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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. Geometry 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: Number Sense
The learner will be able to identify, classify, and compare whole numbers, integers, rational numbers, irrational numbers, and field properties of the real number system with regard to structural characteristics, and build logical arguments using these properties.
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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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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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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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Number Sentences: Relating to Real-World
The learner will be able to explore expressions, equations, and inequalities involving whole numbers, fractions, decimals, and integers within the context of real-world scenarios, identify relationships between the variables and coefficients, and articulate how each relates to a corresponding real-world problem (in coordinate geometry, measurement, career fields, etc.).
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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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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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| Calculus and Pre-Calculus |
| 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. |
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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: 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 |
| 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. |
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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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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 |
| The Functions Unit includes exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular 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: 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: 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: 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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Congruency/Similarity/Proportionality
The learner will be able to demonstrate an understanding of congruency, similarity, and proportionality through deductive reasoning.
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Congruent/Similar: Figures
The learner will be able to demonstrate an understanding of congruent and similar figures by utilizing the properties of these figures to solve problems and to prove solutions.
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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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Angles
The learner will be able to identify, describe, estimate, and apply knowledge of various angles (including adjacent, vertical, straight, acute, right, obtuse, supplementary, and complementary).
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Circle: Determine Properties
The learner will be able to determine properties of circles and their related parts such as arcs, chords, secants, tangents, and other angles, by inductively and deductively formulating and applying logical arguments.
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Circle: Problem Solving
The learner will be able to develop strategies for approaching and solving real-world circle problems (determining relevant factors, discounting irrelevant factors, isolating the problem, using lists, webbing, graphical forms, pictures, and reasoning skills to solve problems and justify solutions).
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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: Understand
The learner will be able to understand transformations including rotations, reflections, translations, and dilations.
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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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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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Reasoning: Inductive/Deductive
The learner will be able to apply appropriate mathematical abilities to use inductive and deductive reasoning to solve real-world problems and confirm solutions.
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Inductive Reasoning: Understand
The learner will be able to apply inductive reasoning to understand and illustrate mathematical and other real-world phenomena.
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Points/Lines/Planes: Compare/Contrast
The learner will be able to explore similarities and differences within the relationships between points, lines, and planes.
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Logic: Applying
The learner will be able to utilize inductive and deductive reasoning to solve real-world scenario problems involving parallelism, perpendicularity, angles, lines, circles, arcs, chords, secants, and tangents.
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Logic: Understanding Concepts
The learner will be able to understand and apply the concepts of facts, indirect and direct proof, hypotheses, conditional statements, and validity.
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Logic: Deductive Arguments
The learner will be able to incorporate definitions, postulates, theorems, and logical reasoning techniques to develop deductive arguments in paragraph or flow chart form, to solve real-world scenario problems.
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Logic: Conditional Statements
The learner will be able to recognize the hypothesis and conclusion of a conditional statement, and be able to state the converse, inverse, and contrapositive of a conditional statement.
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Logic: Applying Arguments
The learner will be able to demonstrate an understanding of logic by applying deductive and inductive arguments to proofs appropriately.
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Logic: Proving Validity
The learner will be able to test the validity of possible solutions by utilizing inverse operations, truth tables, and other methods.
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Symmetry: Pyramids
The learner will be able to explore right hexagonal pyramids, and determine the symmetry planes and the angles of rotational symmetry.
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Connecting: Transformations
The learner will be able to use appropriate mathematical abilities to connect the ideas of symmetry, similarity, and congruence to transformations in problem scenarios.
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Connecting: Geometry/Algebra
The learner will be able to apply geometric concepts to solve problems in algebra by solving systems of equations through graphing and by exploring number sentence relationships (numerical coefficients, slopes, and the y and x intercepts).
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Constructions: Manipulatives
The learner will be able to use manipulatives to identify, describe, and compare polygons and circles, and each of their parts, and to construct two- and three-dimensional figures.
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Constructions: Relating
The learner will be able to use constructions to analyze and draw conclusions about geometric patterns, reflections, rotations, translations, similarity, congruency, and transformations, and concentrate on how these geometric themes relate to each other.
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Properties: Understand/Dimensions/Shapes
The learner will be able to understand dimensions, shapes, and attributes of figures and objects.
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Properties: Identify/Explain
The learner will be able to identify and explain geometric properties and relationships as they are present in nature, art, and other real-world scenarios.
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Problem Solving: Models
The learner will be able to use appropriate mathematical abilities to solve real-life and mathematical problems applying geometric models.
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Problem Solving: Trigonometric Ratios
The learner will be able to use appropriate mathematical abilities to solve problems involving indirect measurement.
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Problem Solving: Transformations
The learner will be able to use appropriate mathematical abilities to solve geometry problems using transformations, coordinates, and vectors.
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Problem Solving: Area/Perimeter
The learner will be able to solve real-world problems (involving the area and perimeter of quadrilaterals) which require logical deductions and reasoning based on geometric properties, and utilize geometric concepts as proof or evidence of a self-generated solution theory.
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Proving: Geometric Properties
The learner will be able to use a coordinate plane, distance, mid-point, and slope formulas to prove the validity of geometric properties.
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Proving: Geometric Principles
The learner will be able to prove that the altitude from the vertex angle of an isosceles triangle contains the midpoint of the opposite side, that translations and rotations are isometries (given that an isometry preserves collinearity, betweenness, and angle measures, and a triangle and its image under an isometry are congruent), and that two triangles (with two sides each and congruent angles) are congruent.
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Spatial Thinking: Geometric Figures
The learner will be able to demonstrate spatial sense by comparing and classifying geometric figures, using representations to describe how two to three dimensional figures compare, solving problems, and justifying solutions by using geometric figures and their properties as proof.
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Exploring: 2-3 D Figures
The learner will be able to explore, compare, and classify two- and three-dimensional figures, and make predictions about the unseen faces of three-dimensional figures based on a working knowledge of geometric properties and spatial sense.
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Triangles: Exploring Properties
The learner will be able to investigate the following triangle issues: the relationship between the bisectors of an interior angle of a triangle and its corresponding exterior angle, the equations of the altitudes and the intersection of two altitudes (for the coordinates of a given triangle), the possible bilateral and rotational symmetry of specific triangles, triangle properties deduced from symmetry information, and Pythagorean implications for triangles.
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Angles/Lines: Properties/Logic
The learner will be able to apply inductive and deductive logical arguments to determine properties of angles and lines.
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