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© 2004 by Bloomsburg Area School District and Scantron Corporation.
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Curriculum Designer by
Scantron Corporation

Bloomsburg Area School District
Math 9-12 10/22/04
Mathematics - Pre-Calculus

Algebraic Concepts

Linear System of Equations: Solve
The learner will be able to find the number of solutions of a system of linear equations, and/or tell whether the system is consistent (independent/dependent) or inconsistent.
Strand Scope Source
Linear Systems of Equations Master PA: Academic Standards, January 16, 1999, Grade 11, p.13,2.8.11.F
  
Operations: Apply
The learner will be able to apply operations such as opposite, reciprocal, absolute value, raising to a power, finding roots, and finding logarithms.
Strand Scope Source
Operations Master PA: Academic Standards, January 16, 1999, Grade 11, p.2,2.1.11.A
  
Algebraic Concepts: Problem Scenarios
The learner will be able to create expressions, equations, inequalities, systems of equations and inequalities, and matrices to represent routine and non-routine problem scenarios.
Strand Scope Source
Algebraic Concepts Master PA: Academic Standards, January 16, 1999, Grade 11, p.13,2.8.11.D
  
Algebraic Concepts
The learner will be able to study and describe systems of equations and inequalities and matrices.
Strand Scope Source
Algebraic Concepts Master PA: Academic Standards, January 16, 1999, Grade 11, p.13,2.8.11.G
  
Algebraic Concepts: Relationship
The learner will be able to show the relationship between algebraic equations and inequalities and the geometry of relations in the coordinate plane.
Strand Scope Source
Algebraic Concepts Master PA: Academic Standards, January 16, 1999, Grade 11, p.14,2.8.11.J
  
Patterns: Analyze
The learner will be able to study a given set of data for the existence of a pattern and illustrate the pattern algebraically and graphically.
Strand Scope Source
Equality/Inequality Master PA: Academic Standards, January 16, 1999, Grade 11, p.13,2.8.11.A
  
Equality/Inequality: Choose/Apply
The learner will be able to choose and apply appropriate methods to solve systems of equations and inequalities using graphing calculators, symbol manipulators, spreadsheets, and other software.
Strand Scope Source
Equality/Inequality Master PA: Academic Standards, January 16, 1999, Grade 11, p.14,2.8.11.H
  
Computation: Develop/Apply
The learner will be able to develop and apply computation ideas, operations and procedures with real numbers in problem solving situations.
Strand Scope Source
Computation Master PA: Academic Standards, January 16, 1999, Grade 11, p.4,2.2.11.A
  
Linear System of Equations: Solve
The learner will be able to calculate solutions to systems of linear equations.
Strand Scope Source
Linear Systems of Equations Master PA: System of School Assessment, 1997, Grade 11, p.12,#5 week tested: 32.
  
Equations: Write
The learner will be able to use a given set of data points to write an equation for a line of best fit.
Strand Scope Source
Equations Master PA: Academic Standards, January 16, 1999, Grade 11, p.14,2.8.11.M
  
Linear Equations: Solve
The learner will be able to obtain solutions to linear equations.
Strand Scope Source
Linear Equations Master PA: Academic Standards, January 16, 1999, Grade 11, p.14,2.8.11.N
  
Linear Equations: Graph/Two-Variables
The learner will be able to graph a linear equation in two variables.
Strand Scope Source
Linear Equations Master PA: Academic Standards, January 16, 1999, Grade 11, p.14,2.8.11.N
  
Inequalities: System
The learner will be able to solve a system of inequalities.
Strand Scope Source
Inequalities Master PA: System of School Assessment, 1997, Grade 11, p.12,#5 week tested: 32.
  
Quadratic Equations: Solving
The learner will be able to solve quadratic equations using the appropriate method.
Strand Scope Source
Quadratic Equations/Formula Master PA: Academic Standards, January 16, 1999, Grade 11, p.14,2.8.11.N
  
Exponents: Solve/Equations
The learner will be able to solve equations involving exponents symbolically and graphically.
Strand Scope Source
Exponents Master PA: Academic Standards, January 16, 1999, Grade 11, p.14,2.8.11.N
  
Rates: Graph/Growth/Decay
The learner will be able to graph rates of growth and decay.
Strand Scope Source
Rates Master PA: Academic Standards, January 16, 1999, Grade 11, p.19,2.11.11.C
  
Rates: Interpret/Growth/Decay
The learner will be able to interpret rates of growth and decay.
Strand Scope Source
Rates Master PA: Academic Standards, January 16, 1999, Grade 11, p.19,2.11.11.C
  
Equality/Inequality/Expression
The learner will be able to interpret equations, expressions, and inequalities using graphs and tables.
Strand Scope Source
Equality/Inequality Master PA: System of School Assessment, 1997, Grade 11, p.12,#5 week tested: 32.
  
Computation: Error/Estimations
The learner will be able to explain the amount of error that is possible when using estimation in computation.
Strand Scope Source
Computation Master PA: Academic Standards, January 16, 1999, Grade 11, p.4,2.2.11.D
  
Nonlinear Equations: Represent/Curves
The learner will be able to represent curves using equations.
Strand Scope Source
Nonlinear Equations Master PA: Academic Standards, January 16, 1999, Grade 11, p.13,2.8.11.E
  
Binomial Expansion: Finding Terms
The learner will be able to find an nth term within a binomial expansion.
Strand Scope Source
Binomial Expansion Master Bloomsburg Area School District
  
Logarithms: Simplifying
The learner will be able to use logarithmic properties to simplify expressions.
Strand Scope Source
Logarithms Master Bloomsburg Area School District
  
Logarithmic Equations
The learner will be able to solve equations involving logarithms.
Strand Scope Source
Logarithms Master Bloomsburg Area School District
  
Binomial Theorem
The learner will be able to apply the binomial theorem.
Strand Scope Source
Binomial Expansion Master Bloomsburg Area School District
  
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Calculus and Pre-Calculus

Matrices: Operations with Matrices
The learner will be able to perform addition, subtraction, multiplication, and scalar multiplication with matrices and find inverse matrices.
Strand Scope Source
Matrices Reinforce PA: Academic Standards, January 16, 1999, Grade 11, p.14,2.8.11.I
  
Matrices: Organize Data
The learner will be able to use matrices to organize real world data.
Strand Scope Source
Matrices Master PA: Academic Standards, January 16, 1999, Grade 11, p.14,2.8.11.I
  
Conic Sections: Hyperbola
The learner will be able to use a given equation of a hyperbola in standard form to find the foci, vertices, and asymptotes and then graph the hyperbola.
Strand Scope Source
Conic Sections Master Bloomsburg Area School District
  
Conic Sections: Ellipse
The learner will be able to use a given equation of an ellipse in standard form to find the center, foci, and vertices, and then graph the ellipse.
Strand Scope Source
Conic Sections Master Bloomsburg Area School District
  
Conic Sections: Parabola
The learner will be able to use a given equation of a parabola to find the vector, focus, and direction and then graph the parabola.
Strand Scope Source
Conic Sections Master Bloomsburg Area School District
  
Conic Sections: Understanding Loci
The learner will be able to use manipulatives, graphs, and technology to demonstrate an understanding of conic sections and loci.
Strand Scope Source
Conic Sections Master Bloomsburg Area School District
  
Conic Sections: Circle
The learner will be able to use a given equation of a circle to find the center and radius and graph the circle.
Strand Scope Source
Conic Sections Master Bloomsburg Area School District
  
Applying: Limits
The learner will be able to analyze and apply the concept of limits.
Strand Scope Source
Applying Calculus Concepts Master Bloomsburg Area School District
  
Connecting: Trigonometric/Circular
The learner will be able to make connections between circular and trigonometric expressions, their functions, and how each translates to graphical form.
Strand Scope Source
Circles Master Bloomsburg Area School District
  
Connecting: Exponential/Logarithmic
The learner will be able to analyze the relationship between exponential and logarithmic functions.
Strand Scope Source
Connecting Master Bloomsburg Area School District
  
Conic Section: Determining Equation
The learner will be able to find the equation of a locus given the description.
Strand Scope Source
Conic Sections Master Bloomsburg Area School District
  
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Functions

Graphing: Linear Functions
The learner will be able to choose, account for, and use a suitable method (such as, slope-intercept, x- and y-intercepts, and graphing calculators) to create a graph of a linear function with two variables.
Strand Scope Source
Graphing Functions Master PA: Academic Standards, January 16, 1999, Grade 11, p.14,2.8.11.K
  
Circular Functions: Display
The learner will be able to display periodic and circular functions using graphing calculators.
Strand Scope Source
Circular Functions Master PA: Academic Standards, January 16, 1999, Grade 11, p.18,2.10.11.A
  
Trigonometric Functions: Graph/Analyze
The learner will be able to analyze the graphs of trigonometric functions.
Strand Scope Source
Trigonometric Functions Master PA: Academic Standards, January 16, 1999, Grade 11, p.18,2.10.11.A
  
Graphing: Functions/Relations
The learner will be able to graph both functions and relations within the coordinate plane.
Strand Scope Source
Graphing Functions Master PA: System of School Assessment, 1997, Grade 11, p.12,#5 week tested: 32.
  
Exploring: Study/Categorize
The learner will be able to study and categorize functions according to their attributes.
Strand Scope Source
Exploring Master PA: Academic Standards, January 16, 1999, Grade 11, p.15,2.8.11.T
  
Representations: Problem Situations
The learner will be able to use functions to represent problem situations.
Strand Scope Source
Representations of Functions Master PA: Academic Standards, January 16, 1999, Grade 11, p.15,2.8.11.R
  
Relations: Domain/Range on Graph
The learner will be able to identify the domain and range for a relation shown on a graph.
Strand Scope Source
Relations Master PA: Academic Standards, January 16, 1999, Grade 11, p.15,2.8.11.O
  
Relations: Domain/Range
The learner will be able to find the domain and range for given relation presented as a set of ordered pairs.
Strand Scope Source
Relations Master PA: Academic Standards, January 16, 1999, Grade 11, p.15,2.8.11.O
  
Functions: Maximum/Minimum
The learner will be able to identify the maximum and minimum values of a function over a specified interval.
Strand Scope Source
Functions Master PA: Academic Standards, January 16, 1999, Grade 11, p.19,2.11.11.A
  
Functions: Interpret
The learner will be able to interpret functions.
Strand Scope Source
Functions Master PA: Academic Standards, January 16, 1999, Grade 11, p.15,2.8.11.R
  
Functions: Analyze
The learner will be able to analyze the general properties and behavior of functions.
Strand Scope Source
Functions Master PA: Academic Standards, January 16, 1999, Grade 11, p.15,2.8.11.S
  
Functional Relationships: Represent
The learner will be able to use tables, charts or graphs to represent a functional relationship.
Strand Scope Source
Functional Relationships Master PA: Academic Standards, January 16, 1999, Grade 11, p.15,2.8.11.Q
  
Trigonometric/Circular Functions: Graph
The learner will be able to graph and analyze the 6 circular and trigonometric functions.
Strand Scope Source
Circles Master Bloomsburg Area School District
  
Trigonometric/Circular Functions: Change
The learner will be able to perform changes to amplitude, period, and phase shift of circular and trigonometric functions.
Strand Scope Source
Trigonometric Equations Master Bloomsburg Area School District
  
Problem Solving: Functions/Inverses
The learner will be able to use the inverse of a trigonometric or circular function to solve a problem.
Strand Scope Source
Problem Solving Master Bloomsburg Area School District
  
Polynomial Functions: Roots
The learner will be able to find both real and complex roots of polynomial functions.
Strand Scope Source
Polynomial Functions Master Bloomsburg Area School District
  
Inverses
The learner will be able to find the inverse of a given function and determine whether that is a function.
Strand Scope Source
Inverses Master Bloomsburg Area School District
  
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Geometry

Circles: Properties/Problem Solving
The learner will be able to identify and apply circle properties in order to solve problems.
Strand Scope Source
Circles Master PA: System of School Assessment, 1997, Grade 11, p.11,#3 week tested: 32.
  
Geometric Concepts
The learner will be able to understand and/or apply the concepts of solid, coordinate, and/or transformational geometry.
Strand Scope Source
Geometric Concepts Master PA: System of School Assessment, 1997, Grade 11, p.11,#3 week tested: 32.
  
Problem Solving: Analytic Geometry
The learner will be able to solve both real world and mathematical problems using concepts of analytic geometry.
Strand Scope Source
Problem Solving Master PA: Academic Standards, January 16, 1999, Grade 11, p.16,2.9.11.G
  
Lines/Angles: Properties
The learner will be able to understand and/or apply properties of lines and/or angles.
Strand Scope Source
Lines/Angles/Polygons Master PA: System of School Assessment, 1997, Grade 11, p.11,#3 week tested: 32.
  
Circles: Problem Solving
The learner will be able to obtain solutions to problems involving circles using the properties of angles, arcs, chords, tangents, and secants.
Strand Scope Source
Circles Master PA: Academic Standards, January 16, 1999, Grade 11, p.16,2.9.11.F
  
Symmetry: Analyze Figures
The learner will be able to study figures in terms of the kinds of symmetries they have.
Strand Scope Source
Symmetry Master PA: Academic Standards, January 16, 1999, Grade 11, p.17,2.9.11.J
  
Problem Solving: Geometric Models
The learner will be able to obtain solutions to problem situations with geometric models.
Strand Scope Source
Problem Solving Master PA: Academic Standards, January 16, 1999, Grade 11, p.17,2.9.11.I
  
Problem Solving: Geometric Models
The learner will be able to geometrically model situations to formulate problems.
Strand Scope Source
Problem Solving Master PA: Academic Standards, January 16, 1999, Grade 11, p.17,2.9.11.I
  
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Mathematics Processes

Mathematical Concepts: Communication
The learner will be able to apply symbols, mathematical terminology, standard notation, rules, graphing and other mathematical illustrations to communicate observations, predictions, ideas procedures, generalizations, and results.
Strand Scope Source
Communication Master PA: Academic Standards, January 16, 1999, Grade 11, p.8,2.5.11.B
  
Communication: Clearly
The learner will be able to communicate mathematical procedures and results clearly, systematically, succinctly and accurately.
Strand Scope Source
Communication Master PA: Academic Standards, January 16, 1999, Grade 11, p.8,2.5.11.C
  
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Area/Perimeter: Problem Solving
The learner will be able to develop an understanding of area and perimeter by applying various problem solving techniques.
Strand Scope Source
Perimeter/Area/Volume Master PA: System of School Assessment, 1997, Grade 11, p.11,#2 week tested: 32.
  
Accuracy
The learner will be able to realize the degree of accuracy necessary in calculations is dependent upon how the results are going to be used and the tools used to find the measurements.
Strand Scope Source
Accuracy Master PA: Academic Standards, January 16, 1999, Grade 11, p.4,2.2.11.E
  
Accuracy: Choose/Apply Tools
The learner will be able to choose and use suitable tools and units to measure to the degree of accuracy required in a particular scenario.
Strand Scope Source
Accuracy Master PA: Academic Standards, January 16, 1999, Grade 11, p.6,2.3.11.A
  
Circumference: Application
The learner will be able to solve real world application problems involving circumference measurements.
Strand Scope Source
Circumference Master PA: System of School Assessment, 1997, Grade 11, p.11,#2 week tested: 32.
  
Measurement: Accuracy
The learner will be able to measure an object to a given degree of accuracy.
Strand Scope Source
Measurement: Application Master PA: Academic Standards, January 16, 1999, Grade 11, p.6,2.3.11.D
  
Angle Measure: Degrees
The learner will be able to measure angles in degrees.
Strand Scope Source
Angle Measurement Master PA: Academic Standards, January 16, 1999, Grade 11, p.6,2.3.11.B
  
Angle Measure: Radians
The learner will be able to measure angles in radians.
Strand Scope Source
Angle Measurement Master PA: Academic Standards, January 16, 1999, Grade 11, p.6,2.3.11.B
  
Angle Measure: Compare
The learner will be able to compare angles in degrees and radians.
Strand Scope Source
Angle Measurement Master PA: Academic Standards, January 16, 1999, Grade 11, p.6,2.3.11.B
  
Area of a Triangle: Oblique
The learner will be able to compute the area of an oblique triangle.
Strand Scope Source
Area of a Triangle Master Bloomsburg Area School District
  
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Number Systems: Operations
The learner will be able to explore, apply, and/or understand operations as they are applied to various number systems.
Strand Scope Source
Number Systems Master PA: System of School Assessment, 1997, Grade 11, p.11,#1 week tested: 32.
  
Number Systems: Applying Properties
The learner will be able to understand and apply number systems and properties to model and solve problems including dealing with special number properties (i.e., 1, and 0).
Strand Scope Source
Number Systems Master PA: System of School Assessment, 1997, Grade 11, p.11,#1 week tested: 32.
  
Number Sense: Display/Knowledge
The learner will be able to display a knowledge of number sense.
Strand Scope Source
Number Sense Master PA: System of School Assessment, 1997, Grade 11, p.11,#1 week tested: 32.
  
Ratio/Proportion: Apply/Real World
The learner will be able to apply ratio and proportion concepts to solve real world scenario problems.
Strand Scope Source
Ratio/Proportion Master PA: System of School Assessment, 1997, Grade 11, p.11,#1 week tested: 32.
  
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Numeration

Estimate/Problems: No Exact Results
The learner will be able to make estimations and/or round-off to obtain problem solutions where exact results are not necessary.
Strand Scope Source
Estimate/Problems Master PA: Academic Standards, January 16, 1999, Grade 11, p.4,2.2.11.B
  
Sequences: Reproduce/Extend/Create
The learner will be able to reproduce, extend, and create sequences.
Strand Scope Source
Sequences Master PA: System of School Assessment, 1997, Grade 11, p.12,#5 week tested: 32.
  
Patterns: Problem Solving/Recognize
The learner will be able to use pattern recognition to solve problems.
Strand Scope Source
Patterns: Problem Solving Master PA: Academic Standards, January 16, 1999, Grade 11, p.13,2.8.11.C
  
Sequences: Sum of Finite
The learner will be able to determine sums of finite sequences of numbers.
Strand Scope Source
Sequences Master PA: Academic Standards, January 16, 1999, Grade 11, p.19,2.11.11.D
  
Series: Sum/Infinite Geometric
The learner will be able to determine the sum of an infinite geometric series.
Strand Scope Source
Series Master PA: Academic Standards, January 16, 1999, Grade 11, p.19,2.11.11.D
  
Patterns: Give Examples/Other Areas
The learner will be able to give examples of patterns that exist in data from other content areas.
Strand Scope Source
Patterns Master PA: Academic Standards, January 16, 1999, Grade 11, p.13,2.8.11.B
  
Sequence/Series: Problem Solving
The learner will be able to apply sequences and series to obtain solutions to word problems.
Strand Scope Source
Sequences/Series Master PA: Academic Standards, January 16, 1999, Grade 11, p.13,2.8.11.C
  
Sequences: Expression/Rule
The learner will be able to find any term in a sequence given an expression or rule for the nth term.
Strand Scope Source
Sequences Master Bloomsburg Area School District
  
Sequences: Determine/Formula
The learner will be able to determine a formula for the nth term given any sequence.
Strand Scope Source
Sequences Master Bloomsburg Area School District
  
Series: Sigma Notation
The learner will be able to show a series in correct sigma notation.
Strand Scope Source
Series Master Bloomsburg Area School District
  
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Number Sense: Applying
The learner will be able to show an intuitive sense of what a percent is, and how percents are used in real world scenarios by completing sentences involving percentages with appropriate and reasonable choices.
Strand Scope Source
Number Sense Master PA: System of School Assessment, 1997, Grade 11, p.11,#1 week tested: 32.
  
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Probability/Statistics

Data: Statistical Measures
The learner will be able to explain data as an example of distribution applying statistical measures of center and spread.
Strand Scope Source
Data Master PA: Academic Standards, January 16, 1999, Grade 11, p.9,2.6.11.A
  
Probability Distribution: Normal Curve
The learner will be able to explain (in non-specific terms) the normal curve and use its attributes in answering questions about data that is assumed to be normally distributed.
Strand Scope Source
Probability Distribution Master PA: Academic Standards, January 16, 1999, Grade 11, p.10,2.6.11.I
  
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Problem Solving

Solutions: Summarize/Evaluate
The learner will be able to finish a solution procedure with a summary of results and evaluate the degree to which the results are acceptable and validate reasoning.
Strand Scope Source
Solution Master PA: Academic Standards, January 16, 1999, Grade 11, p.8,2.5.11.D
  
Strategies: Choose/Apply
The learner will be able to choose and apply appropriate mathematical concepts and strategies from various areas of mathematics and use them to solve non-routine and multi-step problems.
Strand Scope Source
Strategies Master PA: Academic Standards, January 16, 1999, Grade 11, p.8,2.5.11.A
  
Solution: Illustrate
The learner will be able to illustrate mathematical solutions to problems.
Strand Scope Source
Solution Master PA: Academic Standards, January 16, 1999, Grade 11, p.7,2.4.11.E
  
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Real Numbers and the Coordinate Plane

Linear Equations: Graph/Two Points
The learner will be able to determine the equation of a line given the graph of the line or two points on the line.
Strand Scope Source
Linear Equations Master PA: Academic Standards, January 16, 1999, Grade 11, p.14,2.8.11.L
  
Linear Equations: Slope/Point
The learner will be able to determine the equation of a line given the slope and a point on the line.
Strand Scope Source
Linear Equations Master PA: Academic Standards, January 16, 1999, Grade 11, p.14,2.8.11.L
  
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Computers: Show Ability
The learner will be able to show the ability to use scientific and graphing calculators.
Strand Scope Source
Computers Master PA: Academic Standards, January 16, 1999, Grade 11, p.4,2.2.11.F
  
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Problem Solving: Right Triangles
The learner will be able to recognize, create, and solve practical right triangle problems by applying trigonometric functions and the Pythagorean Theorem.
Strand Scope Source
Problem Solving Master PA: Academic Standards, January 16, 1999, Grade 11, p.18,2.10.11.B
  
Trig. Identities
The learner will be able to identify and use the trigonometric identities.
Strand Scope Source
Trigonometric Identities Master Bloomsburg Area School District
  
Trig. Ratios: Law of Sines/Cosines
The learner will be able to use the Law of Sines and Cosines to solve problems.
Strand Scope Source
Trigonometric Ratios Master Bloomsburg Area School District
  
Triangles: SSA Case
The learner will be able to discern whether 0,1, or 2 triangles exist, and what they are in an SSA (side, side, angle) case.
Strand Scope Source
Triangles Master Bloomsburg Area School District
  
Trig. Equations: Solutions
The learner will be able to determine possible solutions for trigonometric equations.
Strand Scope Source
Trigonometric Equations Master Bloomsburg Area School District
  
Trig. Identities: Verifying
The learner will be able to verify identities.
Strand Scope Source
Trigonometric Identities Master Bloomsburg Area School District
  
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