Mathematics Grade 6

EAST LONGMEADOW PUBLIC SCHOOLS
2006 - 2007 DISTRICT CURRICULUM GUIDES

Mathematics - Grade 6

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 6

The Massachusetts Mathematics Curriculum Framework provides learning standards for students in grades 5-6.

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.

Expressions: Evaluate/Symbolic/Algebraic
The learner will be able to evaluate a symbolic algebraic expression for a particular value of the variable involved and simplify expressions.

Strand	Scope	Source
Expressions	Master	MA: Curriculum Framework, 2000, Grade 6, 6.P.2

Operations: Choose/Apply/Suitable
The learner will be able to choose and apply suitable operations to obtain problem solutions involving addition, subtraction, division, multiplication, and positive integer powers with whole numbers, positive fractions, mixed numbers, decimals, and percents.

Strand	Scope	Source
Operations	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.9

Algebraic Concepts: Constant Rate
The learner will be able to recognize and explain the relationships that exist between two variables exhibiting a constant rate of change, and compare this relationship with a varying rate of change.

Strand	Scope	Source
Algebraic Concepts	Master	MA: Curriculum Framework, 2000, Grade 6, 6.P.7

Variables: Create/Interpret/Graphs
The learner will be able to create and interpret graphs that illustrate the relationship between two variables in common situations.

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

Order of Operations: Apply/Expressions
The learner will be able to apply the order of operations in expressions involving addition, subtraction, multiplication, and division with grouping symbols.

Strand	Scope	Source
Order of Operations	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.11

Linear Equations: Solve/Physical Models
The learner will be able to apply physical models to obtain solutions to linear equations.

Strand	Scope	Source
Linear Equations	Master	MA: Curriculum Framework, 2000, Grade 6, 6.P.5

Linear Equations: Solve/Tables
The learner will be able to apply tables to obtain solutions to linear equations.

Strand	Scope	Source
Linear Equations	Master	MA: Curriculum Framework, 2000, Grade 6, 6.P.5

Linear Equations: Solve/Graphs
The learner will be able to apply graphs to obtain solutions to linear equations.

Strand	Scope	Source
Linear Equations	Master	MA: Curriculum Framework, 2000, Grade 6, 6.P.5

Linear Equations: Solve/Paper-Pencil
The learner will be able to apply paper and pencil methods to obtain solutions to linear equations.

Strand	Scope	Source
Linear Equations	Master	MA: Curriculum Framework, 2000, Grade 6, 6.P.5

Exponents: Understand/Positive
The learner will be able to illustrate an understanding of positive integer exponents with base 10.

Strand	Scope	Source
Exponents	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.1

Exponents: Comprehension
The learner will be able to illustrate a comprehension of positive integer exponents.

Strand	Scope	Source
Exponents	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.1

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 6, 6.N.12

Inverse Operations: Apply/Add/Subtract
The learner will be able to apply the inverse relationship between addition and subtraction to simplify computation and obtain problem solutions.

Strand	Scope	Source
Inverse Operations	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.12

Equality: Apply/Properties/Solve
The learner will be able to obtain problem solutions by applying the properties of equality.

Strand	Scope	Source
Equations	Master	MA: Curriculum Framework, 2000, Grade 6, 6.P.3

Computation: Estimate/Results
The learner will be able to estimate the results of calculations with whole numbers, and with positive fractions, mixed numbers, decimals, and percents.

Strand	Scope	Source
Computation	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.16

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. The Data Interpretation Unit includes Competencies/Objectives which focus on the study and use of graphical forms. Students collect and classify data, organize and display data, use logical reasoning, and problem solving.

Circle Graphs: Interpret
The learner will be able to interpret data shown in a circle graph.

Strand	Scope	Source
Circle Graphs	Master	MA: Curriculum Framework, 2000, Grade 6, 6.D.2

Graphs: Construct/Circle Graphs
The learner will be able to construct circle graphs to illustrate data.

Strand	Scope	Source
Circle Graphs	Master	MA: Curriculum Framework, 2000, Grade 6, 6.D.2

Graphs: Interpret/Line Plots
The learner will be able to interpret information which is presented in a line plot.

Strand	Scope	Source
Analyzing/Evaluating Graphical Forms	Master	MA: Curriculum Framework, 2000, Grade 6, 6.D.2

Stem-and-Leaf Plots: Interpret
The learner will be able to interpret data shown in a stem-and-leaf graph.

Strand	Scope	Source
Stem-and-Leaf/Box-and-Whisker Plots	Master	MA: Curriculum Framework, 2000, Grade 6, 6.D.2

Stem-and-Leaf Plots: Create
The learner will be able to create stem-and-leaf plots.

Strand	Scope	Source
Stem-and-Leaf/Box-and-Whisker Plots	Master	MA: Curriculum Framework, 2000, Grade 6, 6.D.2

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. The Decimals Unit includes Competencies/Objectives which focus on number sense and operations with decimals. Students compare and compute decimals, study money, estimate decimals, problem solve using decimals, and reason using decimals.

Addition/Subtraction Decimals
The learner will be able to add and subtract decimal amounts.

Strand	Scope	Source
Add/Subtract Decimals	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.13

Divide Decimals: By 2-Digit Numbers
The learner will be able to divide decimals by two-digit numbers.

Strand	Scope	Source
Divide Decimals	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.13

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.

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 6, 6.N.4

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 6, 6.N.4

Fraction Parts: Comprehend/Whole Number
The learner will be able to develop a comprehension of fractions as a ratio of whole numbers.

Strand	Scope	Source
Fraction Parts	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.4

Fractions: Lowest Terms
The learner will be able to reduce a given fraction to its lowest terms.

Strand	Scope	Source
Fractions	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.14

Fractions: Apply/Arithmetic Operations
The learner will be able to apply the four arithmetic operations on positive fractions and mixed numbers.

Strand	Scope	Source
Fractions	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.14

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.

Circles: Describe/Relationships
The learner will be able to describe the relationships between the radius, diameter, circumference, and area of a circle and apply these ideas to obtain problem solutions.

Strand	Scope	Source
Circles	Master	MA: Curriculum Framework, 2000, Grade 6, 6.M.5

Congruence: Determine
The learner will be able to determine if two geometric shapes are congruent by measuring sides, measuring a combination of sides and angles, applying transformations or a series of transformations.

Strand	Scope	Source
Congruence	Master	MA: Curriculum Framework, 2000, Grade 6, 6.G.8

Shapes: Quadrilateral
The learner will be able to identify quadrilateral shapes.

Strand	Scope	Source
Quadrilaterals	Master	MA: Curriculum Framework, 2000, Grade 6, 6.M.2

Angles: Classify
The learner will be able to classify angles according to angle measure.

Strand	Scope	Source
Angles	Master	MA: Curriculum Framework, 2000, Grade 6, 6.M.2

Transformations: Explain/2-D
The learner will be able to explain transformations of two-dimensional figures.

Strand	Scope	Source
Transformations	Master	MA: Curriculum Framework, 2000, Grade 6, 6.G.6

Transformation: 2-D
The learner will be able to perform transformations on two-dimensional figures.

Strand	Scope	Source
Transformations	Master	MA: Curriculum Framework, 2000, Grade 6, 6.G.6

Transformations: Predict/2-D
The learner will be able to predict transformations of two-dimensional figures.

Strand	Scope	Source
Transformations	Master	MA: Curriculum Framework, 2000, Grade 6, 6.G.6

Point/Line/Plane: Identify/Relationship
The learner will be able to recognize relationships between and among points, lines, and planes.

Strand	Scope	Source
Planes/Points/Lines	Master	MA: Curriculum Framework, 2000, Grade 6, 6.G.3

Symmetries: Line/Rotational
The learner will be able to recognize line and/or rotational symmetry.

Strand	Scope	Source
Symmetry	Master	MA: Curriculum Framework, 2000, Grade 6, 6.G.7

Quadrilaterals: Describe
The learner will be able to describe quadrilaterals.

Strand	Scope	Source
Quadrilaterals	Master	MA: Curriculum Framework, 2000, Grade 6, 6.M.2

Quadrilaterals: Classify
The learner will be able to make classifications of quadrilaterals.

Strand	Scope	Source
Quadrilaterals	Master	MA: Curriculum Framework, 2000, Grade 6, 6.M.2

Quadrilaterals: Construct
The learner will be able to construct quadrilaterals.

Strand	Scope	Source
Quadrilaterals	Master	MA: Curriculum Framework, 2000, Grade 6, 6.M.2

Polygons: Recognize/Properties
The learner will be able to recognize polygons based on their properties, including types of interior angles, perpendicular or parallel sides, and congruence of sides.

Strand	Scope	Source
Polygons	Master	MA: Curriculum Framework, 2000, Grade 6, 6.G.1

Polygons: Determine/Angle Sum
The learner will be able to determine the angle sum in simple polygons (up to eight sides) with and without measuring the angles.

Strand	Scope	Source
Polygons	Master	MA: Curriculum Framework, 2000, Grade 6, 6.M.7

Three-Dimensional Solids: Recognize
The learner will be able to recognize solids based on their properties.

Strand	Scope	Source
Three-Dimensional Solids	Master	MA: Curriculum Framework, 2000, Grade 6, 6.G.2

Solids: Representation/Two-Dimension
The learner will be able to match various two-dimensional illustrations of three-dimensional objects.

Strand	Scope	Source
Three-Dimensional Solids	Master	MA: Curriculum Framework, 2000, Grade 6, 6.G.9

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. The Integers Unit includes Competencies/Objectives which focus on number sense and operations with integers. Students compare integers, perform operations with integers, convert integers to other number forms, use manipulatives to demonstrate integers, and solve problems with integers in real world contexts.

Subtract Integers: Except Negative
The learner will be able to subtract integers, except for subtracting negative integers.

Strand	Scope	Source
Subtract Integers	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.15

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: Illustrate
The learner will be able to illustrate real world scenarios or mathematical relationships through the use physical models, tables, graphs, and rules in words and with symbols.

Strand	Scope	Source
Relationships	Master	MA: Curriculum Framework, 2000, Grade 6, 6.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: Problem Solve
The learner will be able to obtain solutions to problems involving units of measure.

Strand	Scope	Source
Units	Master	MA: Curriculum Framework, 2000, Grade 6, 6.M.3

Perimeter: Apply/Concepts/Solve Problems
The learner will be able to apply perimeter concepts to obtain problem solutions.

Strand	Scope	Source
Perimeter	Master	MA: Curriculum Framework, 2000, Grade 6, 6.M.1

Area of a Parallelogram
The learner will be able to calculate the area of a parallelogram.

Strand	Scope	Source
Area	Master	MA: Curriculum Framework, 2000, Grade 6, 6.M.4

Area: Different Shape/Same Area
The learner will be able to recognize that figures with the same number of sides, but different shape may possess the same area.

Strand	Scope	Source
Area	Master	MA: Curriculum Framework, 2000, Grade 6, 6.M.4

Area: Apply/Concepts/Solve Problems
The learner will be able to apply area concepts to obtain problem solutions.

Strand	Scope	Source
Area	Master	MA: Curriculum Framework, 2000, Grade 6, 6.M.1

Area: Create/Methods/Complex Figures
The learner will be able to create methods to determine the areas of more complex figures.

Strand	Scope	Source
Area	Master	MA: Curriculum Framework, 2000, Grade 6, 6.M.4

Area/Volume: Prisms
The learner will be able to determine the surface area and volume of rectangular prisms.

Strand	Scope	Source
Perimeter/Area/Volume	Master	MA: Curriculum Framework, 2000, Grade 6, 6.M.6

Area of a Triangle: Determine
The learner will be able to find the area of a triangle.

Strand	Scope	Source
Area of a Triangle	Master	MA: Curriculum Framework, 2000, Grade 6, 6.M.4

Formulas: Apply/Appropriate
The learner will be able to apply formulas where appropriate.

Strand	Scope	Source
Formulas	Master	MA: Curriculum Framework, 2000, Grade 6, 6.M.1

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.

Place Value: Understand/Thousandths
The learner will be able to understand place value through the thousandths.

Strand	Scope	Source
Place Value	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.2

Equivalent Forms: Recognize/Common
The learner will be able to recognize common equivalent fractions, mixed numbers, decimals, and percents.

Strand	Scope	Source
Equivalent Forms	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.5

Equivalent Forms: Find/Common
The learner will be able to find common equivalent fractions, mixed numbers, decimals, and percents.

Strand	Scope	Source
Equivalent Forms	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.5

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 6, 6.M.3

Primes/Composites: Application
The learner will be able to apply primes and composites in problem solving situations.

Strand	Scope	Source
Prime/Composite Numbers	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.8

Multiples: LCM
The learner will be able to determine the least common multiple within the context of solving problems.

Strand	Scope	Source
Multiples	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.8

Factors: GCF
The learner will be able to determine the greatest common factor within the context of solving problems.

Strand	Scope	Source
Factors	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.8

Factorization: Prime
The learner will be able to use prime factorization to solve problems.

Strand	Scope	Source
Factors	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.8

Divisibility: Apply/Rules/Problem Solve
The learner will be able to apply the divisibility rules for 2, 3, 4, 5, 6, 9, and 10 to obtain problem solutions.

Strand	Scope	Source
Divisibility	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.8

Number Theory: Problem Solving
The learner will be able to use number theory concepts to solve problems.

Strand	Scope	Source
Number Theory	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.8

Place Value: Understand/Billions
The learner will be able to understand place value through the billions.

Strand	Scope	Source
Place Value	Reinforce	MA: Curriculum Framework, 2000, Grade 6, 6.N.2

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.

Number Lines: Locate/Position
The learner will be able to use a number line to locate and position integers, fractions, mixed numbers, and decimals (negative and positive).

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

Compare/Order
The learner will be able to compare and order integers, positive fractions, mixed numbers, decimals, and percents.

Strand	Scope	Source
Comparing/Ordering	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.7

Patterns: Determine/Analyze/Rules
The learner will be able to determine and analyze the rules that extend symbolic, arithmetic, and geometric patterns and progressions.

Strand	Scope	Source
Patterns: Determining Rules	Master	MA: Curriculum Framework, 2000, Grade 6, 6.P.1

Estimation: Explain/Reasonableness
The learner will be able to explain the reasonableness of approximations.

Strand	Scope	Source
Estimation	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.16

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 6, 6.N.4

Number Lines: Model/Addition/Subtraction
The learner will be able to apply the number line to model the addition and subtraction of integers (not including the subtraction of negative integers).

Strand	Scope	Source
Number Lines	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.10

Compare: Represent/Large/Small/Numbers
The learner will be able to illustrate and compare very large (billions) and very small (thousandths) positive numbers in a variety of forms.

Strand	Scope	Source
Comparison	Master	MA: Curriculum Framework, 2000, Grade 6, 6.N.3

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.).

Mean/Median/Mode/Range: Apply
The learner will be able to apply the concepts of mean, median, mode, range, maximum, and minimum to explain and compare sets of data.

Strand	Scope	Source
Average/Median/Mode/Range	Master	MA: Curriculum Framework, 2000, Grade 6, 6.D.1

Probability: Apply/Ratios/Likelihood
The learner will be able to apply suitable ratios between zero and one to represent the probability of an outcome and relate the probability with the likelihood of events.

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

Counting Methods: Tree Diagrams/Others
The learner will be able to represent possible outcomes or actual outcomes of an event through the use of tree diagrams and other models.

Strand	Scope	Source
Counting Methods	Master	MA: Curriculum Framework, 2000, Grade 6, 6.D.3

Experiments: Conduct/Predictions
The learner will be able to carry out an experiment to test predictions.

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

Experiments: Elementary/Predict
The learner will be able to formulate predictions about the probability of outcomes for elementary experiments.

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

The Real Numbers and the Coordinate Plane Unit includes graphing equations, and making connections between algebraic concepts and their geometric correspondences. 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 Plane: Recognize/Points
The learner will be able to recognize coordinates of points on all four quadrants of the Cartesian coordinate plane.

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

Coordinate Plane: Plot/Points
The learner will be able to plot points on all four quadrants of the Cartesian coordinate plane.

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

Distance: Number Line
The learner will be able to determine the distance between two points on a number line.

Strand	Scope	Source
Distance Formula	Master	MA: Curriculum Framework, 2000, Grade 6, 6.G.5

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.