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Poyen School
Poyen School Curriculum K - 12 2007-2008
Mathematics - Pre-Calculus including Trigonometry

Polynomial and Rational Functions
Graph polynomial and rational functions
The learner will be able to investigate and sketch, with and without appropriate technology, the graphs of polynomial and rational functions using the characteristics of domain and range, upper and lower bounds, maximum and minimum points, asymptotes and end behavior, zeroes multiplicity of zeroes, y - intercepts, and symmetry.
Strand Bloom's Scope Hours Source Activities
Analyze: graphically & algebraically   Master 1.0 2004 Arkansas Mathematics Frameworks PRF.1.PCT.1 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, Lesson 1.3 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 1.4 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 2.1 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 2.2 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 2.3 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 2.5 [Textbook].  
  
Solve polynomial equations
The learner will be able to solve, with and without appropriate technology, polynomial equations utilizing techniquest such as Descartes' Rule of Signs, upper and lower bounds, Intermediate Value Theorem and Rational Root Theorem.
Strand Bloom's Scope Hours Source Activities
Analyze: graphically & algebraically   Master 1.0 2004 Arkansas Mathematics Frameworks PRF.1.PCT.2 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 2.2 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 2.3 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 2.5 [Textbook].  
  
Fund. characteristics:Rational Functions
The learner will be able to describe, with and without appropriate technology, the fundamental characteristics of rational functions: zeroes, discontinuities (including vertical asymptotes), end behavior (including horizontal asymptotes).
Strand Bloom's Scope Hours Source Activities
Analyze: graphically & algebraically   Master 1.0 2004 Arkansas Mathematics Frameworks PRF.1.PCT.3 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 2.2 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 2.3 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 2.6 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 2.7 [Textbook].  
  
Apply Concepts: polynomial & rationa
The learner will be able to apply the concepts of polynomial and rational functions to model real world situations using appropriate technology when needed.
Strand Bloom's Scope Hours Source Activities
Analyze: graphically & algebraically   Master 1.0 2004 Arkansas Mathematics Frameworks PRF.1.PCT.4 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 1.3 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 1.4 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 1.5 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 1.7 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 2.2 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 2.3 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 2.5 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 2.8 [Textbook].  
  
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Exponential and Logarithmic Functions
Inverse relationship: exponential &
The learner will be able to establish the inverse relationship between exponential and logarithmic functions.
Strand Bloom's Scope Hours Source Activities
Graph, Inverse relationship, apply   Master 1.0 2004 Arkansas Mathematics Frameworks ELF.2.PCT.1 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 3.2 [Textbook].  
  
Laws of log/change of base
The learner will be able to develop and apply the laws of logarithms and the change of base formula to simplify and evaluate expressions.
Strand Bloom's Scope Hours Source Activities
Graph, Inverse relationship, apply   Master 1.0 2004 Arkansas Mathematics Frameworks ELF.2.PCT.2 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 3.3 [Textbook].  
  
Solve exponential & log equations
The learner will be able to solve graphically, algebraically, and numerically, with and without appropriate technology, equations and real world problems involving exponential and logarithmic expressions.
Strand Bloom's Scope Hours Source Activities
Graph, Inverse relationship, apply   Master 1.0 2004 Arkansas Mathematics Frameworks ELF.2.PCT.3 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 3.1 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 3.2 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 3.3 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 3.4 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 3.5 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 3.6 [Textbook].  
  
Domain/range/intercepts/asymptotes
The learner will be able to find, with and without appropriate technology, the domain, range, intercepts, and asymptotes of logarithmic and exponential functions.
Strand Bloom's Scope Hours Source Activities
Graph, Inverse relationship, apply   Master 1.0 2004 Arkansas Mathematics Frameworks ELF.2.PCT.4 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 3.1 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 3.2 [Textbook].  
  
Graph log & exponential functions
The learner will be able to draw and analyze, with and without appropriate technology, graphs of logarithmic and exponential functions.
Strand Bloom's Scope Hours Source Activities
Graph, Inverse relationship, apply   Master 1.0 2004 Arkansas Mathematics Frameworks ELF.2.PCT.5 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 3.1 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 3.2 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 3.6 [Textbook].  
  
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Conics
Conic sections
The learner will be able to identify, graph, write, and analyzie equations of conic sections, using properties such as symmetry, intercepts, foci, asympototes, and eccentricity, and when appropriate, use technology.
Strand Bloom's Scope Hours Source Activities
Identify, Analyze, Graph, Equations   Master 1.0 2004 Arkansas Mathematics Frameworks C.3.PCT.1 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 9.1 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 9.2 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 9.3 [Textbook].  
  
Systems of equations & inequalities
The learner will be able to solve, with and without appropriate technology, systems of equations and inequalities involving conics and other types of equations.
Strand Bloom's Scope Hours Source Activities
Identify, Analyze, Graph, Equations   Master 1.0 2004 Arkansas Mathematics Frameworks C.3.PCT.2 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 9.4 [Textbook].  
  
Real world problems: conics
The learner will be able to solve, with and without appropriate technology, real world problems involving conic sections.
Strand Bloom's Scope Hours Source Activities
Identify, Analyze, Graph, Equations   Master 1.0 2004 Arkansas Mathematics Frameworks C.3.PCT.3 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 9.1 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 9.2 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 9.3 [Textbook].  
  
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Sequences and Series
Sequence: recursive
The learner will be able to develop, with and without appropriate technology, a representation of sequences recursively.
Strand Bloom's Scope Hours Source Activities
Represent/analyze/solve: real world   Master 1.0 2004 Arkansas Mathematics Frameworks SS.4.PCT.1 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 8.1 [Textbook].  
  
Arithmetic/geometric:sequences & ser
The learner will be able to define and discriminate between arithmetic and geometric sequences and series and use appropriate technology when needed.
Strand Bloom's Scope Hours Source Activities
Represent/analyze/solve: real world   Master 1.0 2004 Arkansas Mathematics Frameworks SS.4.PCT.2 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 8.2 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 8.3 [Textbook].  
  
Sum: finite & infinite sequences/ser
The learner will be able to solve, with and without appropriate technology, problems involving the sum (including Sigma notation) of finite and infinite sequences and series.
Strand Bloom's Scope Hours Source Activities
Represent/analyze/solve: real world   Master 1.0 2004 Arkansas Mathematics Frameworks SS.4.PCT.3 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 8.1 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 8.2 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 8.3 [Textbook].  
  
Find the nth term of sequence
The learner will be able to determine the nth term of a sequence give a rule or specific terms and use appropriate technology when needed.
Strand Bloom's Scope Hours Source Activities
Represent/analyze/solve: real world   Master 1.0 2004 Arkansas Mathematics Frameworks SS.4.PCT.4 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 8.1 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 8.2 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 8.3 [Textbook].  
  
Solve real world problems
The learner will be able to use, with and without appropriate technology, sequences and series to solve real world problems.
Strand Bloom's Scope Hours Source Activities
Represent/analyze/solve: real world   Master 1.0 2004 Arkansas Mathematics Frameworks SS.4.PCT.5 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 8.1 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 8.2 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 8.3 [Textbook].  
  
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Trigometric Functions
Define 6 trig functions
The learner will be able to define the six trigometric functions as: 1. Circular functions 2. Ratios of sides of right triangles 3. Functions of an angle in standard position when given a point on the terminal side of the angle.
Strand Bloom's Scope Hours Source Activities
Apply/graph/inverses/solve real world   Master 1.0 2004 Arkansas Mathematics Frameworks TF.5.PCT.1 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.2 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.3 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.4 [Textbook].  
  
Interchange degrees and radians
The learner will be able to use degrees and radians interchangeably to represent angle measures.
Strand Bloom's Scope Hours Source Activities
Apply/graph/inverses/solve real world   Master 1.0 2004 Arkansas Mathematics Frameworks TF.5.PCT.2 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.1 [Textbook].  
  
Reference angle/Conterminal angle
The learner will be able to sketch and angle in standard position and determine the reference angle and coterminal angles.
Strand Bloom's Scope Hours Source Activities
Apply/graph/inverses/solve real world   Master 1.0 2004 Arkansas Mathematics Frameworks TF.5.PCT.3 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.1 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.4 [Textbook].  
  
Solve for trig functions
The learner will be able to find the values of the trigometric functions given the value of one trigometric function and an additional piece of qualifying information or given the coordinates of a point on the terminal side of an angle.
Strand Bloom's Scope Hours Source Activities
Apply/graph/inverses/solve real world   Master 1.0 2004 Arkansas Mathematics Frameworks TF.5.PCT.4 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.2 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.3 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.4 [Textbook].  
  
Exact values trig functions
The learner will be able to develop and become fluent in the recall of the exact values of the trigometric funtions for special angles.
Strand Bloom's Scope Hours Source Activities
Apply/graph/inverses/solve real world   Master 1.0 2004 Arkansas Mathematics Frameworks TF.5.PCT.5 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.2 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.3 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.4 [Textbook].  
  
Apply trig functions
The learner will be able to solve, with and without appropriate technology, real world problems involving applications of trigometric functions.
Strand Bloom's Scope Hours Source Activities
Apply/graph/inverses/solve real world   Master 1.0 2004 Arkansas Mathematics Frameworks TF.5.PCT.6 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.3 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.4 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.8 [Textbook].  
  
Graph 6 trig functions
The learner will be able to graph the six trigometric functions, identify domain, range, intercepts, period, amplitude, and asymptotes as applicable and use symmetry to determine whether the function is even or odd through appropriate technology when needed.
Strand Bloom's Scope Hours Source Activities
Apply/graph/inverses/solve real world   Master 1.0 2004 Arkansas Mathematics Frameworks TF.5.PCT.7 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.5 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.6 [Textbook].  
  
Transformations of trig functions
The learner will be able to determine, with and without appropriate technology, the amplitude, period, phase shift, and vertical shift, and sketch the graph of transformations of the trigometric functions.
Strand Bloom's Scope Hours Source Activities
Apply/graph/inverses/solve real world   Master 1.0 2004 Arkansas Mathematics Frameworks TF.5.PCT.8 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.5 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.6 [Textbook].  
  
Inverse of trig functions
The learner will be able to identify and garph, wtih and without appropriate technology, the inverse of trigometric functions including the restrictions on the domain.
Strand Bloom's Scope Hours Source Activities
Apply/graph/inverses/solve real world   Master 1.0 2004 Arkansas Mathematics Frameworks TF.5.PCT.9 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 4.7 [Textbook].  
  
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Oblique Triangles
Oblique triangles
The learner will be able to develop and use the Law of Sines and the Law of Cosines to solve oblique triangles and use appropriate technology when needed.
Strand Bloom's Scope Hours Source Activities
Identify, create, solve real world   Master 1.0 2004 Arkansas Mathematics Frameworks OT.6.PCT.1 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 6.1 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 6.2 [Textbook].  
  
Apply Law of Sines/Cosines
The learner will be able to solve real world problems applying the Law of Sines and the Law of Cosines and appropriate technology when needed.
Strand Bloom's Scope Hours Source Activities
Identify, create, solve real world   Master 1.0 2004 Arkansas Mathematics Frameworks OT.6.PCT.2 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 6.1 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 6.2 [Textbook].  
  
Area of oblique triangle
The learner will be able to determine the area of an oblique triangle by using an appropriate formula and appropriate technology when needed.
Strand Bloom's Scope Hours Source Activities
Identify, create, solve real world   Master 1.0 2004 Arkansas Mathematics Frameworks OT.6.PCT.3 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 6.1 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 6.2 [Textbook].  
  
Use vectors
The learner will be able to use vectors to solve problems and describe addition of vectors and multiplication of a vector by a scalar, both symbolically and geometrically.
Strand Bloom's Scope Hours Source Activities
Identify, create, solve real world   Master 1.0 2004 Arkansas Mathematics Frameworks OT.6.PCT.4 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 6.3 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 6.4 [Textbook].  
  
Vectors to model situations
The learner will be able to use vectors to model situations defined by magnitude and direction and analyze and solve real world problems by using appropriate technology when needed.
Strand Bloom's Scope Hours Source Activities
Identify, create, solve real world   Master 1.0 2004 Arkansas Mathematics Frameworks OT.6.PCT.5 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 6.3 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 6.4 [Textbook].  
  
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Trig Equations and Identities
Trig identities
The learner will be able to develop the Pythagorean Identities and use to verify other identities and simplify expressions.
Strand Bloom's Scope Hours Source Activities
Verify and solve   Master 1.0 2004 Arkansas Mathematics Frameworks TEI.7.PCT.1 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 5.1 [Textbook].  
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 5.2 [Textbook].  
  
Trig formulas
The learner will be able to develop and use trigometric formulas including sum and difference formulas and multiple angle formulas.
Strand Bloom's Scope Hours Source Activities
Verify and solve   Master 1.0 2004 Arkansas Mathematics Frameworks TEI.7.PCT.2 Classroom
  Instructional Resources
 
· PreCalculus with Limits, Houghton Mifflin, 4th Edition, lesson 5.4 [Textbook].  
  
Solve trig equations
The learner will be able to solve trigometric equations algebraically and graphically and use appropriate technology when needed.
Strand Bloom's Scope</