Mathematics Grade 4

EAST LONGMEADOW PUBLIC SCHOOLS
2006 - 2007 DISTRICT CURRICULUM GUIDES

Mathematics - Grade 4

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 4

The Massachusetts Mathematics Curriculum Framework provides learning standards for students in grades 3-4.

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. The Algebraic Concepts Unit includes Competencies/Objectives which focus on algebraic equations and operations. 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.

Variables: Apply/Symbols/Letters
The learner will be able to apply symbols and letter variables to represent unknowns or values that vary in expressions and in equations or inequalities.

Strand	Scope	Source
Variable	Master	MA: Curriculum Framework, 2000, Grade 4, 4.P.2

Algorithms: Comprehend/Add/Subtract
The learner will be able to comprehend and apply the common algorithms for addition and subtraction (up to five-digit numbers) and multiplication (up to three-digits times two-digits).

Strand	Scope	Source
Algorithms	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.14

Algorithms: Comprehend/Understand/Apply
The learner will be able to comprehend and apply the common algorithms for division up to a three-digit number by a one-digit divisor, with or without remainders.

Strand	Scope	Source
Algorithms	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.15

Equations: Solve/Basic
The learner will be able to determine the value of or obtain the solution for a variable in a basic algebraic equation.

Strand	Scope	Source
Solve Equations	Master	MA: Curriculum Framework, 2000, Grade 4, 4.P.3

Inverse Operations: Multiply/Divide
The learner will be able to comprehend the inverse relationship of multiplication and division.

Strand	Scope	Source
Inverse Operations	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.8

Inverse Operation: Apply/Multiply/Divide
The learner will be able to apply the inverse relationship of multiplication and division.

Strand	Scope	Source
Inverse Operations	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.8

Basic Operations: Choose/Apply
The learner will be able to choose and apply the suitable arithmetic operation to obtain problem solutions, including those involving money.

Strand	Scope	Source
Basic Operations	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.10

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. The Fractions Unit includes Competencies/Objectives which focus on number sense and operations with fractions. Students compare and order fractions, study fraction parts, estimate with fractions, reason using fractions, and problem solve using fractions.

Fractions: Models/Mixed Numbers
The learner will be able to choose, apply, and describe models to associate common fractions and mixed numbers.

Strand	Scope	Source
Fractions	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.4

Add Fractions: Models/Objects
The learner will be able to apply physical objects and visual models to assist in the addition of common fractions.

Strand	Scope	Source
Add Fractions	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.18

Subtract Fractions: Models/Objects
The learner will be able to apply physical objects and visual models to assist in the subtraction of common fractions.

Strand	Scope	Source
Subtract Fractions	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.18

Fraction Parts: Comprehend/Whole
The learner will be able to develop a comprehension of fractions as parts of unit wholes.

Strand	Scope	Source
Fraction Parts	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.3

Fraction Parts: Comprehend/Collection
The learner will be able to develop a comprehension of fractions as parts of a collection.

Strand	Scope	Source
Fraction Parts	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.3

Equivalent Fractions: Find/Mixed Numbers
The learner will be able to find equivalent fractions, mixed numbers, and decimals.

Strand	Scope	Source
Equivalent Fractions	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.4

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. The Geometry Unit includes Competencies/Objectives which focus on exploring geometric concepts from multiple perspectives. Students study properties and construction of figures, proofs and theorems, history of geometry, transformations, logic, and problem solving.

Combine/Partition/Fold: Predict/Confirm
The learner will be able to predict and confirm the results of combining, partitioning, and folding plane and solid figures.

Strand	Scope	Source
Combine/Partition/Transform	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.9

Solids: Describe
The learner will be able to describe three-dimensional solids.

Strand	Scope	Source
Three-Dimensional Solids	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.2

Three-Dimensional Solids: Model
The learner will be able to model three-dimensional solids.

Strand	Scope	Source
Three-Dimensional Solids	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.2

Three-Dimensional Solids: Classify
The learner will be able to classify three-dimensional solids.

Strand	Scope	Source
Three-Dimensional Solids	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.2

Three-Dimensional Solids: Compare
The learner will be able to make comparisons of solids.

Strand	Scope	Source
Three-Dimensional Solids	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.2

Three-Dimensional Solids: Analyze
The learner will be able to analyze the attributes of three-dimensional solids.

Strand	Scope	Source
Three-Dimensional Solids	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.1

Solids: Draw
The learner will be able to draw three-dimensional solids.

Strand	Scope	Source
Three-Dimensional Solids	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.2

Solids: Compare Attributes
The learner will be able to compare characteristics of three-dimensional solids.

Strand	Scope	Source
Three-Dimensional Solids	Master	MA: Curriculum Framework, 2000, Grade 4, 4.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 4, 4.G.2

Two-Dimensional Shapes: Analyze
The learner will be able to analyze the attributes of two-dimensional shapes.

Strand	Scope	Source
Two-Dimensional Shapes	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.1

Angles: Acute/Obtuse/Right
The learner will be able to identify acute, obtuse, and right angles.

Strand	Scope	Source
Acute/Right/Obtuse Angles	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.4

Symmetry: Line/Recognize/2-D
The learner will be able to recognize line symmetry present in two-dimensional figures.

Strand	Scope	Source
Symmetry	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.8

Symmetry: Line/Explain/2-D
The learner will be able to explain line symmetry present in two-dimensional figures.

Strand	Scope	Source
Symmetry	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.8

Similarity: Similar Figure/Using Picture
The learner will be able to identify similar figures.

Strand	Scope	Source
Similarity	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.3

Congruence: Describe/Techniques
The learner will be able to describe techniques to determine if two figures are congruent.

Strand	Scope	Source
Congruence	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.7

Congruence: Apply/Techniques
The learner will be able to apply techniques to determine if two figures are congruent.

Strand	Scope	Source
Congruence	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.7

Parallel Lines: Describe
The learner will be able to describe parallel lines.

Strand	Scope	Source
Lines: Parallel/Perpendicular	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.5

Parallel Lines: Draw
The learner will be able to draw parallel lines.

Strand	Scope	Source
Lines: Parallel/Perpendicular	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.5

Perpendicular Lines: Describe
The learner will be able to describe perpendicular lines.

Strand	Scope	Source
Lines: Parallel/Perpendicular	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.5

Perpendicular Lines: Draw
The learner will be able to draw perpendicular lines.

Strand	Scope	Source
Lines: Parallel/Perpendicular	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.5

Shapes: Compare Attributes
The learner will be able to compare characteristics of two-dimensional figures.

Strand	Scope	Source
Two-Dimensional Shapes	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.1

Shapes: Describe
The learner will be able to describe two-dimensional figures.

Strand	Scope	Source
Two-Dimensional Shapes	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.2

Two-Dimensional Shapes: Classify
The learner will be able to classify two-dimensional shapes.

Strand	Scope	Source
Two-Dimensional Shapes	Master	MA: Curriculum Framework, 2000, Grade 4, 4.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 4, 4.G.2

Two-Dimensional Shapes: Model
The learner will be able to model two-dimensional shapes.

Strand	Scope	Source
Two-Dimensional Shapes	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.2

The Mathematics Processes Unit focuses on mathematical connections, communication, modeling, concepts and procedures. The Mathematics Processes Unit includes Competencies/Objectives which focus on mathematical connections. Students communicate and model concepts and procedures.

Relationships: Interpret/Mathematical
The learner will be able to interpret mathematical relationships by applying pictures, models, tables, charts, graphs, words, number sentences, and mathematical notation.

Strand	Scope	Source
Relationships	Master	MA: Curriculum Framework, 2000, Grade 4, 4.P.4

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

Units: Recognize/Apply/Tools/Units
The learner will be able to recognize and apply suitable metric and English units and tools to approximate, measure, and obtain problem solutions involving length, area, volume, weight, time, temperature, and angle size.

Strand	Scope	Source
Units	Master	MA: Curriculum Framework, 2000, Grade 4, 4.M.5

Units: Understand/Attributes
The learner will be able to understand the attributes of length, area, weight, and volume, and choose the suitable measurement unit for each.

Strand	Scope	Source
Units	Master	MA: Curriculum Framework, 2000, Grade 4, 4.M.1

Perimeter/Area: Approximate/Determine
The learner will be able to approximate and determine the area and perimeter of rectangles, triangles, or irregular shapes by applying diagrams, models, grids, or by measuring.

Strand	Scope	Source
Perimeter/Area/Volume	Master	MA: Curriculum Framework, 2000, Grade 4, 4.M.4

Conversion: Within System
The learner will be able to perform simple conversions of units within a measurement system.

Strand	Scope	Source
Converting	Master	MA: Curriculum Framework, 2000, Grade 4, 4.M.2

Time: Calculate/Elapsed Time/Calendar
The learner will be able to calculate elapsed time using a calendar.

Strand	Scope	Source
Time	Master	MA: Curriculum Framework, 2000, Grade 4, 4.M.3

Time: Calculate/Elapsed Time/Clock
The learner will be able to calculate elapsed time using a clock.

Strand	Scope	Source
Time	Master	MA: Curriculum Framework, 2000, Grade 4, 4.M.3

Time: Recognize/Minute/Digital/Analog
The learner will be able to recognize time to the minute on analog and digital clocks applying A.M. and P.M.

Strand	Scope	Source
Time	Master	MA: Curriculum Framework, 2000, Grade 4, 4.M.3

The Number Theory Unit focuses on manipulating number forms and classifications. Students make connections between number forms and their real-world applications. The Number Theory Unit includes Competencies/Objectives which focus on manipulating number forms and classifications. Students make connections between number forms and their real world applications.

Equivalent Forms: Recognize/Generate
The learner will be able to recognize and generate equivalent representations of common decimals and common fractions less than one.

Strand	Scope	Source
Equivalent Forms	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.5

Number Forms: Identify/Classes
The learner will be able to identify number classes in which a number may belong, recognize the numbers in those classes, and apply them when obtaining problem solutions (classes include odds, evens, factors, multiples, and squares).

Strand	Scope	Source
Number Forms: Relationships	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.7

Number Forms: Representing/Large Numbers
The learner will be able to illustrate, order, and compare large numbers to at least 100,000 using a variety of representations, including expanded notation.

Strand	Scope	Source
Number Forms: Representing	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.2

Number System: Understand/Base Ten
The learner will be able to illustrate an understanding of the base ten number system by reading, naming, and writing decimal numbers between 0 and 1 up to the hundredths place.

Strand	Scope	Source
Number Systems	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.6

Number System: Understand/Base Ten
The learner will be able to illustrate an understanding of the base ten number system by reading, modeling, writing, and interpreting whole numbers up to at least 100,000; understanding the values of the digits, and comparing and ordering the numbers.

Strand	Scope	Source
Number Systems	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.1

Proportions: Solve Problems/Relationship
The learner will be able to obtain solutions to problems that involve proportional relationships.

Strand	Scope	Source
Ratio/Proportion	Master	MA: Curriculum Framework, 2000, Grade 4, 4.P.5

Proportions: Solve Problems/Unit Pricing
The learner will be able to solve proportional relationship problems involving unit pricing.

Strand	Scope	Source
Ratio/Proportion	Master	MA: Curriculum Framework, 2000, Grade 4, 4.P.5

Proportions: Solve Problems/Maps
The learner will be able to solve proportional relationship problems involving map interpretation.

Strand	Scope	Source
Ratio/Proportion	Master	MA: Curriculum Framework, 2000, Grade 4, 4.P.5

The Numeration Unit focuses on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships. The Numeration Unit includes Competencies/Objectives which focus on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships.

Estimation Strategies: Choose/Apply
The learner will be able to choose and apply various strategies in estimating quantities, measurements, and the results of whole number calculations up to three-digit whole numbers and $1000 money amounts.

Strand	Scope	Source
Estimation Strategies	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.17

Number Lines: Fractions/Location
The learner will be able to understand fractions as locations on the number line.

Strand	Scope	Source
Number Lines	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.3

Change: Determine
The learner will be able to determine how change in one unknown associates to a change in a second unknown.

Strand	Scope	Source
Change	Master	MA: Curriculum Framework, 2000, Grade 4, 4.P.6

Rounding: Whole Numbers/Through 100,000
The learner will be able to round whole numbers through 100,000 to the nearest ten, hundred, thousand, ten thousand, and hundred thousand.

Strand	Scope	Source
Rounding	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.16

Patterns: Number/Multiplication
The learner will be able to create, describe, and continue multiplication patterns.

Strand	Scope	Source
Patterns: Number	Master	MA: Curriculum Framework, 2000, Grade 4, 4.P.1

Pattern: Geometric/Create
The learner will be able to create geometric patterns.

Strand	Scope	Source
Patterns: Geometric	Master	MA: Curriculum Framework, 2000, Grade 4, 4.P.1

Pattern: Geometric/Describe
The learner will be able to describe a geometric pattern.

Strand	Scope	Source
Patterns: Geometric	Master	MA: Curriculum Framework, 2000, Grade 4, 4.P.1

Patterns: Geometric/Continue
The learner will be able to continue geometric patterns.

Strand	Scope	Source
Patterns: Geometric	Master	MA: Curriculum Framework, 2000, Grade 4, 4.P.1

Patterns: Number/Create
The learner will be able to create patterns using numbers.

Strand	Scope	Source
Patterns: Number	Master	MA: Curriculum Framework, 2000, Grade 4, 4.P.1

Patterns: Number/Describe
The learner will be able to describe number patterns.

Strand	Scope	Source
Patterns: Number	Master	MA: Curriculum Framework, 2000, Grade 4, 4.P.1

Patterns: Number/Extend
The learner will be able to extend patterns of numbers.

Strand	Scope	Source
Patterns: Number	Master	MA: Curriculum Framework, 2000, Grade 4, 4.P.1

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.). The Probability/Statistics Unit includes Competencies/Objectives which focus on data analysis and probability concepts. Students collect, analyze, and make sense of real world data (including overlapping data, inconclusive data, etc.).

Outcomes: List/Combinations
The learner will be able to list and count the possible combinations made from three sets of objects.

Strand	Scope	Source
Outcomes	Master	MA: Curriculum Framework, 2000, Grade 4, 4.D.5

Data Displays: Create/Predict/Conclusion
The learner will be able to create, predict, and form conclusions from a variety of data set displays, including tables, bar graphs, pictographs, line graphs, line plots, and tallies.

Strand	Scope	Source
Data Display	Master	MA: Curriculum Framework, 2000, Grade 4, 4.D.3

Outcomes: Generate/All Possible
The learner will be able to determine all possible outcomes in basic probability activities.

Strand	Scope	Source
Outcomes	Master	MA: Curriculum Framework, 2000, Grade 4, 4.D.4

Experiments: Design/Perform
The learner will be able to apply physical objects in designing and performing experiments to classify outcomes as certain, likely, unlikely, or impossible.

Strand	Scope	Source
Experiments	Master	MA: Curriculum Framework, 2000, Grade 4, 4.D.6

Data Collection: Organize
The learner will be able to collect and organize data through observations, measurements, surveys, or experiments.

Strand	Scope	Source
Data Collection	Master	MA: Curriculum Framework, 2000, Grade 4, 4.D.1

Data Displays: Match
The learner will be able to match data set displays to the actual data set.

Strand	Scope	Source
Data Display	Master	MA: Curriculum Framework, 2000, Grade 4, 4.D.2

Data Management: Display Data
The learner will be able to identify suitable methods to display different types of data.

Strand	Scope	Source
Data Management	Master	MA: Curriculum Framework, 2000, Grade 4, 4.D.1

The Problem Solving Unit focuses on the problem solving effort. This unit includes analyzing problems, evaluating solutions, problem exploration, and strategies. The Problem Solving Unit includes Competencies/Objectives which focus on analyzing problems, evaluating solutions, exploring problems, and developing strategies for solving problems.

Solution: Reasonableness
The learner will be able to evaluate the reasonableness of a given solution.

Strand	Scope	Source
Solution	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.17

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. The Whole Numbers Unit includes Competencies/Objectives which focus on whole number concepts. Students perform operations with whole numbers, use manipulatives to demonstrate whole number concepts, and solve problems with whole numbers in real world contexts.

Multiply/Divide: Facts/12x12
The learner will be able to comprehend the multiplication facts and related division facts (through 12 X 12), and apply these to solve associated multiplication problems and compute related problems.

Strand	Scope	Source
Multiply/Divide Whole Numbers	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.11

Operations: Whole Numbers/Properties
The learner will be able to choose, apply, and describe the commutative, associative, and identity properties of operations in problem solving scenarios involving whole numbers.

Strand	Scope	Source
Operations	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.9

Addition/Subtraction: Six-Digits
The learner will be able to add and subtract whole numbers with no more than five digits.

Strand	Scope	Source
Add/Subtract Whole Numbers	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.12

Multiply 1-3 Digits by 2 Digits
The learner will be able to multiply a one- to three-digit number by a two-digit number.

Strand	Scope	Source
Multiply Whole Numbers	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.12

Divide 1-3 Digits by 1-Digit
The learner will be able to divide one- to three-digit whole number dividends by one-digit divisors.

Strand	Scope	Source
Divide Whole Numbers	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.13

Division: Interpret/Remainders
The learner will be able to interpret the remainder in whole number division.

Strand	Scope	Source
Divide Whole Numbers	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.13

Multiply/Divide Whole Numbers: Models
The learner will be able to choose, apply, and describe the various meanings and models of multiplying and dividing whole numbers.

Strand	Scope	Source
Multiply/Divide Whole Numbers	Master	MA: Curriculum Framework, 2000, Grade 4, 4.N.8

The Real Numbers and the Coordinate Plane Unit includes Competencies/Objectives which focus on graphing concepts. Students graph equations and make connections between algebraic concepts and their geometric correspondences.

Coordinate Geometry: Points/Paths
The learner will be able to graph, locate, and recognize points, and explain paths in the first quadrant applying ordered pairs of numbers and/or letters.

Strand	Scope	Source
Coordinate Geometry	Master	MA: Curriculum Framework, 2000, Grade 4, 4.G.6