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Mathematics

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Chester Township Public Schools
Mathematics Curriculum
Mathematics - Algebra I Extended Learner

Algebraic Concepts

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. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Properties   Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Polynomials/Factoring: Relationships
The learner will be able to demonstrate an understanding of the inverse relationship between multiplying binomials and factoring polynomials. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Polynomials   Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Polynomials: Applying Exponential Laws
The learner will be able to apply the laws of exponents to prove the validity of the simplification of a given polynomial expression. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Polynomials   Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Variables: Problem Solving
The learner will be able to represent situations that involve variable quantities with expressions, equations, and inequalities by setting up number sentences and performing basic operations with rational algebraic expressions and absolute value. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Variable   Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Systems of Equations: Addition
The learner will be able to identify, apply, and analyze steps toward solving a system of equations by addition. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Systems of Equations   Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Connecting: Algebra/Geometry
The learner will be able to determine the relationships between number sentences and lines on the Cartesian plane (numerical coefficients, slopes, y-intercepts). (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Connecting   Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Connecting: Algebra/Geometry
The learner will be able to apply geometric concepts to solve problems in algebra by determining equations of a line (given the graph of the line), by solving quadratic equations by graphing, by solving systems of equations through graphing, by analyzing range, domain, odd/even, relation-functions, zeros of a function, and x and y intercepts, and by exploring relationships. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Connecting   Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Problem Solving: Manipulatives
The learner will be able to demonstrate an understanding of equations by reading or listening to a given scenario, and creating manipulatives to represent the scenario, (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Problem Solving   Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Number Sentences: Represent/Real-World
The learner will be able to explain why a specific number sentence corresponds to a given scenario using manipulatives, graphs, and diagrams. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Number Sentence   Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Translate Problems: Two Variables
The learner will be able to translate a given real-world scenario (delivered orally or in a written prompt) into an equation or inequality with two variables, use order of operations to solve the equation, and apply inverse operations to check the answer. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Relating Number Sentences/Problems   Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Solution Methods: Equation/Inequality
The learner will be able to solve real world situations by using linear equations, inequalities, and multiple representations. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Solution Methods   Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Missing Elements
The learner will be able to determine how to solve for an unknown variable when given the problem in written form. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Missing Information Analysis Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Applications of Learning, January 1999, Chester Township Schools, Grade 8 - Extended Learner - Algebra I Classroom
  
Order of Operations: Decimals
The learner will be able to determine the correct order of operations for an equation containing decimal numbers. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Order of Operations Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Grade 8 - Extended Learner - Algebra I Classroom
  
Order of Operations: Integers
The learner will be able to determine the correct order of operations for an equation containing integers. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Order of Operations Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Order of Operations: Exponents
The learner will be able to determine the correct order of operations for an exponential equation. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Order of Operations Comprehension Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Properties: Distributive
The learner will be able to solve a problem requiring the application of the distributive property. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Properties Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Properties
The learner will be able to identify and apply the following properties of addition and multiplication: multiplication by 0, distributive, associative, reciprocal, adding like terms, property of opposites, commutative, and order of operations. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Properties Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Properties: Identify Uses
The learner will be able to identify the use of properties in solving a problem. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Properties Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Equations: Addition/Subtraction
The learner will be able to use addition or subtraction in one variable equations to determine the value of the variable. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Equations Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Equations: Multiplication/Division
The learner will be able to use multiplication or division in one variable equations to determine the value of the variable. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Equations Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Equations: Errors
The learner will be able to identify errors or incorrect steps in solving an equation. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Solve Equations Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Diagrams with Equations
The learner will be able to use a diagram to demonstrate the meaning of a given equation. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Equations Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Equations: Writing
The learner will be able to develop and write equations based on word problems. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Equations Synthesis Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Number Relation Problems
The learner will be able to translate sentences into algebraic equations and solve the equations. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Solve Equations Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Equations: Two Variables
The learner will be able to solve for the value of a variable in two variable equations. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Solve Equations Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
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. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Inequalities Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Inequalities: Writing
The learner will be able to write inequalities for real-world scenario problems. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Inequalities Synthesis Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Absolute Value
The learner will be able to evaluate expressions, apply the definition of absolute value, recognize absolute value expressions on number lines, and solve equations by finding the solution sets. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Absolute Value Analysis Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Absolute Value Problems
The learner will be able to solve absolute value problems. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Absolute Value Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
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. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Expressions Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
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. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Expressions Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Expressions: Evaluating/Simplifying
The learner will be able to simplify expressions, apply the rules regarding order of operations, and evaluate expressions with one or two unknown variables. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Simplify Expressions Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Expressions with Exponents: Analyzing
The learner will be able to analyze expressions with exponents. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Expressions Analysis Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Polynomials/Equations: Represent
The learner will be able to use manipulatives and geometric area models to represent equations and polynomials. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Polynomials Comprehension Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Polynomials: Addition/Subtraction
The learner will be able to identify and justify each step and rule of adding and subtracting polynomials. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Polynomials Analysis Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Polynomials: Multiplication
The learner will be able to translate sentences into numerical equations including monomials and binomials. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Polynomials Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Polynomials: Division
The learner will be able to divide both monomials and polynomials. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Polynomials Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Radicals: Addition/Subtraction
The learner will be able to combine radical terms, find the simplest radical form, and approximate square roots.
Strand Bloom's Scope Source Activities
Radicals Application Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Quadratic Equations: Real World
The learner will be able to solve quadratic equations in real world situations. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Quadratic Equations/Formula Application Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Exponents: Multiplying
The learner will be able to multiply two whole numbers with different exponents. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Exponents Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Foundations of Learning, January 1999, Chester Township Schools, Grade 8 - Extended Learner - Algebra I Classroom
  
Exponents: Dividing
The learner will be able to divide 2 whole numbers with different exponents. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Exponents Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Foundations of Learning, January 1999, Chester Township Schools, Grade 8 - Extended Learner - Algebra I Classroom
  
Exponential Numbers: Multiply
The learner will be able to multiply exponential numbers that have the same base and integer exponents. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Exponents Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Exponential Numbers: Divide
The learner will be able to divide exponential numbers that have the same base and whole number exponents. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Exponents Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Exponential Equations
The learner will be able to solve equations involving exponents. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Exponents Application Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Inverse Operations: Variable
The learner will be able to apply inverse operations by identifying equivalent expressions with one unknown variable. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Inverse Operations Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Identify Question
The learner will be able to identify the question that is represented in a number sentence. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Identify Question Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Variable/Expression/Equation
The learner will be able to comprehend the concepts of variable, expression, and equation. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Variable Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Proving Theorems
The learner will be able to use mathematical structures such as field properties to prove elementary theorems (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Theorems Application Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Equality/Inequality/Expression: Problems
The learner will be able to solve story problems involving equations, inequalities, and expressions. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Equality/Inequality Application Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Solving Equations/Inequalities
The learner will be able to solve a system of 2 first degree equations or an inequality with 2 variables in a real world situation. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Equality/Inequality Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
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. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Equality/Inequality Application Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
Factoring
The learner will be able to factor trinomials, find the difference of two squares, find missing terms which complete perfect square trinomials, find the length and width of a rectangle when given the area (a trinomial), identify deductive arguments based on principles of factoring, describe the inverse relationship between multiplying polynomials and factoring, and use combined types of factoring. (NJCCCS 4.1, 4.2, 4.3, 4.4, 4.6 4.11).
Strand Bloom's Scope Source Activities
Factoring Analysis Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I Classroom
  
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Data Interpretation

Diagram: Problem Solving
The learner will be able to solve real-world problems using diagrams, (NJCCCS 4.1, 4.2, 4.6).
Strand Bloom's Scope Source Activities
Diagrams Application Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grade 8 - Extended Learner - Algebra I