Chester Township Public Schools
Mathematics Curriculum

Mathematics - Algebra I Extended Learner

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.


The Foundations of Learning (1999) curriculum offers Kindergarten through Grade 12 objectives for the Knowledge and Comprehension levels of Bloom's Taxonomy. EdVISION.com developed this curriculum based on extensive research of standardized and state tests. Additional objectives were added to enhance the content areas.

The Mathematics component of the Foundations of Learning curriculum focuses on basic skills. Objectives primarily involve the identification, recognition, comprehension, or understanding of various math topics.


The Applications of Learning (1999) curriculum offers Kindergarten through Grade 12 objectives for the Application and Analysis levels of Bloom's Taxonomy. EdVISION.com developed this curriculum based on extensive research of standardized and state tests. Additional objectives were added to enhance the content areas.

The Mathematics component of the Applications of Learning curriculum focuses on intermediate skills. The objectives primarily involve the application, examination, or analysis of various math topics.


The Higher Order Learning (1999) curriculum offers Grade 4 through Grade 12 objectives for the Synthesis and Evaluation levels of Bloom's Taxonomy. EdVISION.com developed this curriculum based on extensive research of standardized and state tests. Additional objectives were added to enhance the content areas.

The Mathematics component of the Higher Order Learning curriculum focuses on advanced skills. The objectives primarily involve the synthesis and evaluation of various math topics.


The purpose of New Jersey's statewide assessment program is to measure what students at benchmark grade levels know and are able to do. The Mathematics Content Clusters that are covered in the tests unavoidably contain some overlapping content, since mathematical topics are not disconnected but are part of an interconnected whole.


The New Jersey Curriculum Content Standards for Mathematics is focused on achieving one crucial goal:

"To enable ALL of New Jersey's children to move into the twenty-first century with the mathematical skills, understandings, and attitudes that they will need to be successful in their careers and daily lives."

The environment in the mathematics classroom should reflect the following two standards:

"1. All students' mathematical learning will embody the concepts that engagement in mathematics is essential, and that the decision-making, risk-taking, cooperative work, perseverance, self-assessment, and self-confidence are frequently keys to success."

"2. All students will be evaluated using a diversity of assessment tools and strategies, to provide multiple indicators of the quality of every student's mathematical learning and of overall program effectiveness."

The New Jersey Standards for Mathematics are as follows:

*"All students will develop the ability to pose and solve mathematical problems in mathematics, other disciplines, and everyday experiences."

*"All students will communicate mathematically through written, oral, symbolic, and visual forms of expression."

*"All students will connect mathematics to other learning by understanding the interrelationships of mathematical ideas and the roles that mathematics and mathematical modeling play in other disciplines and in life."

*"All students will develop reasoning ability and will become self-reliant, independent mathematical thinkers."

*"All students will regularly and routinely use calculators, computers, manipulatives, and other mathematical tools to enhance mathematical thinking, understanding, and power."

*"All students will develop number sense and an ability to represent numbers in a variety of forms and use numbers in diverse situations."

*"All students will develop spatial sense and an ability to use geometric properties and relationships to solve problems in mathematics and everyday life."

*"All students will understand, select, and apply various methods of performing numerical operations."

*"All students will develop an understanding of and will use measurement to describe and analyze phenomena."

*"All students will use a variety of estimation strategies and recognize situations in which estimation is appropriate."

*"All students will develop an understanding of patterns, relationships, and functions and will use them to represent and explain real-world phenomena."

*"All students will develop an understanding of statistics and probability and will use them to describe sets of data, model situations, and support appropriate inferences and arguments."

*"All students will develop an understanding of algebraic concepts and processes and will use them to represent and analyze relationships among variable quantities and to solve problems."

*"All students will apply the concepts and methods of discrete mathematics to model and explore a variety of practical situations."

*"All students will develop an understanding of conceptual building blocks of calculus and will use them to model and analyze natural phenomena."

*"All students will demonstrate high levels of mathematical thought through experiences which extend beyond traditional computation, algebra, and geometry."


In this area students concentrate on making mathematical connections and using principles of mathematics to communicate, reason, and solve problems. Students engage in projects which require them to apply number systems, operations, and forms in real-world contexts.

Algebra I Extended Learner

The Foundations of Learning curriculum provides objectives for ninth grade students.

The Applications of Learning curriculum provides objectives for ninth grade students.

The Higher Order Learning curriculum provides objectives for ninth grade students.

In this course students learn advanced applications of algebraic concepts such as number systems, operations, and forms. Students engage in challenging activities which require them to solve number sentences in the forms of ax + b = c, ax + b = cx + d, and ax + b < cx + d, apply formulas, properties, and order of operations rules appropriately, graph and study lines, slopes, and parabolas, utilize exponents and powers, evaluate polynomials, manipulate absolute value and probability functions, and use functional notation and function language. The course emphasizes the need for students to apply, analyze, and synthesize algebraic concepts. The Terra Nova Complete Battery assesses students in eighth grade (Level 18).


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.

    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
Properties Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Polynomials Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Polynomials Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Variable Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
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
  
    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
Connecting Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Connecting Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Problem Solving Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Number Sentence Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
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
  
    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
Solution Methods Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
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
  
    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
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
  
    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
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
  
    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
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
  
    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
Properties Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Properties Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Properties Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Equations Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Equations Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
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
  
    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
Equations Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Equations Synthesis Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
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
  
    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
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
  
    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
Inequalities Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Inequalities Synthesis Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
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
  
    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
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
  
    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
Expressions Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Expressions Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
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
  
    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
Expressions Analysis Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Polynomials Comprehension Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Polynomials Analysis Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Polynomials Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Polynomials Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Radicals Application Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
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
  
    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
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
  
    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
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
  
    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
Exponents Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Exponents Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Exponents Application Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
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
  
    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
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
  
    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
Variable Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
Theorems Application Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    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
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
  
    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
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
  
    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
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
  
    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
Factoring Analysis Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  

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.

This unit includes presenting data in graphical forms and interpreting data given in graphical forms.

    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
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
  

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.

    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. (NJCCCS 4.2, 4.3, 4.4, 4.5).
Strand Bloom's Scope Source
Functions/Relations Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    Function Notation: Reasoning
The learner will be able to use functional notation to justify arguments, and to judge the reasonableness of a given solution. (NJCCCS 4.2, 4.3, 4.4, 4.5).
Strand Bloom's Scope Source
Functions/Relations Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    Function Notation
The learner will be able to review and evaluate a sample student's work, give directions regarding the use of functional notation, understand the formula f(x) = y, find the range of a function, and calculate the values of unknown variables by substitution. (NJCCCS 4.2, 4.3, 4.4, 4.5).
Strand Bloom's Scope Source
Functions/Relations Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    Connecting: Functions
The learner will be able to explore the interrelationships of mathematical functions using tables, graphs, and equations, focusing on the interrelationships, and not on exploring functions as isolated phenomena. (NJCCCS 4.2, 4.3, 4.4, 4.5).
Strand Bloom's Scope Source
Connecting Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    Represent/Translate: Functions
The learner will be able to demonstrate an understanding of functional relationships by applying functional notation to mapping, tables, graphs, and inverse functions, by translating representations of functions from these forms, by analyzing functional relationships, and by articulating how changing one element of functions alters all other elements of functions. (NJCCCS 4.2, 4.3, 4.4, 4.5).
Strand Bloom's Scope Source
Representations of Functions Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    Absolute Value/Quadratic Functions
The learner will be able to examine absolute value and quadratic functions to compare and relate their representations within graph, table, and algebraic form. (NJCCCS 4.2, 4.3, 4.4, 4.5).
Strand Bloom's Scope Source
Absolute Value/Quadratic Functions Comprehension Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  

Geometry
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.

    Connecting: Geometry/Algebra
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 through 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 number sentence relationships (numerical coefficients, slopes, and the y and x intercepts) (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Connecting Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    Connecting: Geometry/Algebra
The learner will be able to demonstrate the ability to make connections between algebra and geometry by determining the relationships between number sentences and lines on the Cartesian plane (numerical coefficients, slopes, y-intercepts). (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Connecting Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    Line Segments: Properties
The learner will be able to apply the basic properties of line segments. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Lines 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
  

Integers
This unit includes comparing integers, performing operations with integers, converting integers to other number forms, using manipulatives to demonstrate integers, and solving problems with integers in real-world contexts.

    Adding: Integer Fractions
The learner will be able to add integer fractions with the same denominator. (NJCCCS 4.1, 4.6).
Strand Bloom's Scope Source
Add Integers Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    Subtraction: Integer Fractions
The learner will be able to subtract integer fractions with the same denominator. (NJCCCS 4.1, 4.6).
Strand Bloom's Scope Source
Subtract Integers Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    Integers: Understanding
The learner will be able to compare integers with ordering symbols (<, >, =) and with phrases. (NJCCCS 4.1, 4.6).
Strand Bloom's Scope Source
Integers Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    Integers: Number Lines
The learner will be able to interpret real-world scenarios involving integers presented on number lines. (NJCCCS 4.1, 4.6).
Strand Bloom's Scope Source
Integers Analysis Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    Integer: Missing Element
The learner will be able to identify the missing element in an integer equation.
Strand Bloom's Scope Source
Integers Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    Multiplying: Integer Fractions
The learner will be able to multiply integer fractions. (NJCCCS 4.1, 4.6).
Strand Bloom's Scope Source
Multiply Integers Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    Division: Integer Fractions
The learner will be able to divide integer fractions. (NJCCCS 4.1, 4.6).
Strand Bloom's Scope Source
Divide Integers Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    Problem Solving: Integers
The learner will be able to solve story problems requiring the addition, subtraction, multiplication, and division of integers, and determine the operations necessary to solve the problems without being cued. (NJCCCS 4.1, 4.6).
Strand Bloom's Scope Source
Problem Solving Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    Number Sense: Uses of Integers
The learner will be able to talk and write about the uses of integers. (NJCCCS 4.1, 4.6).
Strand Bloom's Scope Source
Number Sense Comprehension Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  

Number Theory
The Number Theory Unit focuses on manipulating number forms and classifications. Students make connections between number forms and their real-world applications.

This unit includes manipulating number forms and classifications. Students make connections between number forms and their real-world applications. The Number Theory Unit focuses on manipulating number forms and classifications. Students make connections between number forms and their real-world applications.

    Number Forms
The learner will be able to discuss why a certain number form is used to solve a certain problem. (NJCCCS 4.1, 4,2, 4.6).
Strand Bloom's Scope Source
Number Forms Evaluation Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    Proportion Story Problems
The learner will be able to use proportional reasoning to solve story problems. (NJCCCS 4.1, 4,2, 4.6).
Strand Bloom's Scope Source
Ratio/Proportion Application Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    Primes/Composites: Application
The learner will be able to apply primes and composites in problem solving situations. (NJCCCS 4.1, 4,2, 4.6).
Strand Bloom's Scope Source
Prime/Composite Numbers Application Master 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
  
    Factoring: Represent
The learner will be able to use manipulatives, pictures, and technology to factor polynomials. (NJCCCS 4.1, 4,2, 4.6).
Strand Bloom's Scope Source
Factors Application Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools - Extended Learner - Algebra I
  
    Prime/Factor/Multiple/Divisibility: Uses
The learner will be able to discover the properties of primes, factors, multiples, and divisibility to use in solving real world problems. (NJCCCS 4.1, 4,2, 4.6).
Strand Bloom's Scope Source
Divisibility 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