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approximations of irrational numbers.AZ 2.1 P0 2Organize collected data in an appropriate graphical representation.AZ 2.1 P0 3Display data as lists, tables, matrices, and plots.AZ 2.1 P0 4Construct equivalent displays of the same data.AZ 2.1 P0 5Identify graphic misrepresentations and distortions of sets of data.AZ 2.1 P0 6Identify which of the measures of central tendency is most appropriate in a given situation.AZ 2.1 P0 7Make reasonable predictions based upon linear patterns in data sets or scatter plots.AZ 2.1 P0 8Make reasonable predictions for a set of data, based on patterns.AZ 2.1 P0 9Draw inferences from charts, tables, graphs, plots, or data sets.AZ 2.1 P0 10Apply the concepts of mean, median, mode, range, and quartiles to summarize data sets.AZ 2.1 P0 13Draw a line of best fit for a scatter plot.AZ 2.1 P0 14Determine whether displayed data has positive, negative, or no correlation.AZ 2.2 P0 1Find the probability that a specific event will occur, with or without replacement.AZ 2.2 P0 2Determine simple probabilities related to geometric figures.AZ 2.2 P0 3Predict the outcome of a grade-level appropriate probability experiment.AZ 2.2 P0 4Record the data from a performing a grade-level appropriate probability experiment.AZ 2.2 P0 5Compare the outcome of an experiment to predictions made prior to performing the experiment.AZ 2.2 P0 6Distinguish between independent and dependent events.AZ 2.2 P03Note to FSC: In correlation spreadsheet, add space before final digit (AZ 2.2 P0 3).AZ 2.3 P0 1Determine the number of possible outcomes for a contextual event using a chart, a tree diagram, or the counting principle.AZ 2.3 P0 2Determine when to use combinations versus permutations in counting objects.AZ 2.3 P0 3Use combinations or permutations to solve contextual problems.AZ 3.1 P0 1Communicate a grade-level appropriate iterative or recursive pattern, using symbols or numbers.AZ 3.1 P0 2Find the nth term of an iterative or recursive pattern.AZ 3.2 P0 1Determine if a relationship is a function, given a graph, table, or set of ordered pairs.AZ 3.2 P0 2Describe a contextual situation that is depicted by a given graph.AZ 3.2 P0 3Identify a graph that models a given real-world situation.AZ 3.2 P0 4Sketch a graph that models a given contextual situation.AZ 3.2 P0 5Determine domain and range for a function.AZ 3.2 P0 6Determine the solution to a contextual maximum/minimum problem, given the graphical representation.AZ 3.2 P0 7Express the relationship between two variables using tables/matrices, equations, or graphs.AZ 3.2 P0 8Interpret the relationship between data suggested by tables/matrices, equations, or graphs.AZ 3.2 P0 9Determine from two linear equations whether the lines are parallel, perpendicular, coincident, or intersecting but not perpendicular.AZ 3.3 P0 2Simplify algebraic expressions.AZ 3.3 P0 3Multiply and divide monomial expressions with integral exponents.AZ 3.3 P0 4Translate a written expression or sentence into a mathematical expression or sentence.AZ 3.3 P0 5Translate a sentence written in context into an algebraic equation involving multiple operations.AZ 3.3 P0 6Write a linear equation for a table of values.AZ 3.3 P0 7Write a linear algebraic sentence that represents a data set that models a contextual situation.AZ 3.3 P0 8Solve linear (first degree) equations in one variable (may include absolute value).AZ 3.3 P0 9Solve linear inequalities in one variable.AZ 3.3 P0 10Write an equation of the line given: two points on the line, the slope and a point on the line, or the graph of the line.AZ 3.3 P0 11Solve an algebraic proportion.AZ 3.3 P0 12Solve systems of linear equations in two variables (integral coefficients and rational solutions).AZ 3.3 P0 13Add, subtract, and perform scalar multiplication with matrices.AZ 3.3 P0 14Calculate powers and roots of real numbers, both rational and irrational, using technology when appropriate.AZ 3.3 P0 15Simplify square roots and cube roots with monomial radicands (including those with variables) that are perfect squares or perfect cubes.AZ 3.3 P0 16Solve square root radical equations involving only one radical.AZ 3.3 P0 17Solve quadratic equations.AZ 3.3 P0 18Identify the sine, cosine, and tangent ratios of the acute angles of a right triangle.AZ 3.4 P0 1Determine slope, x-, and y-intercepts of a linear equation.AZ 4.1 P0 1Identify the attributes of special triangles (isosceles, equilateral, right).AZ 4.1 P0 14Solve contextual situations using angle and side length relationships.AZ 4.2 P0 3Determine the new coordinates of a point when a single transformation is performed on a planar geometric figure.AZ 4.3 P0 1Graph a quadratic equation with lead coefficient equal to one.AZ 4.3 P0 2Graph a linear equation in two variables.AZ 4.3 P0 3Graph a linear inequality in two variables.AZ 4.3 P0 4Determine the solution to a system of equations in two variables from a given graph.AZ 4.3 P0 6Determine changes in the graph of a linear function when constants and coefficients in its equation are varied.AZ 4.4 P0 4Compare perimeter, area, or volume of figures when dimensions are changed.AZ 4.4 P0 10Solve applied problems using similar triangles.AZ 4.4 PO 9Solve scale factor problems using ratios and proportions.  Note to FSC:  In correlation spreadsheet and here, change letter O to numeral 0 (AZ 4.4 P0 9).AZ 5.1 PO 1Determine whether a given procedure for simplifying an expression is valid.  Note to FSC:  In correlation spreadsheet and here,  change letter O to numeral 0 (AZ 4.4 P0 9).AZ 5.2 P0 9Identify a counterexample for a given conjecture.AZ 5.2 P0 13Construct a simple formal or informal deductive proof.AZ 5.2 P0 14Verify characteristics of a given geometric figure using coordinate formulas such as distance, mid-point, and slope to confirm parallelism, perpendicularity, and congruency.CO 9.1Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems.CO 9.1.1.aCompare and order sets of rational numbers and common irrational numbers (?2, ?5, and ?.).CO 9.1.1.bRecognize and use equivalent representations of rational numbers* and common irrational numbers (?2, ?5, and ?.), including scientific notationCO 9.1.1.cUse very large and very small numbers in real life situations to solve problems (scientific notation, powers).CO 9.1.2.aVerify and apply the properties of the operation �to the power of�.CO 9.1.3.aUse number sense* to estimate and justify the reasonableness of solutions to problems involving rational numbers* and common irrational numbers (for example, circumference, area of a circle, and PythagoreanTheorem).CO 9.2Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in solving these problems.CO 9.2.1.aModel real world phenomena involving linear and non-linear relationships using multiple representations of rules that can take the form of recursive processes, functions*, equations, or inequalities.CO 9.2.2Represent functional relationships using written explanations, tables, equations, and graphs, and describing the connections among these representationsCO 9.2.2.aRepresent functional relationships using written explanations, tables, equations, and graphs, and describe the connections among these representations.CO 9.2.2.bconvert from one functional representation to another.CO 9.2.2.cInterpret a graphical representation of a real-world situation.CO 9.2.3.aSolve problems involving functions* and relations using calculators, graphs, tables, and algebraic methods.CO 9.2.3.bSolve simple systems of equations using algebraic, graphical or numeric methods.CO 9.2.4Analyze and explain the behaviors, transformations, and general properties of types of equations and functions (for example, linear, quadratic, exponential)CO 9.2.4.aIdentify and interpret x- and y- intercepts in the context of a problem.CO 9.2.4.bUsing a graph, identify the maximum and minimum value within a given domain.CO 9.2.4.cAnalyze the effects of change in the leading coefficient and/or the vertical translation* (for example, given y = kx + c and y = kx^2 + c, how do changes in k and/or c affect the graphs?CO 9.2.5Interpret algebraic equations and inequalities geometrically and describe geometric relationships algebraicallyCO 9.2.5,CO 9.2.3.aNote to FSC: In correlation spreadsheet, add space after comma to separate. Should be two standards.CO 9.2.5.aGraph solutions to equations and inequalities in one-and two-dimensions and determine solutions.CO 9.3Graph solutions to equations and inequalities in one-and two-dimensions and determine solutions.CO 9.3.1Graph solutions to equations and inequalities in one-and two-dimensions and determine solutions.CO 9.3.1.cSelect and use an appropriate display to represent and describe a set of data (for example, scatter  plot, line graph and histogram).CO 9.3.2.aAnalyze a graph, table, or summary for misleading characteristics.CO 9.3.3.aFit curves to scatter plots using informal methods or appropriate technology to make predictions about the data.CO 9.3.3.bFit curves to scatter plots using informal methods or appropriate technology to determine the type (positive, negative, or non-existent) of relationship between two data sets.CO 9.3.4Draw conclusions about distributions of data based on analysis of statistical summaries (for example, the combination of mean and standard deviation, and differences between the mean and median)CO 9.3.4.aDetermine, analyze, and use measure of central tendency* (such as mean, median, and mode) and measures of variability  (such as range and quartiles) in problem-solving situations .CO 9.3.5Use experimental and theoretical probability to represent and solve problems involving uncertainty (for example, the chance of playing professional sports if a student is a successful high school athlete)CO 9.3.5.aDetermine the probability of an identified event using the sample space.CO 9.3.5.bMake predictions using theoretical probability in real-world problems .CO 9.3.6.aUse experimental and theoretical probability to represent and solve problems involving uncertainty (for example, the chance of playing professional sports if a student is a successful high school athlete)CO 9.4Determine the probability of an identified event using the sample space.CO 9.4.1.aUse experimental and theoretical probability to represent and solve problems involving uncertainty (for example, the chance of playing professional sports if a student is a successful high school athlete)CO 9.4.2Determine the probability of an identified event using the sample space.CO 9.4.2.bUse the Pythagorean theorem to solve real-world problems.CO 9.4.3.bUse coordinate geometry to solve problems involving shapes and their properties.CO 9.4.4Use trigonometric ratios in problem-solving situations (for example, finding the height of a building from a given point, if the distance to the building and the angle of elevation are known)CO 9.5.1.aUse appropriate measurements to solve problems indirectly (for example, find the height of a flagpole using similar triangles.CO 9.5.1.bUse measurement to solve real-world problems* involving rate of change (for example, distance traveled using rate and time).CO 9.5.1.cDescribe how changing one attribute of a shape affects its angle measure, perimeter, circumference, area, surface area and volume.CO 9.6.1Use ratios, proportions, and percents in problem-solving situationsCO 9.6.1.aUse ratios, proportions, and percents in problem-solving situations that involve rational numbers.CO 9.6.1.cApply direct variation to problem-solving situations.CO 9.6.2Select and using appropriate methods for computing with real numbers in problem-solving situations from among mental arithmetic, estimation, paper-and-pencil, calculator, and computer methods, and determining whether the results are reasonableCO 9.6.2.aApply appropriate computational methods to solve multi-step problems involving rational numbers.CO 9.6.3Describe the limitations of estimation, and assessing the amount of error resulting from estimation within acceptable limitsCT 1.3a(1)Note to FSC: In correlation spreadsheet, add C before 1.3 (CT C1.3a(1)).CT 2.2a(2)Note to FSC: In correlation spreadsheet, add C before 2.2 (CT C2.2a(2)).CT 4.2a(1)Note to FSC: In correlation spreadsheet, add C before 4.2 (CT C4.2a(1)).CT C1.1aDescribe relationships and make generalizations about patterns and functions.CT C1.1a(1)Identify, describe, create and generalize numeric, geometric and statistical patterns with tables, graphs, words and symbolic rules.CT C1.1a(2)Make and justify predictions based on patterns.CT C1.1a(3)Identify the characteristics of functions and relations, including domain and range.CT C1.1a(4)Describe and compare properties and classes of linear, quadratic and exponential functions.CT C1.2aRepresent and analyze linear and non-linear functions and relations symbolically and with tables and graphs.CT C1.2a(1)Represent functions and relations on the coordinate plane.CT C1.2a(2)Identify an appropriate symbolic representation for a function or relation displayed graphically or verbally.CT C1.2a(3)Recognize and explain the meaning of the slope and x- and y-intercepts as they relate to a context, graph, table or equation.CT C1.2a(4)Evaluate and interpret the graphs of linear, exponential and polynomial functions.CT C1.3(1)Note to FSC: In correlation spreadsheet, insert a before (1) (CT C1.3a(1)).CT C1.3a(1)Model and solve problems with linear, quadratic and absolute value equations and linear inequalities.CT C1.3a(2)Determine equivalent representations of an algebraic equation or inequality to simplify and solve problems.CT C1.3a(3)Solve systems of two linear equations using algebraic or graphical methods.CT C2.1aExtend the understanding of number to include integers, rational numbers and real numbers.CT C2.1a(1)Compare, locate, label and order real numbers on number lines, scales, coordinate grids and measurement tools.CT C2.1a(2)Select and use an appropriate form of number (integer, fraction, decimal, ratio, percent, exponential, scientific notation, irrational) to solve practical problems involving order, magnitude, measures, labels, locations and scales.CT C2.2aDevelop strategies for computation and estimation using properties of number systems to solve problems.CT C2.2a(1)Select and use appropriate methods for computing to solve problems in a variety of contexts.CT C2.2a(2)Solve problems involving scientific notation and absolute value.CT C2.2a(3)Develop and use a variety of strategies to estimate values of formulas, functions and roots; to recognize the limitations of estimation; and to judge the implications of the results.CT C2.2bSolve proportional reasoning problems.CT C2.2b(1)Use dimensional analysis to determine equivalent rates.CT C2.2b(2)Solve problems using direct and inverse variation.CT C3.1a(2)Use geometric properties to solve problems in two and three dimensions.CT C3.1b(2)Create logical arguments to solve problems and determine geometric relationships.CT C3.2aVerify geometric relationships using algebra, coordinate geometry and transformations.CT C3.2a(1)Interpret geometric relationships using algebraic equations and inequalities, and vice versa.CT C3.2a(3)Apply transformations to plane figures to determine congruence, similarity, symmetry and tessellations.CT C3.3a(2)Use indirect methods including the PythagoreanTheorem, trigonometric ratios and proportions in similar figures to solve a variety of measurement problems.CT C4.1aCreate the appropriate visual or graphical representation of real data.CT C4.1a(1)Collect real data and create meaningful graphical representations of the data.CT C4.1a(2)Develop, use and explain applications and limitations of linear and nonlinear models and regression in a variety of contexts.CT C4.2aAnalyze real-world problems using statistical techniques.CT C4.2a(3)Determine and use measures of spread and central tendency to describe and compare sets of data.CT C4.3a(1)Determine outcomes and solve problems involving the probabilities of events.CT C4.3a(3)Apply theoretical and experimental probabilities appropriately to solve problems and predict experimental results.CT E.1.1a(5)Solve problems involving direct and inverse variation.  Note to FSC: In correlation spreadsheet, remove period between E and 1 (CT E1.1a(5)).CT E1.1a(1)Describe and compare properties and classes of functions, including exponential, polynomial, rational, logarithmic and trigonometric.CT E1.1a(2)Analyze essential relations in a problem to determine possible functions that could model the situation.CT E1.1a(4)Solve problems involving financial applications including compound interest, amortization of loans, and investments.CT E1.1a(7)Apply the concepts of limits to sequences and asymptotic behavior of functions.CT E1.2(2)Note to FSC: In correlation spreadsheet, insert a before (2) (CT E1.2a(2)).CT E1.2a(1)Relate the graphical representation of a function to its function family and find equations, intercepts, maximum or minimum values, asymptotes and line of symmetry for that function.CT E1.2a(2)Recognize the effect of changes in parameters on the graphs of functions or relations.CT E1.3a(1)Determine equivalent representations of an algebraic equation or inequality to simplify and solve problems.CT E2.1a(3)Justify mathematical procedures and determine how they apply to invented operations using field properties (closure, associative, commutative, distributive, identity and inverse).CT E2.1a(4)Judge the effects of computations with powers and roots on the magnitude of results.CT E3.1a(1)Recognize the relationships between a conditional statement and its converse, inverse and contrapositive.CT E3.3a(2)Use properties of similarity and techniques of trigonometry to make indirect measurements of lengths and angles to solve a variety of problems.CT E4.2a(1)Determine statistical measures to describe univariate data.CT E4.3a(1)Understand and use permutations, combinations, recursion and mathematical induction to solve problems.CT E4.3a(2)Solve problems using finite graphs.ID AL.01Use algebraic symbolism as a tool to represent mathematical relationships.ID AL.01.aUnderstand and use variables, expressions, equations and inequalities.ID AL.02Evaluate algebraic expressions.ID AL.02.aUnderstand and use procedures for operating on algebraic expressions.ID AL.03Solve algebraic equations and inequalities.ID AL.03.aUnderstand and use appropriate procedures to solve linear equations and inequalities.ID AL.03.bUse appropriate procedures to simplify and solve polynomial equations and inequalities.ID AL.04Solve simple linear systems of equations or inequalities.ID AL.04.aUnderstand and use appropriate procedures to solve simple linear systems of equations and inequalities.ID DA.01.aRead and interpret tables, charts, and graphs (scatter plots, line graphs, dimensional graphs, and pie charts).ID DA.02Collect, organize, and display data.ID DA.02.aCollect and organize data, and display the data in tables, charts, and graphs (scatter diagrams, frequency tables, bar graphs, pie charts).ID DA.03Apply simple statistical measurements.ID DA.03.aUnderstand basic statistical concepts including mean (average), median, mode, range, and standard deviation.ID DA.04Understand the basic concepts of probability.ID DA.04.aUnderstand experimental and theoretical probability.ID DA.04.bDistinguish between independent and dependent events.ID DA.04.cKnow that probability ranges from 0% to 100%.  Understand randomness and chance.ID DA.05Make predictions or decisions based on data.ID F.01Understand the concept of functions.ID F.01.aSolve problems that involve varying quantities with variables, expressions, equations, inequalities, and absolute values.ID F.02Represent equations, inequalities and functions in a variety of formats.ID F.02.aRepresent a set of data in a table, as a graph, and as a mathematical relationship.ID F.03Apply functions to a variety of problems.ID F.03.aModel real-world phenomena using polynomial, rational, and basic exponential functions, noting restricted domains.ID G.01Apply concepts of size, shape, and spatial relationships.ID G.01.aUnderstand congruence and similarity as they apply to reflection, rotation, and translation.ID G.01.bUnderstand scaling as it relates to size variations in one-, two-, and three-dimensional objects, while shape is maintained.ID G.02.aUnderstand the basic concepts of right triangle trigonometry (e.g., basic trigonometry ratios such as sine, cosine, and tangent).ID G.02.bUse trigonometric ratio methods to solve problemsID G.02.cKnow and apply the PythagoreanTheorem to solve real-world problems.ID G.03Apply graphing in two dimensions.ID G.03.aUnderstand concepts of the Cartesian Coordinate System.ID M.01.aDetermine length, area, capacity, weight, time, and temperature, with appropriate units.ID M.02Apply concepts of rates and other derived or indirect measurements.ID M.02.aUnderstand equivalent units, comparable units, and conversions.ID M.03Apply the concepts of ratios and proportions.ID M.03.aUnderstand and use proportions, ratio, and scaling.ID M.05Perform error analysis.ID M.O3.aNote to FSC: In correlation spreadsheet,  replace letter O with numeral 0 (ID M.03.a).ID N.01Understand and use numbers.ID N.01.aUnderstand and use positive and negative numbers, fractions, decimals, percentages, and scientific notation.ID N.01.bUnderstand properties of the real number system.ID N.01.cUnderstand properties of roots, exponents, and logarithms.ID N.01.dUse number theory concepts (divisibility rules, factors, multiples, primes) to solve problems.ID N.02Perform computations accurately.ID N.02.aUse the proper order of operations. Perform operations with real numbers.ID N.02.bUse graphs, matrices, and sequences to represent and solve problems.ID PS.01Understand and use a variety of problem-solving skills.ID PS.01.aUse a variety of methods, including common mathematical formulas, to solve problems drawn from daily life.ID PS.01aNote to FSC: In correlation spreadsheet, add period before final letter (ID PS.01.a).ID PS.02Use reasoning skills to recognize problems and express them mathematically.ID PS.02.aUse inductive and deductive reasoning to set up a problem.ID PS.02.bUse logic to make mathematical proofs.ID PS.02.cMake and evaluate logical arguments.ID PS.03Apply appropriate technology and models to find solutions to problems.ID PS.03.aUnderstand the purpose and capabilities of appropriate technology.ID PS.03.bUnderstand the nature and use of mathematical models.ID PS.04Communicate results using appropriate terminology and methods.ID PS.04.aSelect the appropriate means to communicate mathematical information.ID.AL.03Note to FSC: In correlation spreadsheet, remove period between ID and AL (ID AL.03).ID.PS.02.aNote to FSC: In correlation spreadsheet, remove period between ID and PS (ID PS.02.a).IL 6.11.01Recognize, represent, order, compare real numbers, and locate real numbers on a number line.IL 6.11.02Represent numbers in equivalent forms.IL 6.11.03Use matrices to organize data.IL 6.11.04Apply the rules of order of operations to real-number expressions.IL 6.11.05Simplify or test expressions by applying field properties (commutative, associative, distributive), order properties (transitive, reflexive, symmetric), and properties of equality for the set of real numbers.IL 6.11.06Apply number theory concepts to the solution of problems.IL 6.11.07Determine the effects of operations on the magnitudes of quantities.IL 6.11.08Determine the appropriate solution, including rounding, from a context.IL 6.11.09Solve problems involving estimates or data.IL 6.11.10Perform numerical computations with real numbers.IL 6.11.12Solve problems using simple matrix operations (addition, subtraction, multiplication, scalar multiplication).IL 6.11.13Set up, evaluate, or solve single- and multi-step number sentences and word problems with rational numbers using the four basic operations.IL 6.11.16Simplify numerical problems using absolute value.IL 6.11.17Set up, evaluate, or solve number sentences or word problems involving ratios and proportions with rational numbers.IL 6.11.18Set up, evaluate, or solve common problems involving percent.IL 6.11.19Set up, evaluate, or solve problems stated in terms of direct and inverse variation of simple quantities.IL 6.A.4Identify and apply the associative, commutative, distributive and identity properties of real numbers, including special numbers such as pi and square roots.IL 6.B.4Select and use appropriate arithmetic operations in practical situations including calculating wages after taxes, developing a budget and balancing a checkbook.IL 6.D.4Solve problems involving recipes or mixtures, financial calculations, and geometric similarity using ratios, proportions and percents.IL 6ADemonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings.IL 6BInvestigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships.IL 6CCompute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers.IL 6DSolve problems using comparisons of quantities, ratios, proportions and percents.IL 7.11.01Change from one unit to another within the same system of measurement, including calculations with mixed units.IL 7.11.03Change from one unit in one system of measurement to a unit in another system of measurement, given a conversion factor.IL 7.11.04Determine and calculate to an indicated precision the length, width, height, perimeter/circumference, area, volume, surface area, angle measures, or sums of angle measures of common geometric figures or combinations of common geometric figures.IL 7.11.05Describe the general trends of how the change in one measure affects other measures in the same figure.IL 7.11.06Determine the linear measure, perimeter, area, surface area, and volume of similar figures.IL 7.11.07Determine the ratio of perimeters, area, and volumes of figures.IL 7.A.4aApply units and scales to describe and compare numerical data and physical objects.IL 7.A.4bApply formulas in a wide variety of theoretical and practical real-world measurement applications involving perimeter, area, volume, angle, time, temperature, mass, speed, distance, density and monetary values.IL 7.C.4aMake indirect measurements, including heights and distances, using proportions (e.g., finding the height of a tower by its shadow).IL 7.C.5bStudents will be able to determine how changes in one measure may affect other measures (e.g., what happens to the volume and surface area of a cube when the side of the cube is halved).IL 7CSelect and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.IL 8.11.01Simplify or identify equivalent algebraic expressions.IL 8.11.02Represent mathematical relationships using symbolic algebra.IL 8.11.03Identify essential quantitative relationships in a situation, and determine the class or classes of functions that model the relationships.IL 8.11.04Determine a specific term, a finite sum, or a rule that generates terms of a pattern.IL 8.11.05Model and describe slope as a constant rate of change.IL 8.11.06Evaluate variable expressions and functions.IL 8.11.07Identify an equation of a line or an equation of a line of best fit from given information.IL 8.11.08Recognize and describe the general shape and properties of functions from graphs, tables, or equations.IL 8.11.09Identify slope from an equation, table of values, or graph.IL 8.11.10Interpret the role of the coefficients and constants on the graphs of linear and quadratic functions, given a set of equations.IL 8.11.11Analyze functions by investigating domain, range, rates of change, intercepts, and zeros.IL 8.11.12Create and connect representations that are tabular, graphic, numeric, and symbolic from a set of data.IL 8.11.13Represent quantitative relationships graphically, and interpret the meaning of the graph or a specific part of the graph as it relates to the situation represented by the graph.IL 8.11.14Model problems using mathematical functions and relations.IL 8.11.15Interpret the graph of a system of equations and inequalities, including cases where there are no solutions.IL 8.11.16Solve linear equations and inequalities, including selecting and evaluating formulas.IL 8.11.17Solve systems of equations and inequalities.IL 8.11.19Solve quadratic equations over the complex number system, including selecting and evaluating formulas.IL 8.11.21Recognize and apply mathematical and algebraic axioms, theorems of algebra, and deductive reasoning.IL 8.11.22Identify equivalent forms of equations, inequalities, and systems of equations.IL 8.A.4aStudents will be able to use algebraic methods to convert repeating decimals to fractions.IL 8.A.4bRepresent mathematical patterns and describe their properties using variables and mathematical symbols.IL 8.B.4aRepresent algebraic concepts with physical materials, words, diagrams, tables, graphs, equations, and inequalities and use appropriate technology.IL 8.B.4bUse the basic functions of absolute value, square root, linear, quadratic and step to describe numerical relationships.IL 8.C.4aAnalyze and report the effects of changing coefficients, exponents and other parameters on functions and their graphs.IL 8.C.4bApply algebraic properties and procedures with matrices, vectors, functions and sequences using data found in business, industry and consumer situations.IL 8.D.4Formulate and solve linear and quadratic equations and linear inequalities algebraically and investigate nonlinear inequalities using graphs, tables, calculators and computers.IL 8ADescribe numerical relationships using variables and patterns.IL 8BInterpret and describe numerical relationships using tables, graphs and symbols.IL 8CSolve problems using systems of numbers and their properties.IL 8DUse algebraic concepts and procedures to represent and solve problems.IL 9.11.01Apply the Pythagorean theorem.IL 9.11.02Identify and represent transformations (rotations, reflections, translations, dilations) of an object in the plane, and describe the effects of transformations on points in words or coordinates.IL 9.11.03Determine how changing the scale factor affects the size and position of a figure in the plane.IL 9.11.05Identify, apply, or solve problems that require knowledge of geometric properties of plane figures.IL 9.11.09Solve problems that involve calculating distance, midpoint, and slope using coordinate geometry.IL 9.11.12Solve problems involving similar figuresIL 9.11.14Describe how two or more objects are related in space.IL 9.11.16Recognize and apply the conditions that assure congruence and similarity.IL 9.11.18Identify a counter-example to disprove a conjecture.IL 9.11.19Determine distances and angle measures using indirect measurement.IL 9.11.20Solve problems using 45?-45?-90? and 30?-60?-90? triangles.IL 9.11.22Define, identify, and evaluate trigonometric ratios.IL 9.11.23Use trigonometric identities.IL 9.B.4Recognize and apply relationships within and among geometric figures.IL 9.C.4aConstruct and test logical arguments for geometric situations using technology where appropriate.IL 9.C.4bConstruct and communicate convincing arguments for geometric situations.IL 9.D.4Analyze and solve problems involving triangles (e.g., distances which cannot be measured directly) using trigonometric ratios.IL 9ADemonstrate and apply geometric concepts involving points, lines, planes and space.IL 9BIdentify, describe, classify and compare relationships using points, lines, planes and solids.IL 9CConstruct convincing arguments and proofs to solve problems.IL 9DUse trigonometric ratios and circular functions to solve problems.IL 10.11.01Read, interpret, predict, interpolate, extrapolate, and use information from a variety of graphs, charts, and tables.IL 10.11.02Translate from one representation of data to another.IL 10.11.05Calculate, interpret, and use measures of central tendency and dispersion.IL 10.11.08Compute probabilities for compound events.IL 10.11.10Apply counting techniques.IL 10.A.4aRepresent and organize data by creating lists, charts, tables, frequency distributions, graphs, scatter plots and box plots.IL 10.A.4bAnalyze data using mean, median, mode, range, variance and standard deviation of a data set, with and without the use of technology.IL 10.C.4bDesign and conduct simulations (e.g., waiting times at restaurants, probabilities of births, likelihood of game prizes), with and without the use of technology.IL 10.C.5aCompute conditional probabilities and the probabilities of independent events.IL 10CDetermine, describe and apply the probabilities of events.KS 1.4The student models, performs, and explains computation with real numbers and polynomials in a variety of situations.KS AI 1.1.1The student generates and/or solves real-world problems using equivalent representations of real numbers and algebraic expressions.KS AI 1.2.1aThe student generates and/or solves real-world problems with real numbers using the concepts of these properties to explain reasoning: commutative, associative, distributive, and substitution properties.KS AI 1.2.1bThe student generates and/or solves real-world problems with real numbers using the concepts of these properties to explain reasoning: identity and inverse properties of addition and multiplication.KS AI 1.2.1dThe student generates and/or solves real-world problems with real numbers using the concepts of these properties to explain reasoning: addition and multiplication properties of equality.KS AI 1.2.1eThe student generates and/or solves real-world problems with real numbers using the concepts of these properties to explain reasoning: zero product property.KS AI 1.3.4The student explains the impact of estimation on the result of a real-world problem (underestimate, overestimate, range of estimates).KS AI 1.4.1aThe student generates and/or solves multi-step real-world problems with real numbers and algebraic expressions using computational procedures (addition, subtraction, multiplication, division, roots, and powers excluding logarithms), and mathematical concepts with: applications from business, chemistry, and physics that involve addition, subtraction, multiplication, division, squares, and square roots when the formulae are given as part of the problem and variables are defined.KS AI 1.4.1cThe student generates and/or solves multi-step real-world problems with real numbers and algebraic expressions using computational procedures (addition, subtraction, multiplication, division, roots, and powers excluding logarithms), and mathematical concepts with:  probabilities.KS AI 1.4.1dThe student generates and/or solves multi-step real-world problems with real numbers and algebraic expressions using computational procedures (addition, subtraction, multiplication, division, roots, and powers excluding logarithms), and mathematical concepts with:  application of percents.KS AI 1.4.1eThe student generates and/or solves multi-step real-world problems with real numbers and algebraic expressions using computational procedures (addition, subtraction, multiplication, division, roots, and powers excluding logarithms), and mathematical concepts with: simple exponential growth and decay (excluding logarithms) and economics.KS AI 2.1.1The student recognizes the same general pattern presented in different representations [numeric (list or table), visual (picture, table, or graph), and written].KS AI 2.1.2The student solves real-world problems with arithmetic or geometric sequences by using the explicit equation of the sequence.KS AI 2.2.1The student recognizes the same general pattern presented in different representations [numeric (list or table), visual (picture, table, or graph), and written].KS AI 2.2.2aThe student solves real-world problems with arithmetic or geometric sequences by using the explicit equation of the sequence.KS AI 2.2.2bThe student recognizes the same general pattern presented in different representations [numeric (list or table), visual (picture, table, or graph), and written].KS AI 2.2.2cThe student solves real-world problems with arithmetic or geometric sequences by using the explicit equation of the sequence.KS AI 2.2.2dThe student recognizes the same general pattern presented in different representations [numeric (list or table), visual (picture, table, or graph), and written].KS AI 2.2.2eThe student solves real-world problems with arithmetic or geometric sequences by using the explicit equation of the sequence.KS AI 2.3.1The student recognizes the same general pattern presented in different representations [numeric (list or table), visual (picture, table, or graph), and written].KS AI 2.3.2The student solves real-world problems with arithmetic or geometric sequences by using the explicit equation of the sequence.KS AI 2.3.3aThe student recognizes the same general pattern presented in different representations [numeric (list or table), visual (picture, table, or graph), and written].KS AI 2.3.3cThe student analyzes how changes in the constants and/or coefficients within a quadratic function in the form of y = ax2 + c affects the appearance of a graph.KS AI 2.4.1aThe student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships.  Mathematical models include:  process models (concrete objects, pictures, diagrams, number lines, hundred charts, measurement tools, multiplication arrays, division sets, or coordinate grids) to model computational procedures, algebraic relationships, and mathematical relationships and to solve equations.KS AI 2.4.1bThe student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships.  Mathematical models include: factor trees to model least common multiple, greatest common factor, and prime factorization.KS AI 2.4.1cThe student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships.  Mathematical models include: algebraic expressions to model relationships between two successive numbers in a sequence or other numerical patterns.KS AI 2.4.1dThe student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships.  Mathematical models include: equations and inequalities to model numerical and geometric relationships.KS AI 2.4.1eThe student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships.  Mathematical models include: function tables to model numeric and algebraic relationships.KS AI 2.4.1gThe student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include: constructions to model geometric theorems and properties.KS AI 2.4.1hThe student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships.  Mathematical models include: two- and three-dimensional geometric models (geoboards, dot paper, coordinate plane, nets, or solids) and real-world objects to model perimeter, area, volume, and surface area, properties of two- and three-dimensional figures, and isometric views of three-dimensional figures.KS AI 2.4.1iThe student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships.  Mathematical models include: scale drawings to model large and small real-world objects.KS AI 2.4.2The student uses the mathematical modeling process to analyze and make inferences about real-world situations.KS AI 3.1.1aThe student solves real-world problems by using the properties of corresponding parts of similar and congruent figures, e.g., scale drawings, map reading, or proportions.KS AI 3.1.1bThe student solves real-world problems by applying the PythagoreanTheorem.KS AI 3.2.1aThe student solves real-world problems by converting within the customary and the metric systems.KS AI 3.2.1dThe student solves real-world problems by using the Pythagorean theorem.KS AI 3.2.1eThe student solves real-world problems by using rates of change.KS AI 3.2.3The student uses indirect measurements to measure inaccessible objects.KS AI 3.4.2The student translates between the written, numeric, algebraic, and geometric representations of a real-world problem.KS AI 3.4.3The student recognizes and explains the effects of scale changes on the appearance of the graph of an equation involving a line or parabola.KS AI 3.4.4The student analyzes how changes in the constants and/or leading coefficients within the equation of a line or parabola affects the appearance of the graph of the equation.KS AI 4.1.1The student translates between the written, numeric, algebraic, and geometric representations of a real-world problem.KS AI 4.1.2aThe student recognizes and explains the effects of scale changes on the appearance of the graph of an equation involving a line or parabola.KS AI 4.1.3The student compares theoretical probability (expected results) with empirical probability (experimental results) of two independent and/or dependent events and understands that the larger the sample size, the greater the likelihood that experimental results will match theoretical probability.KS AI 4.1.4The student uses conditional probabilities of two dependent events in an experiment, simulation, or situation to make predictions and analyze decisions.KS AI 4.2.1aThe student organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including, a title, labels, categories, and rational number intervals using these data displays: frequency tables and line plots.KS AI 4.2.1eThe student organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including, a title, labels, categories, and rational number intervals using these data displays: frequency tables and line plots.KS AI 4.2.1fThe student organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including, a title, labels, categories, and rational number intervals using these data displays: frequency tables and line plots.KS AI 4.2.1gThe student organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including, a title, labels, categories, and rational number intervals using these data displays: frequency tables and line plots.KS AI 4.2.6The student approximates a line of best fit given a scatter plot, makes predictions, and analyzes decisions using the equation of that line.KS KBI 1.1.1The student knows, explains, and uses equivalent representations for real numbers and algebraic expressions including integers, fractions, decimals, percents, ratios; rational number bases with integer exponents; rational numbers written in scientific notation; absolute value; time; and moneyKS KBI 1.1.2The student compares and orders real numbers and/or algebraic expressions and explains the relative magnitude between themKS KBI 1.1.3aThe student knows and explains what happens to the product or quotient when a real number is multiplied or divided by: a rational number greater than zero and less than one.KS KBI 1.1.3bThe student knows and explains what happens to the product or quotient when a real number is multiplied or divided by a rational number greater than one.KS KBI 1.1.3cThe student knows and explains what happens to the product or quotient when a real number is multiplied or divided by a rational number less than zero.KS KBI 1.2.1The student explains and illustrates the relationship between the subsets of the real number system [natural (counting) numbers, whole numbers, integers, rational numbers, irrational numbers] using mathematical models.KS KBI 1.2.2The student identifies all the subsets of the real number system [natural (counting) numbers, whole numbers, integers, rational numbers, irrational numbers] to which a given number belongs.KS KBI 1.2.3aThe student names, uses, and describes these properties with the real number system and demonstrates their meaning including the use of concrete objects: commutative, associative, distributive, and substitution properties.KS KBI 1.2.3bThe student names, uses, and describes these properties with the real number system and demonstrates their meaning including the use of concrete objects: identity properties for addition and multiplication and inverse properties of addition and multiplication.KS KBI 1.2.3cThe student names, uses, and describes these properties with the real number system and demonstrates their meaning including the use of concrete objects: symmetry property of equality.KS KBI 1.2.3dThe student names, uses, and describes these properties with the real number system and demonstrates their meaning including the use of concrete objects: addition and multiplication properties of equality and inequalities.KS KBI 1.2.3eThe student names, uses, and describes these properties with the real number system and demonstrates their meaning including the use of concrete objects: zero product property.KS KBI 1.3.1The student explains and illustrates the relationship between the subsets of the real number system [natural (counting) numbers, whole numbers, integers, rational numbers, irrational numbers] using mathematical models.KS KBI 1.3.2The student identifies all the subsets of the real number system [natural (counting) numbers, whole numbers, integers, rational numbers, irrational numbers] to which a given number belongs.KS KBI 1.3.3The student names, uses, and describes these properties with the real number system and demonstrates their meaning including the use of concrete objects: commutative, associative, distributive, and substitution properties.KS KBI 1.3.4The student names, uses, and describes these properties with the real number system and demonstrates their meaning including the use of concrete objects: identity properties for addition and multiplication and inverse properties of addition and multiplication.KS KBI 1.4.1The student computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology.KS KBI 1.4.2aThe student performs and explains these computational procedures: N addition, subtraction, multiplication, and division using the order of operations.KS KBI 1.4.2b.iThe student performs and explains these computational procedures: multiplication or division to find a percent of a number.KS KBI 1.4.2b.iiThe student performs and explains these computational procedures: multiplication or division to find percent of increase and decrease.KS KBI 1.4.2b.iiiThe student performs and explains these computational procedures: multiplication or division to find percent one number is of another number.KS KBI 1.4.2b.ivThe student performs and explains these computational procedures: multiplication or division to find a number when a percent of the number is given.KS KBI 1.4.2dThe student performs and explains these computational procedures: simplification of radical expressions (without rationalizing denominators) including square roots of perfect square monomials and cube roots of perfect cubic monomials.KS KBI 1.4.2eThe student performs and explains these computational procedures: simplification or evaluation of real numbers and algebraic monomial expressions raised to a whole number power and algebraic binomial expressions squared or cubed.KS KBI 1.4.2fThe student performs and explains these computational procedures: simplification of products and quotients of real number and algebraic monomial expressions using the properties of exponents.KS KBI 1.4.2gThe student performs and explains these computational procedures: matrix addition.KS KBI 1.4.3The student finds prime factors, greatest common factor, multiples, and the least common multiple of algebraic expressions.KS KBI 2.1.1aThe student identifies, states, and continues the following patterns using various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written: arithmetic and geometric sequences using real numbers and/or exponents.KS KBI 2.1.1bThe student identifies, states, and continues the following patterns using various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written: patterns using geometric figures.KS KBI 2.1.1cThe student identifies, states, and continues the following patterns using various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written: algebraic patterns including consecutive number patterns or equations of functions.KS KBI 2.1.2The student generates and explains a pattern.KS KBI 2.1.3The student classifies sequences as arithmetic, geometric, or neither.KS KBI 2.1.4aThe student defines: a recursive or explicit formula for arithmetic sequences and finds any particular term.KS KBI 2.1.4bThe student defines: a recursive or explicit formula for geometric sequences and finds any particular term.KS KBI 2.2.1The student knows and explains the use of variables as parameters for a specific variable situation.KS KBI 2.2.2The student manipulates variable quantities within an equation or inequality.KS KBI 2.2.3aThe student solves:  N linear equations and inequalities both analytically and graphically.KS KBI 2.2.3bThe student solves: quadratic equations with integer solutions (may be solved by trial and error, graphing, quadratic formula, or factoring).KS KBI 2.2.3cThe student solves: N systems of linear equations with two unknowns using integer coefficients and constants.KS KBI 2.2.3dThe student solves: radical equations with no more than one inverse operation around the radical expression.KS KBI 2.2.3eThe student solves: equations where the solution to a rational equation can be simplified as a linear equation with a nonzero denominator.KS KBI 2.2.3fThe student solves: equations and inequalities with absolute value quantities containing one variable with a special emphasis on using a number line and the concept of absolute value.KS KBI 2.3.1The student evaluates and analyzes functions using various methods, including mental math, paper and pencil, concrete objects, and graphing utilities or other appropriate technology.KS KBI 2.3.2The student matches equations and graphs of constant and linear functions and quadratic functions limited to y = ax2 + c.KS KBI 2.3.3The student determines whether a graph, list of ordered pairs, table of values, or rule represents a function.KS KBI 2.3.4The student determines x- and y-intercepts and maximum and minimum values of the portion of the graph that is shown on a coordinate plane.KS KBI 2.3.5aThe student identifies domain and range of relationships given the graph or table.KS KBI 2.3.5bThe student identifies domain and range of linear, constant, and quadratic functions given the equation(s).KS KBI 2.3.6The student recognizes how changes in the constant and/or slope within a linear function changes the appearance of a graph.KS KBI 2.3.7The student uses function notation.KS KBI 2.3.8The student  evaluates function(s) given a specific domain.KS KBI 2.3.9The student describes the difference between independent and dependent variables and identifies independent and dependent variables.KS KBI 2.4.1The student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships.KS KBI 2.4.1aThe student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships.  Mathematical models include:  process models (concrete objects, pictures, diagrams, number lines, hundred charts, measurement tools, multiplication arrays, division sets, or coordinate grids) to model computational procedures, algebraic relationships, and mathematical relationships and to solve equations.KS KBI 2.4.1bThe student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships.  Mathematical models include: factor trees to model least common multiple, greatest common factor, and prime factorization.KS KBI 2.4.1cThe student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships.  Mathematical models include: algebraic expressions to model relationships between two successive numbers in a sequence or other numerical patterns.KS KBI 2.4.1dThe student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships.  Mathematical models include: equations and inequalities to model numerical and geometric relationships.KS KBI 2.4.1eThe student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships.  Mathematical models include: function tables to model numeric and algebraic relationships.KS KBI 2.4.1fThe student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships.  Mathematical models include: coordinate planes to model relationships between ordered pairs and equations and inequalities and linear and quadratic functions.KS KBI 2.4.1iThe student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships.  Mathematical models include: scale drawings to model large and small real-world objects.KS KBI 2.4.1kThe student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships.  Mathematical models include: geometric models (spinners, targets, or number cubes), process models (concrete objects, pictures, diagrams, or coins), and tree diagrams to model probability.KS KBI 2.4.1lThe student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships.  Mathematical models include: frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, charts, tables, single and double stem-and-leaf plots, scatter plots, box-and-whisker plots, histograms, and matrices to organize and display data.KS KBI 2.4.1mThe student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships.  Mathematical models include: Venn diagrams to sort data and show relationships.KS KBI 3.1.4The student recognizes that similar figures have congruent angles, and their corresponding sides are proportional.KS KBI 3.1.5aThe student uses the PythagoreanTheorem to determine if a triangle is a right triangle.KS KBI 3.1.5bThe student uses the PythagoreanTheorem to find the missing side of a right triangle.KS KBI 3.2.4cThe student states, recognizes, and applies formulas for volume of rectangular solids.KS KBI 3.2.5The student uses given measurement formulas to find perimeter, area, volume, and surface area of two- and three-dimensional figures (regular and irregular)KS KBI 3.2.6The student recognizes and applies properties of corresponding parts of similar and congruent figures to find measurements of missing sides.KS KBI 3.2.7The student knows, explains, and uses ratios and proportions to describe rates of change.KS KBI 3.3.1The student describes and performs single and multiple transformations [refection, rotation, translation, reduction (contraction/shrinking), enlargement (magnification/growing) on two- and three-dimensional figures.KS KBI 3.4.3The student calculates the slope of a line from a list of ordered pairs on the line and explains how the graph of the line is related to its slope.KS KBI 3.4.4The student finds and explains the relationship between the slopes of parallel and perpendicular lines.KS KBI 3.4.6The student recognizes the equation of a line and transforms the equation into slope-intercept form in order to identify the slope and y-intercept and uses this information to graph the line.KS KBI 3.4.7The student recognizes the equation y = ax2 + c as a parabola; represents and identifies characteristics of the parabola including opens upward or opens downward, steepness (wide/narrow), the vertex, maximum and minimum values, and line of symmetry; and sketches the graph of the parabola.KS KBI 3.4.8The student explains the relationship between the solution(s) to systems of equations and systems of inequalities in two unknowns and their corresponding graphs, e.g., for equations, the lines intersect in one point, no points, or infinite points; and for inequalities, all points in double-shaded areas are solutions for both inequalities.KS KBI 4.1.3The student explains the relationship between probability and odds and computes one given the other.KS KBI 4.2.1aThe student organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including, a title, labels, categories, and rational number intervals using these data displays: frequency tables and line plots.KS KBI 4.2.1bThe student organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including, a title, labels, categories, and rational number intervals using these data displays: bar, line, and circle graphs.KS KBI 4.2.1eThe student organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including, a title, labels, categories, and rational number intervals using these data displays: stem-and-leaf plots (single and double).KS KBI 4.2.1fThe student organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including, a title, labels, categories, and rational number intervals using these data displays: scatter plots.KS KBI 4.2.1gThe student organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including, a title, labels, categories, and rational number intervals using these data displays: box-and-whisker plots.KS KBI 4.2.1hThe student organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including, a title, labels, categories, and rational number intervals using these data displays: histograms.KS KBI 4.2.5The student approximates a line of best fit given a scatter plot and makes predictions using the graph or the equation of that line.MA A1.8bNote to FSC: In correlation spreadsheet, add P. before 8b (MA A1.P.8b).MA A1.D.1Select, create, and interpret an appropriate graphical representation (e.g., scatter plot, table, stem-and-leaf plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) for a set of data and use appropriate statistics to communicate information about the data.They will use these notions to compare different sets of data.MA A1.D.2Approximate a line of best fit (trend line) given a set of data (e.g., scatter plot).They will use technology when appropriate.MA A1.M.1Note to FSC: In correlation spreadsheet, delete MA A1.M.1   there is no such standard.MA A1.N.1aIdentify and use the properties of operations on real numbers, including the associative, commutative, and distributive properties.MA A1.N.1bIdentify and use the identity and inverse elements for addition and multiplication.MA A1.N.1cIdentify and use nth roots of positive real numbers for any positive integer n.MA A1.N.1dIdentify and use the inverse relationship between taking the nth root of and the nth power of a positive real number.MA A1.N.2Simplify numerical expressions, including those involving positive integer exponents or the absolute value e.g., 3(24 - 1) = 45, 4|3 - 5| + 6 = 14; apply such simplifications in the solution of problems.MA A1.N.3Find the approximate value for solutions to problems involving square roots and cube roots without the use of a calculator.MA A1.N.4Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers.MA A1.P.1Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative, recursive (e.g., Fibonacci Numbers), linear, quadratic, and exponential functional relationships.MA A1.P.2Use properties of the real number system to judge the validity of equations and inequalities, to prove or disprove statements, and to justify every step in a sequential argument.MA A1.P.3Demonstrate an understanding of relations and functions.They will identify the domain, range, dependent, and independent variables of functions.MA A1.P.4Translate between different representations of functions and relations: graphs, equations, point sets, and tabular.MA A1.P.5Demonstrate an understanding of the relationship between various representations of a line.MA A1.P.5aDetermine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line.MA A1.P.5bFind a linear equation describing a line from a graph or a geometric description of the line, by using the point-slope or slope-intercept formulas. Explain the significance of positive, negative, zero, or undefined slope.MA A1.P.5cExplain the significance of a positive, negative, zero, or undefined slope.MA A1.P.6Find linear equations that represent lines either perpendicular or parallel to a given line and through a point, e.g., by using the point-slope form of the equation.MA A1.P.7Add, subtract, and multiply polynomials.They will divide polynomials by monomials.MA A1.P.8aDemonstrate facility in symbolic manipulation of polynomial and rational expressions by rearranging and collecting terms.MA A1.P.8bDemonstrate facility in symbolic manipulation of polynomial and rational expressions by factoring (e.g., a2 - b2 = (a + b)(a - b), x2 + 10x + 21 = (x + 3)(x + 7), 5x4 + 10x3 - 5x2 = 5x2 (x2 + 2x - 1)).MA A1.P.8cDemonstrate facility in symbolic manipulation of polynomial and rational expressions by identifying and canceling common factors in rational expressions.MA A1.P.8dDemonstrate facility in symbolic manipulation of polynomial and rational expressions by applying the properties of positive integer exponents.MA A1.P.9Find solutions to quadratic equations (with real roots) by factoring, completing the square, or using the quadratic formula.They will demonstrate an understanding of the equivalence of the methods.MA A1.P.10Solve equations and inequalities including those involving absolute value of linear expressions (e.g., |x � 2| > 5) and apply to the solution of problems.MA A1.P.11Solve everyday problems that can be modeled using linear, reciprocal, quadratic, or exponential functions; apply appropriate tabular, graphical, or symbolic methods to the solution; and use technology.MA A1.P.12Solve everyday problems that can be modeled using systems of linear equations or inequalities; apply algebraic and graphical methods to the solution; and use technology.MA A1.P7Note to FSC: In correlation spreadsheet,  add period before final number (MA A1.P.7).MA A1.P10Note to FSC: In correlation spreadsheet, add period before final number (MA A1.P.10).MA A1.P11Note to FSC: In correlation spreadsheet, add period before final number (MA A1.P.11).MP A1.P.11Note to FSC: In correlation spreadsheet, prefix should be MA, not MP (MA A1.P.11).MD 1.1The student will analyze a wide variety of patterns and functional relationships using the language of mathematics and appropriate technology.MD 1.1.1The student will recognize, describe, and/or extend patterns and functional relationships that are expressed numerically, algebraically, and/or geometrically.MD 1.1.2The student will represent patterns and/or functional relationships in a table, as a graph, and/or by mathematical expression.MD 1.1.3The student will apply addition, subtraction, multiplication, and/or division of algebraic expressions to mathematical and real-world problems.MD 1.1.4The student will describe the graph of a non-linear function and discuss its appearance in terms of the basic concepts of maxima and minima, zeros (roots), rate of change, domain and range, and continuity.MD 1.2The student will model and interpret real-world situations using the language of mathematics and appropriate technology.MD 1.2.1The student will determine the equation for a line, solve linear equations, and/or describe the solutions using numbers, symbols, and/or graphs.MD 1.2.2The student will solve linear inequalities and describe the solutions using numbers, symbols, and/or graphs.MD 1.2.3The student will solve and describe using numbers, symbols, and/or graphs if and where two straight lines intersect.MD 1.2.4The student will describe how the graphical model of a non-linear function represents a given problem and will estimate the solution.MD 1.2.5The student will apply formulas and/or use matrices (arrays of numbers) to solve real-world problems.MD 2.1.4The student will construct and/or draw and/or validate properties of geometric figures using appropriate tools and technology.MD 2.2.1The student will identify and/or verify congruent and similar figures and/or apply equality or proportionality of their corresponding parts.MD 2.2.2The student will solve problems using two-dimensional figures and/or right-triangle trigonometry.MD 2.2.3The student will use inductive or deductive reasoning.MD 2.3.1The student will use algebraic and/or geometric properties to measure indirectly.MD 3.1The student will collect, organize, analyze, and present data.MD 3.1.2The student will use the measures of central tendency and/or variability to make informed conclusions.MD 3.1.3The student will calculate theoretical probability or use simulations or statistical inference from data to estimate the probability of an event.MD 3.2The student will apply the basic concepts of statistics and probability to predict possible outcomes of real-world situations.MD 3.2.2The student will interpret data and/or make predictions by finding and using a line of best fit and by using a given curve of best fit.MD 3.2.3The student will communicate the use and misuse of statistics.MI I.1.1To comeMI I.1.2To comeMI I.1.3To comeMI I.1.4To comeMI I.1.5To comeMI I.2.1To comeMI I.2.2To comeMI I.2.3To comeMI I.2.4To comeMI I.2.5To comeMI I.2.6To comeMI II.1.1To comeMI II.1.6To comeMI II.2.2To comeMI II.2.3To comeMI II.2.5To comeMI II.3.2To comeMI II.3.3To comeMI II.3.4To comeMI II.3.5To comeMI II.3.6To comeMI III.1.2To comeMI III.1.3To comeMI III.1.4To comeMI III.2.1To comeMI III.2.2To comeMI III.2.3To comeMI III.3.1To comeMI III.3.4To comeMI IV.1.1To comeMI IV.1.3To comeMI IV.1.4To comeMI IV.2.1To comeMI IV.2.2To comeMI IV.2.5To comeMI IV.3.1To comeMI IV.3.2To comeMI IV.3.3To comeMI IV.3.4To comeMI IV.3.5To comeMI V.1.1To comeMI V.1.2To comeMI V.1.3To comeMI V.1.4To comeMI V.2.1To comeMI V.2.2To comeMI V.2.3To comeMI V.2.4To comeMI V.2.5To comeMI VI 2.5To comeMI VI.1.1To comeMI VI.1.2To comeMI VI.1.3To comeMI VI.1.5To comeMI VI.2.1To comeMI VI.2.5To comeMN I.A.3To comeMN I.A.4To comeMN I.D.1To comeMN II.ATo comeMN II.B.1To comeMN II.B.2To comeMN III.ATo comeMN III.A.1To comeMN III.A.2To comeMN III.A.3To comeMN III.A.4To comeMN III.A.5To comeMN III.BTo comeMN III.B.1To comeMN III.B.2To comeMN III.B.3To comeMN III.B.4To comeMN III.B.5To comeMN III.B.6To comeMN III.B.7To comeMN III.B.8To comeMN III.B.9To comeMN III.B.10To comeMN III.B.11To comeMN III.B.12To comeMN IV.ATo comeMN IV.A.1To comeMN IV.A.2To comeMN IV.A.3To comeMN IV.A.6To comeMN IV.B.1To comeMN IV.B.4To comeMN IV.B.6To comeMN V.BTo comeMN V.B.1To comeMN V.B.3To comeMN V.B.4To comeMN V.B.5To comeMN V.B.6To comeD2Cgiven a scatterplot, determine an equation for a line of best fit.  Note to FSC: In correlation spreadsheet,  this should be MO D.2.c.9.MO A.1.b.9generalize patterns using explicitly or recursively defined functionsMO A.1.c.9compare and contrast various forms of representations of patternsMO A.1.d.9understand and compare the properties of linear and exponential functions (include intercepts)MO A.1.e.9describe the effects of parameter changes on linear functionsMO A.2.a.9use symbolic algebra to represent and solve problems that involve linear relationships, including absolute value and recursive relationshipsMO A.2.b.9describe and use algebraic manipulations, including factoring and rules of integer exponentsMO A.2.c.9use and solve equivalent forms of equations and inequalities (linear)MO A.2.d.9use and solve systems of linear equations with 2 variablesMO A.3.a.9identify quantitative relationships and determine the type(s) of functions that might model the situation to solve the problemMO A.4.a.9analyze linear functions by investigating rates of change and interceptsMO D.1.c.9select, create and use appropriate graphical representation of dataMO D.2.a.9apply statistical concepts to solve problemsMO D.2.b.9given one- variable quantitative data, display the distribution and describe its shapeMO D.3.a.9describe how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference.  Note to FSC: In correlation spreadsheet, replace 9 with 10 (MO D.3.a.10).MO D.4.a.9construct sample spaces and distributionsMO G.1.a.9solve problems involving angle relationships (supplementary, complementary angles) and PythagoreanTheoremMO G.1.b.9apply geometric properties and relationships, such as similarity, to solve multi-step problems in 2 dimensionsMO G.3.a.9represent translations, reflections, rotations, and dilations of objects in the coordinate planeMO G.3.b.9translate and reflect linear functionsMO G.4.b.9draw or use visual models to represent and solve problemsMO M.1.a.9identify and justify appropriate units of measure for velocityMO M.2.d.9analyze effects of computation on precisionMO M.2.e.9use unit analysis to solve problems involving ratesMO N.1.a.9compare and order rational and irrational numbers, including finding their approximate locations on a number lineMO N.2Understand meanings of operations and how they relate to one anotherMO N.2.b.9describe the effects of operations, such as multiplication, division, and computing powers and roots on the magnitude of quantitiesMO N.2.c.9apply properties of exponents (including order of operations) to simplify expressionsMO N.2.d.9apply operations to real numbers, using mental computation or paper-and-pencil calculations for simple cases and technology for more complicated casesMO N.3.c.9apply all operations on real numbersMO N.3.d.9judge the reasonableness of numerical computations and their resultsMO N.3.e.9solve problems involving proportionsMS A1.1Recognize, classify, and use real numbers and their properties.MS A1.1.aDescribe the real number system using a diagram to show the relationships of component sets of numbers that compose the set of real numbers.MS A1.1.bModel properties and equivalence relationships of real numbers.MS A1.1.cDemonstrate and apply properties of real numbers to algebraic expressions.MS A1.1.dPerform basic operations on square roots excluding rational denominators.MS A1.2Recognize, create, extend, and apply patterns, relations, and functions and their applications.MS A1.2.aAnalyze relationships between two variables, identify domain and range, and determine whether a relation is a function.MS A1.2.bExplain and illustrate how change in one variable may result in a change in another variable.MS A1.2.cDetermine the rule that describes a pattern and determine the pattern given the rule.MS A1.3Simplify algebraic expressions, solve and graph equations, inequalities and systems in one and two variables.MS A1.3.aSolve, check, and graph linear equations and inequalities in one variable, including rational coefficients.MS A1.3.bGraph and check linear equations and inequalities in two variables.MS A1.3.cSolve and graph absolute value equations and inequalities in one variable.MS A1.3.dUse algebraic and graphical methods to solve systems of linear equations and inequalities.MS A1.3.eTranslate problem-solving situations into algebraic sentences and determine solutions.MS A1.4.aClassify polynomials and determine the degree.MS A1.4.bAdd, subtract, multiply, and divide polynomial expressions.MS A1.4.cFactor polynomials using algebraic methods and geometric models.MS A1.4.dInvestigate and apply real-number solutions to quadratic equations algebraically and graphically.MS A1.4.fApply polynomial operations to problems involving perimeter and area.MS A1.5Utilize various formulas in problem-solving situations.MS A1.5.aEvaluate and apply formulas (e.g., circumference, perimeter, area, volume, PythagoreanTheorem, interest, distance, rate, and time).MS A1.5.eUse formulas (e.g., point-slope and slope-intercept) to write equations of lines.MS A1.6.aRecognize and demonstrate the appropriate use of terms, symbols, and notations.MS A1.6.bDistinguish between linear and non-linear equations.MS A1.6.cTranslate between verbal expressions and algebraic expressions.MS A1.6.dApply the operations of addition, subtraction, and scalar multiplication to matrices.MS A1.6.eUse scientific notation to solve problems.MS A1.6.fUse appropriate algebraic language to justify solutions and processes used in solving problems.MS A1.7Interpret and apply slope as a rate of change.MS A1.7.aDefine slope as a rate of change using algebraic and geometric representations.MS A1.7.bInterpret and apply slope as a rate of change in problem-solving situations.MS A1.7.cUse ratio and proportion to solve problems including direct variation.MS A1.7.dApply the concept of slope to parallel and perpendicular lines.MS A1.8Analyze data and apply concepts of probability.MS A1.8.aCollect, organize, graph, and interpret data sets, draw conclusions, and make predictions from the analysis of data.MS A1.8.bDefine event and sample spaces and apply to simple probability problems.MS A1.8.cUse counting techniques, permutations, and combinations to solve probability problems.ADP ADP I.1.4Note to FSC: In correlation spreadsheet, delete extra ADP.ADP I.1.1Add, subtract, multiply and divide integers, fractions and decimals.ADP I.1.2Calculate and apply ratios, proportions, rates and percentages to solve problems.ADP I.1.3Use the correct order of operations to evaluate arithmetic expressions, including those containing parentheses.ADP I.1.4Explain and apply basic number theory concepts such as prime number, factor, divisibility, least common multiple and greatest common divisor.ADP I.1.5Multiply and divide numbers expressed in scientific notation.ADP I.2.1Locate the position of a number on the number line, know that its distance from the origin is its absolute value and know that the distance between two numbers on the number line is the absolute value of their difference.ADP I.2.2Determine the relative position on the number line of numbers and the relative magnitude of numbers expressed in fractional form, in decimal form, as roots or in scientific notation.ADP I.3Understand that to solve certain problems and equations, number systems need to be extended from whole numbers to the set of all integers (positive, negative and zero), from integers to rational numbers, from rational numbers to real numbers (rational and irrational numbers) and from real numbers to complex numbers; define and give examples of each of these types of numbers.ADP I.4.1Use calculators appropriately and make estimations without a calculator regularly to detect potential errors.ADP I.4.2Use graphing calculators and computer spreadsheets.ADP J.1.1Understand the properties of integer exponents and roots and apply these properties to simplify algebraic expressions.ADP J.1.3Add, subtract and multiply polynomials; divide a polynomial by a lowdegree polynomial.ADP J.1.4Factor polynomials by removing the greatest common factor; factor quadratic polynomials.ADP J.1.5Add, subtract, multiply, divide and simplify rational expressions.ADP J.1.6Evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified values of their variables.ADP J.2.1Recognize whether a relationship given in symbolic or graphical form is a function.ADP J.2.2Determine the domain of a function represented in either symbolic or graphical form.ADP J.2.3Understand functional notation and evaluate a function at a specified point in its domain.ADP J.3.1Solve linear equations and inequalities in one variable including those involving the absolute value of a linear function.ADP J.3.3Solve systems of two linear equations in two variables.ADP J.3.5Solve quadratic equations in one variable.ADP J.4.1Graph a linear equation and demonstrate that it has a constant rate of change.ADP J.4.2Understand the relationship between the coefficients of a linear equation and the slope and x- and y-intercepts of its graph.ADP J.4.3Understand the relationship between a solution of a system of two linear equations in two variables and the graphs of the corresponding lines.ADP J.4.4Graph the solution set of a linear inequality and identify whether the solution set is an open or a closed half-plane; graph the solution set of a system of two or three linear inequalities.ADP J.4.5Graph a quadratic function and understand the relationship between its real zeros and the x-intercepts of its graph.ADP J.4.7Graph exponential functions and identify their key characteristics.ADP J.4.8Read information and draw conclusions from graphs; identify properties of a graph that provide useful information about the original problem.ADP J.5.1Recognize and solve problems that can be modeled using a linear equation in one variable, such as time/rate/distance problems, percentage increase or decrease problems, and ratio and proportion problems.ADP J.5.2Recognize and solve problems that can be modeled using a system of two equations in two variables, such as mixture problems.ADP J.5.3Recognize and solve problems that can be modeled using a quadratic equation, such as the motion of an object under the force of gravity.ADP J.5.4Recognize and solve problems that can be modeled using an exponential function, such as compound interest problems.ADP J.5.6Recognize and solve problems that can be modeled using a finite geometric series, such as home mortgage problems and other compound interest problems.ADP K.1.1Identify, explain the necessity of and give examples of definitions, axioms and theorems.ADP K.1.2State and prove key basic theorems in geometry such as the Pythagorean theorem, the sum of the angles of a triangle is 180 degrees, and the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.ADP K.2.1Identify and apply properties of and theorems about parallel lines and use them to prove theorems such as two lines parallel to a third are parallel to each other and to perform constructions such as a line parallel to a given line through a point not on the line.ADP K.2.2Identify and apply properties of and theorems about perpendicular lines and use them to prove theorems such as the perpendicular bisectors of line segments are the set of all points equidistant from the two end points and to perform constructions such as the perpendicular bisector of a line segment.ADP K.2.3Identify and apply properties of and theorems about angles and use them to prove theorems such as two lines are parallel exactly when the alternate interior angles they make with a transversal are equal and to perform constructions such as the bisector of an angle.ADP K.3Know the basic theorems about congruent and similar triangles and use them to prove additional theorems and solve problems.ADP K.5Apply the Pythagorean theorem, its converse and properties of special right triangles to solve problems.ADP K.6Use rigid motions (compositions of reflections, translations and rotations) to determine whether two geometric figures are congruent and to create and analyze geometric designs.ADP K.7Know about the similarity of figures and use the scale factor to solve problems.ADP K.8.1Understand that numerical values associated with measurements of physical quantities must be assigned units of measurement or dimensions; apply such units correctly in expressions, equations and problem solutions that involve measurements; and convert a measurement using one unit of measurement to another unit of measurement.ADP K.8.2Determine the perimeter of a polygon and the circumference of a circle; the area of a rectangle, a circle, a triangle and a polygon with more than four sides by decomposing it into triangles; the surface area of a prism, a pyramid, a cone and a sphere; and the volume of a rectangular box, a prism, a pyramid, a cone and a sphere.ADP K.8.3Know that the effect of a scale factor k on length, area and volume is to multiply each by k, k� and k�, respectively.ADP K.10.1Express the intuitive concept of the �slant� of a line in terms of the precise concept of slope, use the coordinates of two points on a line to define its slope, and use slope to express the parallelism and perpendicularity of lines.ADP K.10.2Describe a line by a linear equation.ADP K.11.1Understand how similarity of right triangles allows the trigonometric functions sine, cosine and tangent to be defined as ratios of sides and be able to use these functions to solve problems.ADP K.11.2Apply the trigonometric functions sine, cosine and tangent to solve for an unknown length of a side of a right triangle, given one of the acute angles and the length of another side.ADP L.1.1Organize and display data using appropriate methods (including spreadsheets) to detect patterns and departures from patterns.ADP L.1.2Read and interpret tables, charts and graphs.ADP L.1.3Compute and explain summary statistics for distributions of data including measures of center (mean, median) and spread (range, percentiles, variance, standard deviation).ADP L.1.4Compare data sets using graphs and summary statistics.ADP L.1.5Create scatter plots, analyze patterns and describe relationships in paired data.ADP L.2.1Evaluate reports based on data published in the media by considering the source of the data, the design of the study, and the way the data are analyzed and displayed.ADP L.2.2Identify and explain misleading uses of data.ADP L.2.3Recognize when arguments based on data confuse correlation with causation.ADP L.3.2Design simple experiments or investigations to collect data to answer questions of interest.ADP L.3.4Construct a scatter plot of a set of paired data, and if it demonstrates a linear trend, use a graphing calculator to find the regression line that best fits this data; recognize that the correlation coefficient measures goodness of fit and explain when it is appropriate to use the regression line to make predictions.ADP L.4.1Explain how probability quantifies the likelihood that an event occurs in terms of numbers.ADP L.4.2Explain how the relative frequency of a specified outcome of an event can be used to estimate the probability of the outcome.ADP L.4.4Apply probability concepts such as conditional probability and independent events to calculate simple probabilities.ADP L.4.5Apply probability concepts to practical situations to make informed decisions.NAEP 2005 A1aRecognize, describe, or extend arithmetic, geometric progressions or patterns using words or symbols.NAEP 2005 A1bExpress the function in general terms, given a table, verbal description, or some terms of a sequence.NAEP 2005 A1eIdentify or analyze distinguishing properties of linear, quadratic, inverse or exponential functions from tables, graphs, or equations.NAEP 2005 A1gDetermine the domain and range of functions given various contexts.NAEP 2005 A1hRecognize and analyze the general forms of linear, quadratic, inverse, or exponential functions.NAEP 2005 A1iExpress linear and exponential functions in recursive and explicit form given a table or verbal description.NAEP 2005 A2aTranslate between different representations of algebraic expressions using symbols, graphs, tables, diagrams, or written descriptions.NAEP 2005 A2bAnalyze or interpret relationships expressed in symbols, graphs, tables, diagrams, or written descriptions.NAEP 2005 A2cGraph or interpret points that are represented by one or more ordered pairs of numbers on a rectangular coordinate system.NAEP 2005 A2dPerform or interpret transformations on the graphs of linear and quadratic functions.NAEP 2005 A2eUse algebraic properties to develop a valid mathematical argument.NAEP 2005 A2fUse an algebraic model of a situation to make inferences or predictions.NAEP 2005 A2gGiven a real-world situation, determine if a linear, quadratic, inverse, or exponential function fits the situation.NAEP 2005 A2hSolve problems involving exponential growth and decay.NAEP 2005 A3aWrite algebraic expressions, equations, or inequalities to represent a situation.NAEP 2005 A3bPerform basic operations, using appropriate tools, on algebraic expressions.NAEP 2005 A3cWrite equivalent forms of algebraic expressions, equations, or inequalities to represent and explain mathematical relationships.NAEP 2005 A4aSolve linear, rational, or quadratic equations or inequalities.NAEP 2005 A4cAnalyze situations or solve problems using linear or quadratic equations or inequalities symbolically or graphically.NAEP 2005 A4dRecognize the relationship between the solution of a system of linear equations and its graph.NAEP 2005 A4gSolve or interpret systems of equations or inequalities.NAEP 2005 D1aRead or interpret data, including interpolating or extrapolating from dataNAEP 2005 D1bGiven a set of data, complete a graph and then solve a problem using the data in the graph.NAEP 2005 D1cSolve problems by estimating and computing with univariate or bivariate data.NAEP 2005 D1eCompare and contrast the effectiveness of different representations of the same data.NAEP 2005 D2aCalculate, interpret, or use mean, median, mode, range, interquartile range, or standard deviation.NAEP 2005 D2dCompare two or more data sets using mean, median, mode, range, interquartile range, or standard deviation describing the same characteristic for two different populations or subsets of the same population.NAEP 2005 D2eGiven a set of data or a scatterplot, visually choose the line of best fit and explain the meaning of the line. Use the line to make predictions.NAEP 2005 D2gGiven a scatterplot, make decisions or predictions involving a line or curve of best fit.NAEP 2005 D2hGiven a scatterplot, estimate the correlation coefficient.NAEP 2005 G2eJustify relationships of congruence and similarity, and apply these relationships using scaling and proportional reasoning.NAEP 2005 G3dUse the Pythagorean theorem to solve problems in two- or three-dimensional situations.NAEP 2005 G3fAnalyze properties or relationships of triangles, quadrilaterals, and other polygonal plane figures.NAEP 2005 G3f; ADP I.4.1Note to FSC: In correlation spreadsheet, change semicolon to comma, which should separate these two standareds.NAEP 2005 G3gDescribe or analyze properties and relationships of parallel, perpendicular, or intersecting lines including the angle relationships that arise in these cases.NAEP 2005 G5aMake, test, and validate geometric conjectures using a variety of methods including deductive reasoning and counterexamples.NAEP 2005 G5a; ADP L.4.1Note to FSC: In correlation spreadsheet, change semicolon to comma, which should separate these two standareds.NAEP 2005 M1; NAEP 2005 M2fNote to FSC: In correlation spreadsheet, change semicolon to comma, which should separate these two standareds.NAEP 2005 M1ADP K.Note to FSC: In correlation spreadsheet, change semicolon to comma, which should separate these two standareds.NAEP 2005 M1eSolve problems involving the coordinate plane such as the distance between two points, the midpoint of a segment, or slopes of perpendicular or parallel lines.NAEP 2005 M1e; ADP J.1.6Note to FSC: In correlation spreadsheet, change semicolon to comma, which should separate these two standareds.NAEP 2005 M1fSolve problems of angle measure, including those involving triangles or other polygons or parallel lines cut by a transversal.NAEP 2005 M1hSolve mathematical or real-world problems involving perimeter or area of plane figures such as polygons, circles, or composite figures.NAEP 2005 M1kSolve problems involving indirect measurement such as finding the height of a building by finding the distance to the base of the building and the angle of elevation to the top.NAEP 2005 M1lSolve problems involving rates such as speed, density, population density, or flow rates.NAEP 2005 M1mUse trigonometric relations in right triangles to solve problems.NAEP 2005 M2bSolve problems involving conversions within or between measurement systems, given the relationship between the units.NAEP 2005 M2eDetermine appropriate accuracy of measurement in problem situations (e.g., the accuracy of measurement of the dimensions to obtain a specified accuracy of area) and find the measure to that degree of accuracy.NAEP 2005 M2fConstruct or solve problems involving scale drawings.NAEP 2005 M2gCompare lengths, areas, or volumes of similar figures using proportions.NAEP 2005 N1dWrite, rename, represent, or compare real numbers.NAEP 2005 N1fRepresent very large or very small numbers using scientific notation in meaningful contexts.NAEP 2005 N1gFind or model absolute value or apply to problem situations.NAEP 2005 N1jOrder or compare real numbers, including very large or small real numbers.NAEP 2005 N2dEstimate square or cube roots of numbers less than 1,000 between two whole numbers.NAEP 2005 N3aPerform computations with real numbers including common irrational numbers or the absolute value of numbers.NAEP 2005 N3gSolve application problems involving numbers, including rational and common irrationals, using exact answers or estimates as appropriate.NAEP 2005 N4bUse proportions to model problems.NAEP 2005 N4cUse proportional reasoning to solve problems.NAEP 2005 N4dSolve problems involving percentagesNAEP 2005 N5bSolve problems involving factors, multiples, or prime factorization.NAEP 2005 N5eApply basic properties of operations.NAEP 2005 N5fProvide a mathematical argument about a numerical property or relationship.NE 12.1.1By the end of twelfth grade, students will describe and compare the relationships between subsets of real numbers. Example indicators: draw Venn diagrams including, but not limited to, natural, whole, integers, rational, irrational, and real numbers; find intersection and union of two sets of numbers; given a number, identify to which subset it belongs; justify why a number does not belong to a specific set.NE 12.1.2By the end of twelfth grade, students will express the equivalent forms of numbers using exponents, radicals, scientific notation, absolute values, fractions, decimals, and percents.NE 12.2.1By the end of twelfth grade, students will solve theoretical and applied problems using numbers in equivalent forms, radicals, exponents, scientific notation, absolute values, fractions, decimals, and percents, ratios and proportions, order of operations, and properties of real numbers.NE 12.2.3By the end of twelfth grade, students will perform estimations and computations of real numbers mentally, with paper and pencil, and with technology.NE 12.4.1By the end of twelfth grade, students will calculate perimeter and area of two-dimensional shapes and surface area and volume of three-dimensional shapes.NE 12.4.3By the end of twelfth grade, students will evaluate characteristics and properties of two- and three-dimensional geometric shapes. Example indicators: Classify and compare attributes of two- and three-dimensional shapes; classify shapes in terms of congruence and similarity and apply these relationships; determine the effects of changing dimensions on perimeter, area, and volume; investigate and deduce geometric properties using transformations such as translations, rotations, and reflections.NE 12.4.5By the end of twelfth grade, students will apply right triangle trigonometry to find length and angle measures.NE 12.4.6By the end of twelfth grade, students will apply geometric properties to solve problems. Example indicator: Find missing angles and lengths of geometric shapes using geometric properties (Properties may include but are not limited to similarity, parallel and line-transversal.)NE 12.4.7By the end of twelfth grade, students will apply deductive reasoning to arrive at a conclusion. Example indicators: Justify steps when solving an algebraic equation using properties of real numbers; use logic statements, paragraph proof, two-column proof, or algebraic proof to arrive at a conclusion.NE 12.5.2By the end of twelfth grade, students will write equations and make predictions from sets of data. Example indicators: Display data in a scatter plot, describe its shape, and estimate how close the data comes to fitting an equation; relate the slope of a regression line to the rate of change for the data set; determine what the y-intercept or beginning value indicates about the data; determine the validity of predictions made from regression equations.NE 12.5.3By the end of twelfth grade, students will apply theoretical probability to represent problems and make decisions. Example indicator: Explain the likelihood of the next event based on theoretical probabilities.NE 12.5.4By the end of twelfth grade, students will evaluate how transformations on data affect the measures of central tendency and variability. Example indicators: Describe how adding the same amount to each score changes the mean, median, mode, range, outliers, interquartile points, maximum, and minimum; describe how dropping an outlier changes the other measures.NE 12.5.6By the end of twelfth grade, students will calculate probabilities of independent events. Example indicator: Calculate probabilities using the fundamental counting principle and permutations.NE 12.6.1By the end of twelfth grade, students will graph and interpret algebraic relations and inequalities. Example indicators: Describe a graph by identifying intercepts, slopes, maximum, minimum, increasing, decreasing, parallel, and perpendicular; use families of curves to describe the effect of changing coefficients of an equation.NE 12.6.2By the end of twelfth grade, students will solve problems involving equations and inequalities. Example indicator: Use appropriate methods to solve linear and quadratic equations.NE 12.6.3By the end of twelfth grade, students will solve problems involving systems of two equations and systems of two or more inequalities.  Example indicator: Solve systems by graphing, substitution, elimination or matrices.NE 12.6.4By the end of twelfth grade, students will solve problems using patterns and functions. Example indicators: Apply direct and indirect variations; recognize the properties of families of functions; recognize patters of exponential growth and decay and their significance to real-life situations; represent a problem in multiple formats (words, tables, graphs, and symbols).NE 12.62Note to  FSC: In correlation spreadsheet, insert period between last two numerals (NE 12.6.2).8 NJ 4.5.E.1cCreate and use representations to organize, record, and communicate mathematical ideas: symbolic representations (e.g., a formula).  Note to FSC: In correlation spreadsheet, remove space after 8.8NJ 4.5 C.2Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).  Note to FSC: In correlation spreadsheet, replace space before C with period.8NJ 4.5 C.4Apply mathematics in practical situations and in other disciplines.  Note to FSC: In correlation spreadsheet, replace space before C with period.8NJ 4.5 D.4Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of problem solutions.  Note to FSC: In correlation spreadsheet, replacespace before D with period8NJ 4.5 E.1aCreate and use representations to organize, record, and communicate mathematical ideas: concrete representations (e.g., base-ten blocks or algebra tiles.  Note to FSC: In correlation spreadsheet, replace space before E with period8NJ 4.5 E.1bCreate and use representations to organize, record, and communicate mathematical ideas: pictorial representations (e.g., diagrams, charts, or tables.  Note to FSC: In correlation spreadsheet, replace space before E with period8NJ 4.5 E.1cCreate and use representations to organize, record, and communicate mathematical ideas: symbolic representations (e.g., a formula).  Note to FSC: In correlation spreadsheet, insert period before E.8NJ 4.5 E.1dCreate and use representations to organize, record, and communicate mathematical ideas: graphical representations (e.g., a line graph).  Note to FSC: In correlation spreadsheet, replace space before E with period8NJ 4.5 E.2Select, apply, and translate among mathematical representations to solve problems.  Note to FSC: In correlation spreadsheet, replace space before E with period8NJ 4.5 E.3Use representations to model and interpret physical, social, and mathematical phenomena.  Note to FSC: In correlation spreadsheet, replace space before E with period8NJ 4.5 F.3Use graphing calculators and computer software to investigate properties of functions and their graphs.  Note to FSC: In correlation spreadsheet, replace space before F with period8NJ 4.5 F4Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).  Note to FSC: In correlation spreadsheet, s/b (NJ 4.5.F.4).8NJ 4.5.A.2dSolve problems that arise in mathematics and in other contexts: problems that can be solved in several ways.8NJ 4.5.A.3Select and apply a variety of appropriate problem-solving strategies (e.g., try a simpler problem or make a diagram) to solve problems.8NJ 4.5.A.5Monitor progress and reflect on the process of problem solving activity.8NJ 4.5.B.1aUse communication to organize and clarify mathematical thinking: reading and writing.8NJ 4.5.C.1Recognize recurring themes across mathematical domains (e.g., patterns in number, algebra, and geometry).8NJ 4.5.C.2Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).8NJ 4.5.D.1Recognize that mathematical facts, procedures, and claims must be justified.8NJ 4.5.D.3Select and use various types of reasoning and methods of proof.8NJ 4.5.D.4Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of problem solutions.8NJ 4.5.E.1bCreate and use representations to organize, record, and communicate mathematical ideas: pictorial representations (e.g., diagrams, charts, or tables).8NJ 4.5.E.1cCreate and use representations to organize, record, and communicate mathematical ideas: symbolic representations (e.g., a formula).8NJ 4.5.E.1dCreate and use representations to organize, record, and communicate mathematical ideas: graphical representations (e.g., a line graph).  Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).8NJ 4.5.E.2Select, apply, and translate among mathematical representations to solve problems.  Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).8NJ 4.5.E.3Use representations to model and interpret physical, social, and mathematical phenomena.8NJ 4.5.F.4Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).NJ 4.1.12 A.1Extend understanding of the number system to all real numbers.NJ 4.1.12 A.2Compare and order rational and irrational numbers.NJ 4.1.12 A.3Develop conjectures and informal proofs of properties of number systems and sets of numbers.NJ 4.1.12 A2Note to FSC: In correlation spreadsheet, add period before final number (NJ 4.1.12 A.2).NJ 4.1.12 B.1Extend understanding and use of operations to real numbers and algebraic procedures.NJ 4.1.12 B.2Develop, apply, and explain methods for solving problems involving rational and negative exponents.NJ 4.1.12 B.3aPerform operations on matrices: addition and subtractionNJ 4.1.12 B.3bPerform operations on matrices: scalar multiplication.NJ 4.1.12 B.4Understand and apply the law of exponents to simplify expressions involving numbers raised to powers.NJ 4.1.12 B1Note to FSC: In correlation spreadsheet, add period before final number (NJ 4.1.12 B.1).NJ 4.1.12 B4Note to FSC: In correlation spreadsheet, add period before final number (NJ 4.1.12 B.4).NJ 4.1.12 C.1Recognize the limitations of estimation, assess the amount of error from estimation, and determine whether the error is within acceptable tolerance limits.NJ 4.2.12 A.1Use geometric models to represent real-world situations and objects and to solve problems using those models (e.g., use PythagoreanTheorem to decide whether an object can fit through a doorway).NJ 4.2.12 A.4aUse reasoning and some form of proof to verify or refute conjectures and theorems: verification or refutation of proposed proofsNJ 4.2.12 B.1Determine, describe, and draw the effect of a transformation, or a sequence of transformations, on a geometric or algebraic object, and, conversely, determine whether and how one object can be transformed to another by a transformation or a sequence of transformations.NJ 4.2.12 C.1cUse coordinate geometry to represent and verify properties of lines: finding the intersection of two linesNJ 4.2.12 C.1dUse coordinate geometry to represent and verify properties of lines: lines with the same slope are parallel.NJ 4.2.12 C.1eUse coordinate geometry to represent and verify properties of lines: lines that are perpendicular have slopes whose product is �1.NJ 4.2.12 D.2aChoose appropriate tools and techniques to achieve the specified degree of precision and error needed in a situation: degree of accuracy of a given measurement toolNJ 4.2.12 E.1aUse techniques of indirect measurement to represent and solve problems: similar triangles,NJ 4.2.12 E.1bUse techniques of indirect measurement to represent and solve problems: Pythagorean theorem,NJ 4.2.12 E.1cUse techniques of indirect measurement to represent and solve problems: right triangle trigonometry (sine, cosine, tangent).NJ 4.2.12 E.2cUse a variety of strategies to determine perimeter and area of plane figures and surface area and volume of 3D figures: estimation of area, perimeter, volume, and surface area.NJ 4.3.12 A.1aUse models and algebraic formulas to represent and analyze sequences and series: explicit formulas for nth terms.NJ 4.3.12 A.3Use inductive reasoning to form generalizations.NJ 4.3.12 B.1Understand relations and functions and select, convert flexibly among, and use various representations for them, including equations or inequalities, tables, and graphs.NJ 4.3.12 B.2aAnalyze and explain the general properties and behavior of functions of one variable, using appropriate graphing technologies: slope of a line or curveNJ 4.3.12 B.2bAnalyze and explain the general properties and behavior of functions of one variable, using appropriate graphing technologies: domain and rangeNJ 4.3.12 B.2cAnalyze and explain the general properties and behavior of functions of one variable, using appropriate graphing technologies: interceptsNJ 4.3.12 B.2dAnalyze and explain the general properties and behavior of functions of one variable, using appropriate graphing technologies: continuityNJ 4.3.12 B.2eAnalyze and explain the general properties and behavior of functions of one variable, using appropriate graphing technologies: Maximum/minimumNJ 4.3.12 B.2fAnalyze and explain the general properties and behavior of functions of one variable, using appropriate graphing technologies: estimating roots of equationsNJ 4.3.12 B.2gAnalyze and explain the general properties and behavior of functions of one variable, using appropriate graphing technologies: intersecting points as solutions of systems of equationsNJ 4.3.12 B.2hAnalyze and explain the general properties and behavior of functions of one variable, using appropriate graphing technologies: rates of change.NJ 4.3.12 B.4aUnderstand and compare the properties of classes of functions, including exponential, polynomial, rational, and trigonometric functions: linear vs. non-linearNJ 4.3.12 B.4bUnderstand and compare the properties of classes of functions, including exponential, polynomial, rational, and trigonometric functions: symmetryNJ 4.3.12 B1Note to FSC: In correlation spreadsheet, add period before final number (NJ 4.3.12 B.1).NJ 4.3.12 C.1aUse functions to model real-world phenomena and solve problems that involve varying quantities: linear, quadratic, exponential, periodic (sine and cosine), and step functions (e.g., price of mailing a first-class letter over the past 200 years)NJ 4.3.12 C.1cUse functions to model real-world phenomena and solve problems that involve varying quantities: absolute valueNJ 4.3.12 C.1dUse functions to model real-world phenomena and solve problems that involve varying quantities: expressions, equations, and inequalities; same function can model variety of phenomenaNJ 4.3.12 C.1eUse functions to model real-world phenomena and solve problems that involve varying quantities: growth/decay and change in the natural worldNJ 4.3.12 C.1fUse functions to model real-world phenomena and solve problems that involve varying quantities: applications in mathematics, biology, and economics (including compound interest).NJ 4.3.12 C.2Analyze and describe how a change in an independent variable leads to a change in a dependent one.NJ 4.3.12 D.1aEvaluate and simplify expressions: add and subtract polynomialsNJ 4.3.12 D.1bEvaluate and simplify expressions: multiply a polynomial by a monomial or binomialNJ 4.3.12 D.1cEvaluate and simplify expressions: divide a polynomial by a monomialNJ 4.3.12 D.2aSelect and use appropriate methods to solve equations and inequalities: linear equations -- algebraicallyNJ 4.3.12 D.2bSelect and use appropriate methods to solve equations and inequalities: quadratic equations -- factoring (when the coefficient of x2 is 1) and using the quadratic formulaNJ 4.3.12 D.2cSelect and use appropriate methods to solve equations and inequalities: all types of equations using graphing, computer, and graphing calculator techniques.NJ 4.4.12 A.3Design a statistical experiment, conduct the experiment, and interpret and communicate the outcome.NJ 4.4.12 A.4Estimate or determine lines of best fit (or curves of best fit if appropriate) with technology, and use them to interpolate within the range of data.NJ 4.4.12 B.3Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models, and solve problems using these models.NJ 4.4.12 B.4cDetermine probabilities in complex situations: dependent and independent events.NJ 4.4.12 B.5Estimate probabilities and make predictions based on experimental and theoretical probabilities.NJ 4.4.12 C.1Calculate combinations with replacement (e.g., the number of possible ways of tossing a coin 5 times and getting 3 heads) and without replacement (e.g., number of possible delegations of 3 out of 23 students).NJ 4.4.12 C.2Apply the multiplication rule of counting in complex situations, recognize the difference between situations with replacement and without replacement, and recognize the difference between ordered and unordered counting situations.NJ 4.4.12 C.3Justify solutions to counting problems.NJ 4.5.D.4Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of problem solutions.NJ.2.12 E.1cNote to FSC: In correlation spreadsheet, add  4 before the first period (NJ 4.2.12 E.1c).NJ.4.1.12 B.1Note to FSC: In correlation spreadsheet, delete first period (NJ 4.1.12 B.1).2.C.4d. NM 2.C.8Note to FSC: In correlation spreadsheet, these should be two separate standards--NM 2.C.4d and NM 2.C.8--standards are added below--cells shaded green:NM 2.ARepresent and analyze mathematical situations and structures using algebraic symbols.NM 2.A.1Classify numbers and members of the following sets:  natural, whole, integers, rationals, irrationals.NM 2.A.2Simplify numerical expressions using the order of operations, including exponents.NM 2.A.3Evaluate the numerical value of expressions of one or more variables that are: polynomial, rational, radical.NM 2.A.3,NM 2.A.7fNote to FSC: In correlation spreadsheet, these should be two separate standards--add space after comma.NM 2.A.4Simplify algebraic monomial expressions raised to a power (e.g.,[5 x y2]3) and algebraic binomial (e.g.,[5x2 + y]2) expressions raised to a powerNM 2.A.5Compare and order polynomial expressions by degree.NM 2.A.6Represent and analyze relationships using written and verbal expressions, tables, equations, and graphs, and describe the connections among those representations: translate from verbal expression to algebraic formulae; given data in a table, construct a function that represents these data (linear only); given a graph, construct a function that represents the graph (linear only).NM 2.A.7eKnow, explain, and use equivalent representations for the same real number, including: scientific notation.NM 2.A.7fKnow, explain, and use equivalent representations for the same real number, including: numbers with integer exponents.NM 2.A.8Simplify algebraic expressions using the distributive property.NM 2.A.9Explain and use the concept of absolute value.NM 2.A.10Know, explain, and use equivalent representations for algebraic expressions.NM 2.A.11Simplify square roots and cube roots with monomial radicands that are perfect squares or perfect cubes (e.g., 9a2 x 2x4).NM 2.A.12Calculate powers and roots of real numbers, both rational and irrational.NM 2.A.14Factor polynomials, difference of squares and perfect square trinomials, and the sum and difference of cubes.NM 2.A.15Simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms.NM 2.A.16Manipulate simple expressions with + and � exponents.NM 2.A.17Use the four basic operations (+, �, x, �) with: linear expressions, polynomial expressions, rational expressions.NM 2.A.17,NM 2.D.4Note to FSC: In correlation document, these should be two separate standards, add space after comma--NM 2.A.17 is above; NM 2.D.4 has been added below and is shaded greenNM 2.A.141Note to FSC: Delete final 1 from code.NM 2.B.1Distinguish between the concept of a relation and a function.NM 2.B.2Determine whether a relation defined by a graph, a set of ordered pairs, a table of values, an equation, or a rule is a function.NM 2.B.3Describe the concept of a graph of a function.NM 2.B.4Translate among tabular, symbolic, and graphical representations of functions.NM 2.B.5Explain and use function notation.NM 2.B.6Determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression.NM 2.B.7Identify the independent and dependent variables from an application problem (e.g., height of a child).NM 2.B.8Describe the concept of a graph of an equation.NM 2.B.10Analyze and describe middle and end (asymptotic) behavior of linear, quadratic, and exponential functions, and sketch the graphs of functions.NM 2.B.12Use the quadratic formula and factoring techniques to determine whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points.NM 2.B.13Apply quadratic equations to physical phenomena (e.g., the motion of an object under the force of gravity).NM 2.B.13. NM 2.C.1Note to FSC: In correlation document, these should be two separate standards. Change period after 13 to a commaNM 2.CUse mathematical models to represent and understand quantitative relationships.NM 2.C.1Model real-world phenomena using linear and quadratic equations and linear inequalities (e.g., apply algebraic techniques to solve rate problems, work problems, and percent mixture problems; solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest; apply quadratic equations to model throwing a baseball in the air).NM 2.C.2Use a variety of computational methods (e.g., mental arithmetic, paper and pencil, technological tools).NM 2.C.3Express the relationship between two variables using a table with a finite set of values and graph the relationship.NM 2.C.4aExpress the relationship between two variables using an equation and a graph: graph a linear equation and linear inequality in two variablesNM 2.C.4bExpress the relationship between two variables using an equation and a graph: solve linear inequalities and equations in one variableNM 2.C.4cExpress the relationship between two variables using an equation and a graph: solve systems of linear equations in two variables and graph the solutionsNM 2.C.4dExpress the relationship between two variables using an equation and a graph: solve use the graph of a system of equations in two variables to help determine the solution.NM 2.C.5Solve applications involving systems of equations.NM 2.C.6Evaluate numerical and algebraic absolute value expressions.NM 2.C.7Create a linear equation from a table of values containing co-linear data.NM 2.C.8Determine the solution to a system of equations in two variables from a given graph.NM 2.C.9Generate an algebraic sentence to model real-life situations.NM 2.C.10Write an equation of the line that passes through two given points.NM 2.C.11Understand and use: such operations as taking the inverse, finding the reciprocal, taking a root, and raising to a fractional power; the rules of exponents.NM 2.C.12Verify that a point lies on a line, given an equation of the line, and be able to derive linear equations by using the point-slope formula.NM 2.D.1Analyze the effects of parameter changes on these functions: linear, quadratic, exponential, polynomial.NM 2.D.2bSolve routine two- and three-step problems relating to change using concepts such as factoring.NM 2.D.2cSolve routine two- and three-step problems relating to change using concepts such as ratio.NM 2.D.2dSolve routine two- and three-step problems relating to change using concepts such as proportion.NM 2.D.2eSolve routine two- and three-step problems relating to change using concepts such as average.NM 2.D.3Calculate the percentage of increase and decrease of a quantity.NM 2.D.4Analyze the general shape of polynomial expressions and equations for different degree polynomialsNM 2.D.5Estimate the rate of change of a function or equation by finding the slope between two points on the graph.NM 2.D.6Evaluate the estimated rate of change in the context of the problem.NM 3.A.1Interpret and draw two-dimensional objects and find the area and perimeter of basic figures (e.g., rectangles, circles, triangles, other polygons[e.g., rhombi, parallelograms, trapezoids).NM 3.A.4Interpret and draw three-dimensional objects and find the surface area and volume of basic figures (e.g., spheres, rectangular solids, prisms, polygonal cones), and calculate the surface areas and volumes of these figures as well as figures constructed from unions of rectangular solids and prisms with faces in common, given the formulas for these figures.NM 3.A.5aDemonstrate an understanding of simple aspects of a logical argument: identify the hypothesis and conclusion in logical deduction.NM 3.A.5bDemonstrate an understanding of simple aspects of a logical argument: use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion.NM 3.A.6aDemonstrate an understanding of inductive and deductive reasoning, explain the difference between inductive and deductive reasoning, and identify and provide examples for inductive reasoning, demonstrate understanding that showing a statement is true for a finite number of examples does not show it is true for all cases.NM 3.B.3Given two linear equations, determine whether the lines are parallel, perpendicular, or coincide.NM 3.C.1Describe the effect of rigid motions on figures in the coordinate plane and space that include rotations, translations, and reflections: determine whether a given pair of figures on a coordinate plane represents the effect of a translation, reflection, rotation, and/or dilation; sketch the planar figure that is the result of a given transformation of this type.NM 3.DUse visualization, spatial reasoning, and geometric modeling to solve problems.NM 3.D.1Solve real-world problems using congruence and similarity relationships of triangles (e.g., find the height of a pole given the length of its shadow).NM 3.D.3Solve problems involving the perimeter, circumference, area, volume, and surface area of common geometric figures.NM 3.D.4Solve problems using the Pythagorean theorem.NM 3.D.5Understand and use elementary relationships of basic trigonometric functions defined by the angles of a right triangle.NM 3.D.6Use trigonometric functions to solve for the length of the second leg of a right triangle given the angles and the length of the first leg.NM 5.B.3For univariate data, be able to display the distribution and describe its shape using appropriate summary statistics, and understand the distinction between a statistic and a parameter: construct and interpret frequency tables, histograms, stem-and-leaf plots, and box-and-whisker plots; calculate and apply measures of central tendency (mean, median, and mode) and measures of variability (range, quartiles, standard deviation); compare distributions of univariate data using back-to-back stem and leaf plots and parallel box-and-whisker plots.NM 5.B.4For bivariate data, be able to display a scatter plot and describe its shape: fit a linear model to a set of data using technological tools; describe and interpret the relationship/correlation between two variables using technological tools.NM 5.B.31Note to FSC: In correlation spreadsheet, delete the 1 following the 3.NM 5.C.2Draw conclusions concerning the relationships among bivariate data: make predictions from a linear pattern in data; determine the strength of the relationship between two sets of data by examining the correlation; understand that correlation does not imply a cause-and-effect relationship.NM 5.C.3Use simulations to explore the variability of sample statistics from a known population and construct sampling distributions.NM 5.D.2Understand the concept of probability as relative frequency.NM 5.D.3Use simulations to compute the expected value and probabilities of random variables in simple cases.NM 5.D.4Distinguish between independent and dependent events.NM 5.D.5Understand how to compute the probability of an event using the basic rules of probability: complement rule, addition rule (disjoint and joint events), multiplication rule (independent events), conditional probability.NV 1.12.1Apply the laws of exponents to perform operations on expressions with integral exponents and expressions in  scientific notation.NV 1.12.2Apply the properties and theories of the real number system to everyday situations.NV 1.12.3Perform simple operations on matrices.NV 1.12.5Represent and solve problems using discrete structures including graphs and matrices, with and without technology.NV 2.12.2Create and use different forms of a variety of equations, proportions, and/or formulas (e.g., I=PRT or R=I/PT), solving for the needed variable as necessary in given situations.NV 2.12.3Add, subtract, multiply, and factor (1st and 2nd degree) polynomials, describing each step in the process and the connection between the algebraic process and the arithmetic process; use simple quadratic equations with integer roots to solve practical and mathematical problems.NV 2.12.4Model practical problems from everyday situations with a variety of models that includes matrices, translating among tabular, symbolic and graphical representations of functions, with and without technology.NV 2.12.5Determine the domain and range of linear relations given a graph or a set of ordered pairs; explain their importance in problem solving situations.NV 2.12.6Solve systems of two linear equations, both algebraically and graphically; use graphing calculators as a primary tool in solving these problems and to verify solutions found by other methods.NV 2.12.7Calculate and estimate sums, differences, products, quotients, powers, and roots using mental math, formulas, and algorithms.NV 3.12.5Use relationships (e.g., proportions) and formulas (indirect measurement) to determine the measurement of unknown dimensions, angles, areas, and volumes to solve problems.NV 4.12.5Use coordinate geometry to graph linear equations, determine slopes of lines, identify parallel and perpendicular lines and find possible solutions to sets of equations; use algebraic techniques to solve problems determined by geometric relationships.NV 4.12.7Apply the PythagoreanTheorem, its converse, properties of special right triangles, and right triangle trigonometry to solve practical problems.NV 4.12.9Construct, justify and defend mathematical conclusions using logical, sequential, deductive reasoning supported by established mathematical principles.NV 5.12.1Use calculators and computers to create and manipulate tables, graphs, and matrices to communicate statistical information; use the shape of graphs of normal distributions to compare and analyze information.NV 5.12.2Design, conduct, analyze, and communicate the results of multi-stage probability experiments.NV 5.12.3Distinguish between and apply permutations and combinations using a variety of methods, includingThe Fundamental Counting Principle.NV 5.12.4Select and use the measures of central tendency such as mean, median, mode and variability including range, distribution and possible outliers that are appropriate for given situations.NV 5.12.5Analyze the validity of statistical conclusions noting various sources of bias, misuse, and abuse of data caused by a wide variety of factors including choices of scale, probability versus odds, inappropriate uses of measures of central tendency, inaccurate curve fitting and inappropriate uses of controls or sample groups.NV 5.12.6Design, construct, analyze, and select an appropriate type of graph to represent data to communicate the results of statistical experiments (e.g., write a survey question and analyze and communicate the findings).NV 6.1Select, modify, develop, and apply strategies to solve a variety of mathematical and practical problems and to investigate and understand mathematical concepts.NV 6.5Verify, interpret, and evaluate results with respect to the original problem situation, determining an efficient strategy for the given situation.NV 6.7Apply multi-step, integrated, mathematical problem-solving strategies, persisting until a solution is found or until it is clear that no solution exists.NV 6.9Generalize solutions and strategies from earlier problems to new problem situations.NV 6.10Interpret and solve a variety of mathematical problems by paraphrasing, identifying necessary and extraneous information, selecting and justifying efficient methods and/or strategies, and ensuring the answer is reasonable.NV 6.11Apply combinations of proven strategies and previous knowledge to solve non-routine problems.NV 6.14Use technology, including calculators, to investigate, define, and describe quantitative relationships such as patterns and functions.NV 7.9Model and explain mathematical relationships using oral, written, graphical, and algebraic methods.NV 7.11Make conjectures and present arguments in discussions of mathematical ideas.NV 7.14Explain and evaluate thinking about mathematical ideas and solutions based on the role of definitions, properties, common rules, and symbols in solving problems.NV 7.17Use mathematical notation to communicate and explain mathematical situations.NV 8.3Construct, justify, and defend mathematical conclusions using logical arguments, in situations related to mathematics, science, and technology.NV 8.4Use patterns and relationships to analyze mathematical situations; draw logical conclusions about mathematical problems.NV 8.5Follow a logical argument and judge its validity.NV 8.7Recognize and apply deductive and inductive reasoning in both concrete and abstract contexts.NV 8.9Review and refine the assumptions and steps used to derive conclusions in mathematical arguments.NV 8.10Construct valid arguments; make and test conjectures about algebraic and geometric properties based on mathematical principles.NV 9.2Use mathematical ideas from one area of mathematics to explain an idea from another area of mathematics.NV 9.4Use the connections among mathematical topics to develop multiple approaches to problems.NY A.A.1Translate a quantitative verbal phrase into an algebraic expression.NY A.A.3Distinguish the difference between an algebraic expression and an algebraic equation.NY A.A.4Translate verbal sentences into mathematical equations or inequalities.NY A.A.5Write algebraic equations or inequalities that represent a situation.NY A.A.6Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable.NY A.A.7Analyze and solve verbal problems whose solution requires solving systems of linear equations in two variables.NY A.A.8Analyze and solve verbal problems that involve quadratic equations.NY A.A.9Analyze and solve verbal problems that involve exponential growth and decay.NY A.A.10Solve systems of two linear equations in two variables algebraically. (See A.G.7)NY A.A.12Multiply and divide monomial expressions with a common base, using the properties of exponents. Note: Use integral exponents only.NY A.A.13Add, subtract, and multiply monomials and polynomials.NY A.A.14Divide a polynomial by a monomial or binomial, where the quotient has no remainder.NY A.A.15Find values of a variable for which an algebraic fraction is undefined.NY A.A.16Simplify fractions with polynomials in the numerator and denominator by factoring both and renaming them to lowest terms.NY A.A.17Add or subtract fractional expressions with monomial or like binomial denominators.NY A.A.18Multiply and divide algebraic fractions and express the product or quotient in simplest form.NY A.A.19Identify and factor the difference of two perfect squares.NY A.A.20Factor algebraic expressions completely, including trinomials with a lead coefficient of one (after factoring a GCF).NY A.A.21Determine whether a given value is a solution to a given linear equation in one variable or linear inequality in one variable.NY A.A.22Solve all types of linear equations in one variable.NY A.A.23Solve literal equations for a given variable.NY A.A.24Solve linear inequalities in one variable.NY A.A.25Solve equations involving fractional expressions.  Note: Expressions which result in linear equations in one variable.NY A.A.26Solve algebraic proportions in one variable which result in linear or quadratic equations.NY A.A.27Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients and integral roots.NY A.A.28Understand the difference and connection between roots of a quadratic equation and factors of a quadratic expression.NY A.A.32Explain slope as a rate of change between dependent and independent variables.NY A.A.33Determine the slope of a line, given the coordinates of two points on the line.NY A.A.34Write the equation of a line, given its slope and the coordinates of a point on the line.NY A.A.35Write the equation of a line, given the coordinates of two points on the line.NY A.A.36Write the equation of a line parallel to the x- or y-axis.NY A.A.37Determine the slope of a line, given its equation in any form.NY A.A.38Determine if two lines are parallel, given their equations in any form.NY A.A.40Determine whether a given point is in the solution set of a system of linear inequalities.NY A.A.41Determine the vertex and axis of symmetry of a parabola, given its equation. (See A.G.10)NY A.A.42Find the sine, cosine, and tangent ratios of an angle of a right triangle, given the lengths of the sides.NY A.A.44Find the measure of a side of a right triangle, given an acute angle and the length of another side.NY A.A.45Determine the measure of a third side of a right triangle using the PythagoreanTheorem, given the lengths of any two sides.NY A.CM.1Communicate verbally and in writing a correct, complete, coherent, and clear design (outline) and explanation for the steps used in solving a problem.NY A.CM.2Use mathematical representations to communicate with appropriate accuracy, including numerical tables, formulas, functions, equations, charts, graphs, Venn diagrams, and other diagrams.NY A.CM.3Present organized mathematical ideas with the use of appropriate standard notations, including the use of symbols and other representations when sharing an idea in verbal and written form.NY A.CM.4Explain relationships among different representations of a problem.NY A.CM.5Communicate logical arguments clearly, showing why a result makes sense and why the reasoning is valid.NY A.CM.11Represent word problems using standard mathematical notation.NY A.CM.12Understand and use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and rationale.NY A.CM.13Draw conclusions about mathematical ideas through decoding, comprehension, and interpretation of mathematical visuals, symbols, and technical writing.NY A.CN.1Understand and make connections among multiple representations of the same mathematical idea.NY A.CN.2Understand the corresponding procedures for similar problems or mathematical concepts.NY A.CN.3Model situations mathematically, using representations to draw conclusions and formulate new situations.NY A.CN.4Understand how concepts, procedures, and mathematical results in one area of mathematics can be used to solve problems in other areas of mathematics.NY A.CN.5Understand how quantitative models connect to various physical models and representations.NY A.CN.6Recognize and apply mathematics to situations in the outside world.NY A.CN.7Recognize and apply mathematical ideas to problem situations that develop outside of mathematics.NY A.G.2Use formulas to calculate volume and surface area of rectangular solids and cylinders.NY A.G.3Determine when a relation is a function, by examining ordered pairs and inspecting graphs of relations.NY A.G.4Identify and graph linear, quadratic (parabolic), absolute value, and exponential functions.NY A.G.5Investigate and generalize how changing the coefficients of a function affects its graph.NY A.G.6Graph linear inequalities.NY A.G.7Graph and solve systems of linear equations and inequalities with rational coefficients in two variables. (See A.A.10)NY A.G.8Find the roots of a parabolic function graphically. Note: Only quadratic equations with integral solutions.NY A.G.9Solve systems of linear and quadratic equations graphically.  Note: Only use systems of linear and quadratic equations that lead to solutions whose coordinates are integers.NY A.G.10Determine the vertex and axis of symmetry of a parabola, given its graph. (See A.A.41) Note:The vertex sill have an ordered pair of integers and the axis of symmetry will have an integral value.NY A.M.1Calculate rates using appropriate units (e.g., rate of a spaceship versus the rate of a snail).NY A.M.2Solve problems involving conversions within systems, given the relationship between the units.NY A.M.3Calculate the relative error in measuring square and cubic units, when there is an error in the linear measure.NY A.N.1Identify and apply the properties of real numbers (closure, commutative, associative, distributive, identity, inverse). Note: Students do not need to identify groups and fields, but students should be engaged in the ideas.NY A.N.2Simplify radical terms (no variable in the radicand).NY A.N.3Perform the four arithmetic operations using like and unlike radical terms and express the results in simplest form.NY A.N.4Understand and use scientific notation to compute products and quotients of numbers.NY A.N.5Solve algebraic problems arising from situations that involve fractions, decimals, percents (decrease/increase and discount), and proportionality/direct variation.NY A.N.6Evaluate expressions involving factorial(s), absolute value(s), and exponential expression(s).NY A.N.7Determine the number of possible events, using counting techniques or the Fundamental Principle of Counting.NY A.N.8Determine the number of possible arrangements (permutations) of a list of items.NY A.PS.1Use a variety of problem solving strategies to understand new mathematical content.NY A.PS.2Recognize and understand equivalent representations of a problem situation or a mathematical concept.NY A.PS.3Observe and explain patterns to formulate generalizations and conjectures.NY A.PS.4Use multiple representations to represent and explain problem situations (e.g., verbally, numerically, algebraically, graphically).NY A.PS.5Choose an effective approach to solve a problem from a variety of strategies (numeric, graphic, algebraic).NY A.PS.6Use a variety of strategies to extend solution methods to other problems.NY A.PS.8Determine information required to solve a problem, choose methods for obtaining the information, and define parameters for acceptable solutions.NY A.PS.9Interpret solutions within the given constraints of a problem.NY A.PS.10Evaluate the relative efficiency of different representations and solution methods of a problem.NY A.R.1Use physical objects, diagrams, charts, tables, graphs, symbols, equations, or objects created using technology as representations of mathematical concepts.NY A.R.2Recognize, compare, and use an array of representational forms.NY A.R.3Use representation as a tool for exploring and understanding mathematical ideas.NY A.R.4Select appropriate representations to solve problem situations.NY A.R.5Investigate relationships between different representations and their impact on a given problem.NY A.R.6Use mathematics to show and understand physical phenomena (e.g., find the height of a building if a ladder of a given length forms a given angle of elevation with the ground).NY A.R.7Use mathematics to show and understand social phenomena (e.g., determine profit from student and adult ticket sales).NY A.R.8Use mathematics to show and understand mathematical phenomena (e.g., compare the graphs of the functions represented by the equations y = x2 and y = -x2).NY A.RP.1Recognize that mathematical ideas can be supported by a variety of strategies.NY A.RP.4Develop, verify, and explain an argument, using appropriate mathematical ideas and language.NY A.RP.5Construct logical arguments that verify claims or counterexamples that refute them.NY A.RP.5 (ex. 54�60)Note to FSC: In correlation spreadsheet, delete (ex 54-60) .NY A.RP.6Present correct mathematical arguments in a variety of forms.NY A.RP.9Devise ways to verify results or use counterexamples to refute incorrect statements.NY A.RP.9 (ex. 54�60)Note to FSC: In correlation spreadsheet, delete (ex 54-60) .NY A.RP.10Extend specific results to more general cases.NY A.RP.12Apply inductive reasoning in making and supporting mathematical conjectures.NY A.S.4Compare and contrast the appropriateness of different measures of central tendency for a given data set.NY A.S.7Create a scatter plot of bivariate data.NY A.S.8Construct manually a reasonable line of best fit for a scatter plot and determine the equation of that line.NY A.S.10Evaluate published reports and graphs that are based on data by considering: experimental design, appropriateness of the data analysis, and the soundness of the conclusions.NY A.S.12Identify the relationship between the independent and dependent variables from a scatter plot (positive, negative, or none).NY A.S.17Use a reasonable line of best fit to make a prediction involving interpolation or extrapolation.NY A.S.18Know the definition of conditional probability and use it to solve for probabilities in finite sample spaces.NY A.S.19Determine the number of elements in a sample space and the number of favorable events.NY A.S.20Calculate the probability of an event and its complement.NY A.S.21Determine empirical probabilities based on specific sample data.NY A.S.21,NY A.S.22Note to FSC: In correlation document, these should be two separate standards.  Add a space after comma;  Standard for NY A.S.22 added below--cell shaded green.NY A.S.22Determine, based on calculated probability of a set of events, if: some or all are equally likely to occur; one is more likely to occur than another; whether or not an event is certain to happen or not to happen.NY A.S.23Calculate the probability of: a series of independent events; a series of dependent events; two mutually exclusive events; two events that are not mutually exclusive.0H 9D4Note to FSC: In correlation document, this should begin with the letter O, not the number 0.OH 9D1Classify data as univariate (one variable) or bivariate (two variables) and as quantitative (measurement) or qualitative (categorical) data.OH 9D2Create a scatter plot for a set of bivariate data, sketch a line of best fit, and interpret the slope of the line of best fit.OH 9D3Analyze and interpret frequency distributions based on spread, symmetry, skewness, clusters and outliers.OH 9D4Describe and compare various types of studies (survey, observation, experiment), and identify possible misuses of statistical data.OH 9D6Make inferences about relationships in bivariant data, and recognize the difference between evidence of relationship (correlation) and causation.OH 9D7Use counting techniques and the Fundamental Counting Principle to determine the total number of possible outcomes for mathematical situations.OH 9D8Describe, create and analyze a sample space and use it to calculate probability.OH 9D9Identify situations involving independent and dependent events, and explain differences between, and common misconceptions about, probabilities associated with those events.OH 9D10Use theoretical and experimental probability, including simulations or random numbers, to estimate probabilities and to solve problems dealing with uncertainty; e.g., compound events, independent events, simple dependent events.OH 9G1Define the basic trigonometric ratios in right triangles: sine, cosine and tangent.OH 9G2Apply proportions and right triangle trigonometric ratios to solve problems involving missing lengths and angle measures in similar figures.OH 9G3Analyze two-dimensional figures in a coordinate plane; e.g., use slope and distance formulas to show that a quadrilateral is a parallelogram.OH 9M1Convert rates within the same measurement system; e.g., miles per hour to feet per second; kilometers per hour to meters per second.OH 9M2Use unit analysis to check computations involving measurement.OH 9M3Use the ratio of lengths in similar two-dimensional figures or three-dimensional objects to calculate the ratio of their areas or volumes respectively.OH 9M4Use scale drawings and right triangle trigonometry to solve problems that include unknown distances and angle measures.OH 9M5Solve problems involving unit conversion for situations involving distances, areas, volumes and rates within the same measurement system.OH 9M5,OH 9N3Note to FSC: In correlation document, these should be two separate standards. Add space after commaOH 9N1Identify and justify whether properties (closure, identity, inverse, commutative, and associative) hold for a given set and operations; e.g., even integers and multiplication.OH 9N2Compare, order and determine equivalent forms for rational and irrational numbers.OH 9N3Explain the effects of operations such as multiplication or division, and of computing powers and roots on the magnitude of quantities.OH 9N4Demonstrate fluency in computations using real numbers.OH 9N5Estimate the solutions for problem situations involving square and cube roots.OH 9P1Define function with ordered pairs in which each domain element is assigned exactly one range element.OH 9P2Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations.OH 9P3Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations.OH 9P4Demonstrate the relationship among zeros of a function, roots of equations, and solutions of equations graphically and in words.OH 9P5Describe and compare characteristics of the following families of functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum.OH 9P6Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope-intercept form.OH 9P7Use formulas to solve problems involving exponential growth and decay.OH 9P8Find linear equations that represent lines that pass through a given set of ordered pairs, and find linear equations that represent lines parallel or perpendicular to a given line through a specific point.OH 9P9Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology.OH 9P10Solve quadratic equations with real roots by factoring, graphing, using the quadratic formula and with technology.OH 9P11Add, subtract, multiply and divide monomials and polynomials (division of polynomials by monomials only).OH 9P12Simplify rational expressions by eliminating common factors and applying properties of integer exponents.OH 9P13Model and solve problems involving direct and inverse variation using proportional reasoning.OH 9P14Describe the relationship between slope and the graph of a direct variation and inverse variation.OH 9P15Describe how a change in the value of a constant in a linear or quadratic equation affects the related graphsOH 10D1Describe measures of center and the range verbally, graphically and algebraically.OH 10D2Represent and analyze bivariate data using appropriate graphical displays (scatter plots, parallel box-and-whisker plots, histograms with more than one set of data, tables, charts, spreadsheets) with and without technology.OH 10D3Display bivariate data where at least one variable is categorical.OH 10D4Identify outliers on a data display; e.g., use interquartile range to identify outliers on a box-and-whisker plot.OH 10D5Provide examples and explain how a statistic may or may not be an attribute of the entire population; e.g., intentional or unintentional bias may be present.OH 10D6Interpret the relationship between two variables using multiple graphical displays and statistical measures; e.g., scatter plots, parallel box-and-whisker plots, and measures of center and spread.OH 10D8Differentiate and explain the relationship between the probability of an event and the odds of an event, and compute one given the other.OH 10G6Identify the reflection and rotation symmetries of two- and three-dimensional figures.OH 10M1Explain how a small error in measurement may lead to a large error in calculated results.OH 10M2Calculate relative error.OH 10M3Explain the difference between absolute error and relative error in measurement.OH 10N1Connect physical, verbal and symbolic representations of irrational numbers; e.g., construct (the square root of) 2 as a hypotenuse or on a number line.OH 10N3Use factorial notation and computations to represent and solve problem situations involving arrangements.OH 10P1Define function formally and with f(x) notation.OH 10P2Describe and compare characteristics of the following families of functions: square root, cubic, absolute value and basic trigonometric functions; e.g., general shape, possible number of roots, domain and range.OH 10P6Solve equations and inequalities having rational expressions as coefficients and solutions.OH 10P7Solve systems of linear inequalities.OH 10P9Recognize and explain that the slopes of parallel lines are equal and the slopes of perpendicular lines are negative reciprocals.OH 10P10Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.OH 10P11Solve real-world problems that can be modeled using systems of linear equations and inequalities.PA M11.A.1Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers and number systems.PA M11.A.1.1Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, exponents and scientific notation).PA M11.A.1.1.1Find the square root of an integer to the nearest tenth using either a calculator or estimation.PA M11.A.1.1.2Express numbers and/or simplify expressions using scientific notation (including numbers less than 1).PA M11.A.1.1.3Simplify square roots.PA M11.A.1.2Apply number theory concepts to show relationships between real numbers in problem solving settings.PA M11.A.1.2.1Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.PA M11.A.1.3Estimate the value of an irrational number.PA M11.A.1.3.2Compare and/or order any real numbers (rational and irrational may be mixed).PA M11.A.2Understand the meanings of operations, use operations and understand how they relate to each other.PA M11.A.2.1.1Solve problems using operations with rational numbers including rates and percents (single and multi-step and multiple procedure operations) (e.g., distance, work and mixture problems).PA M11.A.2.1.2Solve problems using direct and inverse proportions.PA M11.A.2.1.3Identify and/or use proportional relationships in problem solving settings.PA M11.A.2.2Use exponents, roots and/or absolute value to solve problems.PA M11.A.2.2.1Simplify/evaluate expressions involving positive and negative exponents, roots and/or absolute value (may contain all types of real numbers -- exponents should not exceed power of 10).PA M11.A.2.2.2Simplify/evaluate expressions involving multiplying with exponents (e.g., x6 x x7 = x13), powers of powers (e.g., (x6)7 = x42) and powers of products (2x2)3 = 8x6 (positive integers only).PA M11.A.3.1Apply the order of operations in computations and in problem-solving situations.PA M11.A.3.1.1Simplify/evaluate expressions using the order of operations to solve problems (any rational numbers may be used).PA M11.B.1Apply appropriate techniques, tools and formulas to determine measurements.PA M11.C.1.3Use properties of congruence, correspondence and similarity in problem-solving settings involving two- and three-dimensional figures.PA M11.C.1.3.1Identify and/or use properties of congruent and similar polygons or solids.PA M11.C.1.4Solve problems involving right triangles using the PythagoreanTheorem.PA M11.C.1.4.1Find the measure of a side of a right triangle using the PythagoreanTheorem.PA M11.C.2Locate points or describe relationships using the coordinate plane.PA M11.C.2.1Solve problems using analytic geometry.PA M11.C.2.1.2Relate slope to perpendicularity and/or parallelism (limit to linear algebraic expressions).PA M11.D.1.1Analyze and/or use patterns or relations.PA M11.D.1.1.1Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.PA M11.D.1.1.2Determine if a relation is a function given a set of points or a graph.PA M11.D.1.1.3Identify the domain, range or inverse of a relation (may be presented as ordered pairs or a table).PA M11.D.2Represent and/or analyze mathematical situations using numbers, symbols, words, tables and/or graphs.PA M11.D.2.1Write, solve and/or graph linear equations and inequalities using various methods.PA M11.D.2.1.1Solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities).PA M11.D.2.1.2Identify or graph functions, linear equations, or linear inequalities on a coordinate plane.PA M11.D.2.1.3Write, solve, and/or apply a linear equation (including problem situations).PA M11.D.2.1.4Write and/or solve systems of equations using graphing, substitution and/or elimination (limit systems to 2 equations).PA M11.D.2.1.5Solve quadratic equations using factoring (integers only -- not including completing the square or the Quadratic Formula).PA M11.D.2.2Simplify expressions involving polynomials.PA M11.D.2.2.1Add, subtract and/or multiply polynomial expressions (express answers in simplest form --nothing larger than a binomial multiplied by a trinomial).PA M11.D.2.2.2Factor algebraic expressions, including differences of squares and trinomials (trinomials limited to the form ax2 + bx + c where a is not equal to 0).PA M11.D.3.1Describe and/or determine change.PA M11.D.3.1.1Identify, describe and/or use constant or varying rates of change.PA M11.D.3.1.2Determine how a change in one variable relates to a change in a second variable (e.g., y = 4/x; if x doubles, what happens to y?)/PA M11.D.3.2Computer and/or use the slope of a line.PA M11.D.3.2.1Apply the formula for the slope of a line to solve problems.PA M11.D.3.2.3Compute the slope and/or y-intercept represented by a linear equation or graph.PA M11.D.4.1Interpret and/or use linear, quadratic and exponential functions and their equations, graphs or tables.PA M11.D.4.1.1Match the graph of a given function to its table or equation.PA M11.E.1.1.1Create and/or use appropriate graphical representations of data, including box-and-whisker plots, stem-and-leaf plots or scatter plots.PA M11.E.2.1.2Calculate or select the appropriate measure of central tendency (mean, mode or median) of a set of data given or represented on a table, line plot or stem-and-leaf plot.PA M11.E.2.1.3Calculate and/or interpret the range, quartiles and interquartile range of data.PA M11.E.3.1.1Find probabilities for independent, dependent or compound events and represent as a fraction, decimal or percent).PA M11.E.3.1.2Find, convert and/or compare the probability and/or odds of a simple event.PA M11.E.3.2Apply counting techniques in problem-solving settings.PA M11.E.3.2.1Determine the number of permutations and/or combinations or apply the fundamental counting principle.PA M11.E.4Develop and/or evaluate inferences and predictions or draw conclusions based on data or data displays.PA M11.E.4.1Make predictions using data displays and probability.PA M11.E.4.2Analyze and/or interpret data on a scatter plot and/or use a scatter plot to make predictions.PA M11.E.4.2.1Draw, find and/or write an equation for a line of best fit for a scatter plot.PA M11.E.4.2.2Make predictions using the equations or graphs of best-fit lines of scatter plots.PA M11D.3.2.2Given the graph of the line, 2 points on the line, or the slope and a point on a line, write or identify the linear equation in point-slope form, standard and/or slope-intercept form.  Note to FSC: In correlation spreadsheet and here, insert space before D.PA. M11.D.3Analyze change in various contexts.  Note to FSC: In correlation spreadsheet and here, delete period after PA.PA. M11.E.2.1.1Use measures of central tendency to describe a set of data.  Note to FSC: In correlation spreadsheet, delete period after PA.TX TEKS 8.1BThe student understands that different forms of numbers are appropriate for different situations. The student is expected to select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships.TX TEKS 8.3BThe student identifies proportional or non-proportional linear relationships in problem situations and solves problems. The student is expected to estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates.TX TEKS 8.6AThe student uses transformational geometry to develop spatial sense. The student is expected to generate similar figures using dilations including enlargements and reductions.TX TEKS 8.9AThe student uses indirect measurement to solve problems. The student is expected to use the Pythagorean Theorem to solve real-life problems.TX TEKS 8.9BThe student uses indirect measurement to solve problems. The student is expected to use proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements.TX TEKS 8.11AThe student applies concepts of theoretical and experimental probability to make predictions. The student is expected to find the probabilities of dependent and independent eventsTX TEKS 8.11BThe student applies concepts of theoretical and experimental probability to make predictions. The student is expected to use theoretical probabilities and experimental results to make predictions and decisions.TX TEKS 8.12AThe student uses statistical procedures to describe data. The student is expected to select the appropriate measure of central tendency or range to describe a set of data and justify the choice for a particular situation.TX TEKS 8.16BThe student uses logical reasoning to make conjectures and verify conclusions. The student is expected validate his/her conclusions using mathematical properties and relationships.TX TEKS A.1AThe student is expected to describe independent and dependent quantities in functional relationshipsTX TEKS A.1BThe student is expected to gather and record data and use data sets, to determine functional relationships between quantitiesTX TEKS A.1CThe student is expected to describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situationsTX TEKS A.1DThe student is expected to represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalitiesTX TEKS A.1EThe student is expected to interpret and make decisions, predictions, and critical judgments from functional relationshipsTX TEKS A.2AThe student is expected to identify and sketch the general forms of linear (y = x) and quadratic (y = x2) parent functionsTX TEKS A.2BThe student is expected to identify mathematical domains and ranges and determine  reasonable domain and range values for given situations, both continuous and discreteTX TEKS A.2CThe student is expected to interpret situations in terms of given graphs or create situations that fit given graphsTX TEKS A.2DThe student is expected to collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgmentsTX TEKS A.3AThe student is expected to use symbols to represent unknowns and variablesTX TEKS A.3BThe student is expected to look for patterns and represent generalizations algebraicallyTX TEKS A.4AThe student is expected to find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situationsTX TEKS A.4BThe student is expected to use the commutative, associative, and distributive properties to simplify algebraic expressionsTX TEKS A.4CThe student is expected to connect equation notation with function notation, such as  y = x + 1 and f(x) = x + 1TX TEKS A.5AThe student is expected to determine whether or not given situations can be represented by linear functionsTX TEKS A.5BThe student is expected to determine the domain and range for linear functions in given situationsTX TEKS A.5CThe student is expected to use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions.TX TEKS A.6AThe student is expected to develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representationsTX TEKS A.6BThe student is expected to interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphsTX TEKS A.6DThe student is expected to graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y?intercept.TX TEKS A.6EThe student is expected to determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations b.TX TEKS A.6FThe student is expected to interpret and predict the effects of changing slope and y-intercept in applied situations.TX TEKS A.6GThe student is expected to relate direct variation to linear functions and solve problems involving proportional changeTX TEKS A.7AThe student is expected to analyze situations involving linear functions and formulate linear equations or inequalities to solve problems.TX TEKS A.7BThe student is expected to investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalitiesTX TEKS A.7CThe student is expected to interpret and the reasonableness of solutions to linear equations and inequalities.TX TEKS A.8AThe student is expected to analyze situations and formulate systems of linear equations in two unknowns to solve problemsTX TEKS A.8BThe student is expected to solve systems of linear equations using concrete models, graphs, tables and algebraic methodsTX TEKS A.8CThe student is expected to interpret and determine the reasonableness of solutions to systems of linear equationsTX TEKS A.9AThe student is expected to determine the domain and range for quadratic equations in given situationsTX TEKS A.9BThe student is expected to investigate, describe, and predict the effects of changes in a on the graph of y= ax2 + cTX TEKS A.9CThe student is expected to investigate, describe, and predict the effects of changes in c on the graph of y = x2 + cTX TEKS A.9DThe student is expected to analyze graphs of quadratic functions and draw conclusionsTX TEKS A.10AThe student is expected to solve quadratic equations using concrete models, tables, graphs, and algebraic methodsTX TEKS A.10BThe student is expected to make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts x-intercepts) of the graph of the functionsTX TEKS A.11AThe student is expected to use patterns to generate the laws of exponents and apply them in problem-solving situationsTX TEKS A.11BThe student is expected to analyze data and represent situations involving inverse variation using concrete models, tables, graphs, or algebraic methodsTX TEKS A.11CThe student is expected to analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methodsUT 1Students will acquire number sense and perform operations with real numbers.UT 1.1Compute fluently and make reasonable estimates.UT 1.1.1Estimate solutions to problems.UT 1.1.3Determine the reasonableness of an answer by relating it to the problem.UT 1.2Represent real numbers in a variety of ways.UT 1.2.1Compare and order real numbers.UT 1.2.2Choose appropriate and convenient forms of real numbers for solving problems and representing answers, e.g., radical form, multiples of pi, decimal, fraction, or percent.UT 1.3Identify relationships among real numbers and operations involving these numbers.UT 1.3.1Classify numbers as rational or irrational in the realnumber system.UT 1.3.2Relate properties and operations of rational numbers to irrational numbers.UT 1.3.3Simplify numerical expressions and solve problems using real numbers.UT 2Students will represent and analyze mathematical situations and properties using patterns, relations, functions, and algebraic symbols.UT 2.1Use patterns, relations, and functions to represent mathematical situations.UT 2.1.1Write algebraic expressions or equations to generalize visual patterns, numerical patterns, relations, data sets, or scatter plots.UT 2.1.2Represent linear equations in slope-intercept form, y = mx + b, or standard form, ax + by = c.UT 2.1.3Distinguish between linear and non-linear functions or equations by examining a table, equation, or graph.UT 2.1.4Identify the slope of a linear function as an average rate of change in real-world situations.UT 2.2Evaluate, solve, and analyze mathematical situations using algebraic properties and symbols.UT 2.2.1Solve real-world problems involving constant rates of change, e.g., rates of travel, hourly wages, or rates of interest.UT 2.2.2aSolve multi-step equations and inequalities Numerically; e.g., from a table or guess and check.UT 2.2.2bSolve multi-step equations and inequalities Algebraically, including the use of manipulatives.UT 2.2.2cSolve multi-step equations and inequalities Graphically.UT 2.2.2dSolve multi-step equations and inequalities Using technology.UT 2.2.3bSolve systems of two linear equations or inequalities Algebraically.UT 2.2.3cSolve systems of two linear equations or inequalities Graphically.UT 2.2.4Determine the number of possible solutions for a system of two linear equations.UT 2.2.5Evaluate numerical expressions (including exponents and square roots), algebraic expressions, formulas, and equations.UT 2.2.7Simplify algebraic expressions, including those having integer exponents.UT 2.2.8Solve proportions that include algebraic first-degree expressions.UT 2.2.9Determine the number of solutions for a system of linear equations.UT 2.3Represent quantitative relationships using mathematical models and symbols.UT 2.3.1aIdentify the slope of a line when given A set of two ordered pairs.UT 2.3.1bIdentify the slope of a line when given An equation of a linear function.UT 2.3.1cIdentify the slope of a line when given The graph of a linear function.UT 2.3.2aWrite the equation of a line when given A set of ordered pairs.UT 2.3.2bWrite the equation of a line when given The slope and a point on the line.UT 2.3.2cWrite the equation of a line when given The graph of a line.UT 2.3.3Identify horizontal and vertical lines given the equations.UT 2.3.5Determine the effect of parameter changes on the graphs of linear relations.UT 2.3.6Determine whether two lines are parallel, perpendicular, or neither, given the equations.UT 2.3.7 Determine the x- and y-intercepts from an equation or graph of a line.UT 2.3.8aGraph linear functions By plotting points.UT 2.3.8bGraph linear functions By finding x- and y-intercepts.UT 2.3.8cGraph linear functions Using the slope-intercept form of a line.UT 2.3.8dGraph linear functions Using the slope and any point on the line.UT 2.3.9Graph linear inequalities and identify the boundary line and solution area.UT 2.3.11Use direct variation to model rates of change, e.g., if income = 40 hours times rate of pay, then increasing the rate of pay increases income.UT 3 Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling.UT 3.2.3Solve problems for areas, perimeters, volumes, and surface areas using formulas.UT 3.3.1Solve problems using the PythagoreanTheorem.UT 3.3.2Find missing parts of geometric figures using proportional reasoning and geometric relationships.UT 3.3.3Illustrate multiplication of polynomials using area models, e.g., (a + b)2 , x(x + 2), or (x + a)(x + b).UT 3.3.4aFactor polynomials using area models To identify the greatest common monomial factor.UT 3.3.4bFactor polynomials using area models Of the form ax2 + bx + c when a = 1.UT 4.1.1Solve problems and express answers using appropriate units of measure.UT 4.2.2Express the rate of change as a ratio of two different measures.UT 5.1.1Collect, record, organize, and display a set of data.UT 5.1.2Determine whether the pattern of the data is linear nonlinear when given in a list, table, or graph.UT 5.1.3 Interpret the correlation between two variables positive, negative, or having no correlation.UT 5.1.4Find a line of best fit by estimation, choosing two or using technology for a given set of data.UT 5.2.1Determine and express the probability of an event as a fraction, percent, ratio, or decimal.UT 5.2.2Identify the probability of an event as being between zero (event not possible) and one (event certain).UT 5.2.3Recognize that the sum of the probability of an event andthe probability of its complement is equal to one.WA 5.1.1Note to FSC: These appear to belong in Washington. Please move to WA columnWA 5.1.2Note to FSC: These appear to belong in Washington. Please move to WA columnWA 1.1.1Understand and apply scientific notation.WA 1.1.1aRead and use scientific and exponential notation.WA 1.1.1cUse scientific or exponential notation to simplify a problem.WA 1.1.1dIllustrate the meaning of scientific notation using pictures, diagrams, or numbers.WA 1.1.1eRead and translate numbers represented in scientific notation from calculators and other technology, tables, and charts.WA 1.1.4Apply understanding of direct and inverse proportions to solve problems.WA 1.1.4aExplain a method for determining whether a real-world problem involves direct proportion or inverse proportion.WA 1.1.4bExplain a method for solving a real-world problem involving direct proportion.WA 1.1.4cExplain a method for solving a real-world problem involving inverse proportion.WA 1.1.4dSolve problems using direct or inverse models (e.g., similarity, age of car vs. worth).WA 1.1.4eExplain, illustrate, or describe examples of direct proportion.WA 1.1.4fExplain, illustrate, or describe examples of inverse proportion.WA 1.1.4gUse direct or inverse proportion to determine a number of objects or a measurement in a given situation.WA 1.1.6Apply strategies to compute fluently with rational numbers in all forms including whole number exponents.WA 1.1.6aComplete multi-step computations using order of operations in situations involving combinations of rational numbers including whole number exponents and square roots of square numbers.WA 1.1.6bCalculate using order of operations on all forms of rational numbers.WA 1.1.6cUse properties to reorder and rearrange expressions to compute more efficiently.WA 1.1.8Apply estimation strategies to determine the reasonableness of results in situations involving multi-step computations with rational numbers including whole number powers and square and cube roots.WA 1.1.8dDescribe various strategies used during estimation involving integers, rational numbers.WA 1.1.8eUse estimation to predict or to verify the reasonableness of calculated results.WA 1.2.1Analyze how changes in one or two dimensions of an object affect perimeter, area, surface area, and volume.WA 1.2.1aDescribe and compare the impact that a change in one or more dimensions has on objects (e.g., how doubling one dimension of a cube affects the surface area and volume).WA 1.2.1dCompare a given change in one or two dimensions on the perimeter, area, surface area, or volumes of two objects.WA 1.2.3Understand how to convert units of measure within systems (U.S. or metric).WA 1.2.3bConvert within a system to a unit size appropriate to a given situation.WA 1.2.5bUse a formula to find the volume of a prism or cylinder.WA 1.2.6dEstimate derived units of measure (e.g., miles per hour, people/year, grams/cubic centimeters).WA 1.3.2dUse the properties of two-dimensional and three-dimensional shapes to solve mathematical problems e.g., find the width of a river based on similar triangles; given a set of parallel lines, a transversal, and an angle, find the other angles).WA 1.3.3Apply understanding of geometric properties and location of points to figures.WA 1.3.3aUse coordinates to describe or identify the location of objects on coordinate grids.WA 1.3.3cDescribe the location of points that satisfy given conditions (e.g., the set of points equidistant from a given point; a point equidistant from a given set of points).WA 1.3.3fIdentify, interpret, and use the meaning of slope of a line as a rate of change using physical, symbolic, and technological models.WA 1.3.4Apply understanding of multiple transformations.WA 1.3.4aApply multiple transformations to create congruent and similar figures in any or all of the four quadrants.WA 1.3.4a,WA 3.1.1aNote to FSC: These should be two separate standards. Add space after comma.WA 1.3.4bUse multiple transformations (combinations of translations, reflections, or rotations) to draw an image.WA 1.3.4cUse dilation (expansion or contraction) of a given shape to form a similar shape.WA 1.3.4dDetermine the final coordinates of a point after a series of transformations.WA 1.3.4eExamine figures to determine rotational symmetry about the center of the shape.WA 1.3.4fDefine a set of transformations that would map one onto the other given two similar shapes.WA 1.4.1aCompare the probabilities of dependent and independent events.WA 1.4.1bDetermine and justify whether the outcome of a first event affects the probability of a later event (e.g., drawing cards from a deck with or without replacement).WA 1.4.1cExplain the difference between dependent and independent events.WA 1.4.1dExplain and give examples of compound events.WA 1.4.2Apply understanding of dependent and independent events to calculate probabilities.WA 1.4.2aDetermine probabilities of dependent and independent events.WA 1.4.2bGenerate the outcomes and probability of multiple independent and dependent events using a model or procedure (e.g., tree diagram, area modeling, counting procedures).WA 1.4.2cGenerate the outcomes and probability of events using a counting procedure (e.g., the number of license plates that can be made with three letters and three numbers; winning the lottery).WA 1.4.2dExplain the relationship between theoretical probability and empirical frequency of dependent events using simulations with and without technology.WA 1.4.2gDetermine the sample space for independent or dependent events.WA 1.4.3Apply appropriate methods and technology to collect data or evaluate methods used by others for given research questions.WA 1.4.3bEvaluate methods and technology used to investigate a research question.WA 1.4.4Understand and apply techniques to find the equation for a reasonable linear model.WA 1.4.4bDetermine the equation of a line that fits the data displayed on a scatter plot.WA 1.4.4cUse technology to determine the line of best fit for a set of data.WA 1.4.4dMatch an equation with a set of data.WA 1.4.4eMatch an equation with a graphic display.WA 1.4.4fCreate a graph based on the equation for the line.WA 1.4.5aDetermine whether a straight line is an appropriate way to describe a trend in a set of bivariate data.WA 1.4.5bDetermine whether the underlying model for a set of data is linear.WA 1.4.5eUse technology to generate data to fit a linear model.WA 1.4.6Apply understanding of statistics to make, analyze, or evaluate a statistical argument.WA 1.4.6aIdentify trends in a set of data in order to make a prediction based on the information.WA 1.4.6bJustify a prediction or an inference based on a set of data.WA 1.4.6gDetermine whether statistics have been used or misused to support a point of view or argument and support the evaluation with data.WA 1.5.1Apply processes that use repeated addition (linear) or repeated multiplication (exponential).WA 1.5.1aRecognize, extend, or create a pattern or sequence between sets of numbers and/or linear patterns.WA 1.5.1bIdentify, extend, or create a geometric or arithmetic sequence or pattern.WA 1.5.1cTranslate among equivalent numerical, graphical, and algebraic forms of a linear function.WA 1.5.2Analyze a pattern, table, graph, or model involving repeated addition (linear) or repeated multiplication (exponential) model to write an equation or rule.WA 1.5.2aFind the equation of a line in a variety of ways (e.g., from a table, graph, slope-intercept, point-slope, two points).WA 1.5.2bGenerate and use rules for a pattern to make predictions about future events (e.g., population growth, future sales, growth of corn stalks, future value of savings account).WA 1.5.2cIdentify or write an equation or rule to describe a pattern, sequence, and/or linear function.WA 1.5.2dWrite an equation for a line given a set of information (e.g., two points, point-slope, etc.).WA 1.5.2eWrite a recursive definition of a geometric pattern (e.g., Start and New = Old Number).WA 1.5.2fRepresent systems of equations and inequalities graphically.WA 1.5.2hWrite an expression, equation, or inequality with two variables representing a linear model of a real-world problem.WA 1.5.4Apply understanding of equations, tables, or graphs to represent situations involving relationships that can be written as repeated addition (linear) or repeated multiplication (exponential).WA 1.5.4aRepresent variable quantities through expressions, equations, inequalities, graphs, and tables to represent linear situations involving whole number powers and square and cube roots.WA 1.5.4bIdentify and use variable quantities to read and write expressions and equations to represent situations that can be described using repeated addition (e.g., models that are linear in nature).WA 1.5.4cIdentify and use variable quantities to read and write expressions and equations to represent situations that can be described using repeated multiplication (e.g., models that are exponential such as savings accounts and early stages of population growth).WA 1.5.4dRecognize and write equations in recursive form for additive models (e.g., starting value, New = Old + some number).WA 1.5.4eSelect an expression or equation to represent a given real-world situation.WA 1.5.5Apply procedures to simplify expressions.WA 1.5.5aSimplify expressions and evaluate formulas involving exponents.WA 1.5.5bJustify a simplification of an expression involving exponents.WA 1.5.5cUse multiple mathematical strategies and properties to simplify expressions.WA 1.5.6Apply procedures to solve equations and systems of equations.WA 1.5.6bSolve real-world situations involving linear relationships and verify that the solution makes sense in relation to the problem.WA 1.5.6cFind the solution to a system of linear equations using tables, graphs, and symbols.WA 1.5.6dInterpret solutions of systems of equations.WA 1.5.6eSolve multi-step equations.WA 1.5.6fUse systems of equations to analyze and solve real-life problems.WA 1.5.6gDetermine when two linear options yield the same outcome (e.g., given two different investment or profit options, determine when both options will yield the same result).WA 2.2.1aUse strategies to become informed about the situation (e.g., listing information; examine the table for patterns; create a scatter plot to look for patterns; asking questions).WA 2.2.2Apply mathematical tools to solve the problem.WA 2.2.2bUse mathematics to solve the problem (e.g., use algebra to write equations for the two linear models, solve the system of equations using either symbols or technology).WA 2.2.2dCheck the solution to see if it works (e.g., the solution may be a partial year [i.e., 2003.6]; decide how to deal with this and also if the year is reasonable [i.e., 1925 does not make sense given the context]).WA 3.1.1Apply skill of conjecturing and analyze conjectures by formulating a proof or constructing a counter example.WA 3.1.1aUse the properties of two-dimensional and three-dimensional figures to solve mathematical problems (e.g., find the width of a river based on similar triangles; given a set of parallel lines, a transversal, and an angle, find the other angles).WA 3.2.2Analyze information to draw conclusions and support them using inductive and deductive reasoning.WA 3.2.2cIdentify trends in a set of data in order to make a prediction based on the information.WA 3.2.3Analyze procedures to determine appropriateness of claims and arguments.WA 3.3.1Analyze results using inductive and deductive reasoning.WA 4.2.1Analyze mathematical information to organize, clarify, and refine an argument.WA 4.2.2Understand how to express ideas and situations using mathematical language and notation.WA 4.2.2aExplain how division of measurements produces a derived unit of measurement (e.g., miles traveled divided by hours traveled yields the derived unit [miles per hour]).WA 4.2.2bDescribe the location of points that satisfy given conditions (e.g., the set of points equidistant from a given point; a point equidistant from a given set of points).WA 4.2.2cDescribe and compare the impact that a change in one or more dimensions has on objects (e.g., doubling the edge of a cube affects the surface area).WA 4.2.2dExplain the relationship between theoretical probability and empirical frequency of dependent events using simulations with and without technology.WA 5.1.1Apply multiple mathematical concepts and procedures in a given problem or situation.WA 5.1.1aEstimate derived units of measure (e.g., miles per hour, people/year, grams/cubic centimeters).WA 5.1.1bDetermine the final coordinates of a point after a series of transformations.WA 5.1.2Understand how to use different mathematical models and representations in the same situation.WA 5.1.2aIdentify, interpret, and use the meaning of slope of a line as a rate of change using concrete, symbolic, and technological models.WA 5.1.2cFind the equation of a line in a variety of ways (e.g., from a table, graph, slope-intercept, point-slope, two points).WA 5.1.2dFind the solution to a system of linear equations using tables, graphs, and symbols.WA 5.2.1Analyze mathematical patterns and ideas to extend mathematical thinking and modeling in other disciplines.WA 5.2.1aJustify a prediction or an inference based on a set of data.WA 5.3.1aExplain a method for determining whether a real-world problem involves direct proportion or inverse proportion.WI A.12.1bStudents will use reason and logic to perceive patterns.WI A.12.1cStudents will use reason and logic to identify relationships.WI A.12.1dStudents will use reason and logic to formulate questions, pose problems, and make and test conjectures.WI A.12.1eStudents will use reason and logic to pursue ideas that lead to further understanding and deeper insight.WI A.12.2bStudents will communicate logical arguments and clearly show why the reasoning is or is not valid.WI A.12.3Students will analyze non-routine problems and arrive at solutions by various means, including models and simulations, often starting with provisional conjectures and progressing, directly or indirectly, to a solution, justification, or counter-example.WI A.12.5Students will organize work and present mathematical procedures and results clearly, systematically, succinctly, and correctly.WI B.12.1Students will use complex counting procedures such as union and intersection of sets and arrangements (permutations and combinations) to solve problems.WI B.12.2aStudents will compare real numbers using order relations (>, <) and transitivity.WI B.12.2bStudents will compare real numbers using ordinal scales including logarithmic (e.g., Richter, pH rating).WI B.12.2dStudents will compare real numbers using arithmetic differences.WI B.12.3Students will compare real numbers using ratios, proportions, percents, rates of change.WI B.12.4aStudents will perform and explain operations on real numbers (add, subtract, multiply, divide, raise to a power, extract a root, take opposites and reciprocals, determine absolute value).WI B.12.4bStudents will, in problem-solving situations involving the application of different number systems (natural, integers, rational, real), select and use appropriate computational procedures.WI B.12.4cStudents will, in problem-solving situations involving the application of different number systems (natural, integers, rational, real), select and use appropriate properties (e.g., commutativity, associativity, inverses).WI B.12.5Students will, in problem-solving situations involving the application of different number systems (natural, integers, rational, real), select and use appropriate modes of representation (e.g., rationals as repeating decimals, indicated roots as fractional exponents).WI B.12.6aStudents will create and critically evaluate numerical arguments presented in a variety of classroom and real-world situations (e.g., political, economic, scientific, social).WI B.12.6bStudents will routinely assess the acceptable limits of error when evaluating strategies.WI C.12.2Students will use geometric models to solve mathematical and real-world problems.WI C.12.3aStudents will present convincing arguments by means of demonstration, informal proof, counter-examples, or any other logical means to show the truth of statements (e.g., these two triangles are not congruent).WI C.12.3bStudents will present convincing arguments by means of demonstration, informal proof, counter-examples, or any other logical means to show the truth of generalizations (e.g., the Pythagorean theorem holds for all right triangles).WI C.12.4Students will use the two-dimensional rectangular coordinate system and algebraic procedures to describe and characterize geometric properties and relationships such as slope, intercepts, parallelism, and perpendicularity.WI C.12.5Students will identify and demonstrate an understanding of the three ratios used in right-triangle trigonometry (sine, cosine, tangent).WI D.12.1Students will identify, describe, and use derived attributes (e.g., density, speed, acceleration, pressure) to represent and solve problem situations.WI D.12.2Students will select and use tools with appropriate degree of precision to determine measurements directly within specified degrees of accuracy and error (tolerance).WI D.12.3aStudents will determine measurements indirectly, using estimation.WI D.12.3bStudents will determine measurements indirectly, using proportional reasoning, including those involving squaring and cubing (e.g., reasoning that areas of circles are proportional to the squares of their radii).WI D.12.3cStudents will determine measurements indirectly, using techniques of algebra, geometry, and right triangle trigonometry.WI D.12.3dStudents will determine measurements indirectly, using formulas in applications (e.g., for compound interest, distance formula).WI D.12.3eStudents will determine measurements indirectly, using geometric formulas to derive lengths, areas, or volumes of shapes and objects (e.g., cones, parallelograms, cylinders, pyramids).WI D.12.3fStudents will determine measurements indirectly, using geometric relationships and properties of circles and polygons (e.g., size of central angles, area of a sector of a circle).WI D.12.3gStudents will determine measurements indirectly, using conversion constants to relate measures in one system to another (e.g., meters to feet, dollars to Deutschmarks).WI E.12.1dStudents will work with data in the context of real-world situations by using technology to generate displays, summary statistics, and presentations.WI E.12.2cStudents will organize and display data from statistical investigations using line of best fit (estimated regression line).WI E.12.3cStudents will interpret and analyze information from organized and displayed data when given measures of correlation.WI E.12.5aStudents will determine the likelihood of occurrence of complex events by using a variety of strategies (e.g., combinations) to identify possible outcomes.WI E.12.5bStudents will determine the likelihood of occurrence of complex events by conducting an experiment.WI E.12.5cStudents will determine the likelihood of occurrence of complex events by designing and conducting simulations.WI E.12.5dStudents will determine the likelihood of occurrence of complex events by applying theoretical probability.WI F.12.1Students will analyze and generalize patterns of change (e.g., direct and inverse variation) and numerical sequences, and then represent them with algebraic expressions and equations.WI F.12.2aStudents will use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of ways, including recognizing that a variety of mathematical and real-world phenomena can be modeled by the same type of function.WI F.12.2bStudents will use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of ways, including translating different forms of representing them (e.g., tables, graphs, functional notation, formulas).WI F.12.2cStudents will use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of ways, including describing the relationships among variable quantities in a problem.WI F.12.3aStudents will solve linear and quadratic equations, linear inequalities, and systems of linear equations and inequalities numerically.WI F.12.3bStudents will solve linear and quadratic equations, linear inequalities, and systems of linear equations and inequalities graphically, including use of appropriate technology.WI F.12.3cStudents will solve linear and quadratic equations, linear inequalities, and systems of linear equations and inequalities symbolically, including use of the quadratic formula.WI F.12.4Students will model and solve a variety of mathematical and real-world problems by using algebraic expressions, equations, and inequalities.