# Types of Triangles Templates - Excel

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```					                               Pleasant Valley Community School District
Standard 1: Understands and applies concepts of numbers and operations
Interval Benchmark 1: Describes the properties of numbers and number systems
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

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Pleasant Valley Community School District
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
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
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
Vocabulary            Information                           Skills            Classroom Resources
Benchmark

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Pleasant Valley Community School District
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
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
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
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

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Pleasant Valley Community School District
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
• Knows rounding
rules

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Pleasant Valley Community School District
Standard 2: Understands and applies concepts of algebra
Interval Benchmark 1: Represents, analyzes, and generalizes patterns
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
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

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Pleasant Valley Community School District
Interval Benchmark 3: Uses expressions and symbols to represent mathematical relationships
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
subtraction,
multiplication, and
division

Interval Benchmark 4: Uses models to represent mathematical situations
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

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Pleasant Valley Community School District
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
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
Standard 3: Understands and applies the concepts of geometry
Interval Benchmark 1: Uses properties of figures to describe relationships
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,
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
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

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Pleasant Valley Community School District
Interval Benchmark 3: Applies the concepts of transformation and symmetry
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

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Pleasant Valley Community School District
Interval Benchmark 4: Uses geometric reasoning to solve problems
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)

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Pleasant Valley Community School District
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
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
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

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Pleasant Valley Community School District
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
Standard 5: Understands and applies concepts of data analysis and probability
Interval Benchmark 1: Collects, organizes, and displays data to test a hypothesis
Vocabulary               Information                   Skills            Classroom Resources
Benchmark
a: Gathers data to  • convenience            • Understands the         • Formulates a question
• 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
misinterpretation

11/14/2010                                                                                          Page 13 of 19
Pleasant Valley Community School District
Interval Benchmark 2: Uses statistical methods to describe data
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
Interval Benchmark 3: Reads and interprets data
Vocabulary             Information                   Skills               Classroom Resources
Benchmark
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)

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

11/14/2010                                                                                              Page 15 of 19
Pleasant Valley Community School District
Interval Benchmark 4: Uses probability concepts
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
Standard 6: Understands and applies problem-solving strategies
Interval Benchmark 1: Uses a variety of strategies to solve problems
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
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
Standard 7: Communicates and reasons mathematically
Interval Benchmark 1: Comprehends mathematical language
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
• Uses graphic
organizers to
understand
mathematical terms

Interval Benchmark 2: Expresses ideas using mathematical terms and representations
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
level content
• Presents solutions
using mathematical
terms and
representations

11/14/2010                                                                                        Page 18 of 19
Pleasant Valley Community School District
Interval Benchmark 3: Analyzes and evaluates mathematical thinking
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
regarding solutions

Interval Benchmark 4: Uses technology to enhance mathematical learning
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

11/14/2010                                                                                       Page 19 of 19

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