Math Grade 11  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: Uses a variety of strategies to understand new mathematical content   ITED ***	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 Knows the same situation can often be represented in more than one way Knows different problems may be solved using the same method	Extracts the main idea of a problem (ITED) Chooses appropriate strategies to solve problems in the context of the problem situation (ITED) Uses previously learned strategies, skills, knowledge, and concepts to solve problems (ITED) Identifies pertinent and irrelevant information (ITED) Translates words to numbers to symbolic expressions (ITED) Generalizes solutions to new problem situations (ITED)		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: Specifies the kind of information and resources used to solve a problem	verification conjecture validation algorithm justification evidence valid argument invalid argument counter example	Understands how to make an argument for a solution Knows that conjectures are subject to verification Knows ways to verify a conjecture Knows that one counter example disproves a conjecture	Formulates conjectures and argues why they must be true Uses conjectures previously justified to solve a problem Generalizes conjectures to new problem situations		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: Understands properties of real numbers and its subsystems   ITED **	relative magnitude absolute value natural numbers integers rational numbers irrational numbers real numbers subsystem	Knows the relationships among the subsystems of the real numbers system Understands the type of equations that can and cannot be solved within each subsystem	Represents numbers within each subsystem (ITED) Uses the appropriate number system representation for given problem situations (ITED) Interprets numerical answers on a calculator or computer display		AEA9 AEA16
b: Explores new number systems, such as vectors and matrices	matrix vector scalar multiplication magnitude direction	Knows what operation properties hold for operations with matrices and vectors	Determines what operation properties hold for matrix addition and multiplication Calculates sums, differences, and products of matrices Determines what operation properties hold for vector addition and subtraction Calculates vector addition and multiplication		AEA9 AEA16
c: Uses the appropriate form of a rational number (fraction, decimal, percent) in computations   ITED ***	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	Converts fractions, decimals, and percents to equivalent forms (ITED) Identifies the appropriate rational number to use in a problem situation (ITED)		AEA9 AEA16
d: Uses the properties of roots, exponents in computations   ITED **	squaring square root exponent base expanded notation	Knows squaring is the product of a whole number multiplied by itself Knows squaring and square root are inverse operations Knows an exponent tells how many times a base is used as a factor Knows the rules for multiplying an dividing numbers with exponents Knows the rules for raising a number with an exponent to a power	Finds the square root of any number Writes exponents in expanded notation Simplifies expressions containing exponents (ITED) Writes expressions using scientific notation (ITED)		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	identity property inverse property distributive property associative property commutative property squaring square root	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	Simplifies equations using properties of operations Explains the meaning of adding, subtracting, multiplying, and dividing integers Uses inverse properties and relationships to solve problems Finds the square root of any number		AEA9 AEA16
b: Uses the properties of operations to solve problems   ITED ***	like terms order of operations grouping inverse operations	Recognizes like terms Understands rules for combining variables Knows the order of operations Knows the inverse relationship between properties of operations	Uses order of operation, including grouping symbols, to solve problems (ITED)		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 a variety of operations on expressions containing complex numbers   ITED ***	simplify complex number	Knows the algorithms of operations for complex numbers	Adds, subtracts, multiplies, divides, and simplifies expressions of complex numbers (ITED)		AEA9 AEA16
b: Uses estimation strategies for computing complex numbers   ITED ***	complex numbers estimation exact answer mental computation rounding	Knows when an estimate or an exact answer is more appropriate Knows how to judge the reasonableness of an answer Understands that rounding and estimation inherently add discrepancy Understands appropriate places to round when estimating	Checks answers using estimation strategies (ITED) Uses the appropriate places when estimating answers (ITED) Makes reasonable estimates (ITED)		AEA9 AEA16
Standard 3: Understands and applies concepts of measurement
Interval Benchmark 1: Understands measurable attributes and the process of measurement
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses indirect and derived measures to express measures of attributes   ITED *	attribute indirect measure derived measure rate increasing approximation	Knows some attributes can only be measured indirectly Knows some measures are derived measures Knows some measurements of attributes are determined by a sequence of increasing approximations	Selects the appropriate indirect approach to solve a problem situation Calculates attributes using indirect measures (ITED) Uses rates as a measure of attributes Uses increasing approximations to determine measures of attributes (ITED)		AEA9 AEA16
b: Applies the measurement process	process attribute appropriate comparison	Understands the process to be used when measuring attributes	Calculates error Identifies the attribute to be measured Chooses an appropriate unit Compares the unit with the object to be measured		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: Converts measurements between systems   ITED *	measurement system dimensional analysis	Knows units should be reported along with numerical values Understands the meaning of equivalent forms of units Knows units can be used to organize conversions	Uses dimensional analysis to organize conversions and computations (ITED) Converts measurements from one system to another (ITED)		AEA9 AEA16
b: Understands the importance of scale selection	viewing window scale logarithmic scale	Knows choices about scale and/or viewing windows help solve problems more effectively Knows choices about scale and/or viewing windows can distort solutions	Uses the appropriate scale and/or viewing window to solve a problem		AEA9 AEA16
c: Uses formulas to find perimeter, area, and volume of various figures   ITED **	formula perimeter circumference area surface area lateral area volume composite figures	Knows the formulas for perimeter, circumference, area, surface area, and volume Knows how to solve a formula for a given variable	Computes the perimeter of various figures (ITED) Computes the circumference of a circle (ITED) Computes the area of various figures (ITED) Computes the volume of various figures (ITED)		AEA9 AEA16
d: Makes reasonable estimates about the accuracy of solutions   ITED *	degree of accuracy degree of precision approximation	Knows measurements of continuous quantities are approximations Knows the degree of precision for a solution is dependent upon the accuracy of the measurement	Uses the appropriate degree of accuracy for reporting solutions (ITED) Estimates answers to check accuracy of a solution		AEA9 AEA16
Standard 4: Understands and applies properties of geometry
Interval Benchmark 1: Uses properties of figures to verify relationships
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Describes figures by their characteristics	polygon triangle circle quadrilateral rhombuse kite rectangle square trapezoid cone cylinder prism pyramid sphere Venn Diagram	Knows the characteristics of figures	Describes geometric figures using their characteristics Classifies figures by their discrete characteristics		AEA9 AEA16
b: Uses properties of lines to describe relationsips between figures	line segment ray parallel lines perpendicular lines skew lines intersection bisecting midpoint collinear coplanar	Knows the properties of line segments Knows the midpoint of a line segment divides the line into two equal parts Knows how to find the length of line segments	Describes relationships of figures using line properties		AEA9 AEA16
c: Uses properties of angles to describe relationships between figures	vertical angle adjacent angle complementary angle supplementary angle right angle interior angle exterior angle corresponding angle parallel line transversal	Knows the properties of angles Understands the relationship of angles when two parallel lines are cut by a transversal Knows the relationship between the number of sides of a polygon and the measure of its interior angles	Describes relationships of figures using angle properties		AEA9 AEA16
d: Uses properties of circles to describe relationships between figures	circle diameter radius arc chord secant inscribed angle semicircle	Knows the properties of circles	Describes relationships of figures using properties of circles		AEA9 AEA16
e: Uses congruence and similarity to describe relationships among figures	congruent similar corresponding parts proportionality similar figures congruent figures	Knows the properties of congruent and similar figures Knows the difference between similarity and congruence Knows the ratio for corresponding sides of similar triangles are the same	Recognizes figures as congruent or similar Uses proportionality to show similarity		AEA9 AEA16
Interval Benchmark 2: Uses coordinate geometry to verify relationships
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses the coordinate plane to show how geometric relationships correspond directly to algebraic concepts	coordinate plane distance formula midpoint formula slope formula vertex-edge graph	Knows selecting the origins of a figure makes the calculations easier Knows the formulas for distance, midpoint, and slope	Finds the distance and midpoints of segments in the coordinate plane Compares the slopes and distances of line segments to verify a figure classification Uses vertex-edge graphs to model and solve problems involving paths, networks, or relationships among a finite number of objects		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: Uses various representations to describe transformations	transformation image preimage isometry orientation translation composition rotation reflection dilation matrix	Knows that a transformation is a one-to-one correspondence Knows the difference between the types of transformations Knows how to describe position using matrices	Represents transformations using sketches, coordinates, vectors, function notation, and matrices Identifies the types of transformations that make up a composition Uses matrices to represent transformations		AEA9 AEA16
b: Describes figures in terms of their symmetry	symmetry reflectional symmetry rotational symmetry point symmetry	Knows the difference among the types of symmetry	Identifies the type of symmetry in figures		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 proofs to build logical reasoning skills	conjecture proof theorem postulate axiom inductive reasoning deductive reasoning	Knows the difference between a definition, theorem, and a postulate Knows the steps for completing a proof	Uses inductive and deductive reasoning to verify properties and relationships Uses proofs to write convincing arguments Establishes the validity of conjectures		AEA9 AEA16
b: Uses formulas for perimeter, area, and volume of various figures   ITED ***	formula perimeter circumference area surface area lateral area volume composite figure	Knows the formulas for perimeter, area, surface area, and volume Knows how to solve a formula for any given variable	Computes the perimeter of various figures (ITED) Finds the circumference of a circle and the length of an arc (ITED) Computes the area of various figures (ITED) Computes the volume of various figures (ITED)	Mathematical Thinking	AEA9 AEA16
c: Uses properties of triangles to prove and verify relationships	Pythagorean Theorem 30-60-90 triangles 45-45 triangles right triangles	Knows the Pythagorean Theorem Knows the properties of special triangles	Uses the Pythagorean Theorem and its converse to find segment lengths Uses the properties of special right triangles to solve problems		AEA9 AEA16
d: Uses trigonometric relationships to determine lengths and angle measurements	trigonometry sine cosine tangent inverse sine inverse cosine inverse tangent	Knows the trigonometric ratios	Determines the appropriate trigonometric ratio for a specific problem Uses trigonometric ratios to find lengths and angle measurements		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	convenience sampling survey sampling random sampling bias sampling error	Knows different ways to collect a sample and the inherent bias in each Knows how to formulate a questions that can be verified by data collection Knows factors which add or detract from certainty of a data set	Formulates a question that can be answered by data collection Collects data using a sampling technique 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 Identifies possible bias in sampling		AEA9 AEA16
b: Represents data to convey results   ITED ***	bar graph line graph circle graph stem-and-leaf plot box-and-whisker plot frequency table histogram scatter plot 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 (ITED) Identifies misleading representations of data Extracts data from one graph and redisplays the data with a more appropriate representation (ITED) Reads data from graphs (ITED) Draws conclusions from data represented in a graph (ITED) Makes predictions from data represented in a graph (ITED)		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   ITED *	central tendency outlier variability quartile range interquartile range correlation	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 Knows correlations can be causally related or incidental	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 Interprets representations of central tendency and variability (ITED) Recognizes correlations as causal or incidental Calculates correlations for a given data set		AEA9 AEA16
b: Describes factors that affect measures of central tendency   ITED *	central tendency outlier gap cluster distribution	Knows adding 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 (ITED) Describes how the inclusion/exclusion of outliers affects measures of central tendency Identifies gaps and clusters in a data set		AEA9 AEA16
c: Uses different curve fitting methods to "fit" data	normal curve central limit theorem curve fitting lines of best fit regression line least squares regression	Knows the significance of quartile divisions under the normal curve Knows the properties of the normal curve and how it can be used to describe dta Knows the advantages and disadvantages of curve fitting methods	Identifies data sets in which the results would be expected to approximate the normal curve Chooses the best method of curve fitting for a given data set		AEA9 AEA16
Interval Benchmark 3: Reads and interprets data
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses sampling distribution to make informal inferences   ITED *	sampling distribution confidence interval undertainty bias parameter statistic margin of error	Knows how bias can affect the interpretation of data Knows possible sources of sampling error Knows what constitutes a representative sample	Finds confidence intervals Estimates statistical uncertainty Draws inferences about a population from a sample (ITED) Describes population parameters based on sample statistics		AEA9 AEA16
Interval Benchmark 4: Uses probability concepts
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses a variety of methods to determine probabilities   ITED *	simulation theoretical model experimental model Monte Carlo probability combinations	Knows the advantages and disadvantages of experimental, simulation, and theoretical methods for determining probability Knows experimental probabilities tend to mirror theoretical probabilities Knows the distinction between theoretical and experimental probability Knows how combinations are calculated to determine an outcome	Uses a variety of methods to determine probability of events Determines the best method for determining probability for a given situation Compares theoretical probabilities with experimental probabilities for dependent events, independent events, and mutually exclusive events Uses combinations to represent a given situation (ITED)		AEA9 AEA16
b: Applies the concepts of conditional probability and independent events   ITED *	independent event dependent event simple event compound event conditional event	Knows how to find the probability of two disjoint events Knows how to find the probability of one independent event followed by another independent event Knows the probability for some outcomes depends upon one or more other events occurring	Identifies simple and compound events Identifies dependent and independent events (ITED) Computes the probability of conditional and independent events		AEA9 AEA16
Standard 6: Understands and applies concepts of algebra and functions
Interval Benchmark 1: Represents patterns and relationships in a variety of ways
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses patterns and relationships to analyze mathematical situations   ITED *	sequences series recursive pattern iterative patterns	Knows sequences and series can be used to model problems	Uses words, tables, and graphs and symbolic rules to describe patterns (ITED) Describes the relationship of sequences symbolically Generates formulas to describe a pattern		AEA9 AEA16
Interval Benchmark 2: Describes the properties and characteristics of functions
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Describes functions and their properties using function notation   ITED *	function domain range one-to-one correspondence function notation	Knows for every value in the domain of a function, there is one and only one corresponding value in the range Understands the concept of a function as the correspondence between the elements of two sets Understands the definition of a function: domain, range, function, non-function	Identifies the domain, range, and rule of a function Describes functions and their properties using function notation Recognizes the graphs of non-linear functions (ITED) Describes from a graph the relationship between two variables (ITED)		AEA9 AEA16
b: Explores the properties of different classes of functions   ITED **	function domain range one-to-one correspondence function notation polynomial exponential rational logarithmic periodic parameter	Knows the same function can be represented in a variety of forms Knows the limitations of non-linear functions Understands the concept of a class of functions	Identifies functions expressed numerically or algebraically as linear or non-linear (ITED) Recognizes properties of families of functions and how the values of parameters shape the graphs (ITED) Compares properties of various functions to find common characteristics		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: Rewrites algebraic expression in equivalent forms   ITED **	equivalent forms dimensional analysis	Recognizes like terms Knows rules to simplify expressions Knows the order of operations Understands the meaning of equivalent forms of expressions	Simplifies algebraic expressions by combining like terms and applying appropriate properties Uses dimensional analysis to organize conversions and computations (ITED) Operates fluently on algebraic expressions by combining them and re-expressing them in alternate forms (ITED)		AEA9 AEA16
b: Manipulates polynomial expressions	monomial binomial polynomial common monomial factor factoring perfect square binomials	Knows the various methods to factor polynomial expressions Knows the properties of combining polynomials: addition, subtraction, multiplication, and division Knows some polynomials cannot be solved precisely	Adds, subtracts, multiplies, and divides monomials and polynomials Applies basic factoring techniques to second and simple third-degree polynomials Simplifies fractions with polynomials in the numerator and denominator Finds the number and type of roots of a polynomial equation		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 a variety of methods to solve equations   ITED ***	multi-step problems	Recognizes like terms Understands rules for combining variables Knows the order of operations Knows the inverse relationship between addition and subtraction and multiplication and division Understands such operations as taking the opposite, finding the reciprocal, taking the square root	Solves equations for a specified variable (ITED) Solves multi-step problems (ITED) Writes an equation for a specific problem (ITED)		AEA9 AEA16
b: Uses a variety of methods to solve quadratic equations	quadratic equation factoring completing the square quadratic formula roots discriminant	Knows the strengths and limitations of each method Understands the roots of a quadratic equation are given by the quadratic formula Knows the quadratic formula gives exact values Knows the discriminant can provide information about the roots of a quadratic equation	Solves quadratic equations by graphing, factoring, completing the square, and the quadratic formula Analyzes problem situations to decide which method of solving quadratic equations is appropriate		AEA9 AEA16
c: Uses a variety of methods to graph linear equations and inequalities   ITED *	linear equation inequality slope x-intercept y-intercept general line equation dependent variable independent variable	Knows how the slope and y-intercept of a graph are related to the equation Knows the algebraic significance of the parts of a graph Understands properties of graphs and relationships between a graph and its corresponding expression Knows the numerical value of the slope Knows the numerical value of y-intercept	Graphs a linear equation and inequality Recognizes a linear equation and inequality from its graph (ITED) Finds the slope, x-intercept, and y-intercept of a line given its graph, its equation, or two points on the line (ITED) Writes equations in the General Line equation format Identifies the dependent and independent variables Graphs a linear equation and computes the x- and y-intercepts Verifies a point lies on a line given an equation of the line		AEA9 AEA16
d: Uses a variety of methods to solve systems of equations	system of equations substitution elimination	Knows the strengths and limitations of each method Knows whether a system of equations has one solution, no solutions, or infinitely many solutions	Uses a graph to find the solution of a system of equations Uses substitution to solve a system of equations Uses elimination to solve a system of equations		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 a variety of representations to analyze change   ITED *	rates of change attribute slope	Understands change can be described mathematically Understands how rates of change can be described numerically and graphically	Represents constant rates as the slope of a straight line graph (ITED) Interprets slope as the amount of one quantity (y) per unit amount of another (x) (ITED) Expresses rate of change graphically (ITED) Predicts rate of change from numerical and graphical data (ITED)		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		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 rules 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