Math Grade 8  Download an editable version (RTF file)

Standard 1: Understands and applies problem solving strategies
Interval Benchmark 1: Uses a variety of strategies to solve problems
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Applies problem solving strategies   ITBS ***	pertinent information irrelevant information insufficient information act it out make or use a model find or use a pattern draw a picture guess and check make a chart, table, graph, or organized list use logical reasoning	Knows the general problem solving strategies	Extracts the main idea of a problem Chooses appropriate strategies to solve problems in the context of the problem situation Uses previously learned strategies, skills, knowledge, and concepts to solve problems (ITBS) Identifies pertinent and irrelevant information (ITBS) Uses number sentences to represent information Translates words to numbers to symbolic expressions Generalizes solutions to new problem situations	The Mangoes Problem Math Problems & Warm-ups	AEA9 AEA16
Interval Benchmark 2: Justifies the process used to solve a numerical problem
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Provides a clear justification of a solution	justification evidence valid argument invalid argument counter example	Understands how to make an argument for a solution	Formulates conjectures and argues why they must be true	Ideas with Food	AEA9 AEA16
Standard 2: Understands and applies concepts of numbers and operations
Interval Benchmark 1: Describes the properties of numbers and number systems
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses the appropriate form of a rational number (fraction, decimal, percent) in computations   ITBS **	rational number fraction decimal percent equivalent formats	Understands fractions, decimals, and percents can be expressed in various ways Knows which rational number is most appropriate based on the context of the problem Knows percents can be greater than 100 and less than 1	Identifies the appropriate rational number to use in a problem situation (ITBS) Places expressions on a number line (ITBS)	Model for Solving % Problems	AEA9 AEA16
b: Understands the use of negative and positive numbers in computations   ITBS *	negative number positive number absolute value	Knows absolute value of a number is its distance from zero on a number line Knows negative numbers are the opposite of positive numbers Knows applications for negative numbers	Finds the absolute value of given numbers (ITBS) Simplifies expressions involving integers (ITBS) Represents a change in a word problem with an integer (ITBS)		AEA9 AEA16
c: Compares fractions, decimals, and percents   ITBS *	fraction decimal percent equivalent formats	Understands fractions, decimals, and percents can be expressed in various ways Knows percents can be greater than 100 or less than 1	Converts fractions, decimals, and percents to equivalent forms (ITBS)	Rational Numbers & Proportions	AEA9 AEA16
d: Uses ratios and proportions to represent quantitative relationships   ITBS *	ratio proportion percent	Knows a ratio is a comparison of two numbers Knows a/b, a to b, and a:b are all ways to express a ratio Knows a percentage is a ratio of a number to 100 Knows a proportion is a comparison of two ratios	Writes a ratio in a variety of ways (ITBS) Sets up a proportion correctly	Rational Numbers & Proportions	AEA9 AEA16
e: Expresses numbers using exponents   ITBS *	exponent base expanded notation powers	Knows an exponent tells how many times a base is used as a factor	Writes exponents in expanded notation Simplifies expressions containing exponents (ITBS)	It's in the Cards	AEA9 AEA16
f: Understands number theory   ITBS *			Finds a multiple of a number (ITBS)		AEA9 AEA16
Interval Benchmark 2: Understands the properties of operations
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses the properties of operations to simplify computations   ITBS *	identity property inverse property distributive property associative property commutative property squaring square root perfect square	Knows the inverse operations undo each other Knows the identity properties of addition and multiplication Knows the distributive, associative, and commutative properties of addition and multiplication Knows squaring and square root are inverse operations Knows a perfect square is the product of a whole number multiplied by itself	Simplifies equations using properties of operations (ITBS) Explains the meaning of adding, subtracting, multiplying, and dividing integers Uses inverse properties and relationships to solve problems Finds the square root of perfect squares Approximates the square root of non-perfect squares	Plus or Minus Algebraic Transformations	AEA9 AEA16
b: Uses order of operations, including grouping symbols, to simplify computations   ITBS *	order of operations grouping	Knows the order of operations	Simplifies equations using order of operations Applies the order of operations to perform computations (ITBS)		AEA9 AEA16
Interval Benchmark 3: Computes fluently and makes reasonable estimates
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses appropriate methods to compute with fractions   ITBS *	numerator denominator common denominator least common multiple reciprocal lowest terms	Knows adding and subtracting fractions requires expression terms with a common denominator Knows finding a common denominator uses the same process for finding a least common multiple Knows the rules for adding, subtracting, multiplying, and dividing fractions Knows a fraction must be reduced to lowest terms	Adds, subtracts, multiplies, and divides fractions (ITBS)	Least Common Multiple Multiply Decimals & Mixed Numbers	AEA9 AEA16
b: Uses appropriate methods to compute with decimals and percents   ITBS *	decimal decimal places	Knows to add or subtract decimals the decimal points must line up vertically Knows the rules for adding, subtracting, multiplying, and dividing decimals Knows the rules for finding the percent of a number	Adds, subtracts, multiplies, and divides decimals Finds a percent of a number (ITBS)	Estimate	AEA9 AEA16
c: Uses appropriate methods to compute with integers   ITBS *	integer negative number positive number absolute value	Knows the absolute value of a number is its distance from zero on a number line Knows negative numbers are the opposite of positive numbers Knows the rules for adding, subtracting, multiplying, and dividing integers	Adds, subtracts, multiplies, and divides integers	Guess the Number Plus	AEA9 AEA16
d: Uses appropriate methods to solve proportions   ITBS *	ratio proportion cross-multiplication	Knows a/b, a to b, and a:b are all ways to represent a ratio Knows a proportion is a comparison of two ratios Knows the cross-multiplication method	Converts from one form of a ratio to another (ITBS) Solves for unknown numbers in a proportion		AEA9 AEA16
e: Uses estimation strategies for computing rational numbers   ITBS ***	estimation exact answer mental computation rounding	Knows when an estimate or an exact answer is more appropriate Knows how to judge the reasonable of an answer Knows rounding rules	Checks answers using estimation strategies (ITBS) Uses standard rounding to estimate (ITBS) Uses order of magnitude to estimate (ITBS) Uses number sense (ITBS)	Count On Math for Number Sense	AEA9 AEA16
Standard 3: Understands and applies concepts of measurement
Interval Benchmark 1: Understands the measurable attributes and the process of measurement
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses derived measures to express measures of attributes	attribute indirect measure derived measure rate	Knows some measures are derived measures	Uses rates as a measure of attributes Calculates rates in various contexts	Constant Dimensions	AEA9 AEA16
b: Applies the measurement process   ITBS **	process attribute appropriate comparison	Understands the process to be used when measuring attributes	Identifies the attribute to be measured Chooses an appropriate unit (ITBS) Compares the unit with the object to be measured	Mathematics at the Mall	AEA9 AEA16
Interval Benchmark 2: Uses a variety of techniques for measurement
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Understands the link between attribute measured and its dimension   ITBS *	dimension unit cubed squared conversion factor	Knows the dimensions of measurements Understands when using a conversion factor to change units, the factor may change the dimension of the units Knows appropriate units for perimeter, area, and volume	Labels perimeter with a single-dimensional unit Labels area with a two-dimensional unit Labels volume with a three-dimensional unit Classifies units by the dimension Converts units of measurement (ITBS)	Faster? Link Length, Perimeter, Area, Volume	AEA9 AEA16
b: Compares figures using perimeter and area   ITBS *	formula perimeter are radius diameter circumference pi congruent similar	Knows the formulas for perimeter and area of various figures Understands the meaning of the variables in each formula Knows how perimeter and area are used to describe similar and congruent figures	Computes the perimeter of various figures Computes the area of various figures Finds the difference in perimeter and area of a figure, if the dimensions of that figure are increased or decreased (ITBS) Compares the area and perimeter of similar and congruent figures	Mathematics at the Mall Area Formula Lab Chocolate	AEA9 AEA16
c: Makes reasonable estimates about the accuracy of solutions   ITBS *	gradations degree of accuracy degree of precision	Understands the gradations of measuring tool determine the precision of a measurement Understands situation where precision is not needed	Estimates answers to check accuracy of a solution Uses the appropriate degree of accuracy for reporting solutions (ITBS)	Tour of Measurement	AEA9 AEA16
Standard 4: Understands and applies properties of geometry
Interval Benchmark 1: Uses properties of figures to describe relationships
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Applies the properties of lines and angles to describe relationships   ITBS *	parallel lines transversal corresponding angles alternate interior angles adjacent angles vertical angles theorem	Understands a line that intersects two parallel lines is a transversal Knows the relationship between angles when two parallel lines are cut by a transversal	Identifies corresponding angles, alternate interior angles, adjacent angles, vertical angles Finds the measure of angles when two parallel lines are cut by a transversal Finds the measure of various angles using definitions and theorems Recognizes the properties of angles and triangles (ITBS)	Geometry in the Middle Grades Interactive Geometry Dictionary	AEA9 AEA16
Interval Benchmark 2: Uses coordinate geometry to describe relationships
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses the coordinate plane to prove geometric relationships   ITBS *	lines x-coordinate y-coordinate slope parallel lines perpendicular lines	Knows the uses of slope and intercepts Knows the slopes of parallel lines are equal Knows the slopes of perpendicular lines are negative reciprocals	Determines if lines are parallel or perpendicular using slope Verifies figures using slope Locates specific coordinate pairs on a grid (ITBS)	Printing Books	AEA9 AEA16
Interval Benchmark 3: Applies the concepts of transformation and symmetry
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Identifies transformations more exactly using distance and angle measurements	orientation magnitude composed transformations preimage image transformations	Understands the mathematical basis of transformations Knows each point in a reflection is the same distance from the line of relfection as the corresponding point in the preimages Knows corresponding vertices in the preimage and image are the same distance from the center of rotation	Draws complex transformations of figures Identify a transformation using length and angle measurements Describes the relationship among lines of reflection, centers of rotation, and positions of preimages and images		AEA9 AEA16
b: Uses congruence and similarity to describe relationships among figures   ITBS *	dilation scale factor similarity	Knows a dilation of a figure affects the length of side by a constant scale factor Knows a dilation of a figure does not affect the orientation or magnitude of angles Knows a dilation is a similarity transformation	Determines the scale factor of a dilation Uses scale factor to find dimensions in a similar figure (ITBS)	Geometry in the Middle Grades	AEA9 AEA16
Interval Benchmark 4: Uses geometric reasoning to solve problems
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses the Pythagorean Theorem to explain how geometric relationships correspond to algebraic concepts	theorem pythagorean theorem right triangle hypotenuse diagonal	Knows the Pythagorean Theorem only applies to right triangles Knows the hypotenuse is opposite the right angle Knows the Pythagorean Theorem can be written as c²=a²+b², where c is the hypotenuse	Represents the Pythagorean Theorem using a variety of formats Uses the Pythagorean Theorem to find the length of an unknown side Finds the length of a diagonal of a square	Pythagorean Theorem	AEA9 AEA16
b: Compares figures using perimeter, area, and volume   ITBS *	formula perimeter area radius circumference pi congruent similar volume height	Knows the formulas for perimeter and area of various figures Understands the meaning of the variables in each formula Knows how perimeter and area are used to describe similar and congruent figures	Computes the volume of various figures (ITBS) Computes the perimeter of various figures Computes the area of various figures (ITBS) Finds the difference in perimeter and area of a figure if the dimensions of that figure are increased or decreased Compares the perimeter, area, and volume of similar and congruent figures (ITBS)	Linking Length, Perimeter Area &Volume	AEA9 AEA16
Standard 5: Understands and applies concepts of data analysis and probability
Interval Benchmark 1: Collects, organizes, and displays data to answer a question
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Gathers data to answer questions   ITBS *	convenience sampling survey sampling random sampling bias sampling error certainty	Understands the different ways to collect a sample and the inherent bias in each Knows how to formulate a question that can be verified by data collection Knows which factors add or detract from certainty of a data set	Formulates a question that can be answered through data collection Collects data using a sampling technique (ITBS) Compares data from two or more samples to determine how sampling can influence results Uses knowledge of sampling, certainty, and data gathering to ascertain the certainty of the data	Using Math in Everyday Life	AEA9 AEA16
b: Represents data to convey results	bar graph line graph circle graph stem-and-leaf plot box-and-whisker plot frequency table histogram errors misrepresentation	Knows the basic types of charts, graphs, and tables Knows different types of graphs convey different messages Knows the criteria for selecting a graphical representation for a set of data Knows types of errors in data representation that can lead to misinterpretation	Creates graphical representations appropriate for data type Identifies misleading representations of data Extracts data from one graph and redisplays the data with a more appropriate representation	Exploring Linear Data Box Plotter	AEA9 AEA16
Interval Benchmark 2: Uses statistical methods to describe data
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Describes data using central tendency and other statistical terms   ITBS *	central tendency outlier variability quartile range interquartile range	Knows when to remove outliers from a data set Knows an outlier may represent an error in data collection or a significant variation in the data set Knows the variability of a data set describes the "spread" of the numbers	Explains the mean's sensitivity to outliers Determines the best measure of central tendency to describe a data set Calculates and compares measures of central tendency in two data sets (ITBS) Interprets representations of central tendency and variability (ITBS)	Statistics Polls: What do the numbers tell us?	AEA9 AEA16
b: Describes factors that affect measures of central tendency	central tendency outlier gap cluster distribution	Knows adding additional numbers to a data set can affect measures of central tendency Knows an outlier is a data point that does not correspond with the trend in the data set Knows outliers can affect measures of central tendency Knows gaps are an area of the distribution where there are no data points Knows a cluster is a group of localized points	Identifies situations in which the mean, mode, or median would contain the most relevant information Calculates measures of central tendency with and without outliers Describes how the inclusion/exclusion of outliers affects measures of central tendency Identifies gaps and clusters in a data set	Statistics Polls: What do the numbers tell us? Baseball Stats Linear Regression	AEA9 AEA16
Interval Benchmark 3: Reads and interprets data
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Reads information from graphs   ITBS **	ratio quantity axes scales sector	Knows how to read quantities on a variety of graphs Knows how to combine sectors on a circle graph to determine a total in a larger group	Reads quantities on a graph using the scales, axes, labels, and title (ITBS) Compares quantities on a graph using ratios (ITBS) Compares quantities on a graph using sums and differences (ITBS)		AEA9 AEA16
b: Reads information from tables   ITBS **	tables cell rank quantity	Knows how to read information from a cell in a table	Reads information from a specific cell in a table (ITBS) Compares quantities in a table to determine rank of items (ITBS)	Trips	AEA9 AEA16
c: Interprets information from graphs and tables   ITBS ***	interpretation trends functional relationship generalization	Knows what constitutes an obvious trend in data Knows a functional relationship exists if one variable changes in a consistent way in relation to another variable Knows types of conclusions that can be made about data	Identifies trends in line graphs (ITBS) Draws conclusions about what data represents (ITBS) Finds functional relationships in data in graphs or tables (ITBS) Makes generalizations based on an underlying or functional relationship in the data (ITBS)	Right or Left Handed? Epidemic Proportionss	AEA9 AEA16
Interval Benchmark 4: Uses probability concepts
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Makes predictions based on probabilities   ITBS **	dependent event independent event mutually exclusive event complementary event theoretical probability experimental probability	Knows experimental probabilities tend to mirror theoretical probabilities Understands the distinction between theoretical and experimental probability Understands probability can be represented as a ratio, proportion, or percentage Knows how to find the probability of two disjointed events Knows how to find the probability of one independent event followed by another independent event	Compares theoretical probabilities with experimental probabilities for dependent events and mutually exclusive events (ITBS) Uses appropriate terminology to describe complementary and mutually exclusive events Represents probability as a fraction, a ratio, or proportion Uses ratio to calculate the total when the probability is known for an event (ITBS) Translates experimental and written information into numeric probabilities (ITBS)	Choice and Chance in Life Birthday Paradox Using Monte Carlo Simulation	AEA9 AEA16
Standard 6: Understands and applies concepts of algebra and functions
Interval Benchmark 1: Represents, analyzes, and generalizes patterns
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses patterns and relationships to analyze mathematical situations	recursive relationship prediction rules	Knows how patterns change from one element to the next	Uses relationships in patterns to make predictions Describes a "rule" for an observed pattern Uses a variety of formats to represent patterns	Bridges to Algebraic Thinking	AEA9 AEA16
b: Understands the properties of arithmetic sequences   ITBS *	arithmetic sequence	Understands an arithmetic sequence is where each term is the sum of the previous term plus a constant	Identifies and extends a simple arithmetic sequence (ITBS) Expresses simple arithmetic sequences numerically and with symbols Formulates simple arithmetic sequences		AEA9 AEA16
Interval Benchmark 2: Identifies functions as linear or non-linear
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Describes linear functions using slope and y-intercept	linearity slope y-intercept	Understands the importance of the slope and y-intercept to a linear function Knows how slope and y-intercept determine the "shape" of a linear function	Recognizes the strengths and limitations of representing a linear function using a graph, table, or equation Identifies the y-intercept from a graph or table Uses the slope and y-intercept to describe and compare linear functions	Printing Books Taking Its Toll	AEA9 AEA16
Interval Benchmark 3: Uses expressions and symbols to represent mathematical relationships
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses operation properties to simplify expressions   ITBS **	identity property inverse property distributive property associative property cummutative property	Recognizes like terms Knows rules to simplify expressions	Uses algebraic symbols correctly in a variety of problem situations (ITBS) Simplifies expressions using operations properties (ITBS) Orders operations in an expression (ITBS)		AEA9 AEA16
b: Explores characteristics of polynomials	monomial binomial polynomial	Knows the definition of a polynomial Knows the properties of combining polynomials: addition, subtraction, multiplication, and division	Identifies an expression as a polynomial Adds, subtracts, multiplies, and divides monomials and polynomials		AEA9 AEA16
Interval Benchmark 4: Uses models to represent mathematical situations
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses order of operations, including grouping symbols, to solve problems   ITBS *	like terms order of operations grouping	Recognizes like terms Understands rules for combining variables Knows the order of operations	Uses order of operations, including grouping symbols, to solve problems (ITBS)		AEA9 AEA16
b: Solves equations involving algebraic expressions   ITBS ***	multi-step problems inverse operations identity inverse distributive associative commutative	Recognizes like terms Knows rules to simplify Understands the process of working backwards to solve linear equations (strategy of undoing)	Solves multiple-step problems (ITBS)	Pan Balance-Expressions	AEA9 AEA16
c: Applies properties of exponents, squares, and square roots to solve problems   ITBS *	exponents squares square roots	Understands the inverse relationship of squares and square roots (strategy of undoing) Understands rules for expanding exponents	Uses squares and square roots to solve equations Uses exponential notation (ITBS)	Spreadsheet and Graphing Tool	AEA9 AEA16
d: Solves simple inequalities and linear equations   ITBS *	inequality sign	Understands procedures and rules for moving numbers across the inequality sign Knows inequalities with one variable have a range of answers Knows different techniques for solving linear equations, such as algebraically, graphically Understands the process of working backwards to solve linear equations (strategy of undoing)	Solves inequalities and linear equations using a variety of methods (ITBS) Solves inequalities and linear equations by working backwards (strategy of undoing) (ITBS) Identifies the equation for a line graphed on a coordinate plane (ITBS)		AEA9 AEA16
Interval Benchmark 5: Analyzes change in a variety of situations
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses line graphs to analyze change	linear relationship slope rate of change	Understands slope as the amount of one quantity (y) per unit amount of another (x) Knows the shape of a graph provides insights into the nature of change	Represents change using words, tables, graphs, or symbols Compares the rates of change of two different graphs		AEA9 AEA16
Standard 7: Communicates and reasons mathematically
Interval Benchmark 1: Comprehends mathematical language
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Comprehends mathematical texts	graphic organizers	Knows strategies to help learn vocabulary Knows the text is set up to help vocabulary understanding	See Integrating Standards website for Reading: http://integratingstandards.com/standards/reading/index.html Uses graphic organizers to understand mathematical terms		AEA9 AEA16
Interval Benchmark 2: Expresses ideas using mathematical terms and representations
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Connects ideas to mathematical terms	grade level mathematical terms	Knows expressions represent ruls and generalizations Knows strategies to organize ideas Knows the characteristics of a well-written solution	Organizes mathematical ideas for understanding by a third party Writes coherent solutions Uses correct mathematical terms, language, and drawings for grade level content Presents solutions using mathematical terms and representations		AEA9 AEA16
Interval Benchmark 3: Analyzes and evaluates mathematical thinking
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Reviews mathematical thinking	clarity reasons evidence solutions characteristics	Knows strategies to organize ideas Knows mathematicians defend solutions Knows the characteristics of a well-written solution	Organizes work and labels drawings to make meaning clear Checks for clarity in solutions and revises Gives reasons for decisions made while solving a problem Considers the solutions of others and learns from them Supports solutions with evidence Answers questions regarding solutions		AEA9 AEA16
Interval Benchmark 4: Uses technology to enhance mathematical learning
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses tools and technology to solve problems	tools and technology appropriate at grade level	Knows how to use the tools and technology Understands a type of tool or technology is more appropriate in certain contexts	Identifies the appropriate tools or technology for the problem situation Uses tools or technology to simplify the task		AEA9 AEA16