Chester Township Public Schools
Mathematics Curriculum

Mathematics - Grade 6

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 6

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

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

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

In this course students explore the world of numbers, algorithms, patterns, shapes, data, and spatial sense. Students engage in activities involving whole numbers, decimals, fractions, percents, integers, rational numbers, number sentences, measurement, estimation, coordinate geometry, making sense of real-world data (collecting, discussing, and making conclusions about data), conceptualizing and converting numbers in various forms, and justifying mathematics solutions by articulating the reasons behind the solutions. Course work includes using manipulatives to represent algebraic concepts. The course emphasizes the need for students to make mathematical connections and to use mathematics principles to communicate, reason, and solve problems. The Terra Nova Complete Battery assesses students in sixth grade (Level 16).


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.

    Order of Operations: Apply
The learner will be able to correctly use the rules for order of operations. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Order of Operations Application Introduce Applications of Learning, January 1999, National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grade 6
  
    Order of Operations: Determine
The learner will be able to determine the correct order of calculations when more than one operation is to be performed.
Strand Bloom's Scope Source
Order of Operations Application Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Properties: Number System
The learner will be able to apply the properties of the number system to evaluate the validity of results. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Properties Evaluation Introduce Higher-Order Learning, January 1999, National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grade 6
  
    Multiple Step Story Problems
The learner will be able to solve multiple step word problems using whole numbers and decimals. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Multiple-step Problems Application Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    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.
Strand Bloom's Scope Source
Inequalities Application Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Basic Operations: Whole Numbers
The learner will be able to explain the concepts involved in basic operations. NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Basic Operations Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Inverse Operations: Checking
The learner will be able to check the correctness of an answer by using the inverse operation.
Strand Bloom's Scope Source
Inverse Operations Comprehension Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Inverse Operations
The learner will be able to ""work backwards" to solve story problems. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Solution Methods Analysis Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Solution Methods: Applying
The learner will be able to use mental arithmetic and estimation to solve problems. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Solution Methods Comprehension Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Solution Tools: Analysis
The learner will be able to analyze which solution tool would best solve a problem: calculator, pencil and paper, mental math. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Solution Methods Analysis Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  

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.

    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, 4.2, 4.6).
Strand Bloom's Scope Source
Communicating Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    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. (NJCCCS 4.1, 4.2, 4.6).
Strand Bloom's Scope Source
Analyzing/Evaluating Graphical Forms Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Circle Graphs: Predictions
The learner will be able to make predictions using information given in a circle graph. (NJCCCS 4.1, 4.2, 4.6).
Strand Bloom's Scope Source
Circle Graphs Synthesis Reinforce Higher-Order Learning, January 1999, Grade 6
  
    Circle Graphs: Sum
The learner will be able to determine the number represented by the sum of two sections of a circle graph given in percents. (NJCCCS 4.1, 4.2, 4.6).
Strand Bloom's Scope Source
Circle Graphs Comprehension Reinforce Foundations of Learning, January 1999, Grade 6
  
    Circle Graphs: Interpret
The learner will be able to draw logical conclusions from interpreting data in a circle graph. (NJCCCS 4.1, 4.2, 4.6).
Strand Bloom's Scope Source
Circle Graphs Analysis Reinforce Applications of Learning, January 1999, Grade 6
  
    Bar Graphs: Identify/Compare
The learner will be able to identify or compare amounts in a bar graph. (NJCCCS 4.1, 4.2, 4.6).
Strand Bloom's Scope Source
Bar Graphs Knowledge Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Bar Graphs: Analyze
The learner will be able to analyze simple stacked graphs (bar and pictographs). (NJCCCS 4.1, 4.2, 4.6).
Strand Bloom's Scope Source
Bar Graphs Analysis Master Applications of Learning, January 1999, National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Chester Township Schools, Grade 6
  
    Bar Graphs: Addition/Subtraction
The learner will be able to add or subtract information presented in the form of a bar graph. (NJCCCS 4.1, 4.2, 4.6).
Strand Bloom's Scope Source
Bar Graphs Comprehension Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Line Graphs
The learner will be able to identify, compare, and analyze points on a line graph. (NJCCCS 4.1, 4.2, 4.6).
Strand Bloom's Scope Source
Line Graphs Analysis Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grade 6
  
    Line/Circle Graphs
The learner will be able to interpret data from circle/pie and line graphs, including identifying values from the graph, determining that addition or subtraction is needed to find an answer, and comparing values from the graph. (NJCCCS 4.1, 4.2, 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, Chester Township Schools, Sixth Grade
  
    Table: Compute
The learner will be able to identify values from the graph, compare values from the graph, determine the value of multiple entries, and perform the necessary calculations to find the missing parts of a table. (NJCCCS 4.1, 4.2, 4.6).
Strand Bloom's Scope Source
Tables/Charts Analysis Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grade 6
  
    Table/Graph: Properties/Relationships
The learner will be able to identify properties and relationships from tables and graphs. (NJCCCS 4.1, 4.2, 4.6).
Strand Bloom's Scope Source
Tables/Charts Analysis Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, Applications of Learning, January 1999, Chester Township Schools, Grade 6
  
    Logical Reasoning: Draw Conclusion
The learner will be able to draw a logical conclusion based on data presented in graphical format. (NJCCCS 4.1, 4.2, 4.6).
Strand Bloom's Scope Source
Logical Reasoning Analysis Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Graphs: Construct
The learner will be able to construct charts and graphs. (NJCCCS 4.1, 4.2, 4.6).
Strand Bloom's Scope Source
Graphing Synthesis Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Graphs/Maps: Interpretation
The learner will be able to read and interpret maps, scattergrams, box and whisker graphs, and stem-and-leaf charts. (NJCCCS 4.1, 4.2, 4.6).
Strand Bloom's Scope Source
Analyzing/Evaluating Graphical Forms Analysis Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  

Decimals
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.

    Problem Solving: Application
The learner will be able to use manipulatives, calculators, and symbols to solve real-world scenario problems which call for the rounding, addition, subtraction, multiplication, and division of decimals. This process includes evaluating a given problem scenario, identifying the problem, determining the relevant elements and the required operation, setting up a number sentence, and solving the problem. (NJCCCS 4.1, 4.2).
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, Sixth Grade
  
    Number Sense: Place Value
The learner will be able to articulate (in terms of place value) the reasoning behind placing the decimal point in the appropriate position when evaluating number sentences involving operations on decimals. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Number Sense Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Addition Story Problems
The learner will be able to solve story problems involving adding 3 numbers with decimals. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Add Decimals Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Subtraction Story Problems
The learner will be able to solve story problems involving subtracting decimals. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Subtract Decimals Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Addition/Subtraction Decimals
The learner will be able to solve either a story or numerical problem requiring addition or subtraction of decimals. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Add/Subtract Decimals Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Multiplication Story Problems
The learner will be able to solve real-world story problems by determining that multiplication is required, by regrouping the numbers, and by multiplying the appropriate decimals up to the hundredths position. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Multiply Decimals Application Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Multiplication/Division Decimals
The learner will be able to multiply, divide, and compare decimals using the correct order of operations when necessary. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Multiply/Divide Decimals Analysis Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Decimals: Rounding
The learner will be able to round decimal numbers to the nearest whole number, tenths, and hundredths place, in the context of a problem involving money amounts. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Decimals Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Money: Story Problems/Add/Subtract
The learner will be able to solve story problems which involve the addition and subtraction of money amounts written in decimal form. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Money Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Money: Story Problems/Multiply/Divide
The learner will be able to solve story problems which involve the multiplication and division of money amounts written in decimal form. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Money Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Division Story Problems
The learner will be able to solve story problems by dividing decimals up to the hundredths position. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Divide Decimals Application Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Compare Decimals: Up to 0.0001
The learner will be able to compare decimals up to the ten-thousandths place (0.0001). (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Compare Decimals Analysis Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  

Fractions
The Fractions Unit includes Competencies/Objectives which focus on number sense and operations with fractions. The Fractions Unit includes comparison, ordering, fractions parts, estimation, reasoning and problem solving.

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

    Problem Solving
The learner will be able to demonstrate a sense of how operations with fractions manipulate numbers by recognizing a real-world situation which calls for specific operations (addition, subtraction, multiplication, or division) with fractions, evaluating the situation, articulating the nature and elements of the problem, and solving the problem without being cued that the calculations involved would require fractions. (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, Chester Township Schools, Sixth Grade
  
    Connecting: Using Fractions
The learner will be able to make connections between the functions of numerators and the functions of denominators by exploring fractions (i.e., drawing conclusions about fractions a/b, b/c, c/b, a/c, b/a, and c/a, when a > b > c). (NJCCCS 4.1).
Strand Bloom's Scope Source
Connecting Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Number Sense: Using Fractions
The learner will be able to have an intuitive sense of fractions, the portions they represent, and how fractions are used to solve problems and to communicate proportions and ideas in real-world settings. (NJCCCS 4.1).
Strand Bloom's Scope Source
Number Sense Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Subtraction Story Problems
The learner will be able to subtract two fractions, either mixed fractions, same denominators, or with different denominators, in the context of a story problem. (NJCCCS 4.1).
Strand Bloom's Scope Source
Subtract Fractions Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Addition/Subtraction Fractions
The learner will be able to solve story problems requiring the addition or subtraction of fractions and reduce answers to lowest terms. (NJCCCS 4.1).
Strand Bloom's Scope Source
Add/Subtract Fractions Application Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Multiply 2 Fractions
The learner will be able to multiply 2 fractions. (NJCCCS 4.1).
Strand Bloom's Scope Source
Multiply Fractions Knowledge Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Multiplication Story Problems
The learner will be able to utilize multiplication of fractions to determine the fractional part of a whole number. (NJCCCS 4.1).
Strand Bloom's Scope Source
Multiply Fractions Application Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Divide 2 Fractions
The learner will be able to divide two fractions. (NJCCCS 4.1).
Strand Bloom's Scope Source
Divide Fractions Knowledge Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Division Story Problems
The learner will be able to solve real-world scenario problems where the division of fractions, mixed fractions, and whole numbers is involved. (NJCCCS 4.1).
Strand Bloom's Scope Source
Divide Fractions Application Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Compare Fractions: To 1
The learner will be able to compare a fraction to 1. (NJCCCS 4.1).
Strand Bloom's Scope Source
Compare Fractions Analysis Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Compare Fractions: Equivalent/Mixed
The learner will be able to compare 2 equivalent fractions and equivalent and mixed fractions. (NJCCCS 4.1).
Strand Bloom's Scope Source
Compare Fractions Analysis Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  

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.

    Geometry Terms: Communicating
The learner will be able to communicate solutions to problems across the mathematics curriculum using the language of geometry where appropriate. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Geometric Vocabulary Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Problem Solving: Geometric Properties
The learner will be able to solve real-world problems which require logical deductions and reasoning based on geometric properties without being cued about the properties which would apply to the problem, and utilize geometric concepts as proof or evidence of a self-generated solution theory. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Problem Solving Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Communicating: Spatial Sense
The learner will be able to develop spatial sense by speaking, writing, and using models and diagrams to explain such terms and concepts as transformation, congruency, similarity, points, lines, and the properties of two- and three-dimensional figures. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Communicating Spatial Sense Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Solids: Cube
The learner will be able to identify a cube. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Three-Dimensional Solids Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Solids: Sphere
The learner will be able to identify a sphere. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Three-Dimensional Solids Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Figures: Identify
The learner will be able to identify squares, circles, triangles, rectangles, ovals, cubes, spheres. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Figures: Identify Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Figures: Terms
The learner will be able to apply the following geometric terms in discussing and comparing figures and shapes: symmetry, curves, and lines. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Figures: Vocabulary Comprehension Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Figures: Terms
The learner will be able to apply the following geometric terms in discussing and comparing figures and shapes: parallel, perpendicular, intersection, similar, and circumference. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Figures: Vocabulary Comprehension Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Figures: Terms
The learner will be able to apply the following geometric terms in discussing and comparing figures and shapes: congruent, area, perimeter, and volume. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Figures: Vocabulary Comprehension Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Figures: Comparison
The learner will be able to compare the properties of two and three dimensional shapes. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Properties of Figures Analysis Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Congruency/Similarity: Identify/Solve
The learner will be able to identify the corresponding sides of two congruent figures and, using the proportional relationship between the sides of two similar figures, calculate an unknown side length. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Congruence/Similarity/Symmetry Comprehension Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Lines: Perpendicular/Parallel
The learner will be able to identify and apply properties of both perpendicular and parallel lines. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Lines: Parallel/Perpendicular Application Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Lines
The learner will be able to describe the relationships between different lines and identify properties of intersecting, diagonal, horizontal, vertical, parallel, and perpendicular lines. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Lines Comprehension Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Angles: Identify
The learner will be able to identify and label specific parts of an angle: the vertex, rays, interior and exterior. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Angles Knowledge Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Circle: Parts
The learner will be able to identify and define circle parts. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Circles Knowledge Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Symmetry: Symmetrical Lines
The learner will be able to identify lines of symmetry in figures. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Symmetry Knowledge Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Similarity: Similar Figure/No Pictures
The learner will be able to identify similar figures when no pictures are provided. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Similarity Knowledge Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Congruency: Parts
The learner will be able to identify congruent parts of geometric figures. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Congruence Knowledge Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Lines/Angles/Triangles
The learner will be able to draw and describe lines, angles, and triangles using tools such as a ruler, protractor, etc. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Lines/Angles/Polygons Comprehension Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Geometric Models: Problem Solve
The learner will be able to solve problems using two-dimensional geometric models. (NJCCCS 4.2, 4.4, 4.6).
Strand Bloom's Scope Source
Geometric Models Application Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  

Integers
The Integers Unit includes Competencies/Objectives which focus on number sense and operations with 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.

    Problem Solving: Application
The learner will be able to recognize real-world situations which call for operations with integers, and apply an understanding of integers to solve problems in such areas as temperature, coordinate geometry, number lines, algebra, and statistics, and analyze real-world scenarios, set up number sentences, and solve problems. (NJCCCS 4.1, 4.6).
Strand Bloom's Scope Source
Problem Solving Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Addition: Number Line
The learner will be able to add integers using a number line. (NJCCCS 4.1, 4.6).
Strand Bloom's Scope Source
Add Integers Knowledge Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Addition/Subtraction: Represent
The learner will be able to use manipulatives and number lines to understand addition and subtraction of integers. (NJCCCS 4.1, 4.6).
Strand Bloom's Scope Source
Add/Subtract Integers Comprehension Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Addition/Subtraction Integers
The learner will be able to add and subtract integer numbers. (NJCCCS 4.1, 4.6).
Strand Bloom's Scope Source
Add/Subtract Integers Knowledge Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    Integers: Understand Meaning
The learner will be able to comprehend the meaning of positive and negative integers by applying them to explain real world scenarios. (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, Sixth Grade
  
    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 Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    . Integers: Define Set
The learner will be able to identify what constitutes the set of integers (NJCCCS 4.1, 4.6).
Strand Bloom's Scope Source
Integers Knowledge Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    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 Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  
    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 Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Sixth Grade
  

Measurement
The Measurement Unit includes Competencies/Objectives which focus on measurement concepts, applications, and analysis. The Measurement Unit includes concepts of length, area, circumference, perimeter, volume, weight, formulas, distance, calendar, money, tools, accuracy, units, constructions, patterns and problem solving.

This unit includes experimenting with formal, informal, customary, and metric units of measurement, and distinguishing between situations which call for exact measurement and those which call for estimation.

    Problem Solving: Applications
The learner will be able to solve real-world scenario problems (involving perimeter, area, or length) by using manipulatives to isolate the nature of the problem, by articulating how a given m