Chester Township Public Schools
Mathematics Curriculum

Mathematics - Grade 2

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 2

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


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


In this course students explore the world of numbers, algorithms, patterns, shapes, data, and spatial sense. Students engage in activities which require them to make sense of real-world data (collecting, discussing, and making conclusions about data), to conceptualize the symbolic value of numbers in various forms (including fractions and decimals), to perform operations with numbers, and to use manipulatives as representative objects. The course emphasizes the need for students to make mathematical connections and to use mathematics principles to communicate, reason, and solve problems.


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.

    Number Sense: Manipulatives
The learner will be able to use manipulatives to demonstrate the following algebraic concepts: sets, elements of sets (a different shaped or colored manipulative can be used to represent a set of manipulatives), equal sets, variables representing unequal values (specific manipulatives can be used to equal five of another kind of manipulative), and the symbolic nature of algebra. (NJCCCS 4.2, 4.3).
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, Second Grade.
  
    Identify Sentence: Picture
The learner will be able to determine the number sentence depicted in a picture. (NJCCCS 4.2, 4.3).
Strand Bloom's Scope Source
Identify Sentence Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Fact Families: Components
The learner will be able to identify all of the components completing a fact family. (NJCCCS 4.2, 4.3).
Strand Bloom's Scope Source
Fact Families Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Properties: Missing Number
The learner will be able to identify the missing number in an equation. (NJCCCS 4.2, 4.3).
Strand Bloom's Scope Source
Missing Information Knowledge Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Verify Computation
The learner will be able to verify correct computation of another student's work. (NJCCCS 4.2, 4.3).
Strand Bloom's Scope Source
Verify Analysis Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Equalities/Inequalities: Represent
The learner will be able to use manipulatives to represent equalities and inequalities. (NJCCCS 4.2, 4.3).
Strand Bloom's Scope Source
Equality/Inequality Comprehension Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second 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.

    Data Collection
The learner will be able to discuss problems with and solutions for various ways of collecting data. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Data Collection and Classification Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Analyzing: Graphical Forms
The learner will be able to demonstrate the ability to interpret graphical forms (tables, charts, graphs, diagrams, etc.) of data by transferring information from one graphical form to another. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Analyzing/Evaluating Graphical Forms Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Bar Graph: Plot Data
The learner will be able to plot data on a bar graph that already has a scale and axis labels. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Bar Graphs Comprehension Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Bar Graphs: Identify/Compare
The learner will be able to identify or compare amounts in a bar graph. (NJCCCS 4.1, 4.2).
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, Second Grade.
  
    Pictographs: Identify
The learner will be able to identify data on a simple pictograph. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Pictographs Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Chart/Graph: Labels/Interpret
The learner will be able to understand labels given on graphs, tables, and charts. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Tables/Charts Application Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Table: Compare
The learner will be able to read and compare information in a table. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Tables/Charts Analysis Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Graphs: Construct
The learner will be able to construct graphs recording information in tables, bar graphs, line graphs, and pictographs. (NJCCCS 4.2, 4.3).
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, Second 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.

    Division: Equal Parts
The learner will be able to solve a problem requiring the division of an object into equal parts. (NJCCCS 4.6).
Strand Bloom's Scope Source
Divide Fractions Application Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Fraction Parts: Equal Parts/Represent
The learner will be able to divide a given shape into equal parts. (NJCCCS 4.6).
Strand Bloom's Scope Source
Fraction Parts Application Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Fraction Parts: Part of a Whole
The learner will be able to identify parts of a whole (including 1/2, 1/3, and 1/4). (NJCCCS 4.6).
Strand Bloom's Scope Source
Fraction Parts Knowledge Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Fraction Parts: Unit/Represent
The learner will be able to use manipulatives and pictures to show unit fractions. (NJCCCS 4.6).
Strand Bloom's Scope Source
Fraction Parts Comprehension Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second 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.

    Patterns: Analyzing Visual
The learner will be able to analyze visual patterns in geometric figures by exploring how placing different figures on different sized backgrounds in rows creates different combinations of figures within each row. (NJCCCS 4.7).
Strand Bloom's Scope Source
Geometric Patterns Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Spatial Thinking: Manipulatives
The learner will be able to practice modeling, drawing, and explaining shapes and their properties using manipulatives and exploring the shapes in a real-world context. (NJCCCS 4.7).
Strand Bloom's Scope Source
Spatial Thinking Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Shapes: Visualize
The learner will be able to visualize a 2 dimensional figure given a description. (NJCCCS 4.7).
Strand Bloom's Scope Source
Two-Dimensional Shapes Analysis Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Figures: Relationships
The learner will be able to identify size, shape, and/or position relationships among various objects. (NJCCCS 4.7).
Strand Bloom's Scope Source
Figures: Relationships Knowledge Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Figures: Orally Described
The learner will be able to identify an object based on an oral description. (NJCCCS 4.7).
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, Second Grade.
  
    Figures: Real World Shapes
The learner will be able to identify shapes in real world objects and drawings. (NJCCCS 4.7).
Strand Bloom's Scope Source
Figures: Real World Comprehension Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Figures: Classify/Attributes
The learner will be able to identify geometric attributes used for classification of figures. (NJCCCS 4.7).
Strand Bloom's Scope Source
Figures: Attributes Knowledge Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second 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 4.7).
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, Second Grade.
  
    Symmetry
The learner will be able to determine if a given shape is symmetrical. (NJCCCS 4.7).
Strand Bloom's Scope Source
Symmetry Application Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second 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: Manipulatives
The learner will be able to listen to or read a given scenario involving measurement, and articulate how the problem can be solved using manipulatives. (NJCCCS 4.9, 4.10).
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, Second Grade.
  
    Communicating: Measurement Concepts
The learner will be able to use measurement terms, articulate how and when measurement is used in real-world situations, and give examples of situations which call for either estimation or exact measurement. (NJCCCS 4.9, 4.10).
Strand Bloom's Scope Source
Communicating Measurement Concepts Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Problem Solving
The learner will be able to solve story problems dealing with measurement. (NJCCCS 4.9, 4.10).
Strand Bloom's Scope Source
Problem Solving Application Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Calendar: Days
The learner will be able to identify positions of the days of the week. (NJCCCS 4.2).
Strand Bloom's Scope Source
Calendar Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Calendar: Time Passage/Relating
The learner will be able to discuss the passage of calendar time (days, weeks, months, and years) in relation to personal experiences. (NJCCCS 4.2).
Strand Bloom's Scope Source
Calendar Comprehension Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Calendar: Sequence
The learner will be able to identify chronological sequence within calendar time. (NJCCCS 4.2).
Strand Bloom's Scope Source
Calendar Knowledge Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Calendar: Read
The learner will be able to identify the day of the week, the month, and the year by reading a calendar. (NJCCCS 4.2).
Strand Bloom's Scope Source
Calendar Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Calendar: Convert Weeks/Days
The learner will be able to convert time between weeks and days. (NJCCCS 4.2).
Strand Bloom's Scope Source
Calendar Comprehension Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Length: Ruler
The learner will be able to accurately read the appropriate scale on a ruler. (NJCCCS 4.9, 4.10).
Strand Bloom's Scope Source
Length Knowledge Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.,
  
    Time: Quarter Hour
The learner will be able to tell time to the nearest quarter hour. (NJCCCS 4.2).
Strand Bloom's Scope Source
Time Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Time: Rounding/Quarter Hour
The learner will be able to round time to the nearest quarter hour. (NJCCCS 4.9, 4.10).
Strand Bloom's Scope Source
Time Comprehension Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Money: Equivalent Values
The learner will be able to determine an equivalent value of money given a specific amount. (NJCCCS 4.1).
Strand Bloom's Scope Source
Money Comprehension Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Money: Add Coins
The learner will be able to determine correct number of coins needed to purchase an item. (NJCCCS 4.1).
Strand Bloom's Scope Source
Money Comprehension Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Temperature: Terms
The learner will be able to compare temperatures using terms such as warmer than, cooler than, etc. (NJCCCS 4.9, 4.10).
Strand Bloom's Scope Source
Temperature Comprehension Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Weight: Metric Instrument
The learner will be able to measure an object's weight using the appropriate metric instrument. (NJCCCS 4.9, 4.10).
Strand Bloom's Scope Source
Weight Application Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Mass/Capacity: Measuring
The learner will be able to measure mass and capacity using both metric and standard units. (NJCCCS 4.9, 4.10).
Strand Bloom's Scope Source
Weight Comprehension Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Measurement: Speak/Write
The learner will be able to talk and write about measurement. (NJCCCS 4.2).
Strand Bloom's Scope Source
Measurement: Application Comprehension Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Measuring: Rounding
The learner will be able to round measurements to the nearest whole unit to the nearest "10". (NJCCCS 4.10).
Strand Bloom's Scope Source
Measurement: Application Comprehension Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Area of a Square: Using Models
The learner will be able to use models to find the area of a square. (NJCCCS 4.1).
Strand Bloom's Scope Source
Area of a Square Application Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Estimate Measurements: Metric/Standard
The learner will be able to estimate length, weight, temperature, and capacity using both metric and standard units. (NJCCCS 4.9, 4.10).
Strand Bloom's Scope Source
Measurement: Estimation Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Conversion: Metric/Application
The learner will be able to apply metric conversion skills (converting within the metric system) to solve real-world application problems. (NJCCCS 4.9, 4.10).
Strand Bloom's Scope Source
Converting Application Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  

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: Nature of Different Forms
The learner will be able to investigate numbers by engaging in activities which address the nature of different number forms, how different operations (addition, subtraction, multiplication, division) manipulate numbers, and which require the student to formulate analysis level questions. (NJCCCS 4.1, 4.2, 4.4).
Strand Bloom's Scope Source
Number Forms Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    One-to-one Correspondence
The learner will be able to identify group showing a specific quantity. (NJCCCS 4.1, 4.2, 4.4).
Strand Bloom's Scope Source
One-to-one Correspondence Knowledge Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Place Value: Ten's Place
The learner will be able to determine the place value of a number in the ten's place. (NJCCCS 4.1, 4.2, 4.4).
Strand Bloom's Scope Source
Place Value Comprehension Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Place Value: Equivalent Forms
The learner will be able to identify equivalent values of numbers written with irregularly grouped units, such as 16 tens and 11 ones being equal to 171. (NJCCCS 4.1, 4.2, 4.4).
Strand Bloom's Scope Source
Place Value Comprehension Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Odd/Even: Identifying to 20
The learner will be able to identify odd and even numbers up to 20. (NJCCCS 4.1, 4.2, 4.4).
Strand Bloom's Scope Source
Odd/Even Knowledge Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Number Sense: Represent/Less Than 1000
The learner will be able to use manipulatives to find the size, position, and order of numbers less than 1000. (NJCCCS 4.1, 4.2, 4.4).
Strand Bloom's Scope Source
Number Sense Application Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  

Numeration
The Numeration Unit focuses on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships.

This unit includes exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships. The Numeration Unit focuses on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships.

    Pattern: Problem Solving
The learner will be able to solve problems by recognizing and extending pictorial, concrete, and numerical patterns. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Patterns: Problem Solving Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Number Values: Manipulatives
The learner will be able to demonstrate a conceptualization of number values and how these values relate to each other by using manipulatives (articulating how adding or taking away specific manipulatives changes the quantity of the remaining manipulatives), and see numbers in terms of what they represent (in quantity, values, etc.) in context. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Number Values Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Pattern: Relationship
The learner will be able to determine the relationship (a pattern) between the numbers in two separate columns. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Patterns: Number Analysis Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Pattern: Geometric Shapes
The learner will be able to identify the next shape in a geometric pattern. (NJCCCS 4.1, 4.2, 4.7).
Strand Bloom's Scope Source
Patterns: Geometric Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Pattern: Evaluate/Represent
The learner will be able to use manipulatives to evaluate and complete patterns, utilizing shape, size, and rotation. (NJCCCS 4.1).
Strand Bloom's Scope Source
Patterns: Geometric Analysis Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Greater Than/Less Than
The learner will be able to determine which of two numbers is greater than or less than the other. (NJCCCS 4.1).
Strand Bloom's Scope Source
Comparison Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Counting: Word Names
The learner will be able to identify the word name for a missing number in a given counting series. (NJCCCS 4.1).
Strand Bloom's Scope Source
Counting Comprehension Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Counting: Forward/Backward
The learner will be able to start with any three digit number and count forward or backward by ones. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Counting Knowledge Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Counting: Problem Solving
The learner will be able to solve problems using counting. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Counting Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Symbolic/Concrete Patterns: Creating
The learner will be able to create concrete and symbolic patterns. (NJCCCS 4.1, 4.2, 4.7).
Strand Bloom's Scope Source
Concrete Patterns/Symbolic Patterns Synthesis Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Skip Counting: 25's, 50's, 100's
The learner will be able to skip count by 25's, 50's, and 100's.
Strand Bloom's Scope Source
Skip Counting Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade. (NJCCCS 4.1, 4.2)
  
    Pattern: Missing Element Position
The learner will be able to determine the correct place of a missing element in a numerical pattern. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Patterns Analysis Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Ordering: 1-100
The learner will be able to order numbers from 1 to 100. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Ordering Numbers Knowledge Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Ordering: Whole Numbers
The learner will be able to order whole numbers in the correct sequence. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Ordering Numbers Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Estimate Size: Represent
The learner will be able to use manipulatives and pictures to estimate relative size. (NJCCCS 4.1, 4.2, 4.5).
Strand Bloom's Scope Source
Estimation Application Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Estimate Sum: Whole Numbers
The learner will be able to estimate sums of whole numbers. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Estimation Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Estimate Difference: Whole Numbers
The learner will be able to estimate subtraction problems using whole numbers. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Estimate/Problems Comprehension Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Estimation: Justify
The learner will be able to give a justification for the reasonableness of an estimate. (NJCCCS 4.1, 4.2).
Strand Bloom's Scope Source
Estimation Analysis Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Rounding: Tens
The learner will be able to round whole numbers to the nearest ten. (NJCCCS 4.1, 4.2, 4.8).
Strand Bloom's Scope Source
Rounding Knowledge Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Mental Math
The learner will be able to use mental arithmetic and calculators to find sums, differences, and products. (NJCCCS 4.1, 4.2, 4.8).
Strand Bloom's Scope Source
Mental Math Application Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  

Probability/Statistics
This unit includes collecting, analyzing, and making sense of real-world data (including overlapping data, inconclusive data, etc.). The Probability/Statistics Unit focuses on data analysis and probability concepts. This unit includes collecting, analyzing, and making sense of real-world data (including overlapping data, inconclusive data, etc.

    Data: Problem Analysis
The learner will be able to listen to a given real-world scenario problem involving probability and statistics, describe the problem the scenario presents, collect or list the necessary data, and refer to the data to make predictions about how the problem can be solved. (NJCCCS 4.3, 4.7, 4.12).
Strand Bloom's Scope Source
Data Reinforce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Data: Unclear
The learner will be able to deal with real-world problems which don't have clear cut answers, including adding outlying data to graphs or diagrams which represent conclusions. (NJCCCS 4.3, 4.7, 4.12).
Strand Bloom's Scope Source
Data Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Communicating: Pictograms
The learner will be able to create pictograms which convey information such as the following about the class: how much milk did the class drink in one week, how many hours were spent sleeping by the entire class in one week, etc. (NJCCCS 4.3, 4.7, 4.12).
Strand Bloom's Scope Source
Communicating Master National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.
  
    Data Analysis: Solutions
The learner will be able to listen to a given real-world scenario problem involving probability and statistics, describe the problem the scenario presents, formulate a hypothesis, collect the necessary data, create graphs to organize the collected data, and refer to the graphs to make predictions about how the problem can be solved. (NJCCCS 4.3, 4.7, 4.12).
Strand Bloom's Scope Source
Data Analysis Introduce National Council of Teachers of Mathematics Curriculum and Evaluation Standards, New Jersey Core Curriculum, Chester Township Schools, Second Grade.