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Chester Township Public Schools Mathematics The National Council of Teachers of Mathematics Curriculum and Evaluation Standards provide educators with goals for school mathematics and guidelines for achieving these goals. The fifty-four standards are presented as a vision for school mathematics based on societal goals, student goals, research on teaching and learning, and professional guidelines. Math Analysis The Foundations of Learning curriculum provides objectives for eleventh grade students. |
| Algebraic Concepts |
| The Algebraic Concepts Unit includes Competencies/Objectives which focus on algebraic equations and operations. This unit includes studying number systems, operations, and forms. Students explore the symbolic nature of algebraic concepts by identifying and extending patterns in algebra, by following algebraic procedures, and by proving theorems with properties. |
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Properties: Rational/Real Numbers
The learner will be able to show their comprehension of, and/or apply properties as they apply to rational and/or real numbers.
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Properties: Operations
The learner will be able to conceptually understand the properties of operations, including zero (additive, multiplicative), one (multiplicative), grouping (associative), and order (commutative).
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Expressions: Powers/Roots/Factorials
The learner will be able to simplify expressions that contain powers, roots, and factorials.
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Radicals: Simplifying
The learner will be able to simplify negative and positive radicals, translate sentences into radicals, identify radical equations that do not represent real numbers, and find the nth root of radical equations.
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Algebraic Concepts: Apply
The learner will be able to use appropriate mathematical abilities to apply absolute values, exponents, and estimations for roots of numbers in real-life problem situations.
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Algebraic Concepts: Real-World
The learner will be able to accurately describe, study and model real-world situations using algebraic concepts and processes.
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Order of Operations: Exponents
The learner will be able to determine the correct order of operations for an exponential equation.
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Equations: Story Problems
The learner will be able to determine equations for and solve problems in the context of real world scenarios.
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Absolute Value: Understand
The learner will be able to understand absolute value.
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Exponents: Roots
The learner will be able to understand exponents and roots.
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Exponential Equations
The learner will be able to solve equations involving exponents.
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Exponents: Integral and Square Roots
The learner will be able to apply laws of integral exponents and/or square roots to simplify and/or evaluate algebraic expressions.
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Fundamental Theorem of Algebra
The learner will be able to identify and use the Fundamental Theorem of Algebra.
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Remainder/Factor Theorems
The learner will be able to apply the remainder and factor theorems.
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Logarithms: Simplifying
The learner will be able to use logarithmic properties to simplify expressions.
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Logarithmic Equations
The learner will be able to solve equations involving logarithms.
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Binomial Theorem
The learner will be able to identify and apply the binomial theorem.
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| Calculus and Pre-Calculus |
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The Calculus and Pre-Calculus Unit includes studying the following concepts: limits, matrix algebra, functions, vectors, conic sections, mathematical induction, and sequence and series using graphical calculators, computers, and models. This unit includes studying the following concepts: limits, matrix algebra, functions, vectors, conic sections, mathematical induction, and sequence and series using graphical calculators, computers, and models. |
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Problem Solving: Central Limit Theorem
The learner will be able to apply the Central Limit Theorem to solve real-world scenario problems.
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Derivatives: Deriving Formulas
The learner will be able to use the definition of the derivative as the limit of a sum to derive formulas for the derivatives.
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Derivatives: Derived Function
The learner will be able to find a derived function given the definition.
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Complex Numbers: Polar Form
The learner will be able to write complex numbers in polar form.
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Complex Numbers: Trig Form
The learner will be able to apply the trigonometric form of complex numbers.
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Complex Numbers: Absolute Value
The learner will be able to determine absolute value of complex numbers and relate that to real numbers.
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Complex Numbers: DeMoivre's Theorem
The learner will be able to determine powers and roots of complex numbers by using DeMoivre's theorem.
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Complex Numbers: DeMoivre's/Prove
The learner will be able to prove DeMoivre's theorem.
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Matrices: Understand
The learner will be able to understand the concept of matrices.
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Matrices: Scalar Multiplication
The learner will be able to perform scalar multiplication with matrices.
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Matrices: Evaluate Results
The learner will be able to make evaluations of the results of matrix operations.
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Matrices: Analyzing
The learner will be able to evaluate the use of matrices with systems of equations to determine advantages and disadvantages of this solution method.
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Matrices: Interpret Linear Systems
The learner will be able to interpret linear systems of equations as matrices consisting of their coefficients.
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Vectors: Position of Objects
The learner will be able to apply vectors to show the position of an object.
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Vectors: Understand
The learner will be able to understand the concept of vectors.
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Parametric Equations: Define/Derive
The learner will be able to determine a definition for and derive parametric equations.
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Parametric Equations: Graph
The learner will be able to sketch the graph of a set of parametric equations.
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Parametric Equations: Problem Solving
The learner will be able to solve problems using parametric equations, using technology when necessary.
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| Data Interpretation |
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The Data Interpretation Unit includes Competencies/Objectives which focus on the study and use of graphical forms. The Data Interpretation Unit includes data collection and classification, organization and display of data, logical reasoning and problem solving. This unit includes presenting data in graphical forms and interpreting data given in graphical forms. |
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Scatterplots: Construct
The learner will be able to create a scatterplot of data.
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Scatterplot: Draw/Line of Best Fit
The learner will be able to sketch a line of best fit.
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Scatterplot: Understand
The learner will be able to understand the concept of a scatterplot.
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Line of Best Fit: Understand
The learner will be able to understand the concept of line of best fit.
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Bar Graphs: Proportional Relationships
The learner will be able to use proportional relationships to extrapolate values on a bar graph.
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Line Graphs: Compare/Analyze
The learner will be able to identify values from a line graph, determine that addition or subtraction is needed to find an answer, compare values, and use critical thinking skills to analyze the graph.
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Graphs: Evaluate Appropriateness
The learner will be able to evaluate the appropriateness of a given graphical form for a given set of data.
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Data Collection
The learner will be able to collect data.
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Data Collection: Organization
The learner will be able to organize data in many different ways.
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Graphs: Identify Question
The learner will be able to analyze a given graph and determine what question can be answered using this information.
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Graphs: Evaluate Data Analysis
The learner will be able to determine the validity of an argument based on a given set of data.
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| Discrete Mathematics |
| The Discrete Mathematics Unit includes the concepts of discrete math, matrices and recursion. |
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Discrete Mathematics: Apply Concepts
The learner will be able to apply the concepts and methods of discrete mathematics to illustrate and investigate many different practical scenarios.
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Discrete Math: Interative/Recursive
The learner will be able to apply iterative and recursive patterns and processes to illustrate many different practical scenarios and solve problems.
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| Fractions |
| The Fractions Unit includes Competencies/Objectives which focus on number sense and operations with fractions. The Fractions Unit includes comparison, ordering, fractions parts, estimation, reasoning and problem solving. |
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Fractions: Understand
The learner will be able to understand fractions.
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| Functions |
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The Functions Unit includes exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions. This unit includes exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions. The Functions Unit includes exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions. |
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Trigonometric/Circular Functions
The learner will be able to analyze trigonometric and circular functions by graphing these functions, differentiating between their domains, solving real-world problems involving Laws of Sines and Laws of Cosines, and writing complex numbers in polar form.
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Connecting: Exponential/Logarithmic
The learner will be able to explore the relationship between exponential and logarithmic functions by evaluating graphs of exponential and logarithmic functions, comparing the domain and ranges of exponential and logarithmic functions, solving equations involving exponential and logarithmic functions, using properties of logarithmic functions to simplify expressions, and describing real-world scenarios using exponential and logarithmic functions.
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Problem Solving: Rationals
The learner will be able to analyze and apply rational functions using graphical forms, group study projects, and technology (computers, calculators).
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Problem Solving: Polynomial Functions
The learner will be able to analyze and apply polynomial functions using graphical forms, group study projects, and technology.
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Trigonometric/Circular Functions: Domain
The learner will be able to identify differences between the domains of circular and trigonometric functions.
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Trigonometric/Circular Functions: Graph
The learner will be able to graph and analyze the 6 circular and trigonometric functions.
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Trigonometric/Circular Functions: Relate
The learner will be able to relate between the circular and trigonometric functions.
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Trigonometric/Circular Functions:Inverse
The learner will be able to analyze and graph inverse of both circular and trigonometric functions.
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Trigonometric/Circular Functions: Change
The learner will be able to perform changes to amplitude, period, phase shift, and vertical shift of circular and trigonometric functions.
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Circular Functions: Rotation
The learner will be able to list the values of the 6 circular functions for a specific rotation.
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Circular Functions: Model Real World
The learner will be able to see circular functions as models for periodic, real world functions.
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Exponential Functions: Graph
The learner will be able to graph exponential functions.
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Exponential Functions: Real World
The learner will be able to solve real world problems involving exponential functions.
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Logarithmic Functions: Real World
The learner will be able to solve real world problems involving logarithmic functions.
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Logarithmic Functions: Base 10 and e
The learner will be able to evaluate a logarithmic function with base 10 and e and represent it on a graph.
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Exponential/Logarithmic: Domain/Range
The learner will be able to analyze exponential and logarithmic functions and compare their domains and ranges.
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Exponential/Logarithmic: Relationships
The learner will be able to identify a logarithmic as the inverse of an exponential function.
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Trigonometric Functions/Polar/Complex
The learner will be able to see the relationship between trigonometric functions, polar coordinates, and complex numbers.
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Graphing: Asymptotes/Discontinuity Point
The learner will be able to find both asymptotes and points of discontinuity.
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Rational Functions: Graph/Analyze
The learner will be able to graph and analyze a rational function.
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Rational Functions: Application
The learner will be able to apply rational functions in real world situations.
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Polynomial Functions: Evaluate/Graph
The learner will be able to graph and analyze the polynomial functions such as linear and quadratic.
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Polynomial Functions: Roots
The learner will be able to find both real and complex roots of polynomial functions.
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Polynomial Functions: Application
The learner will be able to solve real world problems using polynomial functions.
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Functions: Illustrate
The learner will be able to apply different types of functions to illustrate mathematical or real-world situations.
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| Geometry |
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The Geometry Unit includes Competencies/Objectives which focus on exploring geometric concepts from multiple perspectives. The Geometry Unit includes properties and construction of figures, proofs and theorems, history of geometry, transformations, logic, and problem solving. This unit includes exploring geometric concepts from multiple perspectives. |
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Figures: Analyze
The learner will be able to use appropriate mathematical abilities to study properties of three-dimensional figures by using models and by drawing and interpreting two-dimensional representations of them in problem scenarios.
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Figures: Recognize/Classify/Explain
The learner will be able to recognize, classify, and explain two- and three-dimensional figures using properties, terms, and relationships.
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Figures: 2-D Illustrations of 3-D Object
The learner will be able to draw two-dimensional illustrations of three-dimensional objects through sketching shadows, projections, perspectives, and map views.
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Congruence/Similarity/Symmetry: Problem
The learner will be able to apply the ideas of symmetry, similarity, and congruence to problem solving.
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Congruence/Similarity/Symmetry
The learner will be able to understand the idea of symmetry, congruence, and similarity.
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Pythagorean Theorem: Problem Solving
The learner will be able to use appropriate mathematical abilities to solve problems applying the Pythagorean Theorem.
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Transformations: Predict/Model
The learner will be able to use appropriate mathematical abilities to predict and model resulting figures when combining, subdividing, and changing figures in problem scenarios.
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Transformations: Sequence
The learner will be able to use appropriate mathematical abilities to identify the sequence of transformations necessary to map one figure onto another figure in problem scenarios.
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Transformations: Understand
The learner will be able to understand transformations including rotations, reflections, translations, and dilations.
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Geometric Concepts: Properties/Pattern
The learner will be able to identify, visualize, study and use geometric properties, relationships, and patterns in real-world and/or problem solving scenarios using models, manipulatives, or technology.
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