Chalkboard
Index
 

Mission Statement
Introduction
Credits


© 2006 by EAST LONGMEADOW PUBLIC SCHOOLS and Scantron Corporation.
All Rights Reserved.

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EAST LONGMEADOW PUBLIC SCHOOLS
2006 - 2007 DISTRICT CURRICULUM GUIDES
Mathematics - Grade 8

Algebraic Concepts

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
  
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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
  
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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
  
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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
  
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Integers: Compute
The learner will be able to perform computations with integers.
Strand Scope Source
Integers Master MA: Curriculum Framework, 2000, Grade 8, 8.N.10
  
Integer: Estimate
The learner will be able to estimate with integers.
Strand Scope Source
Integers Master MA: Curriculum Framework, 2000, Grade 8, 8.N.10
  
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Mathematics Processes

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
  
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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
  
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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
  
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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
  
Estimation: Percents
The learner will be able to estimate percentage amounts.
Strand Scope Source
Estimation Master MA: Curriculum Framework, 2000, Grade 8, 8.N.10
  
Estimation: Decimals
The learner will be able to estimate decimal numbers.
Strand Scope Source
Estimation Master MA: Curriculum Framework, 2000, Grade 8, 8.N.10
  
Estimation: Fractions
The learner will be able to estimate using fractions.
Strand Scope Source
Estimation Master MA: Curriculum Framework, 2000, Grade 8, 8.N.10
  
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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
  
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Probability/Statistics

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: Explain/Spread
The learner will be able to explain the spread of a set of data.
Strand Scope Source
Data Master MA: Curriculum Framework, 2000, Grade 8, 8.D.3
  
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
  
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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
  
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Real Numbers and the Coordinate Plane

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
  
Slope: Apply/Concept/Solve Problems
The learner will be able to obtain solutions to problems by applying the concept of slope.
Strand Scope Source
Slope Master MA: Curriculum Framework, 2000, Grade 8, 8.P.5
  
Linear Equation: Compare/Rate/Intercepts
The learner will be able to make comparisons of rates of change and x- and y- intercepts in different linear patterns.
Strand Scope Source
Linear Equations Master MA: Curriculum Framework, 2000, Grade 8, 8.P.10
  
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Technology as a Tool: Suitable
The learner will be able to apply technology as appropriate.
Strand Scope Source
Technology as a Tool Master MA: Curriculum Framework, 2000, Grade 8, 8.P.9, 8.M.2, 8.M.3
  
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