Types of Triangles Templates - Excel

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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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