematical Induction as a means of mathematical proof.
Strand Bloom's Scope Source Activities
Problem Solving Application Master IN: Academic Standards, 2000, Precalculus, PC.9.6 Classroom
  
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Data Interpretation

Graphs: Create/Analyze
The learner will be able to create and analyze graphs.
Strand Bloom's Scope Source Activities
Graphing   Master IN: Academic Standards, 2000, Precalculus, Standard 4 Classroom
  
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Functions: Linear/Nonlinear
The learner will be able to use linear and nonlinear functions to model data.
Strand Bloom's Scope Source Activities
Functions/Relations   Master IN: Academic Standards, 2000, Precalculus, Standard 8 Classroom
  
Exponential/Logarithmic Functions
The learner will be able to determine the domain, range, intercepts, and asymptotes of logarithmic and exponential functions.
Strand Bloom's Scope Source Activities
Exponential/Logarithmic Functions   Master IN: Academic Standards, 2000, Precalculus, PC.2.2 Classroom
  
Logarithmic/Exponential Function: Define
The learner will be able to define, determine, and check the inverse functions of logarithmic and exponential functions.
Strand Bloom's Scope Source Activities
Exponential/Logarithmic Functions   Master IN: Academic Standards, 2000, Precalculus, PC.2.4 Classroom
  
Graphing: Comprehend/Draw
The learner will be able to comprehend curves defined parametrically and create drawings of their graphs.
Strand Bloom's Scope Source Activities
Graphing Functions   Master IN: Academic Standards, 2000, Precalculus, PC.1.8 Classroom
  
Problem Solving: Model/Solve
The learner will be able to use functions and equations to model and obtain solutions to word problems.
Strand Bloom's Scope Source Activities
Problem Solving   Master IN: Academic Standards, 2000, Precalculus, PC.1.3 Classroom
  
Functions: Determine/Domain/Range
The learner will be able to determine the domain, range, intercepts, zeros, poles, asymptotes, and points of discontinuity of functions, using paper and pencil techniques and graphing calculators.
Strand Bloom's Scope Source Activities
Functions   Master IN: Academic Standards, 2000, Precalculus, PC.1.2 Classroom
  
Functions: Determine/Illustrate
The learner will be able to determine a quadratic, exponential, logarithmic, power, or sinusoidal function to illustrate a set of data and describe the parameters of the model.
Strand Bloom's Scope Source Activities
Functions   Master IN: Academic Standards, 2000, Precalculus, PC.8.3 Classroom
  
Functions: Identify/Graph
The learner will be able to identify and create graphs of different types of functions including polynomial, rational, algebraic, and absolute value using paper and pencil techniques and graphing calculators.
Strand Bloom's Scope Source Activities
Functions   Master IN: Academic Standards, 2000, Precalculus, PC.1.1 Classroom
  
Functions: Apply/Write
The learner will be able to write functions applying polynomial, rational, and algebraic functions, and draw graphs to obtain solutions to word problems, to determine composite and inverse functions, and to study functions and graphs.
Strand Bloom's Scope Source Activities
Functions   Master IN: Academic Standards, 2000, Precalculus, Standard 1 Classroom
  
Inverses: Define
The learner will be able to define the inverse of a function.
Strand Bloom's Scope Source Activities
Inverses Knowledge Master IN: Academic Standards, 2000, Precalculus, PC.1.4 Classroom
  
Inverses: Finding
The learner will be able to find the inverse of a given function.
Strand Bloom's Scope Source Activities
Inverses Application Master IN: Academic Standards, 2000, Precalculus, PC.1.4, Standard 2, Standard 4 Classroom
  
Inverse Functions: Check
The learner will be able to check the inverse of a function.
Strand Bloom's Scope Source Activities
Inverses Evaluation Master IN: Academic Standards, 2000, Precalculus, PC.1.4 Classroom
  
Exponential Functions: Word Problems
The learner will be able to obtain solutions to word problems involving exponential functions.
Strand Bloom's Scope Source Activities
Exponential Functions Application Master IN: Academic Standards, 2000, Precalculus, Standard 2, PC.2.1 Classroom
  
Logarithmic Functions: Word Problems
The learner will be able to obtain solutions to word problems involving logarithmic functions.
Strand Bloom's Scope Source Activities
Logarithmic Functions Application Master IN: Academic Standards, 2000, Precalculus, Standard 2, PC.2.1 Classroom
  
Exponential/Logarithmic Functions: Graph
The learner will be able to graph both exponential and logarithmic functions.
Strand Bloom's Scope Source Activities
Exponential/Logarithmic Functions Application Master IN: Academic Standards, 2000, Precalculus, Standard 2, PC.2.3 Classroom
  
Exponential/Logarithmic: Graph/Analyze
The learner will be able to analyze the graphs of both exponential and logarithmic functions.
Strand Bloom's Scope Source Activities
Exponential/Logarithmic Functions Analysis Master IN: Academic Standards, 2000, Precalculus, Standard 2, PC.2.3 Classroom
  
Trigonometric Functions: Define
The learner will be able to define the six trigonometric functions.
Strand Bloom's Scope Source Activities
Trigonometric Functions Knowledge Master IN: Academic Standards, 2000, Precalculus, PC.4.5 Classroom
  
Trig. Function: Unit Circle
The learner will be able to define the trigonometric functions applying the unit circle.
Strand Bloom's Scope Source Activities
Trigonometric Functions Knowledge Master IN: Academic Standards, 2000, Precalculus, Standard 4 Classroom
  
Trig. Functions: Inverse/Define
The learner will be able to define the inverse of a trigonometric function.
Strand Bloom's Scope Source Activities
Trigonometric Functions Knowledge Master IN: Academic Standards, 2000, Precalculus, PC.4.8 Classroom
  
Trigonometric Functions: Problem Solving
The learner will be able to obtain solutions to word problems by applying trigonometric functions.
Strand Bloom's Scope Source Activities
Trigonometric Functions Application Master IN: Academic Standards, 2000, Precalculus, Standard 4, PC.4.4 Classroom
  
Trigonometric Functions: Inverse/Value
The learner will be able to find the values of inverse trigonometric functions.
Strand Bloom's Scope Source Activities
Trigonometric Functions Application Master IN: Academic Standards, 2000, Precalculus, PC.4.9 Classroom
  
Trigonometric Functions: Graph/Inverse
The learner will be able to graph the inverse of trigonometric functions.
Strand Bloom's Scope Source Activities
Trigonometric Functions Application Master IN: Academic Standards, 2000, Precalculus, PC.4.8 Classroom
  
Trigonometric Functions: Graphing
The learner will be able to graph trigonometric functions.
Strand Bloom's Scope Source Activities
Trigonometric Functions Application Master IN: Academic Standards, 2000, Precalculus, PC.4.5 Classroom
  
Trig. Functions: Translation/Graph
The learner will be able to graph the translation of a given trigonometric function.
Strand Bloom's Scope Source Activities
Trigonometric Functions Application Master IN: Academic Standards, 2000, Precalculus, PC.4.7 Classroom
  
Trigonometric Functions: Attributes
The learner will be able to determine the following attributes for trigonometric functions: domain, range, period, amplitude, intercepts, and asymptotes.
Strand Bloom's Scope Source Activities
Trigonometric Functions Application Master IN: Academic Standards, 2000, Precalculus, PC.4.6 Classroom
  
Trigonometric Functions: Value
The learner will be able to determine the values of trigonometric functions.
Strand Bloom's Scope Source Activities
Trigonometric Functions Application Master IN: Academic Standards, 2000, Precalculus, PC.4.9 Classroom
  
Trig. Functions: Study/Translation
The learner will be able to study the graphs of the translations of trigonometric functions.
Strand Bloom's Scope Source Activities
Trigonometric Functions Analysis Master IN: Academic Standards, 2000, Precalculus, PC.4.7 Classroom
  
Graphing: Symmetry/Describe
The learner will be able to describe how the graphs of functions are symmetrical.
Strand Bloom's Scope Source Activities
Graphing Functions Comprehension Master IN: Academic Standards, 2000, Precalculus, PC.1.5 Classroom
  
Functions: Odd-Even/Identify
The learner will be able to identify odd and even functions.
Strand Bloom's Scope Source Activities
Functions Knowledge Master IN: Academic Standards, 2000, Precalculus, PC.1.6 Classroom
  
Functions: Apply/Transformations
The learner will be able to apply transformations to functions.
Strand Bloom's Scope Source Activities
Functions Application Master IN: Academic Standards, 2000, Precalculus, PC.1.7 Classroom
  
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 Source Activities
Functions Analysis Master IN: Academic Standards, 2000, Precalculus, PC.1.9 Classroom
  
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Inductive Reasoning: Define
The learner will be able to define what is meant by mathematical induction.
Strand Bloom's Scope Source Activities
Reasoning Knowledge Master IN: Academic Standards, 2000, Precalculus, PC.9.6 Classroom
  
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Mathematics Processes

Reasoning: True/False
The learner will be able to determine if a given algebraic statement is true always, never, or occasionally.
Strand Bloom's Scope Source Activities
Reasoning   Master IN: Academic Standards, 2000, Precalculus, PC.9.3 Classroom
  
Math as Reasoning: Create/Evaluate
The learner will be able to create and evaluate mathematical arguments and proofs.
Strand Bloom's Scope Source Activities
Reasoning   Master IN: Academic Standards, 2000, Precalculus, Standard 9 Classroom
  
Modeling: Determine/Linear
The learner will be able to determine linear models applying the median fit and least squares regression methods, and determine which model gives a better fit.
Strand Bloom's Scope Source Activities
Mathematical Modeling   Master IN: Academic Standards, 2000, Precalculus, PC.8.1 Classroom
  
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Sequences: Comprehend/Apply
The learner will be able to comprehend and apply the concept of limit of a sequence or function as the independent variable approaches infinity or a number.
Strand Bloom's Scope Source Activities
Sequences   Master IN: Academic Standards, 2000, Precalculus, PC.7.5 Classroom
  
Sequences: Define/Recursively
The learner will be able to recursively define sequences.
Strand Bloom's Scope Source Activities
Sequences Knowledge Master IN: Academic Standards, 2000, Precalculus, PC.7.4 Classroom
  
Sequences: Convergent/Divergent
The learner will be able to determine whether a given sequence converges or diverges.
Strand Bloom's Scope Source Activities
Sequences Application Master IN: Academic Standards, 2000, Precalculus, PC.7.5 Classroom
  
Series: Sum/Infinite Geometric
The learner will be able to determine the sum of an infinite geometric series.
Strand Bloom's Scope Source Activities
Series Application Master IN: Academic Standards, 2000, Precalculus, PC.7.2 Classroom
  
Series: Prove/Finite/Infinite
The learner will be able to prove the sum formulas for arithmetic series, as well as for finite and infinite geometric series.
Strand Bloom's Scope Source Activities
Series Evaluation Master IN: Academic Standards, 2000, Precalculus, PC.7.3 Classroom
  
Sequence/Series: Define
The learner will be able to give definitions of both arithmetic and geometric sequences and series.
Strand Bloom's Scope Source Activities
Sequences/Series Knowledge Master IN: Academic Standards, 2000, Precalculus, Standard 7 Classroom
  
Sequence/Series: Apply
The learner will be able to apply both arithmetic and geometric sequences and series.
Strand Bloom's Scope Source Activities
Sequences/Series Application Master IN: Academic Standards, 2000, Precalculus, Standard 7 Classroom
  
Sequence/Series: Problem Solving
The learner will be able to apply sequences and series to obtain solutions to word problems.
Strand Bloom's Scope Source Activities
Sequences/Series Application Master IN: Academic Standards, 2000, Precalculus, Standard 7, PC.7.6 Classroom
  
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Probability/Statistics

Correlation: Coefficient
The learner will be able to evaluate the "best-fit" line using the correlation coefficient and residuals.
Strand Bloom's Scope Source Activities
Correlation/Deviation/Variance   Master IN: Academic Standards, 2000, Precalculus, PC.8.2 Classroom
  
Summation Notation: Comprehend
The learner will be able to comprehend summation notation.
Strand Bloom's Scope Source Activities
Average/Median/Mode/Range Comprehension Master IN: Academic Standards, 2000, Precalculus, PC.7.1 Classroom
  
Summation Notation: Apply
The learner will be able to apply summation notation.
Strand Bloom's Scope Source Activities
Average/Median/Mode/Range Application Master IN: Academic Standards, 2000, Precalculus, PC.7.1 Classroom
  
Correlation: Coefficient/Compute
The learner will be able to compute the correlation coefficient for collected data.
Strand Bloom's Scope Source Activities
Correlation/Deviation/Variance Application Master IN: Academic Standards, 2000, Precalculus, PC.8.2 Classroom
  
Correlation: Coefficient/Interpret
The learner will be able to interpret the correlation coefficient for collected data.
Strand Bloom's Scope Source Activities
Correlation/Deviation/Variance Analysis Master IN: Academic Standards, 2000, Precalculus, PC.8.2 Classroom
  
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Problem Solving

Solutions: Evaluate Reasonableness
The learner will be able to evaluate the reasonableness of a given solution within the context of the original problem.
Strand Bloom's Scope Source Activities
Solution Evaluation Master IN: Academic Standards, 2000, Precalculus, PC.9.2 Classroom
  
Strategies: Use
The learner will be able to use a variety of strategies to solve problems.
Strand Bloom's Scope Source Activities
Strategies Application Master IN: Academic Standards, 2000, Precalculus, Standard 9, PC.9.1 Classroom
  
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Real Numbers and the Coordinate Plane

Properties: Apply
The learner will be able to apply the properties of number systems as well as the order of operations to justify the process of simplifying functions and obtaining solutions to equations.
Strand Bloom's Scope Source Activities
Real Number Properties   Master IN: Academic Standards, 2000, Precalculus, PC.9.4 Classroom
  
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Trigonometric Ratios: Sine/Cosine
The learner will be able to know the exact sine, cosine and tangent values for 0, pi/6, pi/4, pi/3, and pi/2 and multiples of pi, and apply those values to determine other trigonometric values.
Strand Bloom's Scope Source Activities
Trigonometric Ratios   Master IN: Academic Standards, 2000, Precalculus, PC.4.3 Classroom
  
Connecting: Functions/Polar/Complex
The learner will be able to define polar coordinates and complex numbers and comprehend the relationship with trigonometric functions.
Strand Bloom's Scope Source Activities
Connecting   Master IN: Academic Standards, 2000, Precalculus, Standard 6 Classroom
  
Connecting: Triangle/Trig./Circular
The learner will be able to make connections between concepts of ratios within right triangles, the trigonometric functions, and circular functions.
Strand Bloom's Scope Source Activities
Connecting   Master IN: Academic Standards, 2000, Precalculus, PC.4.11 Classroom
  
Trigonometric Identities
The learner will be able to comprehend and apply formulas for double angles and half angles for sines, cosines, and tangents.
Strand Bloom's Scope Source Activities
Trigonometric Identities   Master IN: Academic Standards, 2000, Precalculus, PC.5.4 Classroom
  
Trig. Ratios: Sine/Cosine/Tangent
The learner will be able to comprehend the addition formulas for sines, cosines, and tangents.
Strand Bloom's Scope Source Activities
Trigonometric Ratios Comprehension Master IN: Academic Standards, 2000, Precalculus, PC.5.3 Classroom
  
Trig. Ratios: Apply/Addition/Formulas
The learner will be able to apply the addition formulas for sines, cosines, and tangents.
Strand Bloom's Scope Source Activities
Trigonometric Ratios Application Master IN: Academic Standards, 2000, Precalculus, PC.5.3 Classroom
  
Trigonometric Ratios: Apply
The learner will be able to apply the laws of sines and cosines.
Strand Bloom's Scope Source Activities
Trigonometric Ratios Application Master IN: Academic Standards, 2000, Precalculus, Standard 3 Classroom
  
Trig. Ratios: Law of Sines/Cosines
The learner will be able to use the Law of Sines and Cosines to solve problems.
Strand Bloom's Scope Source Activities
Trigonometric Ratios Application Master IN: Academic Standards, 2000, Precalculus, PC.3.2 Classroom
  
Triangles: Determine/Area
The learner will be able to determine the area of a triangle knowing the two sides and the included angle.
Strand Bloom's Scope Source Activities
Triangles Application Master IN: Academic Standards, 2000, Precalculus, PC.3.3 Classroom
  
Triangles: Word Problems
The learner will be able to obtain solutions to word problems involving triangle trigonometry.
Strand Bloom's Scope Source Activities
Triangles Application Master IN: Academic Standards, 2000, Precalculus, Standard 3 Classroom
  
Triangles: Oblique/Problem Solve
The learner will be able to obtain solutions to word problems using oblique triangles.
Strand Bloom's Scope Source Activities
Triangles Application Master IN: Academic Standards, 2000, Precalculus, PC.3.1 Classroom
  
Trigonometric Identities: Knowledge
The learner will be able to know the following trig identity: cosine squared + sine squared = 1.
Strand Bloom's Scope Source Activities
Trigonometric Identities Comprehension Master IN: Academic Standards, 2000, Precalculus, PC.5.1 Classroom
  
Trig. Identities: Apply
The learner will be able to apply basic trigonometric identities to simplify expressions.
Strand Bloom's Scope Source Activities
Trigonometric Identities Application Master IN: Academic Standards, 2000, Precalculus, PC.5.2 Classroom
  
Trig. Identities: Apply
The learner will be able to apply basic trigonometric identities to verify other identities.
Strand Bloom's Scope Source Activities
Trigonometric Identities Application Master IN: Academic Standards, 2000, Precalculus, PC.5.2 Classroom
  
Trig. Identities: Verifying
The learner will be able to verify the trigonometric identities.
Strand Bloom's Scope Source Activities
Trigonometric Identities Application Master IN: Academic Standards, 2000, Precalculus, Standard 5 Classroom
  
Trigonometric Identities: Proving
The learner will be able to prove that the identity cos(x) squared + sine(x) squared = 1 is equivalent to the Pythagorean Theorem.
Strand Bloom's Scope Source Activities
Trigonometric Identities Evaluation Master IN: Academic Standards, 2000, Precalculus, PC.5.1 Classroom
  
Trig. Equations: Solving
The learner will be able to calculate solutions for trigonometric equations.
Strand Bloom's Scope Source Activities
Trigonometric Equations Application Master IN: Academic Standards, 2000, Precalculus, Standard 5, PC.5.5 Classroom
  
Trigonometric Equations: Problem Solving
The learner will be able to apply trigonometric equations and/or inequalities in obtaining word problem solutions.
Strand Bloom's Scope Source Activities
Trigonometric Equations Application Master IN: Academic Standards, 2000, Precalculus, Standard 5, PC.5.6 Classroom
  
Angles: Degrees/Radians
The learner will be able to apply degrees and radians.
Strand Bloom's Scope Source Activities
Radians/Angles Application Master IN: Academic Standards, 2000, Precalculus, Standard 4 Classroom
  
Angle Measures: Degree/Radian
The learner will be able to convert angle measures between degrees and radians.
Strand Bloom's Scope Source Activities
Radians/Angles Synthesis Master IN: Academic Standards, 2000, Precalculus, PC.4.2 Classroom
  
Polar Coordinates: Define
The learner will be able to give a definition of polar coordinates.
Strand Bloom's Scope Source Activities
Polar Forms/Equations/Graphs Knowledge Master IN: Academic Standards, 2000, Precalculus, PC.6.1 Classroom
  
Polar Equations: Graph
The learner will be able to create graphs of equations in the polar coordinate plane.
Strand Bloom's Scope Source Activities
Polar Forms/Equations/Graphs Application Master IN: Academic Standards, 2000, Precalculus, PC.6.3 Classroom
  
Polar Forms/Equations: Represent
The learner will be able to display equations given in rectangular coordinates in the context of polar coordinates.
Strand Bloom's Scope Source Activities
Polar Forms/Equations/Graphs Application Master IN: Academic Standards, 2000, Precalculus, PC.6.2 Classroom
  
Polar Form: Relate/Cartesian
The learner will be able to make the connection between polar coordinates and Cartesian coordinates.
Strand Bloom's Scope Source Activities
Polar Forms/Equations/Graphs Analysis Master IN: Academic Standards, 2000, Precalculus, PC.6.1 Classroom
  
Trigonometric Concepts: Tangent/Slope
The learner will be able to understand that the tangent of the angle by a line intersecting the x-axis is the same as the slope of that line.
Strand Bloom's Scope Source Activities
Trigonometric Concepts Comprehension Master IN: Academic Standards, 2000, Precalculus, PC.4.10 Classroom
  
Right Triangles: Trigonometric Functions
The learner will be able to use right triangles to define trigonometric functions.
Strand Bloom's Scope Source Activities
Right Triangles Knowledge Master IN: Academic Standards, 2000, Precalculus, Standard 3 Classroom
  
Right Triangles: Solve/Word Problems
The learner will be able to obtain solutions to word problems using right triangles.
Strand Bloom's Scope Source Activities
Right Triangles Application Master IN: Academic Standards, 2000, Precalculus, PC.3.1 Classroom
  
Unit Circle: Apply/Concept
The learner will be able to apply the concept of unit circle to define sine and cosine.
Strand Bloom's Scope Source Activities
Unit Circle Knowledge Master IN: Academic Standards, 2000, Precalculus, PC.4.1 Classroom
  
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