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Pleasant Valley Community School District GRADE EIGHT - GRADE LEVEL INDICATORS Standard 1: Understands and applies concepts of numbers and operations Interval Benchmark 1: Describes the properties of numbers and number systems Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Uses the • rational number • Understands fractions, • Identifies the appropriate form of • fraction decimals, and percents can appropriate rational be expressed in various a rational number • decimal ways number to use in a (fraction, decimal, • percent • Knows which rational problem situation percent) in • equivalent formats number is most appropriate (ITBS) based on the context of the • Places expressions computations problem • Knows percents can be on a number line greater than 100 and less (ITBS) than 1 b: Understands the • negative number • Knows absolute value • Finds the absolute use of negative and • positive number of a number is its value of given positive numbers in • absolute value distance from zero on a numbers number line • Simplifies computations • Knows negative expressions involving numbers are the opposite of positive integers (ITBS) numbers • Knows applications for negative numbers Compares fractions, • fraction • Understands fractions, • Converts fractions, decimals, and • decimal decimals, and percents decimals, and percents • percent can be expressed in percents to equivalent various ways • equivalent formats forms (ITBS) • Knows percents can be greater than 100 or less than 1 d: Uses ratios and • ratio • Knows a ratio is a • Writes a ratio in a proportions to • proportion comparison of two variety of ways represent • percent numbers (ITBS) • Knows a/b, a to b, and • Sets up a proportion quantitative a:b are all ways to relationships correctly express a ratio • Knows a percentage is a ratio of a number to 100 • Knows a proportion is a comparison of two ratios • Knows an exponent 11/14/2010 Page 1 of 19 Pleasant Valley Community School District GRADE EIGHT - GRADE LEVEL INDICATORS e: Expresses • exponent • Knows an exponent • Writes exponents in expanded notation numbers using • base tells how many times • Simplifies expressions exponents • expanded notation a base is used as a containing exponents • powers • Convert positive and • scientific notation factor negative exponents Interval Benchmark 2: Understands the properties of operations Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Uses the • identity property • Knows the inverse • Simplifies equations properties of • inverse property operations undo each using properties of operations to • distributive property other operations (ITBS) • Knows the identity • Explains the meaning simplify • associative property properties of addition of adding, subtracting, computations • commutative and multiplication multiplying, and property • Knows the dividing integers • squaring distributive, associative, • Uses inverse properties • square root and commutative and relationships to • perfect square properties of addition solve problems and multiplication • Finds the square root • Knows squaring and of perfect of squares square root are inverse • Approximates the operations square root of non- • Knows a perfect perfect squares square is the product of a whole number multiplied by itself b: Uses order of • order of operations • Knows the order of • Simplifies equations operations, • grouping operations using order of including grouping operations symbols, to simplify • Applies the order of computations operations to perform computations (ITBS) Interval Benchmark 3: Computes fluently and makes reasonable estimates Grade Level Vocabulary Information Skills Classroom Resources Benchmark 11/14/2010 Page 2 of 19 Pleasant Valley Community School District GRADE EIGHT - GRADE LEVEL INDICATORS a: Uses appropriate • numerator • Knows adding and • Adds, subtracts, methods to compute subtracting fractions • denominator multiplies, and requires expressions terms with fractions • common with a common divides fractions denominator denominator (ITBS) • least common • Knows finding a common multiple denominator uses the same process for finding a least • reciprocal common multiple • lowest terms • Knows the rules for adding, subtracting, multiplying, and dividing fractions • Knows a fraction must be reduced to lowest terms b: Uses appropriate • decimal • Knows to add or • Adds, subtracts, methods to compute • decimal places subtract decimals the multiplies, and with decimals decimal points must divides decimals line up vertically • Knows the rules for adding, subtracting, multiplying, and dividing decimals c: Uses appropriate • integer • Knows the absolute • Adds, subtracts, methods to compute • negative number value of a number is its multiplies, and with integers • positive number distance from zero on a divides integers • absolute value number line • Knows negative (ITBS) numbers are the opposite of positive numbers • Knows the rules for adding, subtracting, multiplying and dividing integers d: Uses appropriate • ratio • Knows a/b, a to b, • Converts from one methods to solve • proportion and a:b are all ways to form of a ratio to problems • cross-multiplication represent a ratio another • Knows a proportion • Solves for unknown is a comparison of numbers in a two ratios proportion • Knows the cross- multiplication method 11/14/2010 Page 3 of 19 Pleasant Valley Community School District GRADE EIGHT - GRADE LEVEL INDICATORS e: Uses estimation • estimation • Knows when an • Checks answers strategies for • exact answer estimate or an exact using estimation computing rational • mental computation answer is more strategies numbers • rounding appropriate • Knows how to judge the reasonableness of an answer • Knows rounding rules 11/14/2010 Page 4 of 19 Pleasant Valley Community School District GRADE EIGHT - GRADE LEVEL INDICATORS Standard 2: Understands and applies concepts of algebra Interval Benchmark 1: Represents, analyzes, and generalizes patterns Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Uses patterns and • prediction • Knows how patterns • Uses relationships in relationships to • rules change from one patterns to make analyze element to the next predictions mathematical • Describes a "rule" situations for an observed pattern • Uses a variety of formats to represent patterns b: Understands the • arithmetic sequence • Understands an • Identifies and properties of • geometric sequence arithmetic sequence is extends a simple arithmetic where each term is the arithmetic sequence sequences sum of the previous (ITBS) term plus a constant • Expresses simple • Understands a arithmetic and geometric sequence is geometric sequences where the ratio numerically and with between any two symbols successive terms is • Formulates simple the same. arithmetic and geometric sequences Interval Benchmark 2: Identifies functions as linear or non-linear Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Describes linear • linearity • Understands the • Recognizes the functions using • slope importance of the strengths and slope and y- • y-intercept slope and y-intercept limitations of to a linear function representing a linear intercept function using a • Knows how slope graph, table, or and y-intercept equation determine the "shape" • Identifies the y- of a linear function intercept from a graph or table • Uses the slope and y-intercept to describe and compare linear functions 11/14/2010 Page 5 of 19 Pleasant Valley Community School District GRADE EIGHT - GRADE LEVEL INDICATORS Interval Benchmark 3: Uses expressions and symbols to represent mathematical relationships Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Uses operation • identity property • Recognizes like • Uses algebraic properties to • inverse property terms symbols correctly in a simplify expressions • distributive property • Knows rules to variety of problem • associative property simplify expressions situations (ITBS) • cummutative • Simplifies property expressions using operations properties • Orders operations in an expression (ITBS) b: Explores • monomial • Knows the • Identifies an characteristics of • binomial definition of a expression as a polynomials • polynomial polynomial polynomial • Knows the • Adds, subtracts, properties of multiplies, and combining divides monomials polynomials: addition, and polynomials subtraction, multiplication, and division Interval Benchmark 4: Uses models to represent mathematical situations Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Uses order of • like terms • Recognizes like • Uses order of operations, • order of operations terms operations, including including grouping • grouping • Understands rules grouping symbols, to symbols, to solve for combining solve problems problems variables (ITBS) • Knows the order of operations b: Solves equations • multi-step problems • Recognizes like • Uses commutative, involving algebraic • inverse operations terms associative, and expressions • identity • Knows rules to distributive, and • inverse simplify properties of 0 and 1 • distributive • Understands the to solve multi-step • associative process of working equations • commutative backwards to solve linear equations (strategy of undoing) • Understands the 11/14/2010 Page 6 of 19 Pleasant Valley Community School District GRADE EIGHT - GRADE LEVEL INDICATORS c: Applies • exponents • Understands the • Uses squares and properties of • squares inverse relationship of square roots to solve exponents, squares, • square roots squares and square equations and square roots to roots (strategy of • Uses exponential solve problems undoing) notation • Understands rules for expanding exponents d: Solves simple • inequality sign • Understands • Solves inequalities inequalities and procedures and rules for and linear equations linear equations moving numbers across using a variety of the inequality sign methods (ITBS) • Knows inequalities with one variable have a • Solve inequalities range of answers and linear equations • Knows different by working techniques for solving backwards (strategy linear equations, such as of undoing) (ITBS) algebraically, graphically • Understands the process of working backwards to solve linear equations (strategy of undoing) Interval Benchmark 5: Analyzes change in a variety of situations Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Uses line graphs • linear relationship • Understands slope as • Represents change to analyze change • slope the amount of one using words, tables, • rate of change quantity (y) per unit graphs, or symbols amount of another (x) • Compares the rates • Knows the shape of of change of two a graph provides different graphs insights into the nature of change 11/14/2010 Page 7 of 19 Pleasant Valley Community School District GRADE EIGHT - GRADE LEVEL INDICATORS Standard 3: Understands and applies the concepts of geometry Interval Benchmark 1: Uses properties of figures to describe relationships Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Applies, • parallel lines • Understands a line • Identifies describes, • transversal that intersects two corresponding angles, constructs, and uses • corresponding parallel lines is a alternate interior angles, angles transversal adjacent angles, vertical the properties of angles lines and angles to • alternate interior • Knows the • Finds the measure of describe angles relationship between angles when two relationships • adjacent angles angles when two parallel lines are cut by • vertical angles parallel lines are cut a transversal • theorem by a transversal • Finds the measure of various angles using definitions and theorems • Recognizes the properties of angles and triangles (ITBS) b: Uses properties • Complementary • Knows complementary of angles and angles angles sum to 90 triangles to describe • Supplementary degrees. angles • Knows supplementary figures angles sum to 180 degrees. • Knows vertical angles are congruent. • Understands an isosceles triangle has 2 sides of equal length. • Understands a right triangle contains 1 90 degree angle. • Uses known angles to find unknown angles in a figure. Interval Benchmark 2: Uses coordinate geometry to describe relationships Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Uses the • lines • Knows the uses of • Determines if lines are coordinate plane to • x-coordinate slope and intercepts parallel using slope prove geometric • y-coordinate • Knows the slopes of • Verifies figures using • slope parallel lines are equal slope relationships • Locates specific • parallel lines coordinate pairs on a • perpendicular lines grid (ITBS) • ordered pairs 11/14/2010 Page 8 of 19 Pleasant Valley Community School District GRADE EIGHT - GRADE LEVEL INDICATORS Interval Benchmark 3: Applies the concepts of transformation and symmetry Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Identifies • orientation • Understands the • Draws complex transformations • magnitude mathematical basis of transformations of more exactly using • composed transformations figures transformations • Knows each point in a • Identify a distance and angle reflection is the same transformation using measurements • preimage distance from the line of length and angle • image reflection as the measurements corresponding point in • Describes the the preimages relationship among lines • Knows corresponding of reflection, centers of vertices in the preimage rotation, and positions and image are the same of preimages and distance from the center images of rotation b: Uses • transformation • Knows a dilation of a • Determines the scale transformations to • symmetry figure affects the length factor of a dilation understand • orientation of side by a constant • magnitude scale factor symmetry • Knows a dilation of a • dilation figure does not affect • scale factor the orientation or magnitude of angles • Knows a dilation is a similarity transformation c: Uses • Congruent • Distinguish between transformations to similar and congruent determine if two figures. figures are congruent 11/14/2010 Page 9 of 19 Pleasant Valley Community School District GRADE EIGHT - GRADE LEVEL INDICATORS Interval Benchmark 4: Uses geometric reasoning to solve problems Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Uses the • theorem • Knows the • Represents the Pythagorean • Pythagorean Pythagorean Theorem Pythagorean Theorem Theorem to explain theorem only applies to right using a variety of • right triangle triangles formats how geometric • Knows the hypotenuse • Uses the Pythagorean relationships • hypotenuse is opposite the right Theorem to find the correspond to • diagonal angle length of an unknown algebraic concepts • Knows the side Pythagorean Theorem • Finds the length of a can be written as c2 = a2 diagonal of a square + b2, where c is the hypotenuse b: Compares figures • formula • Knows the formulas • Computes the volume using perimeter, • perimeter for perimeter and area of of various figures area, and volume • area various figures (ITBS) • radius • Understands the • Computes the meaning of the variables perimeter of various • circumference in each formula figures • pi • Knows how perimeter • Computes the area of • congruent and area are used to various figures (ITBS) • similar describe similar and • Finds the difference in • volume congruent figures perimeter and area of a • height figure if the dimensions of that figure are increased or decreased • Compares the perimeter, area, and volume of similar and congruent figures (ITBS) 11/14/2010 Page 10 of 19 Pleasant Valley Community School District GRADE EIGHT - GRADE LEVEL INDICATORS Standard 4: Understands and applies concepts of measurement Interval Benchmark 1: Uses the measurable attributes of two- and three-dimensional figures and the process of measurement Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Uses derived • attribute • Knows some • Uses rates as a measures to express • indirect measure measures are derived measure of attributes measures of • derived measure measures • Calculates rates in attributes • rate various contexts b: Applies the • process • Understands the • Identifies the measurement • attribute process to be used attribute to be process • appropriate when measuring measured • comparison attributes • Chooses an appropriate unit (ITBS) • Compares the unit with the object to be measured Interval Benchmark 2: Uses a variety of techniques for measurement Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Understands the • dimension • Knows the • Labels perimeter link between • unit dimensions of with a single- attribute measured • cubed measurements dimensional unit and its dimension • squared • Understands when • Labels area with a • conversion factor using a conversion two-dimensional unit factor to change units, • Labels volume with the factor may change a three-dimensional the dimension of the unit units • Classifies units by • Knows appropriate their dimension units for perimeter, area, and volume 11/14/2010 Page 11 of 19 Pleasant Valley Community School District GRADE EIGHT - GRADE LEVEL INDICATORS b: Compares figures • formula • Knows the formulas • Computes the using perimeter and • perimeter for perimeter and area of perimeter of various area • area various figures figures • radius • Understands the • Computes the area of meaning of the variables various figures • diameter in each formula • Finds the difference in • circumference • Knows how perimeter perimeter and area of a • pi and area are used to figure, if the dimensions • congruent describe similar and of that figure are • similar congruent figures increased or decreased (ITBS) • Compares the area and perimeter of similar and congruent figures c: Makes reasonable • degree of accuracy • Understands the • Estimates answers to estimates about the • degree of precision gradations of check accuracy of a accuracy of measuring tool solution solutions determine the • Uses the appropriate precision of a degree of accuracy for measurement reporting solutions • Understands (ITBS) situation where precision is not needed 11/14/2010 Page 12 of 19 Pleasant Valley Community School District GRADE EIGHT - GRADE LEVEL INDICATORS Standard 5: Understands and applies concepts of data analysis and probability Interval Benchmark 1: Collects, organizes, and displays data to test a hypothesis Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Gathers data to • convenience • Understands the • Formulates a question answer questions sampling different ways to that can be answered • survey sampling collect a sample and through data collection • random sampling the inherent bias in • Collects data using a sampling technique • bias each • Compares data from • sampling error • Knows how to two or more samples to • certainty formulate a question determine how sampling that can be verified by can influence results data collection • Uses knowledge of • Knows which sampling, certainty, and factors add or detract data gathering to from certainty of a ascertain the certainty of data set the data b: Represents data • bar graph • Knows the basic types • Creates graphical to convey results • line of charts, graphs, and representations • graph tables appropriate for data • circle graph • Knows different types type of graphs convey • frequency table • Identifies misleading different messages • histogram • Knows the criteria for representations of data • errors selecting a graphical • Extracts data from • misrepresentation representation for a set one graph and of data redisplays the data • Knows types of errors with a more in data representation appropriate that can lead to representation misinterpretation 11/14/2010 Page 13 of 19 Pleasant Valley Community School District GRADE EIGHT - GRADE LEVEL INDICATORS Interval Benchmark 2: Uses statistical methods to describe data Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Describes data • central tendency • Knows when to • Explains the mean's using central • outlier remove outliers from a sensitivity to outliers tendency and other • variability data set • Determines the best • quartile range • Knows an outlier may measure of central statistical terms represent an error in tendency to describe a • interquartile range data collection or a data set significant variation in • Calculates and the data set compares measures of • Knows the variability central tendency in two of a data set describes data sets (ITBS) the "spread" of the • Interprets numbers representations of central tendency and variability (ITBS) b: Describes factors • central tendency • Knows adding • Identifies situations in that affect measures • outlier additional numbers to a which the mean, mode, of central tendency • gap data set can affect or median would • cluster measures of central contain the most tendency relevant information • distribution • Knows an outlier is a • Calculates measures of data point that does not central tendency with correspond with the and without outliers trend in the data set • Describes how the • Knows outliers can inclusion/exclusion of affect measures of outliers affects measures central tendency of central tendency • Knows gaps are an • Identifies gaps and area of the distribution clusters in a data set where there are no data points • Knows a cluster is a group of localized points 11/14/2010 Page 14 of 19 Pleasant Valley Community School District GRADE EIGHT - GRADE LEVEL INDICATORS Interval Benchmark 3: Reads and interprets data Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Reads • ratio • Knows how to read • Reads quantities on a information from • quantity quantities on a variety graph using the scales, graphs • axes of graphs axes, labels, and title • scales • Knows how to (ITBS) • Compares quantities • sector combine sectors on a on a graph using ratios circle graph to (ITBS) determine a total in a • Compares quantities larger group on a graph using sums and differences (ITBS) b: Reads • tables • Knows how to read • Reads information information from • cell information from a from a specific cell in tables • rank cell in a table a table (ITBS) • quantity • Compares quantities in a table to determine rank of items (ITBS) c: Interprets • interpretation • Knows what • Identifies trends in line information from • trends constitutes an obvious graphs (ITBS) graphs and tables • functional trend in data • Draws conclusions relationship • Knows a functional about what data represents (ITBS) • generalization relationship exists if • Finds functional one variable changes relationships in data in in a consistent way in graphs or tables (ITBS) relation to another • Makes generalizations variable based on an underlying • Knows types of or functional conclusions that can relationship in the data be made about data (ITBS) 11/14/2010 Page 15 of 19 Pleasant Valley Community School District GRADE EIGHT - GRADE LEVEL INDICATORS Interval Benchmark 4: Uses probability concepts Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Makes • dependent event • Knows experimental • Compares theoretical predictions based on • independent event probabilities tend to mirror probabilities with theoretical probabilities experimental probabilities probabilities • mutually exclusive • Understands the for dependent events and event distinction between mutually exclusive events • complementary theoretical and (ITBS) event experimental probability • Uses appropriate • Understands probability terminology to describe • theoretical can be represented as a complementary and probability ratio, proportion, or mutually exclusive events • experimental percentage • Represents probability as probability • Knows how to find the a fraction, a ratio, or probability of two proportion disjointed events • Uses ratio to calculate the • Knows how to find the total when the probability probability of one is known for an event independent event (ITBS) followed by another • Translates experimental independent event and written information into numeric probabilities (ITBS) 11/14/2010 Page 16 of 19 Pleasant Valley Community School District GRADE EIGHT - GRADE LEVEL INDICATORS Standard 6: Understands and applies problem-solving strategies Interval Benchmark 1: Uses a variety of strategies to solve problems Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Applies problem • pertinent information • Knows the general • Extracts the main idea of solving strategies • irrelevant information problem solving a problem • insufficient • Chooses appropriate strategies strategies to solve information problems in the context of • act it out the problem situation • make or use a model (ITBS) • find or use a pattern • Uses previously learned • draw a picture strategies, skills, • guess and check knowledge, and concepts • make a chart, table, to solve problems graph, or organized list • Identifies pertinent and • use logical reasoning irrelevant information • work backwards (ITBS) • Uses number sentences to • write algebraic represent information equations • Translates words to numbers to symbolic expressions • Generalizes solutions to new problem situations Interval Benchmark 2: Justifies the process used to solve a numerical problem Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Provides a clear • justification • Understands how to • Formulates justification of a • evidence make an argument for conjectures and solution • valid argument a solution argues why they must • invalid argument be true • counter example 11/14/2010 Page 17 of 19 Pleasant Valley Community School District GRADE EIGHT - GRADE LEVEL INDICATORS Standard 7: Communicates and reasons mathematically Interval Benchmark 1: Comprehends mathematical language Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Comprehends • graphic organizers • Knows strategies to • See Integrating mathematical texts help learn vocabulary Standards website for • Knows the text is set Reading: up to help vocabulary http://integratingstand understanding ards.com/standards/re ading/index.html • Uses graphic organizers to understand mathematical terms Interval Benchmark 2: Expresses ideas using mathematical terms and representations Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Connects ideas to • grade level • Knows expressions • Organizes mathematical terms mathematical terms represent rules and mathematical ideas generalizations for understanding by a • Knows strategies to third party organize ideas • Writes coherent • Knows the solutions characteristics of a • Uses correct well-written solution mathematical terms, language, and drawings for grade level content • Presents solutions using mathematical terms and representations 11/14/2010 Page 18 of 19 Pleasant Valley Community School District GRADE EIGHT - GRADE LEVEL INDICATORS Interval Benchmark 3: Analyzes and evaluates mathematical thinking Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Reviews • clarity • Knows strategies to • Organizes work and labels drawings to make mathematical • reasons organize ideas meaning clear thinking • evidence • Knows • Checks for clarity in • solutions mathematicians solutions and revises • characteristics defend solutions • Gives reasons for • Knows the decisions made while solving a problem characteristics of a • Considers the solutions of well-written solution others and learns from them • Supports solutions with evidence • Answers questions regarding solutions Interval Benchmark 4: Uses technology to enhance mathematical learning Grade Level Vocabulary Information Skills Classroom Resources Benchmark a: Uses tools and • tools and technology • Knows how to use • Identifies the technology to solve appropriate at grade the tools and appropriate tools or problems level technology technology for the • Understands a type problem situation of tool or technology • Uses tools or is more appropriate in technology to simplify certain contexts the task 11/14/2010 Page 19 of 19

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