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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. Algebra II Honors The Foundations of Learning curriculum provides objectives for tenth 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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Polynomials: Factoring/Complex Numbers
The learner will be able to factor polynomials over complex numbers, and apply these concepts to geometry and real-world scenarios.
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Radicals: Multiplication/Division
The learner will be able to translate sentences into radical terms, find the product or quotient, rationalize denominators, and either reduce the answer to simplest radical form or find the approximate square root.
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Radicals: Equations
The learner will be able to translate sentences into numerical radical equations and solve for an unknown number, explain solving radical equations, find the value of an unknown variable, solve radical equations for solution sets, describe the characteristics of radical equations, and step into "teacher" roles to evaluate a sample student's work.
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Systems of Equations: Addition
The learner will be able to identify, apply, and analyze steps toward solving a system of equations by addition.
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Problem Solving: Application
The learner will be able to solve real-world application problems involving polynomials, rational algebraic expressions, radical expressions, real number exponential expressions, and logarithmic expressions, while appropriately utilizing matrices, the binomial theorem, Pascal's triangle, probability, synthetic division, polynomial factoring, and rational root theorems, as means to solving such problems.
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Problem Solving Strategies: Graphing
The learner will be able to approach application problems by using graphical representations of the data to deduce possible solutions (including graphing a function and its inverse on a Cartesian plane, analyzing effects of parameter changes on functions, recognizing the equations and corresponding graphs of the conic sections, graphing exponential and logarithmic functions, and determining the maxima and minima of graphs).
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Translate Problems: Complex Coefficients
The learner will be able to translate a given real-world scenario (delivered orally, through manipulatives, pictures, or in a written prompt) into an equation or inequality involving complex coefficients.
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Missing Elements Order of Operations
The learner will be able to solve for the missing element in a given equation, using the correct order of operations when necessary.
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Order of Operations: Integers
The learner will be able to determine the correct order of operations for an equation containing integers.
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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: Simplifying
The learner will be able to solve equations, with one unknown variable, involving fractions, decimals, and integers, by simplifying terms.
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Equations: Solving
The learner will be able to solve given equations.
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Diagrams with Equations
The learner will be able to use a diagram to demonstrate the meaning of a given equation.
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Equations: Writing
The learner will be able to write equations for real-world scenario problems.
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Equations: Exponential/Log/First Degree
The learner will be able to solve problems with exponents, first degree equations, and logarithmic equations in one variable.
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Inequalities
The learner will be able to solve for the value of a variable given in an inequality and as shown on a graph by manipulating the inequality correctly.
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Inequalities: Writing
The learner will be able to write inequalities for real-world scenario problems.
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Inequality
The learner will be able to identify smallest exponent of two different bases required to validate an inequality.
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Absolute Value Problems
The learner will be able to solve absolute value problems.
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Expressions: Addition/Subtraction
The learner will be able to use addition or subtraction in one variable expressions and equations and determine the number sentence for a written expression.
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Expressions: Multiplication/Division
The learner will be able to use multiplication or division in one variable expressions and equations and determine the number sentence for a written expression.
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Expressions: Real World
The learner will be able to evaluate expressions (and formulas) when the expressions are presented within the context of a real-world problem.
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Polynomials: Addition/Subtraction
The learner will be able to identify and justify each step and rule of adding and subtracting polynomials.
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Polynomials: Multiplication
The learner will be able to translate sentences into numerical equations including monomials and binomials.
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Polynomials: Division
The learner will be able to divide both monomials and polynomials.
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Polynomials: Synthetic Substitution
The learner will be able to solve problems with polynomial equations using synthetic substitution.
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Polynomial Equations: Relationships
The learner will be able to solve problems with polynomial equations by applying relationships between synthetic division, polynomial factoring, and rational root theorems.
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Polynomials: Factoring/Uses
The learner will be able to factor polynomials with complex numbers and state their use within a real life situation.
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Radicals: Addition/Subtraction
The learner will be able to combine radical terms, find the simplest radical form, and approximate square roots.
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Radicals: Variables
The learner will be able to solve a radical equation by substituting for a variable.
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Radical Expressions: Represent/Solve
The learner will be able to use manipulatives, pictures, and technology (i.e., calculators) to solve operations with radical expressions.
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Quadratic Equation: Standard Form
The learner will be able to state a quadratic equation in standard form.
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Quadratic Formula
The learner will be able to describe the discriminant, identify the quadratic formula and solve an equation using the quadratic formula.
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Quadratic Equations: Graphing
The learner will be able to solve quadratic equations with 2 variables by graphing the system on a coordinate plane.
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Quadratic/Linear Equations: Justifying
The learner will be able to solve linear and quadratic equations with 2 variables by graphing and justifying the solution.
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Quadratic Formula: Relating Graphs
The learner will be able to relate graphs of second degree equations to the quadratic formula.
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Quadratic Formula: Number Line/Cartesian
The learner will be able to relate both number line and Cartesian graphs of second degree equations to the quadratic formula.
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Exponential Numbers: Multiply
The learner will be able to multiply exponential numbers that have the same base and integer exponents.
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Exponential Numbers: Divide
The learner will be able to divide exponential numbers that have the same base and whole number exponents.
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Exponential Equations
The learner will be able to solve equations involving exponents.
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Exponents: Multiple Step Problem
The learner will be able to determine the solution to a problem requiring multiple operations involving exponential numbers with the same base.
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Multiple Step Problem: Exponents
The learner will be able to solve a multiple step problem involving both exponents and multiple operations.
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Logarithms/Exponents: Simplifying
The learner will be able to use relationships between logarithms and exponents to simplify expressions.
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Inverse Operations: Variable
The learner will be able to apply inverse operations by identifying equivalent expressions with one unknown variable.
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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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Proving Theorems
The learner will be able to use mathematical structures such as field properties to prove elementary theorems.
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Equalities/Inequalities: Represent
The learner will be able to use manipulatives to represent equalities and inequalities.
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Equality/Inequality: Solution Methods
The learner will be able to use technology (i.e., calculators), matrices, and graphing to solve systems of 2 first degree equations or inequalities with 2 variables in real world situations.
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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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Systems of Equations: Determinants
The learner will be able to solve systems of equations by applying determinants.
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Binomial Expansion: Finding Terms
The learner will be able to find an nth term within a binomial expansion.
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| Calculus and Pre-Calculus |
| 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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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.
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Complex Coefficients: Representing
The learner will be able to create manipulatives to represent a given equation or inequality with complex coefficients by identifying relationships between coefficients, variables, and the real-world counterparts.
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Complex Numbers: Forms/Relationships
The learner will be able to demonstrate the ability to focus on the relationship between number forms by relating the absolute value of complex numbers in algebraic, geometric, and vector representations, and by explaining the relationships between exponential expressions and logarithmic expressions, and real number exponents and radical symbolism.
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Complex Numbers: Representing
The learner will be able to represent situations that involve complex numbers with expressions, equations, and inequalities by setting up number sentences and performing basic operations using diagrams, algebraic procedures, and vector representations.
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Complex Numbers: Exploring
The learner will be able to explore the properties and structural characteristics of the complex number system and its sub-systems, including identifying the sub-systems which are isomorphic.
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Limiting Processes
The learner will be able to explore the following limiting processes by analyzing them graphically: series, sequences, targets, and areas under curves.
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Conic Sections
The learner will be able to identify the graph of a conic section (circle, parabola, ellipse, hyperbola) and use it to solve a problem.
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Complex Numbers: Compare with Real
The learner will be able to determine properties of real and complex numbers and examine their similarities and differences.
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Complex Numbers: Basic Operations
The learner will be able to use pictures, technology (i.e., calculators), and principles of algebra to perform basic operations on complex numbers.
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Complex Numbers: Operations/Vectors
The learner will be able to use vectors to perform basic operations on complex numbers.
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Complex Numbers: Applying Absolute Value
The learner will be able to use vector, geometric, and algebraic representations to apply absolute value to complex numbers.
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Complex Numbers: Equations/Inequalities
The learner will be able to solve equations and inequalities that have complex numbers for coefficients.
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Complex Numbers: Compare Subsets
The learner will be able to recognize and compare subsets of complex numbers.
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Matrices: Basic Operations
The learner will be able to solve problems where performing basic operations on matrices is required.
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Matrices: Operations/Real Numbers
The learner will be able to complete operations on matrices, exponents, and logarithmic expressions with real numbers.
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Matrices: Systems of Equations
The learner will be able to solve problems involving systems of equations using the properties of matrices.
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Problem Solving: Graphs of Maxima/Minima
The learner will be able to find a maxima and minima of a graph and use it to solve a problem.
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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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Circle Graphs: Convert
The learner will be able to determine fractional proportions of a circle graph when given percents on a circle graph.
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Table: Predict
The learner will be able to make predictions and decisions based on real-world data presented in the form of a table.
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Charts: Draw Conclusion
The learner will be able to draw conclusions and make inferences from information presented in charts.
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Graphs: Scales
The learner will be able to determine how to appropriately display data by choosing a relevant scale for the graph.
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Diagrams: Create
The learner will be able to create diagrams to display information.
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Graphs: Poll Results
The learner will be able to infer response of public from graphed results of a poll.
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Graphs: Displayed Data/Analyze
The learner will be able to analyze data given in a variety of graphical formats.
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Graphs: Analyze
The learner will be able to analyze information presented in a variety of graphical forms.
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| 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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Functions/Relations: Discuss
The learner will be able to verbally discuss and analyze relations and functions.
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Functions/Relations: Types
The learner will be able to identify correct methods for discerning functions and relations, find the value of a variable which will make a relation not a function, describe how functions and relations appear on graphs, identify linear functions and their traits, translate sentences into coordinate points for relations and functions, and recognize functions described in sentences.
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Graphing: Functions/Application
The learner will be able to graph the following functions in a Cartesian plane and apply them in real life situations: absolute value, greatest integer, and split domain.
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Representations: Sum/Product/Composition
The learner will be able to represent sums, products, and compositions of functions graphically and algebraically.
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Functions: Properties
The learner will be able to describe both the behavior and properties of functions.
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Inverses: Graphing
The learner will be able to use a Cartesian plane to graph both a function and its inverse.
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Operations: Sums/Products/Compositions
The learner will be able to represent graphically and symbolically the sums, products, and compositions of functions.
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Non-Linear Functions: Represent
The learner will be able to model real life processes with logarithmic, exponential, and other non-linear functions.
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