Mathematics Grade 7

Chester Township Public Schools
Mathematics Curriculum

Mathematics - Grade 7

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.

Grade 7

The National Council of Teachers of Mathematics Curriculum and Evaluation Standards for grades 5-8 include the following thirteen standards: Mathematics as Problem Solving, Mathematics as Communication, Mathematics as Reasoning, Mathematical Connections, Number and Number Relationships, Number Systems and Number Theory, Computation and Estimation, Patterns and Functions, Algebra, Statistics, Probability, Geometry, and Measurement.

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

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

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

The mathematics section of the Grade 8 GEPA assesses students' knowledge and skills in four content clusters of mathematics:

1. Number Sense, Concepts, and Applications
2. Spatial Sense and Geometry
3. Data Analysis, Probability, Statistics, and Discrete Mathematics
4. Patterns, Functions, and Algebra

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 course students learn foundational mathematics concepts involving number systems, operations, and forms. Students engage in activities which require them to perform operations (with whole numbers, decimals, fractions, percents, and number sentences) and apply algebraic properties (such as order of operations, commutative, associative, distributive, integer, and -a = -1(a) properties). The course emphasizes the need for students to identify, approach, understand, and solve problems in real-world contexts. The Terra Nova Complete Battery assesses students in seventh grade (Level 17).

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: Identify
The learner will be able to analyze tables and graphs to identify properties and relationships. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Properties		Introduce	NJ: Core Curriculum Content Standards, May 1996, Grade 7, Standard 4.13.8. National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Equations/Expressions: Analyzing
The learner will be able to demonstrate an understanding of equations and expressions by determining patterns in equations and expressions, by finding missing elements, by matching equations and expressions to models, manipulatives, and pictures, and by distinguishing between expressions and equations by explaining their purposes, (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Equations		Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Equations: Analyzing with Technology
The learner will be able to analyze the nature of equations, their representative value, possible solutions to equations, and how equations can be applied in real-world scenarios using computers, calculators, and other technology.

Strand	Bloom's	Scope	Source
Equations		Master	NJ: Core Curriculum Content Standards, May 1996, Grade 7, Standard 4.13.11, National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Solution Methods
The learner will be able to solve linear equations using trial and error, inspection, and concrete materials. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Linear Equations		Master	NJ: Core Curriculum Content Standards, May 1996, Grade 7, Standard 4.13.10, National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Inequalities: Exploring
The learner will be able to think about and discuss the nature of inequalities, their representative value, and how inequalities apply to real-world scenarios in an informal way. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Inequalities		Reinforce	NJ: Core Curriculum Content Standards, May 1996, Grade 7, Standard 4.13.12, National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Inequalities: Apply
The learner will be able to use appropriate mathematical abilities to apply inequalities to model and explain mathematical situations and real-world phenomena. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Inequalities		Introduce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 8, p.37,IV.B.12 week tested: 34.,National Council of Teachers of Mathematics Curriculum and Evaluation Standard., Applications of Learning, January 1999, Chester Township Schools, Grades 7

Absolute Value: Identify
The learner will be able to identify and understand absolute value of a given number. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Absolute Value		Introduce	NJ: Core Curriculum Content Standards, May 1996, Grade 7, Standard 4.13.7, National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Operations: Inverse Relationships
The learner will be able to demonstrate the inverse relationship of addition/subtraction and multiplication/division to solve problems, and to explain and justify a solution, and read a real-world scenario requiring multiplication, identify the nature of the problem, key elements, and the operation needed, set up the equation, solve the equation, and understand how to divide to prove the solution. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Operations		Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Operational Symbols: Reasoning
The learner will be able to evaluate number sentences such as 348 x 1.5 ? 353, 45 x 1/2 ? 90, and 1/4 x 1/2 ? 8/1, replace the question marks with appropriate comparison symbols (<, =, >), and justify the symbol with a written or oral explanation. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Operations		Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Operations: Analyzing Powers/Roots
The learner will be able to extend an understanding of operations (addition, subtraction, multiplication, division) as they are applied to whole numbers to powers and roots. (NJCCCS 4,8).

Strand	Bloom's	Scope	Source
Basic Operations		Reinforce	NJ: Core Curriculum Content Standards, May 1996, Grade 7, Standard 4.8.9. National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Operations: Analyzing/Rational
The learner will be able to extend an understanding of operations (addition, subtraction, multiplication, division) to fractions, decimals, integers, and other rational numbers. (NJCCCS 4,8).

Strand	Bloom's	Scope	Source
Basic Operations		Reinforce	NJ: Core Curriculum Content Standards, May 1996, Grade 7, Standard 4.8.8. National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Algebraic Concepts: Real-World
The learner will be able to accurately describe, study and model real-world situations using algebraic concepts and processes. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Algebraic Concepts		Reinforce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.9,IV.B, p.37,IV.B week tested: 34., National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Algebraic Concepts: Relationships
The learner will be able to create graphs, charts, tables, rules, and equations to represent algebraic relationships and patterns. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Algebraic Concepts		Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Variable/Expression/Equal./Inequal.
The learner will be able to comprehend and apply the concepts of variables, expressions, equalities and inequalities. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Variable		Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Algorithms: Explore/Solve Problems
The learner will be able to explore problems and formulate, explain and test algorithms for solving optimization problems. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Algorithms		Reinforce	NJ: Core Curriculum Content Standards, May 1996, Grade 7, Standard 4.14.10, National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Algorithms: Create
The learner will be able to use appropriate mathematical abilities to create an algorithm to perform a given task in problem scenarios. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Algorithms		Introduce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.33,III.D.12 week tested: 34., National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Computation: Across Forms
The learner will be able to perform computations with whole numbers, fractions, decimals, integers, and rational numbers. (NJCCCS 4.8.8).

Strand	Bloom's	Scope	Source
Computation		Master	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Computation/Estimation
The learner will be able to create, analyze, apply and explain procedures for computation and estimation with whole numbers, fractions, decimals, integers, and rational numbers. (NJCCCS 4.8.10).

Strand	Bloom's	Scope	Source
Computation		Master	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Number Sense: Representing
The learner will be able to represent numerical situations and number patterns with tables, graphs, verbal rules, concrete materials, and number sentences and translate from one to another. (NJCCCS 4.13.6).

Strand	Bloom's	Scope	Source
Number Sense		Master	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

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).

Strand	Bloom's	Scope	Source
Problem Solving		Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Problem Solving: Evaluating Forms
The learner will be able to recognize a real-world situation which calls for operations (addition, subtraction, multiplication, or division) with fractions, decimals, percents, or integers, evaluate the situation, articulate the nature and elements of the problem, and solve the problem, without being cued about the operations required or number form (fractions, decimals, etc.) (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Problem Solving		Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Problem Solving: Proportions/Percents
The learner will be able to analyze, apply, and discuss methods for solving problems involving proportions and percents. (NJCCCS 4.8.1).

Strand	Bloom's	Scope	Source
Problem Solving		Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Number Sentence: Understand/Open
The learner will be able to understand the concept of a number sentence and open sentence. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Number Sentence	Comprehension	Introduce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.37,IV.B.1 week tested: 34.National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Order of Operations
The learner will be able to demonstrate an understanding of the standard algebraic order of operations. (NJCCCS 4.8.12).

Strand	Bloom's	Scope	Source
Order of Operations	Comprehension	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Order of Operations: Understand
The learner will be able to understand order of operations. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Order of Operations	Comprehension	Reinforce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.37,IV.B.3 week tested: 34.National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Properties: Understand/Operations
The learner will be able to conceptually understand the properties of arithmetic operations. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Properties	Comprehension	Reinforce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.11,I.B.12 week tested: 34.National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Equations: Represent
The learner will be able to use physical models to solve equations. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Solve Equations	Application	Reinforce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.37,IV.B.11 week tested: 34.,National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Equations: Substituting
The learner will be able to solve equations with one unknown variable (where there is no formula to apply) involving fractions, decimals, and integers by substituting. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Solve Equations	Application	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Equations: Understand/Linear/Inequality
The learner will be able to understand linear equations and inequalities. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Linear Equations/Inequalities	Comprehension	Introduce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.37,IV.B.2 week tested: 34., National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Solution Methods
The learner will be able to obtain solutions to elementary linear equations through the use of appropriate paper-and-pencil methods.

Strand	Bloom's	Scope	Source
Linear Equations	Application	Master	NJ: Core Curriculum Content Standards, May 1996, Grade 7, Standard 4.13.10, National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Absolute Value: Identifying
The learner will be able to identify the absolute value of a given number. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Absolute Value	Knowledge	Introduce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.11,I.B.20 week tested: 34.,National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Absolute Value: Understand
The learner will be able to understand absolute value. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Absolute Value	Comprehension	Introduce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.11,I.B.9, p.37,IV.B.4 week tested: 34., National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Expressions: Understand
The learner will be able to understand the concept of an expression. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Expressions	Comprehension	Introduce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.35,IV.A.3, p.37,IV.B.1 week tested: 34., National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Expressions: Variable/Inverse Operations
The learner will be able to apply inverse operations to determine the value of a variable given as a written expression. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Expressions	Comprehension	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Expressions: Translate
The learner will be able to translate sentences into algebraic expressions and/or vice-versa. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Expressions	Comprehension	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Exponents: Roots
The learner will be able to understand exponents and roots. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Exponents	Comprehension	Reinforce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.11,I.B.7, p.11,I.B.8 week tested: 34., National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Exponents: Evaluate Expressions
The learner will be able to evaluate expressions involving powers and/or roots. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Exponents	Synthesis	Introduce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.11,I.B.22 week tested: 34.National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Inverse Operations
The learner will be able to ""work backwards" to solve story problems. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Solution Methods	Analysis	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Formulas: Rules
The learner will be able to understand rules or formulas. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Formulas	Comprehension	Reinforce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.35,IV.A.4 week tested: 34.

Variable
The learner will be able to understand the basic concept of a variable as representing an unknown quantity. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Variable	Comprehension	Reinforce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.35,IV.A.2, p.37,IV.B.1 week tested: 34.National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Algorithms: Understand Concept
The learner will be able to understand the concept of algorithms. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Algorithms	Comprehension	Reinforce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.33,III.D.5 week tested: 34., National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Algorithm: Perform
The learner will be able to perform an algorithm. (NJCCCS 4,1).

Strand	Bloom's	Scope	Source
Algorithms	Comprehension	Reinforce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.33,III.D.9 week tested: 34., National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

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.

Networks: Study/Apply
The learner will be able to use appropriate mathematical abilities to study and apply networks to real-world situations, and determine such things as the shortest path, and traversability. (NJCCCS 4.15).

Strand	Bloom's	Scope	Source
Graph Theory/Networks		Master	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.31,III.C.14 week tested: 34.

Problem Solving: Significant Digits
The learner will be able to comprehend and apply the concept of significant digits to solve problems. (NJCCCS 4.15.9).

Strand	Bloom's	Scope	Source
Problem Solving		Master	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.10,I.A.9 week tested: 34.; NJ: Core Curriculum Content Standards, May 1996, Grade 7, Standard 4.15.9

Networks: Select
The learner will be able to select a suitable network to fit a problem scenario. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Graph Theory/Networks	Analysis	Master	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.31,III.C.9 week tested: 34.

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.

Table: Application
The learner will be able to construct, read and interpret displays of data such as tables and lists. (NJCCCS 4.1, 4.2, 4.6).

Strand	Bloom's	Scope	Source
Tables/Charts		Reinforce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.29,III.B.5, p.29,III.B.6 week tested: 34, National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7.

Graphing: Apply/Appropriate
The learner will be able to choose and apply appropriate graphical forms. (NJCCCS 4.1, 4.2, 4.6).

Strand	Bloom's	Scope	Source
Graphing		Master	NJ: Core Curriculum Content Standards, May 1996, Grade 7, Standard 4.12.10, National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Graphs: Draw/Interpret
The learner will be able to draw and/or interpret graphs which model real-world phenomena. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Graphing		Master	NJ: Core Curriculum Content Standards, May 1996, Grade 7, Standard 4.13.13, National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Communicating: Graphical Forms/Solution
The learner will be able to use graphical forms to show a solution to a probability problem, to provide visual or condensed representation of an idea, to explain mathematical concepts, and to express real-world situations such as population variance, grades, marketing materials, sports statistics, and cultural trends. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Communicating		Master	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Communicating: Graphical Forms/Creating
The learner will be able to communicate complex ideas effectively by creating graphical forms of data, including collecting data from a variety of sources, consolidating raw data, and selecting appropriate elements of the data to organize and include in a logical graphical form.

Strand	Bloom's	Scope	Source
Communicating		Master	National Council of Teachers of Mathematics (NCTM), March, 1989, Seventh Grade

Analyzing: Graphical Forms
The learner will be able to demonstrate the ability to interpret graphical forms of data by evaluating graphical forms in the following areas: accuracy, organization, and appropriateness of the forms given a specific audience and purpose. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Analyzing/Evaluating Graphical Forms		Master	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Analyzing: Graphical Forms
The learner will be able to demonstrate the ability to interpret graphical forms of data by articulating the details, facts, and concepts presented in the forms, and by evaluating the reasonableness of specific graphical forms given the types of information presented in the forms and the specific target . audiences. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Analyzing/Evaluating Graphical Forms		Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Circle Graphs: Convert
The learner will be able to determine number represented by a percent on a given circle graph. (NJCCCS 4.1, 4.7).

Strand	Bloom's	Scope	Source
Circle Graphs	Application	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Scatterplot: Draw/Line of Best Fit
The learner will be able to sketch a line of best fit. (NJCCCS 4.1, 4.6).

Strand	Bloom's	Scope	Source
Scatterplots	Knowledge	Introduce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.29,III.B.7 week tested: 34.National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Line of Best Fit: Understand
The learner will be able to understand the concept of line of best fit. (NJCCCS 4.1, 4.6).

Strand	Bloom's	Scope	Source
Scatterplots	Comprehension	Introduce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.29,III.B.4 week tested: 34, National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grades 7.

Bar Graphs: Interpretation
The learner will be able to interpret information given in the form of a bar graph and interpret the results in a variety of forms (percents, fractions, etc.). (NJCCCS 4.1, 4.6).

Strand	Bloom's	Scope	Source
Bar Graphs	Analysis	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Line Graphs: Compare/Analyze
The learner will be able to identify values from a line graph, determine that addition or subtraction is needed to find an answer, compare values, and use critical thinking skills to analyze the graph. (NJCCCS 4.1, 4.6).

Strand	Bloom's	Scope	Source
Line Graphs	Analysis	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Table: Understand
The learner will be able to understand tables. (NJCCCS 4.1, 4.6).

Strand	Bloom's	Scope	Source
Tables/Charts	Comprehension	Reinforce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.35,IV.A.5 week tested: 34.National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Logical Reasoning: Draw Conclusion
The learner will be able to draw a logical conclusion based on data presented in graphical format. (NJCCCS 4.1, 4.6).

Strand	Bloom's	Scope	Source
Logical Reasoning	Analysis	Reinforce	Mathematics Intermediate Series, Grade 7

Logical Reasoning
The learner will be able to use critical thinking skills to solve problems (including determining the best money management plan or determining unknown information). (NJCCCS 4.1, 4.).

Strand	Bloom's	Scope	Source
Logical Reasoning	Evaluation	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Graphs: Organize Data
The learner will be able to organize data to be displayed in graphical format. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Graphing	Comprehension	Reinforce	NJ: Core Curriculum Content Standards, May 1996, Grade 7, Standard 4.12.9, National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Data Collection
The learner will be able to collect data. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Data Collection and Classification	Knowledge	Introduce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 8, p.9,III.B, p.29,III.B week tested: 34.; NJ: Core Curriculum Content Standards, May 1996, Grade 7, Standard 4.12.9

Data Collection: Organization
The learner will be able to organize data in many different ways. (4.1, 4.6).

Strand	Bloom's	Scope	Source
Data Collection and Classification	Comprehension	Introduce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.9,III.B, p.29,III.B week tested: 34.National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Data: Understand/Sorting
The learner will be able to understand sorting methods. (NJCCCS 4.1, 4.6).

Strand	Bloom's	Scope	Source
Data Collection and Classification	Comprehension	Reinforce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.31,III.C.1 week tested: 34.National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Graphs: Stem-and-Leaf Graphs
The learner will be able to interpret data shown in a stem-and-leaf graph. (NJCCCS 4.1, 4.6).

Strand	Bloom's	Scope	Source
Stem-and-Leaf/Box-and-Whisker Plots	Comprehension	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Graphs: Data/Using Integers
The learner will be able to interpret graphical data involving integers. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Analyzing/Evaluating Graphical Forms	Analysis	Introduce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

The Decimals Unit includes Competencies/Objectives which focus on number sense and operations with decimals. The Decimals Unit includes comparison, computing, money, estimation, problem solving and reasoning.

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

Connecting: Forms
The learner will be able to connect concepts relating decimals, whole numbers, fractions, and percents by demonstrating how these number forms are used to communicate place value, ordinality, and money amounts, and to evaluate the reasonableness of a given problem and solution. (NJCCCS 4.1, 4.2, 4.6).

Strand	Bloom's	Scope	Source
Connecting		Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Estimating
The learner will be able to employ strategies for estimating the range of an answer, or the number of digits in an answer to addition, subtraction, multiplication, or division problems, and articulate these strategies to others. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Reasoning/Estimation		Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Decimals: Non-Terminating
The learner will be able to explore, represent and apply concepts of non-terminating decimals. (NJCCCS 4.1, 4.2).

Strand	Bloom's	Scope	Source
Exploring		Master	NJ: Core Curriculum Content Standards, May 1996, Grade 7, Standard 4.15.6, National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Decimals: Understand/Non-terminating
The learner will be able to conceptually understand non-terminating decimals. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Decimals	Comprehension	Reinforce	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.11,I.B.6 week tested: 34., National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Decimals: Understand
The learner will be able to conceptually understand decimals. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Decimals	Comprehension	Master	NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 7, p.11,I.B.3 week tested: 34., National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Decimal Fractions: Adding
The learner will be able to add decimal fractions and convert the answer to a decimal number format. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Decimal Fractions	Application	Reinforce	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Decimal Fractions: Subtracting
The learner will be able to subtract decimal fractions and convert the answer to a decimal number format. (NJCCCS 4.1).

Strand	Bloom's	Scope	Source
Decimal Fractions	Application	Master	National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Applications of Learning, January 1999, Chester Township Schools, Grades 7

Discrete Mathematics

The Discrete Mathematics Unit includes the concepts of discrete math, matrices and recursion.

Recursion: Apply
The learner will be able to use appropriate mathematical abilities to apply recursive processes to develop game strategies and to determine solutions to real-world problem situations. (NJCCCS 4.1).

Strand

Bloom's

Scope

Source