EAST LONGMEADOW PUBLIC SCHOOLS
2006 - 2007 DISTRICT CURRICULUM GUIDES

Mathematics - Grade 2

Mathematics

The Massachusetts Mathematics Curriculum Framework envisions all students in the Commonwealth achieving mathematical competence through a strong mathematics program that emphasizes problem solving, communicating, reasoning and proof, making connections, and using representations. Acquiring such competence depends in large part on a clear, comprehensive, coherent, and developmentally appropriate set of standards to guide curriculum expectations.

Grade 2

The Massachusetts Mathematics Curriculum Framework provides learning standards for students in grades 1-2.


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.

    Algorithms: Understand/Use/Add/Subtract
The learner will be able to understand and use the algorithms for addition (two 3-digit numbers and three 2-digit numbers) and subtraction (two 3-digit numbers).
Strand Scope Source
Algorithms Master MA: Curriculum Framework, 2000, Grade 2, 2.N.11
  
    Number Sentences: Write/Relationships
The learner will be able to write number sentences representing mathematical relationships in everyday scenarios using the +, -, <, >, and/or = symbols.
Strand Scope Source
Number Sentence Master MA: Curriculum Framework, 2000, Grade 2, 2.P.6
  
    Number Sentence: Solve/Unknown Value
The learner will be able to determine solutions to number sentences with an unknown value.
Strand Scope Source
Number Sentence Master MA: Curriculum Framework, 2000, Grade 2, 2.P.5
  
    Number Sentence: Construct/Variable
The learner will be able to construct number sentences by applying a variable to represent an unknown amount.
Strand Scope Source
Number Sentence Master MA: Curriculum Framework, 2000, Grade 2, 2.P.5
  
    Facts: Understand/Addition/Subtraction
The learner will be able to understand the addition facts (sums to 20) and associated subtractions facts, and apply them to obtain problem solutions.
Strand Scope Source
Fact Families Master MA: Curriculum Framework, 2000, Grade 2, 2.N.9
  
    Operations: Meaning/Addition/Subtraction
The learner will be able to show an understanding of the several meanings for addition and subtraction using the words total, sum, in all, difference, less more, equal and remaining.
Strand Scope Source
Operations: Add/Subtract Master MA: Curriculum Framework, 2000, Grade 2, 2.N.7
  
    Inverse Operations: Add/Subtract
The learner will be able to develop an understanding of the inverse relationship that exists between addition and subtraction.
Strand Scope Source
Inverse Operations Master MA: Curriculum Framework, 2000, Grade 2, 2.N.8
  

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.

    Number Sense: Common Fractions
The learner will be able to recognize and illustrate basic fractions (1/4, 1/3 and 1/2) as parts of a whole, parts of a group, and numbers on the number line.
Strand Scope Source
Number Sense Master MA: Curriculum Framework, 2000, Grade 2, 2.N.3
  

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.

    Figures: Curved
The learner will be able to recognize, explain, draw, and compare curved figures.
Strand Scope Source
Figures Master MA: Curriculum Framework, 2000, Grade 2, 2.G.2
  
    Transformations: Identify
The learner will be able to recognize figures that have undergone transformations such as rotation (turn), reflection (flip), and/or translation (flip).
Strand Scope Source
Transformations Master MA: Curriculum Framework, 2000, Grade 2, 2.G.4
  
    Polygons: Up to Six Sides
The learner will be able to recognize, explain, draw, and compare polygons that have up to six sides.
Strand Scope Source
Polygons Master MA: Curriculum Framework, 2000, Grade 2, 2.G.2
  
    Solids: Explain/Characteristics
The learner will be able to explain the characteristics of three-dimensional solids.
Strand Scope Source
Three-Dimensional Solids Master MA: Curriculum Framework, 2000, Grade 2, 2.G.1
  
    Solids: Explain/Parts
The learner will be able to explain the parts of three-dimensional solids (faces,edges lengths of sides and corners).
Strand Scope Source
Three-Dimensional Solids Master MA: Curriculum Framework, 2000, Grade 2, 2.G.1
  
    Shapes: Explain/Characteristics
The learner will be able to explain the characteristics of two-dimensional shapes.
Strand Scope Source
Two-Dimensional Shapes Master MA: Curriculum Framework, 2000, Grade 2, 2.G.1
  
    Shapes: Explain/Parts
The learner will be able to explain the parts of two-dimensional shapes.
Strand Scope Source
Two-Dimensional Shapes Master MA: Curriculum Framework, 2000, Grade 2, 2.G.1
  
    Shapes: Draw
The learner will be able to create drawings of two dimensional shapes.
Strand Scope Source
Two-Dimensional Shapes Master MA: Curriculum Framework, 2000, Grade 2, 2.G.2
  
    Two-Dimensional Shapes: Compare
The learner will be able to make comparisons of two-dimensional shapes.
Strand Scope Source
Two-Dimensional Shapes Master MA: Curriculum Framework, 2000, Grade 2, 2.G.2
  
    Figures: Identify
The learner will be able to identify two dimensional figures.
Strand Scope Source
Two-Dimensional Shapes Master MA: Curriculum Framework, 2000, Grade 2, 2.G.2
  
    Figures: Describe
The learner will be able to describe two-dimensional figures.
Strand Scope Source
Two-Dimensional Shapes Master MA: Curriculum Framework, 2000, Grade 2, 2.G.2
  
    Transformations: Recognize/Enlarged
The learner will be able to recognize a figure that has been enlarged.
Strand Scope Source
Transformations Master MA: Curriculum Framework, 2000, Grade 2, 2.G.4
  
    Transformations: Explain/Direction
The learner will be able to explain the direction of a translation (translation).
Strand Scope Source
Translations Master MA: Curriculum Framework, 2000, Grade 2, 2.G.4
  
    Symmetry: Identify/Plane Figures
The learner will be able to identify symmetry in two dimensional figures.
Strand Scope Source
Symmetry Master MA: Curriculum Framework, 2000, Grade 2, 2.G.5
  
    Connecting: Geometry/Numbers
The learner will be able to associate geometric concepts to numbers.
Strand Scope Source
Connecting Master MA: Curriculum Framework, 2000, Grade 2, 2.G.7
  
    Congruence: Identify
The learner will be able to recognize congruent figures.
Strand Scope Source
Congruence Master MA: Curriculum Framework, 2000, Grade 2, 2.G.3
  
    Combine/Partition: Predict/Subdivide
The learner will be able to make predictions of the results of subdividing figures.
Strand Scope Source
Combine/Partition/Transform Master MA: Curriculum Framework, 2000, Grade 2, 2.G.6
  
    Combine Figures: Predict
The learner will be able to predict the results of combining figures.
Strand Scope Source
Combine/Partition/Transform Master MA: Curriculum Framework, 2000, Grade 2, 2.G.6
  

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.

    Measurement: Estimation
The learner will be able to apply measurement approximations for time, volume, weight and area.
Strand Scope Source
Measurement: Estimation Master MA: Curriculum Framework, 2000, Grade 2, 2.M.6
  
    Measurement Concepts: Comparison
The learner will be able to compare the length, weight, area, and volume of at least two shapes through direct comparisons.
Strand Scope Source
Direct/Indirect Measure Master MA: Curriculum Framework, 2000, Grade 2, 2.M.3
  
    Measurement Concepts: Measure/Compare
The learner will be able to apply metric and English units of length to measure and compare common objects.
Strand Scope Source
Length Master MA: Curriculum Framework, 2000, Grade 2, 2.M.4
  
    Calendar: Recognize/Parts of Day
The learner will be able to recognize parts of the day.
Strand Scope Source
Calendar Master MA: Curriculum Framework, 2000, Grade 2, 2.M.1
  
    Calendar: Months/Days
The learner will be able to identify days of the week and months of the year.
Strand Scope Source
Calendar Master MA: Curriculum Framework, 2000, Grade 2, 2.M.1
  
    Calendar: Dates
The learner will be able to identify specific dates on a given calendar.
Strand Scope Source
Calendar Master MA: Curriculum Framework, 2000, Grade 2, 2.M.1
  
    Time: Tell/Quarter-Hour/Digital/Analog
The learner will be able to tell time in quarter-hour intervals on analog and digital clocks applying A.M. and P.M.
Strand Scope Source
Time Master MA: Curriculum Framework, 2000, Grade 2, 2.M.2
  
    Time: Apply/Estimates
The learner will be able to apply time estimates.
Strand Scope Source
Time Master MA: Curriculum Framework, 2000, Grade 2, 2.M.6
  
    Time: Estimate
The learner will be able to estimate time.
Strand Scope Source
Time Master MA: Curriculum Framework, 2000, Grade 2, 2.M.6
  
    Money: Count
The learner will be able to count the value of coins and bills up to $5.00.
Strand Scope Source
Money Master MA: Curriculum Framework, 2000, Grade 2, 2.N.6
  
    Money: Recognize/Value/U.S. Coins/Bills
The learner will be able to recognize the value of all the U.S. coins and $1, $5, $10, and $20 bills.
Strand Scope Source
Money Master MA: Curriculum Framework, 2000, Grade 2, 2.N.6
  
    Money: Find/Representations/Up to $5
The learner will be able to find the different ways to represent money amounts up to five dollars.
Strand Scope Source
Money Master MA: Curriculum Framework, 2000, Grade 2, 2.N.6
  
    Money: Apply/Notation
The learner will be able to apply suitable notation for monetary amounts.
Strand Scope Source
Money Master MA: Curriculum Framework, 2000, Grade 2, 2.N.6
  
    Area: Estimate
The learner will be able to estimate area.
Strand Scope Source
Area Master MA: Curriculum Framework, 2000, Grade 2, 2.M.6
  
    Area: Apply/Estimates
The learner will be able to apply area estimates.
Strand Scope Source
Area Master MA: Curriculum Framework, 2000, Grade 2, 2.M.6
  
    Weight: Estimate
The learner will be able to estimate weight.
Strand Scope Source
Weight Master MA: Curriculum Framework, 2000, Grade 2, 2.M.6
  
    Weight: Apply/Estimates
The learner will be able to apply weight estimates.
Strand Scope Source
Weight Master MA: Curriculum Framework, 2000, Grade 2, 2.M.6
  
    Volume: Estimate
The learner will be able to estimate volume.
Strand Scope Source
Volume Introduce MA: Curriculum Framework, 2000, Grade 2, 2.M.6
  
    Volume: Apply/Estimates
The learner will be able to apply volume estimates.
Strand Scope Source
Volume Introduce MA: Curriculum Framework, 2000, Grade 2, 2.M.6
  
    Measurement: Estimation
The learner will be able to make measurement estimations.
Strand Scope Source
Measurement: Estimation Master MA: Curriculum Framework, 2000, Grade 2, 2.M.6
  
    Converting: Explain/Functions
The learner will be able to explain conversion functions, including coin and measurement conversions.
Strand Scope Source
Converting Introduce MA: Curriculum Framework, 2000, Grade 2, 2.P.7
  
    Tools: Use/Appropriate
The learner will be able to use suitable measurement instruments.
Strand Scope Source
Tools/Instruments Master MA: Curriculum Framework, 2000, Grade 2, 2.M.5
  
    Tools: Choose/Appropriate
The learner will be able to choose a suitable measurement instrument.
Strand Scope Source
Tools/Instruments Master MA: Curriculum Framework, 2000, Grade 2, 2.M.5
  

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

    Number Sense: Recognize/Distinguish
The learner will be able to recognize and distinguish between the multiple applications of numbers, including cardinal and ordinal, and numbers as labels and as measurements.
Strand Scope Source
Number Sense Master MA: Curriculum Framework, 2000, Grade 2, 2.N.2
  
    Place Value: Less Than 1000
The learner will be able to identify place value in whole numbers up to 1000.
Strand Scope Source
Place Value Master MA: Curriculum Framework, 2000, Grade 2, 2.N.1
  
    Odd: Identify
The learner will be able to identify odd numbers.
Strand Scope Source
Odd/Even Master MA: Curriculum Framework, 2000, Grade 2, 2.N.5
  
    Even: Identify
The learner will be able to identify even numbers.
Strand Scope Source
Odd/Even Master MA: Curriculum Framework, 2000, Grade 2, 2.N.5
  
    Write Numbers: At Most 1000
The learner will be able to write whole numbers to at most 1000 in numeric form.
Strand Scope Source
Write Numbers Master MA: Curriculum Framework, 2000, Grade 2, 2.N.1
  
    Cardinal Numbers: Determine/Odd/Even
The learner will be able to determine whether a set contains an even or odd cardinality.
Strand Scope Source
Cardinal Numbers Master MA: Curriculum Framework, 2000, Grade 2, 2.N.5
  

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

    Patterns: Recognize/Explain/Extend
The learner will be able to recognize, explain, extend, reproduce, and create basic color, rhythmic, shape, number, and letter patterns.
Strand Scope Source
Patterns: Identify/Describe/Continue Master MA: Curriculum Framework, 2000, Grade 2, 2.P.1
  
    Pattern: Recognize/Hundred Chart
The learner will be able to recognize number patterns on a hundred chart.
Strand Scope Source
Patterns: Number Master MA: Curriculum Framework, 2000, Grade 2, 2.P.2
  
    Patterns: Number/Addition/Explain
The learner will be able to explain addition number patterns.
Strand Scope Source
Patterns: Number Master MA: Curriculum Framework, 2000, Grade 2, 2.P.3
  
    Patterns: Number/Subtraction/Explain
The learner will be able to explain subtraction number patterns.
Strand Scope Source
Patterns: Number Master MA: Curriculum Framework, 2000, Grade 2, 2.P.3
  
    Patterns: Number/Addition/Create
The learner will be able to create addition number patterns.
Strand Scope Source
Patterns: Number Master MA: Curriculum Framework, 2000, Grade 2, 2.P.3
  
    Patterns: Number/Subtraction/Create
The learner will be able to create subtraction number patterns.
Strand Scope Source
Patterns: Number Master MA: Curriculum Framework, 2000, Grade 2, 2.P.3
  
    Skip Counting: Twos/Fives/Tens
The learner will be able to skip count by twos, fives, and tens up to at least 50, beginning from any number.
Strand Scope Source
Skip Counting Master MA: Curriculum Framework, 2000, Grade 2, 2.P.4
  
    Estimation: Exact/Approximate/Describe
The learner will be able to describe the difference between exact and estimated values.
Strand Scope Source
Estimation Master MA: Curriculum Framework, 2000, Grade 2, 2.N.12
  

Probability/Statistics
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: Hypothesis
The learner will be able to make inferences and formulate hypotheses based on data.
Strand Scope Source
Data Master MA: Curriculum Framework, 2000, Grade 2, 2.D.3
  
    Data Analysis
The learner will be able to organize, classify, represent, and interpret data through tallies, charts, tables, bar graphs, pictographs, and Venn diagrams, and interpret the various displays.
Strand Scope Source
Data Analysis Master MA: Curriculum Framework, 2000, Grade 2, 2.D.2
  
    Outcomes: Most Likely
The learner will be able to decide which outcomes are most likely to occur in particular situations.
Strand Scope Source
Outcomes Master MA: Curriculum Framework, 2000, Grade 2, 2.D.4
  
    Data Collection: Interviews/Surveys
The learner will be able to gather data about themselves and their environment through interviews, surveys, and observations.
Strand Scope Source
Data Collection Master MA: Curriculum Framework, 2000, Grade 2, 2.D.1
  

Problem Solving
The Problem Solving Unit focuses on the problem solving effort. This unit includes analyzing problems, evaluating solutions, problem exploration, and strategies.

    Problem Solving: Inverse Relationship
The learner will be able to apply the inverse relationship that exists between addition and subtraction to solve problems and/or verify results.
Strand Scope Source
Problem Solving Master MA: Curriculum Framework, 2000, Grade 2, 2.N.8
  

Whole Numbers
The Whole Numbers Unit includes performing operations with whole numbers, using manipulatives to demonstrate whole number concepts, and solving problems with whole numbers in real-world contexts.

    Problem Solving: Add/Subtract/2-Digit
The learner will be able to perform approximations, computations, and obtain solutions to problems involving the addition, subtraction and regrouping of 2-digit numbers.
Strand Scope Source
Problem Solving Master MA: Curriculum Framework, 2000, Grade 2, 2.N.12
  
    Add/Subtract: 3 Digits
The learner will be able to perform the addition and subtraction of two three-digit whole numbers.
Strand Scope Source
Add/Subtract Whole Numbers Master MA: Curriculum Framework, 2000, Grade 2, 2.N.10
  
    Compare: Terminology
The learner will be able to apply the use of comparative terminology when comparing whole numbers.
Strand Scope Source
Compare/Order Master MA: Curriculum Framework, 2000, Grade 2, 2.N.4
  
    Ordering: Up to 1000
The learner will be able to order whole numbers up to 1000.
Strand Scope Source
Compare/Order Master MA: Curriculum Framework, 2000, Grade 2, 2.N.1
  
    Compare: Whole Numbers/Symbols
The learner will be able to apply symbols to compare whole numbers.
Strand Scope Source
Compare/Order Master MA: Curriculum Framework, 2000, Grade 2, 2.N.4
  
    Whole Numbers: Name/Up to 1000
The learner will be able to name whole numbers up to 1,000.
Strand Scope Source
Whole Numbers Master MA: Curriculum Framework, 2000, Grade 2, 2.N.1
  

© 2006 by EAST LONGMEADOW PUBLIC SCHOOLS and Scantron Corporation.  All Rights Reserved. Made with Curriculum Designer by Scantron Corporation.