Mathematics Grade 8

EAST LONGMEADOW PUBLIC SCHOOLS
2006 - 2007 DISTRICT CURRICULUM GUIDES

Mathematics - Grade 8

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 8

The Massachusetts Mathematics Curriculum Framework provides learning standards for students in grades 7-8.

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.

Operations: Understand/Apply
The learner will be able to illustrate an understanding of the identity (-x)(-y)=xy, and apply this to simplify algebraic expressions.

Strand	Scope	Source
Operations	Master	MA: Curriculum Framework, 2000, Grade 8, 8.P.3

Variables: Describe/Examine/Change
The learner will be able to apply pictures, charts, graphs, or equations to describe and examine (both quantitatively and qualitatively) how a change in one variable of a functional relationship affects another variable.

Strand	Scope	Source
Variable	Master	MA: Curriculum Framework, 2000, Grade 8, 8.P.8

Equality/Inequality: Linear/Set Up/Solve
The learner will be able to apply algebraic methods, models, and graphs to set up and obtain solutions to linear equations and inequalities with one or two variables.

Strand	Scope	Source
Linear Equations/Inequalities	Master	MA: Curriculum Framework, 2000, Grade 8, 8.P.7

Order of Operations: Integers/Roots
The learner will be able to include positive integer exponents and square roots in the order of operations rules.

Strand	Scope	Source
Order of Operations	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.7

Properties: Rational Numbers
The learner will be able to develop an understanding of the properties of operations with rational numbers.

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

Properties: Use/Complete/Rational
The learner will be able to use associative, commutative, identity, inverse, and distributive properties to complete operations involving rational numbers.

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

Absolute Value: Understand
The learner will be able to understand absolute value.

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

Expressions: Evaluating
The learner will be able to evaluate algebraic expressions that are simple for specific values of the variable.

Strand	Scope	Source
Expressions	Master	MA: Curriculum Framework, 2000, Grade 8, 8.P.2

Expressions: Symbolic/Apply
The learner will be able to apply symbolic expressions.

Strand	Scope	Source
Expressions	Master	MA: Curriculum Framework, 2000, Grade 8, 8.P.4

Expressions: Symbolic/Associate
The learner will be able to associate symbolic expressions to verbal, tabular, and graphical representations.

Strand	Scope	Source
Expressions	Master	MA: Curriculum Framework, 2000, Grade 8, 8.P.4

Expressions: Symbolic/Create
The learner will be able to create symbolic expressions.

Strand	Scope	Source
Expressions	Master	MA: Curriculum Framework, 2000, Grade 8, 8.P.4

Radicals: Apply/Rules/Problem Solve
The learner will be able to obtain solutions to problems through the use of the rules of radicals.

Strand	Scope	Source
Radicals	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.7

Exponents: Apply/Rules/Problem Solve
The learner will be able to obtain solutions to problems through the use of the rules of exponents.

Strand	Scope	Source
Exponents	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.7

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 8, 8.N.9

Inverse Operations: Apply/Multiply
The learner will be able to apply the inverse relationship between multiplication and division to simplify computation and obtain problem solutions.

Strand	Scope	Source
Inverse Operations	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.9

Inverse Operations: Apply/Square/Root
The learner will be able to apply the inverse relationship between squaring and taking the square root to simplify computation and obtain problem solutions.

Strand	Scope	Source
Inverse Operations	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.9

Rates: Apply/Models/Solve Problems
The learner will be able to apply models to obtain solutions to basic rate problems.

Strand	Scope	Source
Rates	Master	MA: Curriculum Framework, 2000, Grade 8, 8.M.5

Rates: Apply/Graphs/Solve Problems
The learner will be able to apply graphs to obtain solutions to basic rate problems.

Strand	Scope	Source
Rates	Master	MA: Curriculum Framework, 2000, Grade 8, 8.M.5

Rates: Apply/Formulas/Solve Problems
The learner will be able to apply formulas to obtain solutions to basic rate problems.

Strand	Scope	Source
Rates	Master	MA: Curriculum Framework, 2000, Grade 8, 8.M.5

Variables: Recognize/Role/Equation
The learner will be able to recognize a variable's role in an equation.

Strand	Scope	Source
Variable	Master	MA: Curriculum Framework, 2000, Grade 8, 8.P.6

Computation: Fractions
The learner will be able to perform computations with fractions.

Strand	Scope	Source
Computation	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.10

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.

Computing: Decimals
The learner will be able to perform computations with decimal numbers.

Strand	Scope	Source
Computing	Master	MA: Curriculum Framework, 2000, Grade 8, 8.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: 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 8, 8.N.10

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.

Polygons: Relationship/Sides/Angle Sum
The learner will be able to examine, apply, and describe the relationship between the number of sides and the sums of the interior and exterior angles of a polygon.

Strand	Scope	Source
Polygons	Master	MA: Curriculum Framework, 2000, Grade 8, 8.G.1

Figures: Identify/3D/2D Drawings
The learner will be able to identify the three-dimensional figure illustrated by a two-dimensional drawing.

Strand	Scope	Source
Figures: Identify	Master	MA: Curriculum Framework, 2000, Grade 8, 8.G.8

Representations: Represent 3-D as 2-D
The learner will be able to represent a three-dimensional solid as a two-dimensional drawing.

Strand	Scope	Source
Figures: Representations	Master	MA: Curriculum Framework, 2000, Grade 8, 8.G.8

Three-Dimensional Solids: Recognize
The learner will be able to recognize three-dimensional figures by their physical appearance.

Strand	Scope	Source
Three-Dimensional Solids	Master	MA: Curriculum Framework, 2000, Grade 8, 8.G.7

Three-Dimensional Solids: Recognize
The learner will be able to recognize three-dimensional figures by their distinguishing attributes.

Strand	Scope	Source
Three-Dimensional Solids	Master	MA: Curriculum Framework, 2000, Grade 8, 8.G.7

Three-Dimensional Solids: Recognize
The learner will be able to recognize three-dimensional figures by their spatial relationships.

Strand	Scope	Source
Three-Dimensional Solids	Master	MA: Curriculum Framework, 2000, Grade 8, 8.G.7

Congruence/Similarity: Classification
The learner will be able to classify figures by congruence and/or similarity.

Strand	Scope	Source
Congruence/Similarity/Symmetry	Master	MA: Curriculum Framework, 2000, Grade 8, 8.G.2

Congruence/Similarity: Problem Solve
The learner will be able to apply the relationships of congruence and similarity to obtain problem solutions.

Strand	Scope	Source
Congruence/Similarity/Symmetry	Master	MA: Curriculum Framework, 2000, Grade 8, 8.G.2

Angles: Comprehend/Relationships
The learner will be able to comprehend the relationships between the angles formed by intersecting lines.

Strand	Scope	Source
Angle Relationships	Master	MA: Curriculum Framework, 2000, Grade 8, 8.G.3

Angles: Comprehend/Relationships
The learner will be able to comprehend the relationships between the angles formed by parallel lines cut by a transversal.

Strand	Scope	Source
Angle Relationships	Master	MA: Curriculum Framework, 2000, Grade 8, 8.G.3

Pythagorean Theorem: Understanding
The learner will be able to have knowledge and/or comprehension of the Pythagorean Theorem.

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

Pythagorean Theorem: Problem Solving
The learner will be able to solve problems using the Pythagorean Theorem.

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

Transformation: Draw
The learner will be able to draw the figure that results from a transformation.

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

Transformations: Predict/On a Plane
The learner will be able to predict the results of a transformation performed on unmarked or coordinate planes.

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

Constructions: Draw/Figures
The learner will be able to apply a straight edge, compass, or other tools to draw geometric figures.

Strand	Scope	Source
Constructions	Master	MA: Curriculum Framework, 2000, Grade 8, 8.G.5

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.

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.

Conjectures: Apply/Tools/Create/Test
The learner will be able to apply a straight edge, compass, or other tools to create and test conjectures.

Strand	Scope	Source
Conjecture/Argument	Master	MA: Curriculum Framework, 2000, Grade 8, 8.G.5

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: Choose/Convert/Apply/Scale
The learner will be able to choose, convert (within same system) and apply a suitable scale.

Strand	Scope	Source
Units	Master	MA: Curriculum Framework, 2000, Grade 8, 8.M.1

Measurement Concepts
The learner will be able to comprehend the concepts and apply formulas and techniques for finding measurements, including the area and perimeter/circumference of parallelograms, trapezoids, and circles.

Strand	Scope	Source
Measurement Concepts	Master	MA: Curriculum Framework, 2000, Grade 8, 8.M.3

Units: Choose Appropriate
The learner will be able to choose suitable units of measure.

Strand	Scope	Source
Units	Master	MA: Curriculum Framework, 2000, Grade 8, 8.M.1

Units: Apply/Appropriate
The learner will be able to apply suitable units of measurement.

Strand	Scope	Source
Units	Master	MA: Curriculum Framework, 2000, Grade 8, 8.M.1

Formula: Volume/Cylinders
The learner will be able to apply the formula for the volume of a cylinder.

Strand	Scope	Source
Formulas	Master	MA: Curriculum Framework, 2000, Grade 8, 8.M.3

Formula: Surface Area/Rectangular Prism
The learner will be able to use a formula to determine the surface area of a rectangular prism.

Strand	Scope	Source
Formulas	Master	MA: Curriculum Framework, 2000, Grade 8, 8.M.3

Formula: Volume/Rectangular Prism
The learner will be able to use a formula to determine the volume of a rectangular prism.

Strand	Scope	Source
Formulas	Master	MA: Curriculum Framework, 2000, Grade 8, 8.M.3

Formulas: Surface Area/Cylinder
The learner will be able to use a formula to determine the surface area of a cylinder.

Strand	Scope	Source
Formulas	Master	MA: Curriculum Framework, 2000, Grade 8, 8.M.3

Formulas: Surface Area/Sphere
The learner will be able to use a formula to determine the surface area of a sphere.

Strand	Scope	Source
Formulas	Master	MA: Curriculum Framework, 2000, Grade 8, 8.M.3

Formulas: Volume/Sphere
The learner will be able to use a formula to determine the volume of a sphere.

Strand	Scope	Source
Formulas	Master	MA: Curriculum Framework, 2000, Grade 8, 8.M.3

Conversion: Within System
The learner will be able to convert measurements within a system.

Strand	Scope	Source
Converting	Master	MA: Curriculum Framework, 2000, Grade 8, 8.M.1

Conversion: Different Systems/Formula
The learner will be able to convert from one system of measurement to a different system when presented with the formulas.

Strand	Scope	Source
Converting	Master	MA: Curriculum Framework, 2000, Grade 8, 8.M.2

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.

Ratio/Proportion: Solve Problems
The learner will be able to obtain solutions to problem involving similar plane figures and indirect measurement by applying ratios, proportions, and scale factors.

Strand	Scope	Source
Ratio/Proportion	Master	MA: Curriculum Framework, 2000, Grade 8, 8.M.4

Write Numbers: Scientific Notation
The learner will be able to write numbers in scientific notation.

Strand	Scope	Source
Write Numbers	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.4

Proportions: Model/Linear Equations
The learner will be able to model problems involving proportional relationships through linear equations.

Strand	Scope	Source
Ratio/Proportion	Master	MA: Curriculum Framework, 2000, Grade 8, 8.P.9

Ratio/Proportion: Apply/Rates
The learner will be able to apply ratio and proportion to obtain solutions to problems involving unit rates.

Strand	Scope	Source
Ratio/Proportion	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.3

Ratio/Proportion: Apply/Problem Solve
The learner will be able to apply ratio and proportion to obtain solutions to problems involving scale factors.

Strand	Scope	Source
Ratio/Proportion	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.3, 8.M.4

Ratio/Proportion: Apply/Rate of Change
The learner will be able to apply ratio and proportion to obtain solutions to problems involving rate of change.

Strand	Scope	Source
Ratio/Proportion	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.3

Proportions: Examine/Linear Equations
The learner will be able to examine problems involving proportional relationships through linear equations.

Strand	Scope	Source
Ratio/Proportion	Master	MA: Curriculum Framework, 2000, Grade 8, 8.P.9

Ratio/Proportion: Problem Solving
The learner will be able to obtain problem solutions through the use of ratios and/or proportions.

Strand	Scope	Source
Ratio/Proportion	Master	MA: Curriculum Framework, 2000, Grade 8, 8.M.4

Primes: Solve/Problems
The learner will be able to use relatively prime numbers to obtain problem solutions.

Strand	Scope	Source
Prime/Composite Numbers	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.5

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

Strand	Scope	Source
Factors	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.5

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 8, 8.N.5

Scientific Notation: Operations
The learner will be able to perform computations with numbers in scientific notation.

Strand	Scope	Source
Scientific Notation	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.4

Scientific Notation: Problem Solving
The learner will be able to find solutions to problems that involve scientific notation.

Strand	Scope	Source
Scientific Notation	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.4

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.

Patterns: Continue/Represent/Examine
The learner will be able to continue, represent, examine, and generalize several different patterns (including arithmetic and geometric progressions) using tables, graphs, words, and symbols (when possible).

Strand	Scope	Source
Patterns	Master	MA: Curriculum Framework, 2000, Grade 8, 8.P.1

Estimation: Exact/Suitable
The learner will be able to determine whether exact values or estimations are suitable.

Strand	Scope	Source
Estimation	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.11

Compare/Order: Estimate/Translate
The learner will be able to compare, order, estimate, and translate between integers, fractions and mixed numbers, decimals, and percents.

Strand	Scope	Source
Comparing/Ordering	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.1

Estimation: Apply/Problem Solving
The learner will be able to apply estimation in problem solving.

Strand	Scope	Source
Estimate/Problems	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.11

The Percent Unit focuses on the concept of percent. This unit includes performing operations with percents, converting percents to other number forms, using manipulatives to demonstrate percents, and solving problems with percents in real-world contexts. The Percent Unit includes Competencies/Objectives which focus on the concepts of percent. Students perform operations with percents, convert percents to other number forms, use manipulatives to demonstrate percents, and solve problems with percents in real world contexts.

Estimation: Percents
The learner will be able to estimate with percentages that are less than 1 and greater than 100.

Strand	Scope	Source
Reasoning/Estimation	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.10

Percent: Computation
The learner will be able to perform computations with percents.

Strand	Scope	Source
Calculate Percentages	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.10

Percents: Compute
The learner will be able to compute with percentages that are less than 1 and greater than 100.

Strand	Scope	Source
Calculate Percentages	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.10

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.).

Probability: Calculate/Basic/Compound
The learner will be able to calculate probabilities for basic compound events using tree diagrams, tables, organized lists, the fundamental counting principle, and area models.

Strand	Scope	Source
Probability	Master	MA: Curriculum Framework, 2000, Grade 8, 8.D.4

Data Displays: Graphical/Variety
The learner will be able to choose, construct, interpret, and apply several different tabular data displays.

Strand	Scope	Source
Data Display	Master	MA: Curriculum Framework, 2000, Grade 8, 8.D.2

Data Displays: Tabular/Variety
The learner will be able to choose, construct, interpret, and apply several different graphical data displays.

Strand	Scope	Source
Data Display	Master	MA: Curriculum Framework, 2000, Grade 8, 8.D.2

Data: Determine/Spread
The learner will be able to determine the spread of a group of data.

Strand	Scope	Source
Data	Master	MA: Curriculum Framework, 2000, Grade 8, 8.D.3

Data: Interpret/Spread
The learner will be able to interpret the spread of a group of data.

Strand	Scope	Source
Data	Master	MA: Curriculum Framework, 2000, Grade 8, 8.D.3

Measures of Central Tendency: Explain
The learner will be able to explain the measures of central tendency for a data set.

Strand	Scope	Source
Measures of Central Tendency	Master	MA: Curriculum Framework, 2000, Grade 8, 8.D.3

Measure of Central Tendency: Interpret
The learner will be able to interpret a group of data using the suitable measure of central tendency.

Strand	Scope	Source
Measures of Central Tendency	Master	MA: Curriculum Framework, 2000, Grade 8, 8.D.3

Central Tendency: Determine
The learner will be able to determine measures of central tendency.

Strand	Scope	Source
Measures of Central Tendency	Master	MA: Curriculum Framework, 2000, Grade 8, 8.D.3

Measures of Central Tendency: Compare
The learner will be able to compare different data sets by applying the measures of central tendency and spread.

Strand	Scope	Source
Measures of Central Tendency	Master	MA: Curriculum Framework, 2000, Grade 8, 8.D.3

Sampling: Recognize/Methods
The learner will be able to recognize various types of sampling methods.

Strand	Scope	Source
Sampling	Master	MA: Curriculum Framework, 2000, Grade 8, 8.D.1

Samples: Characteristics/Limitations
The learner will be able to explain the attributes and limitations of samples.

Strand	Scope	Source
Sampling	Master	MA: Curriculum Framework, 2000, Grade 8, 8.D.1

Discrete/Continuous Data: Distinguish
The learner will be able to distinguish between continuous and discrete data.

Strand	Scope	Source
Discrete/Continuous Data	Master	MA: Curriculum Framework, 2000, Grade 8, 8.D.2

Discrete/Continuous Data: Displays
The learner will be able to distinguish between the ways to display discrete and continuous data sets.

Strand	Scope	Source
Discrete/Continuous Data	Master	MA: Curriculum Framework, 2000, Grade 8, 8.D.2

The Rational and Irrational Numbers Unit includes manipulating, comparing, and performing operations with rational numbers. The Rational and Irrational Numbers Unit includes Competencies/Objectives which focus on number concepts. Students manipulate, compare, and perform operations with rational and irrational numbers.

Rational Numbers: Choose/Apply/Operation
The learner will be able to choose and apply the appropriate operations (addition, subtraction, multiplication, division, and positive integer exponents) to obtain solutions to problems involving rational numbers.

Strand	Scope	Source
Rational Numbers	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.12

Irrational Numbers: Define
The learner will be able to define irrational numbers.

Strand	Scope	Source
Irrational Numbers	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.2

Irrational Numbers: Use
The learner will be able to make use of irrational numbers.

Strand	Scope	Source
Irrational Numbers	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.2

Irrational Numbers: Compare
The learner will be able to compare irrational numbers.

Strand	Scope	Source
Irrational Numbers	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.2

Irrational Numbers: Order
The learner will be able to order irrational numbers in the correct sequence.

Strand	Scope	Source
Irrational Numbers	Master	MA: Curriculum Framework, 2000, Grade 8, 8.N.2

Rational Numbers: Apply/Closure
The learner will be able to apply the closure property on a subset of the rational numbers under an operation.

Strand	Scope	Source
Rational Numbers	Introduce	MA: Curriculum Framework, 2000, Grade 8, 8.N.8

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.

Slope: Recognize/Steepness/Rate Change
The learner will be able to recognize the slope of a line as a steepness measure and as a constant rate of change from its equation, graph, or tabular values.

Strand	Scope	Source
Slope	Master	MA: Curriculum Framework, 2000, Grade 8, 8.P.5

Linear Equation: Represent/Compare
The learner will be able to apply tables and graphs to represent and compare patterns of linear growth.

Strand	Scope	Source
Linear Equations	Master	MA: Curriculum Framework, 2000, Grade 8, 8.P.10