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SUT:SGSUTT!TUTST`TUT�T�TUTUUUTdUqUUT�U�UUT5VBVUT�V�VUT�V�VUTWWUT�W�WUT^XkXUT�X�XUT6YBY8AZ 1.1 PO 1Locate rational numbers on a number line.8AZ 1.1 PO 2Identify irrational numbers.8AZ 1.1 PO 3Classify real numbers as rational or irrational.8AZ 1.2 PO 1Select the grade-level appropriate operation to solve word problems.8AZ 1.2 PO 2Solve word problems using grade-level appropriate operations and numbers.8AZ 1.2 PO 3Determine the square of an integer.8AZ 1.2 PO 4Determine the square root of an integer.8AZ 1.2 PO 6Apply grade-level appropriate properties to assist in computation.8AZ 1.2 PO 7 Apply the symbols �?� to represent square root, ��� to represent roots, and �{}� as grouping symbols.8AZ 1.2 PO 8Use grade-level appropriate mathematical terminology.8AZ 1.2 PO 9Calculate the missing value in a percentage problem.8AZ 1.2 PO 10Convert standard notation to scientific notation, and vice versa.8AZ 1.2 PO 11Simplify numerical expressions using the order of operations with grade-appropriate operations on number sets.8AZ 1.3 PO 1Solve grade-level appropriate problems using estimation.8AZ 1.3 PO 2Use estimation to verify the reasonableness of a calculation (e.g., Is 32 the square root of 64?).8AZ 1.3 PO 3Express answers to the appropriate place or degree of precision (e.g., time, money).8AZ 2.1 PO 2Construct box-and-whisker plots.8AZ 2.1 PO 4Interpret box-and-whisker plots, circle graphs, and scatter plots.8AZ 2.1 PO 5Answer questions based on box-and-whisker plots, circle graphs, and scatter plots.8AZ 2.1 PO 6Solve problems in contextual situations using the mean, median, mode, and range of a given data set.8AZ 2.1 PO 7Formulate reasonable predictions based on a given set of data.8AZ 2.1 PO 8Compare trends in data related to the same investigation.8AZ 2.1 PO 9Solve contextual problems using scatter plots, box-and-whisker plots, and double line graphs of continuous data.8AZ 2.1 PO 11Identify a line of best fit for a scatter plot.8AZ 2.2 PO 1Determine the probability that a specific event will occur in a 2-stage probability experiment.8AZ 2.2 PO 2Solve contextual situations using probability (e.g., If the probability of Michelle making a free throw is 0.25, what is the probability that she will make three free throws in a row?).8AZ 2.2 PO 3Predict the outcome of a grade-level appropriate probability experiment.8AZ 2.2 PO 4Record the data from performing a grade-level appropriate probability experiment.8AZ 2.3 PO 1Determine all possible outcomes involving the combination of two or more sets of objects (e.g., If you roll a six-sided number cube 4 times, how many possible outcomes are possible?).8AZ 2.3 PO 2Determine all possible arrangements given a set (e.g., How many ways can you arrange a set of 7 books on a shelf?).8AZ 3.1 PO 1Communicate a grade-level appropriate iterative or recursive pattern, using symbols or numbers.8AZ 3.1 PO 2Extend a grade-level appropriate iterative or recursive pattern.8AZ 3.1 PO 3Solve grade-level appropriate iterative or recursive pattern problems.8AZ 3.2 PO 1Describe the rule used in a simple grade-level appropriate function (e.g., T-chart, input/output model).8AZ 3.2 PO 3Determine whether a graph or table is related to a given equation of the form y = ax2 where a is a natural number.8AZ 3.3 PO 1Evaluate algebraic expressions by substituting rational values for variables [e.g., 2(ab+ac+bc), when a = 2, b = 3/5, and c = 4].8AZ 3.3 PO 2Use variables in contextual situations.8AZ 3.3 PO 3Translate a written sentence or phrase into an algebraic equation or expression, and vice versa (e.g., Three less than twice a number is 2n � 3.).8AZ 3.3 PO 4Translate a sentence written in context into an algebraic equation involving two operations.8AZ 3.3 PO 5Translate a contextual situation into an algebraic inequality (e.g., Joe earns more than $5.00 an hour; therefore, x > 5).8AZ 3.3 PO 7Solve one-step equations with rational numbers as coefficients or as solutions.8AZ 3.3 PO 8Solve one-step equations that model contextual situations.8AZ 3.3 PO 9Solve two-step equations with rational coefficients and integer solutions (e.g., 3x + 5 = 11, 4x - 20 = 8).8AZ 3.3 PO 10Graph an inequality on a number line.8AZ 3.3 PO 11Solve a simple algebraic proportion.8AZ 3.3 PO 12Solve applied problems using the Pythagorean theorem.8AZ 3.4 PO 1Identify the slope of a line as the rate of change (the ratio of rise over run).8AZ 4.1 PO 1Draw a model that demonstrates basic geometric relationships such as parallelism, perpendicularity, similarity/proportionality, and congruence.8AZ 4.1 PO 3Recognize the 3-dimensional figure represented by a net.8AZ 4.1 PO 4Represent the surface area of rectangular prisms and cylinders as the area of their net.8AZ 4.1 PO 5Draw regular polygons with appropriate labels.8AZ 4.1 PO 6Identify the properties of angles created by a transversal intersecting two parallel lines (e.g., corresponding angles are congruent).8AZ 4.2 PO 1Identify the planar geometric figure that is the result of a given rigid transformation.8AZ 4.2 PO 2Model a simple transformation on a coordinate grid (e.g., Translate right four units and down two units.).8AZ 4.3 PO 1Use a table of values to graph a linear equation.8AZ 4.4 PO 1Solve problems for the area of a trapezoid.8AZ 4.4 PO 2Solve problems involving the volume of rectangular prisms and cylinders.8AZ 4.4 PO 3Calculate the surface area of rectangular prisms or cylinders.8AZ 4.4 PO 4Identify rectangular prisms and cylinders having the same volume.8AZ 4.4 PO 6Solve problems using ratios and proportions, given the scale factor.8AZ 4.4 PO 7Calculate the length of a side, given two similar triangles.8AZ 5.1 PO 2Analyze algorithms.8CO 1Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems.8CO 1.1Demonstrate meanings for integers, rational numbers, percents, exponents, square roots and pi (?) using physical materials and technology in problem-solving situations.8CO 1.1.aRecognize and use equivalent representations of positive rational numbers and common irrational numbers (for example, locate rational numbers on a number line and demonstrate the meaning of square roots and perfect squares).8CO 1.2Read, write and order integers, rational numbers and common irrational numbers such as ?2, ?5, and ?.8CO 1.2.aCompare and order sets of integers and rational numbers that are expressed in a variety of ways.8CO 1.3Apply number theory concepts (for example, primes, factors, multiples) to represent numbers in various ways.8CO 1.3.aApply number theory concepts (for example, primes, factors, multiples, exponents) in problem-solving situations.8CO 1.4Use the relationships among fractions, decimals, and percents, including the concepts of ratio and proportion, in problem-solving situations.8CO 1.4.aUse the relationships among fractions, decimals and percents including the concepts of ratio and proportion in problem-solving situations (similarity, scale factor, unit rate).8CO 1.5.aDevelop and test conjectures about properties of integers (Does 3-5 = 5-3?) and rational numbers.8CO 1.6Use number sense to estimate and justify the reasonableness of solutions to problems involving integers, rational numbers, and common irrational numbers such as ?2, ?5, and ?.8CO 1.6.aUse number sense to estimate and justify the reasonableness of solutions to problems involving integers and rational numbers.8CO 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.8CO 2.1Represent, describe, and analyze patterns and relationships using tables, graphs, verbal rules, and standard algebraic notation.8CO 2.1.aRepresent, describe, and analyze patterns (for example, geometric and numeric) and relationships using tables, graphs, verbal rules, and standard algebraic notation.8CO 2.1.bConvert from one functional representation (table, graph, verbal rule, standard algebraic notation) to another.8CO 2.2Describe patterns using variables, expressions, equations, and inequalities in problem-solving situations.8CO 2.2.aDescribe patterns using variables, expressions, equations, and inequalities in problem-solving situations.8CO 2.3Analyze functional relationships to explain how a change in one quantity results in a change in another (for example, how the area of a circle changes as the radius increases, or how a person�s height changes over time).8CO 2.3.aAnalyze functional relationships to explain how a change in one quantity results in a change in another (for example, how a person�s height changes over time).8CO 2.5Solve simple linear equations in problem-solving situations using a variety of methods (informal, formal, and graphical) and a variety of tools (physical materials, calculators, and computers).8CO 2.5.aSolve simple linear equations in problem-solving situations using a variety of methods (informal, formal, and graphic).8CO 3Students use data collection and analysis, statistics, and probability in problem-solving situations and communicate the reasoning used in solving these problems.8CO 3.1Read and construct displays of data using appropriate techniques (for example, line graphs, circle graphs, scatter plots, box plots, stem-and-leaf plots) and appropriate technology.8CO 3.1.aRead and construct displays of data using appropriate techniques (for example, circle graphs, scatter plots, box and whisker plots, stem-and-leaf plots).8CO 3.2Display and use measures of central tendency, such as mean, median and mode and measures of variability, such as range and quartiles.8CO 3.2.aDisplay and use measures of central tendency, (such as mean, median, and mode) and measures of variability, (such as range and quartiles) in problem-solving situations8CO 3.3.aAnalyze a graph, table or summary for misleading characteristics.8CO 3.4Formulate hypotheses, drawing conclusions, and making convincing arguments based on data analysis.8CO 3.5Determine probabilities through experiments or simulations.8CO 3.6Make predictions and compare results using both experimental and theoretical probability drawn from real- world problems.8CO 3.6.aUse a model (list, tree diagram, area model) to determine theoretical probabilities to solve problems involving uncertainty.8CO 3.6.bMake predictions using theoretical probability in real-world problems.8CO 3.7Use counting strategies to determine all the possible outcomes from an experiment (for example, the number of ways students can line up to have their picture taken).8CO 3.7.aUse a model or counting technique to determine all the possible outcomes from an experiment  (for example, the number of ways students can line up to have their picture taken).8CO 4Students use geometric concepts, properties, and relationships in problem-solving situations and communicate the reasoning used in solving these problems.8CO 4.1Construct two-and three-dimensional models using a variety of materials and tools.8CO 4.2Describe, analyze and reason informally about the properties (for example, parallelism, perpendicularity, congruence) of two- and three-dimensional figures.8CO 4.2.aDescribe, analyze and reason informally about properties (for example, parallelism, perpendicularity, congruence, and similarity) of two- and three-dimensional figures.8CO 4.3Apply the concepts of ratio, proportion, and similarity in problem-solving situations8CO 4.3.aApply the concept of ratio, proportion, and similarity in problem-solving situations.8CO 4.4Solve problems using coordinate geometry8CO 4.5Solving problems involving perimeter and area in two dimensions, and involving surface area and volume in three dimensions.8CO 4.5.aSolve problems involving perimeter and area in two dimensions, and involving surface area and volume in three dimensions (include right prisms and cylinders).8CO 4.5.bApply the Pythagorean Theorem to solve real-world problems.8CO 4.6Transform geometric figures using reflections, translations, and rotations to explore congruence8CO 4.6.aTransform geometric figures using reflections, translations, and rotations to determine congruence.8CO 5Students use a variety of tools and techniques to measure, apply the results in problem-solving situations, and communicate the reasoning used in solving these problems.8CO 5.1Estimate, use and describe measures of distance, perimeter, area, volume, capacity, weight, mass, and angle comparison.8CO 5.1.aEstimate and use measures of area, volume, capacity, weight, and angle comparisons to solve problems.8CO 5.2Estimate, make, and use direct and indirect measurements to describe and make comparisons.8CO 5.2.aEstimate, make and use direct and indirect measurements to describe and make comparisons (for example, use a proportion to find the height of a flag pole).8CO 5.3Read and interpret various scales including those based on number lines, graphs, and maps.8CO 5.3.aRead and interpret scales on number lines, graphs and maps (for example, given a map and a scale, determine the distance between two points on the map).8CO 5.4Develop and use formulas and procedures to solve problems involving measurement8CO 5.4.aDevelop and use procedures or formulas to solve problems involving measurement (for example, distance, area, surface area, and volume of right prisms and cylinders).8CO 5.6Select and use appropriate units and tools to measure to the degree of accuracy required in a particular problem- solving situation.8CO 6Students link concepts and procedures as they develop and use computational techniques, including estimation, mental arithmetic, paper-and-pencil, calculators, and computers, in problem-solving situations and communicate the reasoning used in solving these problems.8CO 6.1Use models to explain how ratios, proportions, and percents can be used to solve real-world problems.8CO 6.1.aUse models to explain how ratios, proportions, and percents can be used to solve real-world problems.8CO 6.2Construct, use and explain procedures to compute and estimate with whole numbers, fractions, decimals, and integers.8CO 6.2.aApply order of operations to evaluate simple expressions with integers.8CO 6.3Develop, apply and explain a variety of different estimation strategies in problem-solving situations, and explain why an estimate may be acceptable in place of an exact answer.8CO 6.4Select and use appropriate algorithms for computing with commonly used fractions and decimals, percents, and integers in problem-solving situations and determining whether the results are reasonable.8CO 6.4.aApply computational methods (including ratio and proportion) to solve problems involving commonly used fractions, decimals, percents, and integers (for example, discount, tax, sale price, unit price) and determine whether the results are reasonable.8CT 8:1.1Understand and describe patterns and functional relationships.8CT 8:1.1aAnalyze physical phenomena, functions and patterns to identify relationships and make generalizations.8CT 8:1.1a(1)Write recursive and explicit functions to generalize patterns.8CT 8:1.1a(2)Identify relationships that are linear and nonlinear and compare and contrast their properties using tables, graphs, equations and verbal descriptions.8CT 8:1.2Represent and analyze quantitative relationships in a variety of ways.8CT 8:1.2aDescribe the effects of characteristics of linear relationships on the way the relationships are represented verbally and in tables, graphs and equations.8CT 8:1.2a(1)Determine the constant rate of change in a linear relationship and recognize this as the slope of a line.8CT 8:1.2a(2)Compare and contrast the graphs of lines with the same slope versus those with different slopes.8CT 8:1.2a(3)Interpret slope and y-intercepts from contextual situations, graphs and linear equations.8CT 8:1.2a(4)Given two linear relationships in context, recognize that they may have a common solution.8CT 8:1.3Use operations, properties and algebraic symbols to determine equivalence and solve problems.8CT 8:1.3aSolve problems using various algebraic methods and properties.8CT 8:1.3a(1)Solve multistep equations using algebraic properties.8CT 8:1.3a(2)Use tables, graphs and equations to represent mathematical relationships and solve real-world problems.8CT 8:2.1Understand that a variety of numerical representations can be used to describe quantitative relationships.8CT 8:2.1aCompare and order integers, powers and roots using number lines and grids.8CT 8:2.1a(1)Compare, locate, label and order rational numbers on number lines, scales, coordinate grids and measurement tools.8CT 8:2.1a(2)Identify another rational number between any two rational numbers.8CT 8:2.1a(3)Solve a variety of problems involving integers, powers, roots and scientific notation.8CT 8:2.1bExtend the understanding of scientific notation to very small numbers.8CT 8:2.1b(1)Use powers of ten and negative exponents to write decimal fractions.8CT 8:2.1b(2)Use powers of ten and positive and negative exponents to express and compare magnitude of very large and very small numbers and connect to scientific notation.8CT 8:2.1b(3)Find the results of multiplication and division with powers of ten using patterns in operating with exponents.8CT 8:2.1b(4)Develop, describe and use a variety of methods to operate with very large and very small numbers.8CT 8:2.2Use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities.8CT 8:2.2aSolve problems involving fractions, decimals, ratios and percents.8CT 8:2.2a(1)Estimate and solve problems involving percent of increase and decrease.8CT 8:2.2bMake generalizations about operations with very large and very small numbers.8CT 8:2.2b(1)Use the rules for exponents to multiply and divide with powers of ten, including negative exponents.8CT 8:2.2b(2)Develop, describe and use a variety of methods to estimate and calculate mentally with very large and very small numbers.8CT 8:2.2cConnect the exponential growth and decay models to repeated multiplication by the same factor.8CT 8:2.2c(1)Solve problems that involve repetitive patterns and iterations, such as compound interest, using tables, spreadsheets and calculators.8CT 8:3.1Use properties and characteristics of two- and three-dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems.8CT 8:3.1aExplore the relationships among sides, angles, perimeters, areas, surface areas and volumes of congruent and similar polygons and solids.8CT 8:3.1a(1)Explore the effect of scale factors on the length, area and volume ratios of similar polygons, circles and solids.8CT 8:3.1a(2)Make and test conjectures about the relationships among angles, sides, perimeters and areas of congruent and similar polygons, including the Pythagorean Theorem.8CT 8:3.2Use spatial reasoning, location and geometric relationships to solve problems.8CT 8:3.2aModel geometric relationships in a variety of ways.8CT 8:3.2a(1)Use coordinate geometry to explore and test geometric relationships of parallel and perpendicular lines and polygons and their transformations.8CT 8:3.3Develop and apply units, systems, formulas and appropriate tools to estimate and measure.8CT 8:3.3aUse a variety of concrete methods, including displacement, to find volumes of solids.8CT 8:3.3a(1)Develop measurement strategies to find the surface area and volume of pyramids, cones, spheres and irregular solids.8CT 8:3.3a(2)Use estimation and measurement strategies to solve problems involving the volumes of solids.8CT 8:3.3bSolve problems involving measurement through the use of appropriate tools, techniques and strategies.8CT 8:3.3b(1)Use the Pythagorean Theorem to solve indirect measurement problems.8CT 8:3.3b(2)Describe the accuracy of estimates and measures and the precision of measurement tools.8CT 8:3.3b(3)Solve dimensional analysis problems.8CT 8:4.1Collect, organize and display data using appropriate statistical and graphical methods.8CT 8:4.1aConstruct appropriate representations of data based on the size and kind of data set and the purpose for its use.8CT 8:4.1a(1)Collect, organize, display, compare and analyze large data sets.8CT 8:4.1a(2)Construct a variety of data displays, including box-and-whisker plots, and identify where measures of central tendency and dispersion are found in graphical displays.8CT 8:4.2Analyze data sets to form hypotheses and make predictions.8CT 8:4.2aMake and evaluate statistical claims and justify conclusions with evidence.8CT 8:4.2a(1)Make predictions from scatter plots using or estimating a line-of-best-fit.8CT 8:4.2a(2)Make inferences and evaluate reasonable hypotheses based on experimental data.8CT 8:4.2a(3)Analyze and interpret data using descriptive statistics, including range, mode, median, quartiles, outliers and mean.8CT 8:4.2a(4)Determine the accuracy of statistical claims.8CT 8:4.2a(5)Describe the role of random sampling, random number generation and the effects of sample size in statistical claims.8CT 8:4.3Understand and apply basic concepts of probability.8CT 8:4.3aDetermine possible outcomes using a variety of counting techniques.8CT 8:4.3a(1)Distinguish between combinations and permutations as ways to predict possible outcomes in certain situations.8CT 8:4.3a(2)Use combinations and permutations, trees and networks (counting strategies) in a variety of contexts, and identify when order is irrelevant in determining a solution.8GA M8A1.aRepresent a given situation using algebraic expressions or equations in one variable.8GA M8A1.bSimplify and evaluate algebraic expressions.8GA M8A1.cSolve algebraic equations in one variable, including equations involving absolute values.8GA M8A1.dInterpret solutions in problem contexts.8GA M8A2.aRepresent a given situation using an inequality in one variable.8GA M8A2.bUse the properties of inequality to solve inequalities.8GA M8A2.cGraph the solution of an inequality on a number line.8GA M8A2.dInterpret solutions in problem contexts.8GA M8A3.1Translate among verbal, tabular, graphic, and algebraic representations of functions.8GA M8A3.aRecognize a relation as a correspondence between varying quantities.8GA M8A3.bRecognize a function as a correspondence between inputs and outputs where the output for each input must be unique.8GA M8A3.cDistinguish between relations that are functions and those that are not functions.8GA M8A3.dRecognize functions in a variety of representations and a variety of contexts.8GA M8A4.aInterpret slope as a rate of change.8GA M8A4.bDetermine the meaning of the slope and y-intercept in a given situation.8GA M8A4.cGraph equations of the form y = mx + b.8GA M8A4.dGraph equations of the form ax + by = c.8GA M8A4.eDetermine the equation of a line given a graph, numerical information that defines the line, or a context involving a linear relationship.8GA M8A4.fSolve problems involving linear relationships.8GA M8A5.aGiven a problem context, write an appropriate system of linear equations.8GA M8A5.bSolve systems of equations graphically and algebraically, using technology as appropriate.8GA M8A5.cInterpret solutions in problem contexts.8GA M8D1.aDemonstrate relationships among sets through use of Venn diagrams.8GA M8D2.aUse tree diagrams to find the number of outcomes.8GA M8D2.bApply the addition and multiplication principles of counting.8GA M8D3Students will use the basic laws of probability.8GA M8D3.aFind the probability of simple independent events.8GA M8D3.bFind the probability of compound independent events.8GA M8D4Students will organize, interpret, and make inferences from statistical data8GA M8D4.aGather data that can be modeled with a linear function.8GA M8G1.aInvestigate characteristics of parallel and perpendicular lines both algebraically and geometrically.8GA M8G1.bApply properties of angle pairs formed by parallel lines cut by a transversal.8GA M8G1.dUnderstand the meaning of congruence: that all corresponding angles are congruent and all corresponding sides are congruent.8GA M8G2.aApply properties of right triangles, including the Pythagorean theorem.8GA M8N1Students will understand different representations of numbers including square roots, exponents, and scientific notation.8GA M8N1.aFind square roots of perfect squares.8GA M8N1.bRecognize the (positive) square root of a number as a length of a side of a square with a given area.8GA M8N1.cRecognize square roots as points and as lengths on a number line.8GA M8N1.eRecognize and use the radical symbol to denote the positive square root of a positive number.8GA M8N1.fEstimate square roots of positive numbers.8GA M8N1.gSimplify, add, subtract, multiply, and divide expressions containing square roots.8GA M8N1.hDistinguish between rational and irrational numbers.8GA M8N1.ISimplify expressions containing integer exponents.8GA M8N1.jExpress and use numbers in scientific notation.8GA M8N1.kUse appropriate technologies to solve problems involving square roots, exponents, and scientific notation.8GA M8P1Students will solve problems (using appropriate technology).8GA M8P1.bSolve problems that arise in mathematics and in other contexts.8GA M8P1.cApply and adapt a variety of appropriate strategies to solve problems.8GA M8P2.aRecognize reasoning and proof as fundamental aspects of mathematics.8GA M8P2.bMake and investigate mathematical conjectures.8GA M8P2.dSelect and use various types of reasoning and methods of proof.8GA M8P3Students will communicate mathematically.8GA M8P3.aOrganize and consolidate their mathematical thinking through communication.8GA M8P3.dUse the language of mathematics to express mathematical ideas precisely.8GA M8P4.aRecognize and use connections among mathematical ideas.8GA M8P5.aCreate and use representations to organize, record, and communicate mathematical ideas.8GA M8P5.bSelect, apply, and translate among mathematical representations to solve problems.8GA M8P5.cUse representations to model and interpret physical, social, and mathematical phenomena.8ID AL.01.aUnderstand and use variables in expressions, equations, and inequalities.8ID AL.01.bTranslate simple word statements and story problems into algebraic expressions and equations.8ID AL.01.cUse symbols (<, >, =, ?, ?, ?) to express relationships.8ID AL.02.aUnderstand and use the following properties in evaluating algebraic expressions:  commutative, associative, identity, zero, inverse, distributive, and substitution.8ID AL.02.bUnderstand and use the order of operations in evaluating basic algebraic expressions.8ID AL.02.cSimplify algebraic expressions.8ID AL.03Solve algebraic equations and inequalities.8ID AL.03.aSolve one- and two-step equations and inequalities using inverse operations.8ID AL.03.bExplore graphical representation to show simple linear equations.8ID AL.03aNote to FSC: In the correlation spreadsheet, insert period before last letter. Should be 8ID AL.03.a8ID DA.01Understand data analysis.8ID DA.01.aAnalyze and interpret tables, charts, and graphs (scatter plots, line graphs, bar graphs, pie charts).8ID DA.01.bExplain and justify conclusions drawn from tables, charts, and graphs.8ID DA.01.cUnderstand and use appropriate vocabulary.8ID DA.02.aCollect, organize and display data with appropriate notation in tables, charts, and graphs (scatter plots, line graphs, bar graphs, pie charts).8ID DA.03.aChoose and calculate the appropriate measure of central tendency -- mean, median, and mode.8ID DA.04Understand basic concepts of probability.8ID DA.04.aModel situations of probability using simulations.8ID DA.04.bUnderstand and use the language of probability.8ID DA.05.aMake predictions based on experimental and theoretical probabilities.8ID DA.05.bUnderstand and use appropriate vocabulary.8ID F.01Understand the concept of functions.8ID F.01.aExtend patterns and identify a rule (function) that generates the pattern using real numbers.8ID F.01.bUse functional relationships to explain how a change in one quantity results in a change in another.8ID F.01.cUnderstand and use appropriate vocabulary.8ID F.02Represent equations, inequalities, and functions in a variety of formats.8ID F.02.aRepresent a set of data in a table, as a graph, and as a mathematical relationship.8ID F.03Apply functions to a variety of problems.8ID F.03.aUse patterns and functions to represent and solve problems.8ID G.01Apply concepts of size, shape, and spatial relationships.8ID G.01.aPrecisely describe, classify, and understand relationships among types of one-, two-, and three-dimensional objects using their defining properties.8ID G.01.bConstruct and measure various angles and shapes using appropriate tools.8ID G.01.dRecognize and apply congruence, similarities, and symmetry of shapes.8ID G.01.eApply formulas for perimeter, circumference, and area to polygons and circles.8ID G.01.fUnderstand the concept of surface area and volume (capacity).8ID G.01.gExplore and model the effects of reflections, translations, and rotations on various shapes.8ID G.01.hUse appropriate vocabulary.8ID G.02Apply the geometry of right triangles.8ID G.02.aInvestigate right triangle geometry using the Pythagorean Theorem.8ID G.03.aUse the coordinate plane as it relates to real-world applications.8ID M.01.aSelect and use appropriate units and tools to make formal measurements using both systems.8ID M.01.dSolve problems involving length, perimeter, area, volume (capacity), weight, mass, and temperature.8ID M.01.eConvert unit of measurement within each system.8ID M.01.fUse appropriate vocabulary.8ID M.02.aUse rates to make indirect measurements.8ID M.03.aUnderstand and use proportions, ratios, and scales.8ID M.04.aUnderstand units and their relationship to one another and to real-world applications.8ID N.01.aRead, write, order, and compare real numbers (integers, fractions, decimals, percents, ratios) and absolute values.8ID N.01.bUnderstand and use real numbers, both rational and irrational.8ID N.01.cShow a sense of magnitudes and relative magnitudes of real numbers (integers, fractions, decimals) using scientific notation and exponential numbers.8ID N.01.dDevelop and apply number theory concepts.8ID N.01.eUnderstand the position of real numbers on a number line.8ID N.02.aConsistently and accurately add, subtract, multiply, and divide rational numbers.8ID N.02.bInstantly recall common equivalent fractions, decimals, and percents.8ID N.02.cEvaluate numerical expressions using the order of operations.8ID N.02.dUnderstand and use exponents.8ID N.02.eSelect and use an appropriate method of computation from mental math, paper and pencil, calculator, or a combination of the three.8ID N.02.fUse appropriate vocabulary.8ID N.02bNote to FSC: In correlation spreadsheet, insert period before last letter (8ID N.02.b).8ID N.03.aUse estimation to predict computation results.8ID N.03.dUse appropriate vocabulary.8ID PS.01.aUse a variety of strategies, including common mathematical formulas, to compute problems drawn from real-world situations.8ID PS.01.bRecognize pertinent information for problem solving.8ID PS.01.cMake predictions and decisions based on information.8ID PS.02Use reasoning skills to recognize problems and express them mathematically.8ID PS.02.bApply solutions and strategies to new problem situations.8ID PS.02.cFormulate conjectures and justify (short of formal proof) why they must be or seem to be true.8ID PS01.bNote to FSC: In correlation spreadsheet, insert period between PS and 01 (8ID PS.01.b).8PS.01.cNote to FSC: In correlation spreadsheet, insert ID  between 8 and PS (8ID PS.01.c).ID N.02bNote to FSC: In correlation spreadsheet, insert 8 at beginning of code, insert period before last letter (8ID N.02.b).8IL 6.8.02Read, write, recognize, model, and interpret integers, including translating numerical expressions.8IL 6.8.03Recognize, translate between, and apply multiple representations of rational numbers (decimals, fractions, mixed numbers, percents, and roots).8IL 6.8.04Use scientific notation to represent numbers and solve problems.8IL 6.8.05Represent repeated factors using exponents.8IL 6.8.06Order and compare rational numbers.8IL 6.8.07Identify and locate rational and irrational numbers on a number line.8IL 6.8.08Solve problems involving descriptions of numbers, including characteristics and relationships (e.g., exponents, roots, prime/composite, prime factorization, greatest common factor, least common multiple).8IL 6.8.09Solve problems and number sentences involving addition, subtraction, multiplication, and division using rational numbers, exponents, and roots.8IL 6.8.10Identify and apply order of operations to simplify numeric expressions involving integers (including exponents and roots), fractions, and decimals.8IL 6.8.11Identify and apply the following properties of operations with rational numbers: the commutative and associative properties for addition and multiplication; the distributive property; the additive and multiplicative identity properties; the additive and multiplicative inverse properties; and the multiplicative property of zero.8IL 6.8.13Select, use, and justify appropriate operations, methods, and tools to compute or estimate with rational numbers. Verify solutions and determine the reasonableness of results.8IL 6.8.14Estimate the square or cube root of a number less than 1,000 between two whole numbers.8IL 6.8.15Use ratios to describe problem situations.8IL 6.8.16Use proportional reasoning to model and solve problems.8IL 6.8.17Read, write, recognize, model, and interpret percents, including those less than 1% and greater than 100%.8IL 6.8.18Solve number sentences and problems involving fractions, decimals, and percents.8IL 6.A.3Represent fractions, decimals, percentages, exponents and scientific notation in equivalent forms.8IL 6.B.3aSolve practical computation problems involving whole numbers, integers and rational numbers.8IL 6.B.3bApply primes, factors, divisors, multiples, common factors and common multiples in solving problems.8IL 6.B.3cIdentify and apply properties of real numbers including pi, squares, and square roots.8IL 6.C.3aSelect computational procedures and solve problems with whole numbers, fractions, decimals, percents and proportions.8IL 6.C.3bShow evidence that computational results using whole numbers, fractions, decimals, percents and proportions are correct and/or that estimates are reasonable.8IL 6.D.3Apply ratios and proportions to solve practical problems.8IL 7.8.01Select and use appropriate standard units and tools to solve measurement problems, including measurements of polygons and circles.8IL 7.8.02Solve problems involving perimeter/circumference and area of polygons, circles, and composite figures using diagrams, models, and grids or by measuring or using given formulas (may include sketching a figure from its description).8IL 7.8.03Compare and estimate length (including perimeter/circumference), area, volume, weight/mass, and angles (0� to 360�) using referents.8IL 7.8.04Solve problems involving the volume or surface area of a right rectangular prism, right circular cylinder, or composite shape using an appropriate formula or strategy.8IL 7.8.05Solve problems involving unit conversions within the same measurement system for length, weight/mass, capacity, square units, and measures expressed as rates.8IL 7.8.06Solve problems involving scale drawings, maps, and indirect measurement.8IL 7.A.3bApply the concepts and attributes of length, capacity, weight/mass, perimeter, area, volume, time, temperature and angle measures in practical situations.8IL 7.B.3Select and apply instruments including rulers and protractors and units of measure to the degree of accuracy required.8IL 7.C.3aConstruct a simple scale drawing for a given situation.8IL 7.C.3bUse concrete and graphic models and appropriate formulas to find perimeters, areas, surface areas and volumes of two- and three-dimensional regions.8IL 8.8.01Analyze, extend, and create sequences or linear functions, and determine algebraic expressions to describe the nth term of a sequence.8IL 8.8.02Write an expression using variables to represent unknown quantities.8IL 8.8.03Simplify algebraic expressions.8IL 8.8.05Evaluate or simplify algebraic expressions with one or more rational variable values.8IL 8.8.07Represent linear equations and quantitative relationships on a rectangular coordinate system, and interpret the meaning of a specific part of a graph.8IL 8.8.08Translate between different representations (table, written, graphical, or pictorial) of whole number relationships and linear expressions.8IL 8.8.09Interpret the meaning of slope and intercepts in linear situations.8IL 8.8.10Identify, graph, and interpret up to two inequalities with a single variable (including the intersection or union of these inequalities) on a number line.8IL 8.8.11Represent and analyze problems with linear equations and inequalities.8IL 8.8.12Solve linear equations and inequalities in one variable over the rational numbers.8IL 8.8.13Solve word problems involving unknown quantities.8IL 8.A.3aApply the basic properties of commutative, associative, distributive, transitive, inverse, identity, zero, equality and order of operations to solve problems.8IL 8.A.3bSolve problems using linear expressions, equations and inequalities.8IL 8.B.3Use graphing technology and algebraic methods to analyze and predict linear relationships and make generalizations from linear patterns.8IL 8.D.3aSolve problems using numeric, graphic or symbolic representations of variables, expressions, equations and inequalities.8IL 8.D.3bPropose and solve problems using proportions, formulas and linear functions.8IL 8.D.3cApply properties of powers, perfect squares and square roots.8IL 9.8.01Solve problems involving two� and three�dimensional shapes.8IL 9.8.03Find the length of any side of a right triangle using the Pythagorean theorem (whole number solutions).8IL 9.8.04Identify, describe, and determine the radius, diameter, and circumference of a circle and their relationship to each other and to pi.8IL 9.8.05Graph points, and identify coordinates of points on the Cartesian coordinate plane (all four quadrants).8IL 9.8.06Represent and identify geometric figures using coordinate geometry, including those resulting from transformations.8IL 9.8.08Identify or analyze relationships of angles formed by intersecting lines (including parallel lines cut by a transversal) and angles formed by radii of a circle.8IL 9.8.11Solve problems involving congruent and similar figures.8IL 9.8.12Relate absolute value to distance on the number line.8IL 9.A.3aDraw or construct two- and three- dimensional geometric figures including prisms, pyramids, cylinders and cones.8IL 9.A.3bDraw transformation images of figures, with and without the use of technology.8IL 9.A.3cUse concepts of symmetry, congruency, similarity, scale, perspective, and angles to describe and analyze two- and three-dimensional shapes found in practical applications (e.g., geodesic domes, A-frame houses, basketball courts, inclined planes, art forms, blueprints).8IL 9.B.3Identify, describe, classify and compare two- and three- dimensional geometric figures and models according to their properties.8IL 9.D.3Compute distances, lengths and measures of angles using proportions, the Pythagorean theorem and its converse.8IL 10.8.01Read, interpret (including possible misleading characteristics), and make predictions from data represented in a bar graph, line (dot) plot, Venn diagram (with two or three circles), chart/table, line graph, scatterplot, circle graph, stem�and�leaf plot, or histogram.8IL 10.8.03Create a bar graph, chart/table, line graph, or circle graph and solve a problem using the data in the graph for a given set of data.8IL 10.8.04Identify or draw a reasonable approximation of the line of best fit from a set of data or a scatter plot, and use the line to make predictions.8IL 10.8.05Analyze and apply measures of central tendency (mode, range, median, and mean) in problem�solving situations.8IL 10.8.06Solve problems involving the probability of an event composed of repeated trials, compound events (including independent events), or future events with or without replacement.8IL 10.8.07Represent all possible outcomes (sample space) for simple or compound events.8IL 10.8.08Solve simple problems involving the number of ways objects can be arranged (permutations and combinations).8IL 10.A.3aConstruct, read and interpret tables, graphs (including circle graphs) and charts to organize and represent data.8IL 10.A.3bCompare the mean, median, mode and range, with and without the use of technology.8IL 10.A.3cTest the reasonableness of an argument based on data and communicate their findings.8IL 10.B.3Formulate questions (e.g., relationships between car age and mileage, average incomes and years of schooling), devise and conduct experiments or simulations, gather data, draw conclusions and communicate results to an audience using traditional methods and contemporary technologies.8IL 10.C.3aDetermine the probability and odds of events using fundamental counting principles.8IL 10.C.3bAnalyze problem situations (e.g., board games, grading scales) and make predictions about results.8KS AI 1.1.1Generates and/or solves real-world problems using equivalent representations of rational numbers and simple algebraic expressions.8KS AI 1.1.2Determines whether or not solutions to real-world problems using rational numbers, the irrational number pi, and simple algebraic expressions are reasonable.8KS AI 1.2.1Generates and/or solves real-world problems with rational numbers using the concepts of these properties to explain reasoning:  commutative, associative, distributive, and substitution properties; identity and inverse properties of addition and multiplication; symmetric property of equality; addition and multiplication properties of equality; zero product property.8KS AI 1.2.2Analyzes and evaluates the advantages and disadvantages of using integers, whole numbers, fractions (including mixed numbers), or decimals in solving a given real-world problem.8KS AI 1.3.2Estimates to check whether or not the result of a real-world problem using rational numbers and/or simple algebraic expressions is reasonable and makes predictions based on the information.8KS AI 1.4.1Generates and/or solves one- and two-step real-world problems using computational procedures and mathematic concepts with rational numbers, the irrational number pi as an approximation, applications of percents.8KS AI 2.1.1Generalizes numerical patterns using algebra and then translates between the equation, graph, and table of values resulting from the generalization.8KS AI 2.1.2Recognizes the same general pattern presented in different representations [numeric (list or table), visual (picture, table, or graph), and written].8KS AI 2.2.1aRepresents real-world problems using variables, symbols, expressions, one- or two-step equations with rational number coefficients and constants.8KS AI 2.2.1bRepresents real-world problems using one-step inequalities with rational number coefficients and constants.8KS AI 2.2.2Solves real-world problems with two-step linear equations in one variable with rational number coefficients and constants and rational solutions intuitively, analytically, and graphically.8KS AI 2.3.1Represents a variety of constant and linear relationships using written or oral descriptions of the rule, tables, graphs, and symbolic notation.8KS AI 2.3.2Interprets, describes, and analyzes the mathematical relationships of numerical, tabular, and graphical representations.8KS AI 2.3.3Translates between the numerical, tabular, graphical, and symbolic representations of linear relationships with integer coefficients and constants.8KS AI 2.4.1aRecognizes that various mathematical models can be used to represent the same problem situation.  Mathematical models include process models (concrete objects, pictures, diagrams, flowcharts, number lines, hundred charts, measurement tools, multiplication arrays, division sets, or coordinate grids) to model computational procedures, algebraic relationships, mathematical relationships,  and problem situations and to solve equations.8KS AI 2.4.1dRecognizes that various mathematical models can be used to represent the same problem situation.  Mathematical models include equations and inequalities to model numerical relationships.8KS AI 2.4.1eRecognizes that various mathematical models can be used to represent the same problem situation.  Mathematical models include function tables to model numerical and algebraic relationships.8KS AI 2.4.1fRecognizes that various mathematical models can be used to represent the same problem situation.  Mathematical models include coordinate planes to model relationships between ordered pairs and linear equations and inequalities.8KS AI 2.4.1hRecognizes that various mathematical models can be used to represent the same problem situation.  Mathematical models include scale drawings to model large and small real-world objects.8KS AI 2.4.1jRecognizes that various mathematical models can be used to represent the same problem situation.  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, and histograms to describe, interpret, and analyze data.8KS AI 2.4.3Uses the mathematical modeling process to analyze and make inferences about real-world situations.8KS AI 3.1.1aSolves real-world problems by using the properties of corresponding parts of similar and congruent figures.8KS AI 3.1.1bSolves real-world problems by applying the Pythagorean Theorem.8KS AI 3.2.1aSolves real-world problems by converting within the customary and the metric systems.8KS AI 3.2.1bSolves real-world problems by finding perimeter and area of circles, squares, rectangles, triangles, parallelograms, and trapezoids.8KS AI 3.2.1cSolves real-world problems by finding the volume and surface area of rectangular prisms.8KS AI 3.2.3Estimates to check whether or not measurements or calculations for length, weight, volume, temperature, time, perimeter, area, and surface area in real world problems are reasonable and adjusts original measurement or estimation based on additional information.8KS AI 3.3.3Investigates congruency, similarity, and symmetry of geometric figures using transformations.8KS AI 3.3.4Uses a scale drawing to determine the actual dimensions and/or measurements of a two-dimensional figure represented in a scale drawing.8KS AI 3.4.1Represents, generates, and/or solves distance problems (including the use of the Pythagorean theorem, but not necessarily the distance formula).8KS AI 3.4.2Translates between the written, numeric, algebraic, and geometric representations of a real-world problem.8KS AI 4.1.1Conducts an experiment or simulation with independent or dependent events including the use of concrete objects; records the results in a chart, table, or graph; and uses the results to draw conclusions and make predictions about future events.8KS AI 4.1.2Analyzes the results of an experiment or simulation of two independent events to generate convincing arguments, draw conclusions, and make predictions and decisions in a variety of real-world situations.8KS AI 4.1.3Compares theoretical probability (expected results) with empirical probability (experimental results) in an experiment or simulation with a compound event composed of two independent events and understands that the larger the sample size, the greater the likelihood that the experimental results will equal the theoretical probability.8KS AI 4.1.4Makes predictions based on the theoretical probability of: a simple event in an experiment or simulation; compound events composed of two independent events in an experiment or simulation.8KS AI 4.2.1Uses data analysis (mean, median, mode, range) in real-world problems with rational number data sets to compare and contrast two sets of data, to make accurate inferences and predictions, to analyze decisions, and to develop convincing arguments from these data displays: frequency tables; bar, line, and circle graphs; Venn diagrams and other pictorial displays; charts and tables; stem-and-leaf plots (single and double); scatter plots; box-and-whisker plots; histograms.8KS AI 4.2.2Explains advantages and disadvantages of various data collection techniques (observations, surveys, or interviews), and sampling techniques (random sampling, samples of convenience, biased sampling, or purposeful sampling) in a given situation.8KS AI 4.2.3Recognizes and explains: misleading representations of data; the effects of scale or interval changes on graphs of data sets.8KS KBI 1.1.1Knows, explains, and uses equivalent representations for rational numbers and simple algebraic expressions including integers, fractions, decimals, percents, and ratios; rational number bases with integer exponents; rational numbers written in scientific notation with integer exponents; time; and money.8KS KBI 1.1.2Compares and orders rational numbers, the irrational number pi, and algebraic expressions.8KS KBI 1.1.4Recognizes and describes irrational numbers.8KS KBI 1.1.6Explains and determines the absolute value of real numbers.8KS KBI 1.2.2Identifies all the subsets of the real number system [natural (counting) numbers, whole numbers, integers, rational numbers, irrational numbers] to which a given number belongs.8KS KBI 1.2.3Names, uses, and describes properties with the rational number system and demonstrates their meaning including the use of concrete objects: commutative, associative, distributive, and substitution properties; identity properties for addition and multiplication and inverse properties of addition and multiplication; symmetric property of equality; addition and multiplication properties of equalities; addition property of inequalities; zero product property.8KS KBI 1.3.1Estimates real number quantities using various computational methods, including mental math, paper and pencil, concrete objects, and/or appropriate technology.8KS KBI 1.3.2Uses various estimation strategies and explains how they were used to estimate real number quantities and simple algebraic expressions.8KS KBI 1.4.1Computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology.8KS KBI 1.4.2Performs and explains these computational procedures with rational numbers: addition, subtraction, multiplication, and division of integers; order of operations (evaluates within grouping symbols, evaluates powers to the second or third power, multiplies or divides in order from left to right, then adds or subtracts in order from left to right); approximation of roots of numbers using calculators; multiplication or division to find a percent of a number, percent of increase and decrease, percent one number is of another number, a number when a percent of the number is given; addition of polynomials; simplifies algebraic expressions in one variable by combining like terms or using the distributive property.8KS KBI 1.4.3Finds factors and common factors of simple monomial expressions.8KS KBI 2.1.1Identifies, states, and continues a pattern presented in various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written using these attributes:  counting numbers including perfect squares, cubes, and factors and multiples with positive rational numbers (number theory); rational numbers including arithmetic and geometric sequences; geometric figures; measurements; things related to daily life; variables and simple expressions.8KS KBI 2.1.2Generates and explains a pattern.8KS KBI 2.2.2Simplifies algebraic expressions in one variable by combining like terms or using the distributive property.8KS KBI 2.2.3aSolves one- and two-step linear equations in one variable with rational number coefficients and constants intuitively and/or analytically.8KS KBI 2.2.3bSolves one-step linear inequalities in one variable with rational number coefficients and constants intuitively, analytically, and graphically.8KS KBI 2.2.3cSolves systems of given linear equations with whole number coefficients and constants graphically.8KS KBI 2.2.4Knows and describes the mathematical relationship between ratios, proportions, and percents and how to solve for a missing monomial or binomial term in a proportion.8KS KBI 2.2.5Represents and solves algebraically the number when a percent and a number are given; what percent one number is of another number; the percent of increase or decrease.8KS KBI 2.2.6Evaluates formulas using substitution.8KS KBI 2.3.1Recognizes and examines constant, linear, and nonlinear relationships using various methods including mental math, paper and pencil, concrete objects, and graphing utilities or appropriate technology.8KS KBI 2.3.2Knows and describes the difference between constant, linear, and nonlinear relationships.8KS KBI 2.3.3Explains the concepts of slope and x- and y-intercepts of a line.8KS KBI 2.3.5Identifies ordered pairs from a graph, and/or plots ordered pairs using a variety of scales for the x- and y-axis.8KS KBI 2.4.1aKnows, 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 equations8KS KBI 2.4.1dKnows, 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 factorization8KS KBI 2.4.1eKnows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include: equations and inequalities to model numerical relationships.8KS KBI 2.4.1fKnows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include: function tables to model numerical and algebraic relationships.8KS KBI 2.4.1gKnows, 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 linear equations and inequalities.8KS KBI 2.4.1iKnows, 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.8KS KBI 2.4.1kKnows, 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, and histograms to organize and display data.8KS KBI 2.4.1lKnows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include: Venn diagrams to sort data and to show relationships.8KS KBI 3.1.1Recognizes and compares properties of two- and three-dimensional figures using concrete objects, constructions, drawings, appropriate terminology, and appropriate technology.8KS KBI 3.1.2Discusses properties of triangles and quadrilaterals:  a. sum of the interior angles of any triangle is 180�; sum of the interior angles of any quadrilateral is 360�; parallelograms have opposite sides that are parallel and congruent, opposite angles are congruent; rectangles have angles of 90�, sides may or may not be equal; rhombi have all sides equal in length, angles may or may not be equal; squares have angles of 90�, all sides congruent; trapezoids have one pair of opposite sides parallel and the other pair of opposite sides are not parallel; kites have two distinct pairs of adjacent congruent sides. .8KS KBI 3.1.3Recognizes and describes the rotational symmetries and line symmetries that exist in two-dimensional figures.8KS KBI 3.1.4Recognizes and uses properties of corresponding parts of similar and congruent triangles and quadrilaterals to find side or angle measures using standard notation for similarity and congruence.8KS KBI 3.1.6Uses the Pythagorean theorem to: determine if a triangle is a right triangle; find a missing side of a right triangle where the lengths of all three sides are whole numbers.8KS KBI 3.1.7Recognizes and compares the concepts of a point, line, and plane.8KS KBI 3.1.9Describes and explains angle relationships: when two lines intersect including vertical and supplementary angles; when formed by parallel lines cut by a transversal, including corresponding, alternate interior, and alternate exterior angles.8KS KBI 3.1.10Recognizes and describes arcs and semicircles as parts of a circle and uses the standard notation for arc and circle.8KS KBI 3.2.2Selects and uses measurement tools, units of measure, and level of precision appropriate for a given situation to find accurate real number representations for length, weight, volume, temperature, time, perimeter, area, surface area, and angle measurements.8KS KBI 3.2.3Converts within the customary system and within the metric system.8KS KBI 3.2.5Uses given measurement formulas to find area of parallelograms and trapezoids; surface area of rectangular prisms, triangular prisms, and cylinders; volume of rectangular prisms, triangular prisms, and cylinders.8KS KBI 3.2.6Recognizes how ratios and proportions can be used to measure inaccessible objects.8KS KBI 3.3.1Identifies, describes, and performs single and multiple transformations [reflection, rotation, translation, reduction (contraction/shrinking), enlargement (magnification/growing)] on a two-dimensional figure.8KS KBI 3.3.2Describes a reflection of a given two-dimensional figure that moves it from its initial placement (preimage) to its final placement (image) in the coordinate plane over the x- and y-axis.8KS KBI 3.3.3aDraws three-dimensional figures from a variety of perspectives (top, bottom, sides, corners).8KS KBI 3.3.3cDraws a two-dimensional drawing of a three-dimensional figure.8KS KBI 3.3.4Determines where and how an object or a shape can be tessellated using single or multiple transformations.8KS KBI 3.4.1aUses the coordinate plane to list several ordered pairs on the graph of a line and find the slope of the line.8KS KBI 3.4.1eUses the coordinate plane to solve simple systems of linear equations.8KS KBI 4.1.1Knows and explains the difference between independent and dependent events in an experiment, simulation, or situation.8KS KBI 4.1.2Identifies situations with independent or dependent events in an experiment, simulation, or situation.8KS KBI 4.1.3Finds the probability of a compound event composed of two independent events in an experiment, simulation, or situation.8KS KBI 4.1.4Finds the probability of simple and/or compound events using geometric models (spinners or dartboards).8KS KBI 4.1.5Finds the odds of a desired outcome in an experiment or simulation and expresses the answer as a ratio (2/3 or 2:3 or 2 to 3).8KS KBI 4.2.1Organizes, 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; bar, line, and circle graphs; Venn diagrams and other pictorial displays; charts and tables; stem-and-leaf plots (single and double); scatter plots; box-and-whisker plots; histograms.8KS KBI 4.2.2Recognizes valid and invalid data collection and sampling techniques.8KS KBI 4.2.3Determines and explains the measures of central tendency (mode, median, mean) for a rational number data set.8KS KBI 4.2.4Determines and explains the range, quartiles, and interquartile range for a rational number data set.8KS KBI 4.2.5Explains the effects of outliers on the median, mean, and range of a rational number data set.8KS KBI 4.2.6Makes a scatter plot and draws a line that approximately represents the data, determines whether a correlation exists, and if that correlation is positive, negative, or that no correlation exists.8MA D.1Describe the characteristics and limitations of a data sample. Identify different ways of selecting a sample, e.g., convenience sampling, responses to a survey, random sampling.8MA D.2Select, create, interpret, and utilize various tabular and graphical representations of data, e.g., circle graphs, Venn diagrams, scatter plots, stem-and-leaf plots, box-and-whisker plots, histograms, tables, and charts.  Differentiate between continuous and discrete data and ways to represent them.8MA D.3Find, describe, and interpret appropriate measures of central tendency (mean, median, and mode) and spread (range) that represent a set of data. Use these notions to compare different sets of data.8MA D.4Use tree diagrams, tables, organized lists, basic combinatorics (�fundamental counting principle�), and area models to compute probabilities for simple compound events, e.g., multiple coin tosses or rolls of dice.8MA G.1Analyze, apply, and explain the relationship between the number of sides and the sums of the interior and exterior angle measures of polygons.8MA G.2Classify figures in terms of congruence and similarity, and apply these relationships to the solution of problems.8MA G.3Demonstrate an understanding of the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal.8MA G.4Demonstrate an understanding of the Pythagorean theorem. Apply the theorem to the solution of problems.8MA G.5Use a straight-edge, compass, or other tools to formulate and test conjectures, and to draw geometric figures.8MA G.6Predict the results of transformations on unmarked or coordinate planes and draw the transformed figure, e.g., predict how tessellations transform under translations, reflections, and rotations.8MA G.7Identify three-dimensional figures (e.g., prisms, pyramids) by their physical appearance, distinguishing attributes, and spatial relationships such as parallel faces.8MA G.8Recognize and draw two-dimensional representations of three-dimensional objects, e.g., nets, projections, and perspective drawings.8MA M.1Select, convert (within the same system of measurement), and use appropriate units of measurement or scale.8MA M.2Given the formulas, convert from one system of measurement to another. Use technology as appropriate.8MA M.3Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/ circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms, cylinders, and spheres. Use technology as appropriate.8MA M.4Use ratio and proportion (including scale factors) in the solution of problems, including problems involving similar plane figures and indirect measurement.8MA M.5Use models, graphs, and formulas to solve simple problems involving rates, e.g., velocity and density.8MA N.1Compare, order, estimate, and translate among integers, fractions and mixed numbers (i.e., rational numbers), decimals, and percent.8MA N.2Define, compare, order, and apply frequently used irrational numbers.8MA N.3Use ratios and proportions in the solution of problems, in particular, problems involving unit rates, scale factors, and rate of change.8MA N.4Represent numbers in scientific notation, and use them in calculations and problem situations.8MA N.5Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems.8MA N.6Demonstrate an understanding of absolute value, e.g., |�3| = |3| = 3.8MA N.7Apply the rules of powers and roots to the solution of problems. Extend the Order of Operations to include positive integer exponents and square roots.8MA N.8Demonstrate an understanding of the properties of arithmetic operations on rational numbers. Use the associative, commutative, and distributive properties; properties of the identity and inverse elements (e.g., �7 + 7 = 0; 3/4 x 4/3 =1); and the notion of closure of a subset of the rational numbers under an operation (e.g., the set of odd integers is closed under multiplication but not under addition).8MA N.9Use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems; e.g., multiplying by 1/2 or 0.5 is the same as dividing by 2.8MA N.10Estimate and compute with fractions (including simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1).8MA N.11Determine when an estimate rather than an exact answer is appropriate and apply in problem situations.8MA N.12Select and use appropriate operations�addition, subtraction, multiplication, division, and positive integer exponents�to solve problems with rational numbers (including negatives).8MA P.1Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic expressions. Include arithmetic and geometric progressions, e.g., compounding.8MA P.2Evaluate simple algebraic expressions for given variable values.8MA P.3Demonstrate an understanding of the identity (�x)(�y) = xy. Use this identity to simplify algebraic expressions.8MA P.4Create and use symbolic expressions and relate them to verbal, tabular, and graphical representations.8MA P.5Identify the slope of a line as a measure of its steepness and as a constant rate of change from its table of values, equation, or graph. Apply the concept of slope to the solution of problems.8MA P.6Identify the roles of variables within an equation, e.g., y = mx + b, expressing y as a function of x with parameters m and b.8MA P.7Set up and solve linear equations and inequalities with one or two variables, using algebraic methods, models, and/or graphs.8MA P.8Explain and analyze�both quantitatively and qualitatively, using pictures, graphs, charts, or equations�how a change in one variable results in a change in another variable in functional relationships.8MA P.9Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate.8MA P.10Use tables and graphs to represent and compare linear growth patterns. In particular, compare rates of change and x- and y-intercepts of different linear patterns.8MD 1.A.1Identify, describe, extend, and create patterns, functions and sequences.8MD 1.A.1aDetermine the recursive relationship of arithmetic sequences represented in words, in a table, or in a graph.8MD 1.A.1bDetermine the recursive relationship of geometric sequences represented in words, in a table or in a graph.8MD 1.B.1Write, simplify, and evaluate expressions.8MD 1.B.1aWrite an algebraic expression to represent unknown quantities.8MD 1.B.1bEvaluate an algebraic expression.8MD 1.B.1cEvaluate numeric expressions using the order of operations.8MD 1.B.1dSimplify algebraic expressions by combining like terms.8MD 1.B.2Identify, write, solve, and apply equations and inequalities.8MD 1.B.2aWrite equations or inequalities to represent relationships.8MD 1.B.2bSolve for the unknown in a linear equation.8MD 1.B.2cSolve for the unknown in an inequality.8MD 1.B.2dIdentify or graph solutions of inequalities on a number line.8MD 1.b.2eIdentify equivalent equations.  Note to FSC: In correlations speadsheet B should be uppercase.8MD 1.B.2fApply given formulas to a problem-solving situation.8MD 1.B.2gWrite equations and inequalities that describe real-world problems.8MD 1.C.1Locate points on a number line and in a coordinate plane.8MD 1.C.1aGraph linear equations in a coordinate plane.8MD 1.C.2Analyze linear relationships.8MD 1.C.2aDetermine the slope of a graph in a linear relationship.8MD 1.C.2bDetermine the slope of a linear relationship represented numerically or algebraically.8MD 2.A.1Analyze the properties of plane geometric figures.8MD 2.A.1aIdentify and describe geometric relationships between angles formed when parallel lines are cut by a transversal.8MD 2.A.1bIdentify and describe the relationship among the parts of a right triangle.8MD 2.A.2Analyze geometric relationships.8MD 2.A.2bApply right angle concepts to solve real-world problems.8MD 2.A.2cDetermine whether three given side lengths form a right triangle.8MD 2.C.1Represent plane geometric figures.8MD 2.C.1bConstruct perpendicular line segments.8MD 2.D.1Apply the properties of similar polygons.8MD 2.D.1aDetermine similar parts of polygons.8MD 2.E.1Analyze a transformation on a coordinate plane.8MD 2.E.1aIdentify, describe, and plot the results of multiple transformations on a coordinate plane.8MD 3.C.1Estimate and apply measurement formulas.8MD 3.C.1aEstimate and determine the circumference or area of a circle.8MD 3.C.1bEstimate and determine area of a composite figure.8MD 3.C.1cEstimate and determine the volume of a cylinder.8MD 3.C.1dDetermine the volume of cones, pyramids, and spheres.8MD 3.C.1eDetermine the surface area of cylinders, prisms, and pyramids.8MD 3.C.2Analyze measurement relationships.8MD 3.C.2aUse proportional reasoning to solve measurement problems.8MD 4.A.1Organize and display data.8MD 4.A.1aOrganize and display data to make circle graphs.8MD 4.A.1bOrganize and display data to make box-and-whisker plots.8MD 4.A.1cOrganize and display data to make a scatter plot.8MD 4.B.1Analyze data.8MD 4.B.1aInterpret tables.8MD 4.B.1bInterpret box-and-whisker plots.8MD 4.B.1cInterpret scatter plots.8MD 4.B.1dInterpret circle graphs.8MD 4.B.1eAnalyze multiple box-and-whisker plots using the same scale.8MD 5.A.1Identify a sample space.8MD 5.A.1aDescribe the difference between independent and dependent events.8MD 5.A.1bDetermine the number of outcomes.8MD 5.B.1Determine the probability of an event comprised of no more than 2 independent events.8MD 5.B.1aExpress the probability of an event as a fraction, a decimal, or a percent.8MD 5.B.2Determine the probability of a second event that is dependent on a first event of equally likely outcomes.8MD 5.B.2aExpress the probability as a fraction, a decimal, or a percent.8MD 5.C.1Analyze the results of a survey or simulation.8MD 5.C.1aMake predictions and express the probability of the results as a fraction, a decimal, and a percent with no more than 2 decimal places, or a percent.8MD 5.C.2Conduct a probability experiment.8MD 6.A.1Apply knowledge of rational numbers and place values.8MD 6.A.1aRead, write, and represent rational numbers.8MD 6.A.1bCompare, order, and describe rational numbers with and without relational symbols (<, >, =).8MD 6.C.1Analyze number relations and compute.8MD 6.C.1aAdd, subtract, multiply and divide integers.8MD 6.C.1bCalculate powers of integers and square roots of perfect square whole numbers.8MD 6.C.1cIdentify and use the laws of exponents to simplify expressions.8MD 6.C.1dUse properties of addition and multiplication to simplify expressions.8MD 6.C.2Estimation.8MD 6.C.2aEstimate the square roots of whole numbers.8MD 6.C.3Analyze ratios, proportions, and percents.8MD 6.C.3aDetermine unit rates.8MD 6.C.3bDetermine or use percents, rates of increase and decrease, discount, commission, sales tax, and simple interest in the context of a problem.8MD 6.C.3cSolve problems using proportional reasoning.8MD 7.A.1Apply a variety of concepts, processes, and skills to solve problems.8MD 7.A.1aIdentify the question in the problem.8MD 7.A.1cMake a plan to solve a problem.8MD 7.A.1dApply a strategy, i.e., draw a picture, guess and check, finding a pattern, writing an equation.8MD 7.A.1eSelect a strategy, i.e., draw a picture, guess and check, finding a pattern, writing an equation.8MD 7.A.1fIdentify alternative ways to solve a problem.8MD 7.B.1Justify ideas or solutions with mathematical concepts or proofs.8MD 7.B.1aUse inductive or deductive reasoning.8MD 7.B.1cSupport or refute mathematical statements or solutions.8MD 7.B.1dUse methods of proof, i.e., direct, indirect, paragraph, or contradiction.8MD 7.C.1Present mathematical ideas using words, symbols, visual displays, or technology.8MD 7.C.1aUse multiple representations to express concepts or solutions.8MD 7.C.1cExplain mathematically ideas in written form.8MD 7.C.1dExpress solutions using concrete materials.8MD 7.C.1eExpress solutions using pictorial, tabular, graphical, or algebraic methods.8MD 7.C.1fExplain solutions in written form.8MD 7.D.1Relate or apply mathematics within the discipline, to other disciplines, and to life.8MD 7.D.1aIdentify mathematical concepts in relationship to other mathematical concepts.8MD 7.D.1bIdentify mathematical concepts in relationship to other disciplines.8MD 7.D.1cIdentify mathematical concepts in relationship to life.8MD 7.D.1dUse the relationship among mathematical concepts to learn other mathematical concepts.8MN IApply skills of mathematical representation, communication and reasoning throughout the remaining four content strands.8MN I.1Assess the reasonableness of a solution by comparing the solution to appropriate graphical or numerical estimates or by recognizing the feasibility of a solution in a given context.8MN I.2Appropriately use examples and counterexamples to make and test conjectures, justify solutions and explain results.8MN I.3Translate a problem described verbally or by tables, diagrams or graphs, into suitable mathematical language, solve the problem mathematically and interpret the result in the original context.8MN I.4Support mathematical results by explaining why the steps in a solution are valid and why a particular solution method is appropriate.8MN II.AUse rational and irrational numbers, represented in a variety of ways, to quantify information and to solve real-world and mathematical problems.8MN II.A.1Represent and compare rational and irrational numbers symbolically and on a number line.8MN II.A.2Use rational and irrational numbers to solve real-world and mathematical problems.8MN II.A.3Use scientific notation with positive and negative powers of 10, with appropriate treatment of significant digits, to solve real-world and mathematical problems.8MN II.BCompute fluently and make reasonable estimates with rational and irrational numbers in real-world and mathematical problems. Understand the meanings of the basic operations, including the use of integer exponents and nth roots, and how the operations relate to one another. Appropriately use calculators and other technologies to solve problems.8MN II.B.2Find integer approximations of square roots of positive integers without a calculator.8MN II.B.3Multiply and divide expressions involving exponents with a common base.8MN II.B.4Use the inverse relationship between nth roots and nth powers of rational numbers to solve real-world and mathematical problems.8MN II.B.5Apply the correct order of operations and grouping symbols when using calculators and other technologies.8MN III.AUnderstand and describe progressions. Use graphs and tables to solve real-world and mathematical problems.8MN III.A.1Recognize when a list of numbers forms an arithmetic or geometric progression and be able to determine subsequent terms in the progression.8MN III.A.2Represent quantitative relationships graphically and use the graphs to solve real-world and mathematical problems.8MN III.A.3Generate a table of values from a formula and graph the resulting ordered pairs on a grid.8MN III.BUse algebraic operations to generate equivalent expressions, and use proportional reasoning to solve real-world and mathematical problems. Demonstrate the ability to manipulate an equation by applying arithmetic operations to both sides to maintain equivalence.8MN III.B.1Multiply and divide expressions of the form ax^n.8MN III.B.2Use simple formulas with more than one variable to solve real-world and mathematical problems.8MN III.B.3Use proportions and percents with one unknown quantity to solve real-world and mathematical problems.8MN III.B.4Apply the correct order of operations including addition, subtraction, multiplication, division, grouping symbols and powers, to simplify and evaluate algebraic expressions.8MN IV.ARepresent data and use various measures associated with data to draw conclusions and identify trends.8MN IV.A.1Construct and analyze histograms, circle graphs, stem-and-leaf plots and box-and-whisker plots.8MN IV.A.2Compute the quartiles of a data set.8MN IV.BCalculate and express probabilities numerically and apply probability concepts to solve real-world and mathematical problems.8MN IV.B.1Understand that if p is the probability of an event occurring, then 1 - p is the probability of the event not occurring.8MN IV.B.2Convert between odds and probabilities.8MN IV.B.3Use a variety of experiments to explore the relationship between experimental and theoretical probabilities and the effect of sample size on this relationship.8MN V.ARecognize the relationship between different representations of two- and three-dimensional shapes. Understand the effect of various transformations.8MN V.A.1Use models and visualization to understand and create various two-dimensional diagrams of three-dimensional shapes.8MN V.BUse basic geometric principles and proportional reasoning to solve real-world and mathematical problems.8MN V.B.2Use the concept of similarity in simple two-dimensional figures to solve real-world and mathematical problems involving proportionality.8MN V.B.3Know how to find the volumes of cubes, prisms, spheres and cylinders.8MN V.B.4Know how to find the surface areas of cubes, prisms and cylinders.8MN V.B.5Calculate perimeter and area of two-dimensional figures obtained by putting together triangles, parallelograms, and sectors of circles to solve real-world and mathematical problems.8MN V.CMake calculations of time, length, area and volume within and between standard measuring systems using good judgment in choice of units.8MN V.C.1Find approximate equivalent measures of length, temperature and weight for common units in U.S. customary and metric measuring systems.8MN V.C.2Use arithmetic to solve simple real-world and mathematical problems involving mixed units such as minutes and hours in elapsed time, degrees and minutes in latitude and longitude and feet and inches in distance.8MO A.1Understand patterns, relations and functions8MO A.1.bCreate and analyze patterns8MO A.1.b.8generalize patterns represented graphically or numerically using words or symbolic rules, including recursive notation8MO A.1.cClassify objects and representations8MO A.1.c.8compare and contrast various forms of representations of patterns8MO A.1.dIdentify and compare functions8MO A.1.d.8compare properties of linear functions between or among tables, graphs and equations8MO A.2Represent and analyze mathematical situations and structures using algebraic symbols8MO A.2.aRepresent mathematical situations8MO A.2.a.8use symbolic algebra to represent and solve problems that involve linear relationships, including recursive relationships8MO A.2.bDescribe and use mathematical manipulation8MO A.2.b.8generate equivalent forms for linear expressions8MO A.3Use mathematical models to represent and understand quantitative relationships8MO A.3.aUse mathematical models8MO A.3.a.8model and solve problems, using multiple representations such as graphs, tables, equations or inequalities8MO A.4Analyze change in various contexts8MO A.4.aAnalyze change8MO A.4.a.8analyze the nature of changes (including slope and intercepts) in quantities in linear relationships8MO D.1Formulate questions that can be addressed with data and collect, organize and display relevant data to answer them8MO D.1.aFormulate questions8MO D.1.a.8formulate questions, design studies and collect data about a characteristic8MO D.1.cRepresent and interpret data8MO D.1.c.8select, create and use appropriate graphical representation of data (including scatter plots)8MO D.2Select and use appropriate statistical methods to analyze data8MO D.2.aDescribe and analyze data8MO D.2.a.8find, use and interpret measures of center, outliers and spread, including range and interquartile range8MO D.2.bCompare data representations8MO D.2.b.8compare different representations of the same data and evaluate how well each representation shows important aspects of the data8MO D.3Develop and evaluate inferences and predictions that are based on data8MO D.3.aDevelop and evaluate inferences8MO D.3.bAnalyze basic statistical techniques8MO D.3.b.12describe how basic statistical techniques are used in the workplace.8MO D.4Understand and apply basic concepts of probability8MO D.4.aApply basic concepts of probability8MO D.4.a.8make conjectures (based on theoretical probability) about the results of experiments8MO G..4.a.8create isometric drawings from a given mat plan8MO G.1Analyze characteristics of two- and three- dimensional geometric shapes and develop mathematical arguments about geometric relationships8MO G.1.aDescribe and use geometric relationships8MO G.1.a.8describe, classify and generalize relationships between and among types of a) 2-dimensional objects and b) 3- dimensional objects using their defining properties including � Pythagorean Theorem � cross-section of a 3-dimensional object r8MO G.1.bApply geometric relationships8MO G.1.b.8apply relationships between corresponding sides and corresponding areas of similar polygons to solve problems8MO G.2Specify locations and describe spatial relationships using coordinate geometry and other representational systems8MO G.2.aUse coordinate systems8MO G.2.a.8use coordinate geometry to analyze properties of right triangles and quadrilaterals8MO G.3Apply transformations and use symmetry to analyze mathematical situations8MO G.3.aUse transformations on objects8MO G.3.a.8reposition shapes under formal transformations, such as reflection, rotation and translation8MO G.3.cUse symmetry8MO G.3.c.8identify the number of rotational symmetries of regular polygons8MO G.4Use visualization, spatial reasoning and geometric modeling to solve problems8MO G.4.aRecognize and draw three-dimensional representations8MO G.4.bDraw and use visual models8MO G.4.b.8draw or use visual models to represent and solve problems8MO M.1Draw and use visual models8MO M.1.bdraw or use visual models to represent and solve problems8MO M.1.b.8Draw and use visual models8MO M.2draw or use visual models to represent and solve problems8MO M.2.bDraw and use visual models8MO M.2.cApply geometric measurements8MO M.2.c.8describe how to solve problems involving surface area and/or volume of a rectangular or triangular prism, or cylinder8MO M.2.dAnalyze precision8MO M.2.d.8analyze precision and accuracy in measurement situations and determine number of significant digits8MO M.2.eUse relationships within a measurement system8MO N.1Apply geometric measurements8MO N.1.adescribe how to solve problems involving surface area and/or volume of a rectangular or triangular prism, or cylinder8MO N.1.a.8Analyze precision8MO N.1.banalyze precision and accuracy in measurement situations and determine number of significant digits8MO N.1.b.8Use relationships within a measurement system8MO N.1.cApply geometric measurements8MO N.1.c.8describe how to solve problems involving surface area and/or volume of a rectangular or triangular prism, or cylinder8MO N.1.dAnalyze precision8MO N.1.d.8analyze precision and accuracy in measurement situations and determine number of significant digits8MO N.2Use relationships within a measurement system8MO N.2.bApply geometric measurements8MO N.2.b.8describe how to solve problems involving surface area and/or volume of a rectangular or triangular prism, or cylinder8MO N.2.cAnalyze precision8MO N.2.c.8analyze precision and accuracy in measurement situations and determine number of significant digits8MO N.2.d.8apply the relationship between squares and square roots and cubes and cube roots to solve a problem8MO N.3Compute fluently and make reasonable estimates8MO N.3.cCompute problems8MO N.3.c.8apply all operations on rational numbers8MO N.3.dEstimate and justify solutions8MO N.3.d.8estimate and justify the results of all operations on rational numbers8MO N.3.eUse proportional reasoning8MO N.3.e.8solve problems involving proportions, such as scaling and finding equivalent ratiosMS PA 1Explain, classify, and perform basic operations on the set of real numbers.MS PA 1aClassify numbers as natural, whole, integer, rational, irrational, and real.MS PA 1bIdentify and apply the properties of real numbers (include the use of mental mathematics and estimation methods).MS PA 1cModel absolute value of real numbers as a measure of distance.MS PA 1dCompare and order the real numbers and perform operations with rational numbers.MS PA 1eEvaluate numerical and algebraic expressions using order of operations.MS PA 1fConvert between repeating decimals and fractions.MS PA 1gRecognize and evaluate perfect squares and approximate square roots.MS PA 2Solve, check, and graph linear equations and inequalities in one variable.MS PA 2aRelate the language of mathematics to indicate mathematical operations.MS PA 2bTranslate between verbal expressions and algebraic expressions.MS PA 2cGiven an algebraic expression, write a corresponding real-life situation.MS PA 2dSimplify algebraic expressions by combining like terms and using the distributive property.MS PA 2eSolve, check, and graph one-step and two-step linear equations and inequalities.MS PA 2fSolve and check multi-step linear equations and inequalities with variables on both sides involving the distributive property.MS PA 3Recognize and perform basic operations on polynomials.MS PA 3aClassify types of polynomials.MS PA 3bDetermine the degree of polynomials.MS PA 3cSimplify polynomials by combining like terms.MS PA 3dArrange polynomials in ascending or descending order of a variable.MS PA 3eUse the rules of exponents to multiply and divide monomials.MS PA 3fUse the rules of exponents to multiply monomials by polynomials.MS PA 3gModel and use the distributive property and rules of exponents to multiply binomials by binomials.MS PA 3hMultiply and divide numbers involving scientific notation.MS PA 3iUse manipulative models to demonstrate operations of monomials and polynomials.MS PA 4Use ratios, proportions, and percents to solve problems.MS PA 4aRepresent, convert, and explain relationships among fractions, ratios, decimals, and percents in problem solving.MS PA 4bUse proportions and equations to find part, rate, or base in real-world situations.MS PA 4cExplain solutions and processes orally and in writing.MS PA 5Use concepts of probability and statistics to interpret information.MS PA 5aModel the Fundamental Counting Principle to determine possible outcomes of an event.MS PA 5bUse combinations and permutations in application problems.MS PA 5cCalculate and apply basic probability.MS PA 5dCollect, display, analyze, and draw appropriate conclusions from data.MS PA 5eInterpret and construct stem-and-leaf, box-and-whisker, and scatter plots from data.MS PA 6Solve, check, and graph solutions of equations and inequalities in two variables using the coordinate system.MS PA 6aGiven a set of ordered pairs, draw a coordinate system using an appropriate scale.MS PA 6bCreate a table to graph equations and inequalities that are presented in slope-intercept form.MS PA 6cUse calculators/computers to check accuracy of tables and graphs as needed.MS PA 6dIdentify slope as positive, negative, zero, or undefined from a graph.MS PA 6eCalculate slope from two points graphically and algebraically.MS PA 6fIdentify x- and y-intercepts from a graph.MS PA 6gIdentify the solution of a system of equations from a graph.MS PA 7Use and apply properties and formulas to solve geometric problems.MS PA 7aCalculate perimeter, area, circumference, and volume using appropriate formulas.MS PA 7bRecognize the irrational number pi (?) as the ratio of circumference to diameter of any given circle.MS PA 7cSolve problems involving the use of the Pythagorean Theorem.MS PA 7dClassify triangles by sides and angles.MS PA 7eUse properties of similar triangles to solve problems.MS PA 7fRecognize and determine degree measure of angles formed by parallel lines cut by a transversal.MS PA 7gDevelop, extend, and model the relationships of faces, vertices, and edges of three-dimensional figures.MS PA 7hPerform transformations on plane figures.CAT5.LV18.53Data interpretationNAEP 2005  A3bPerform basic operations, using appropriate tools, on linear algebraic expressions (including grouping and order of multiple operations involving basic operations, exponents, roots, simplifying, and expanding).NAEP 2005  N2dEstimate square or cube roots of numbers less than 1,000 between two whole numbers.NAEP 2005  N3dDescribe the effect of multiplying and dividing by numbers including the effect of multiplying or dividing a rational number by: zero, a number less than zero, a number between zero and one, one, or a number greater than one.NAEP 2005 A1aRecognize, describe, or extend numerical and geometric patterns using tables, graphs, words, or symbols.NAEP 2005 A1bGeneralize a pattern appearing in a numerical sequence or table or graph using words or symbols.NAEP 2005 A1cAnalyze or create patterns, sequences, or linear functions given a rule.NAEP 2005 A1eIdentify functions as linear or non-linear or contrast distinguishing properties of functions from tables, graphs, or equations.NAEP 2005 A2aTranslate between different representations of linear expressions using symbols, graphs, tables, diagrams, or written descriptions.NAEP 2005 A2bAnalyze or interpret linear relationships expressed in symbols, graphs, tables, diagrams, or written descriptions.NAEP 2005 A2cGraph or interpret points that are represented by ordered pairs of numbers on a rectangular coordinate system.NAEP 2005 A2gIdentify or represent functional relationships in meaningful contexts including proportional, linear, and common non-linear in tables, graphs, words, or symbols.NAEP 2005 A3aWrite algebraic expressions, equations, or inequalities to represent a situation.NAEP 2005 A3bPerform basic operations, using appropriate tools, on linear algebraic expressions (including grouping and order of multiple operations involving basic operations, exponents, roots, simplifying, and expanding).NAEP 2005 A4aSolve linear equations or inequalities.NAEP 2005 A4bInterpret �=� as an equivalence between two expressions and use this interpretation to solve problems.NAEP 2005 A4cAnalyze situations or solve problems using linear equations and inequalities with rational coefficients symbolically or graphically.NAEP 2005 A4dInterpret relationships between symbolic linear expressions and graphs of lines by identifying and computing slope and intercepts.NAEP 2005 A4eUse and evaluate common formulas.NAEP 2005 B2dNote to FSC: Delete NAEP 2005 B2d from standards and correlation spreadsheet. This standard does not exist.NAEP 2005 D1aRead or interpret data, including interpolating or extrapolating from data.NAEP 2005 D1bGiven a set of data, complete a graph and then solve a problem using the data in the graph.NAEP 2005 D1dGiven a graph or a set of data, determine whether information is represented effectively and appropriately.NAEP 2005 D1eCompare and contrast the effectiveness of different representations of the same data.NAEP 2005 D2aCalculate, use, or interpret mean, median, mode, or range.NAEP 2005 D2bDescribe how mean, median, mode, range, or interquartile ranges relate to the shape of the distribution.NAEP 2005 D2dUsing appropriate statistical measures, compare two or more data sets describing the same characteristic for two different populations or subsets of the same population.NAEP 2005 D3aGiven a sample, identify possible sources of bias in sampling.NAEP 2005 D3bDistinguish between a random and non-random sample.NAEP 2005 D3dEvaluate the design of an experiment.NAEP 2005 D4aAnalyze a situation that involves probability of an independent event.NAEP 2005 D4bDetermine the theoretical probability of simple and compound events in familiar contexts.NAEP 2005 D4cEstimate the probability of simple and compound events through experimentation or simulation.NAEP 2005 D4dDistinguish between experimental and theoretical probability.NAEP 2005 D4eDetermine the sample space for a given situation.NAEP 2005 D4hDetermine the probability of independent and dependent events.NAEP 2005 G1bIdentify a geometric object given written description of its properties.NAEP 2005 G1cIdentify, define, or describe geometric shapes in the plane and in 3-dimensional space given a visual representation.NAEP 2005 G1eRepresent or describe a three-dimensional situation in a two-dimensional drawing using perspective.NAEP 2005 G1fDemonstrate an understanding about the two- and three-dimensional shapes in our world through identifying, drawing, modeling, building, or taking apart.NAEP 2005 G2cRecognize or informally describe the effect of a transformation on two-dimensional geometric shapes (reflections across lines of symmetry, rotations, translations, magnifications, and contractions).NAEP 2005 G2eJustify relationships of congruence and similarity, and apply these relationships using scaling and proportional reasoning.NAEP 2005 G2fFor similar figures, identify and use the relationships of conservation of angle and of proportionality of side length and perimeter.NAEP 2005 G3bApply geometric properties and relationships in solving simple problems in two- and three-dimensions.NAEP 2005 G3dUse the Pythagorean theorem to solve problems.NAEP 2005 G3fDescribe or analyze simple properties of, or relationships between, triangles, quadrilaterals, and other polygonal plane figures.NAEP 2005 G3gDescribe or analyze properties and relationships of parallel or intersecting lines.NAEP 2005 M1aNote to FSC: Delete NAEP 2005 M1a from standards and correlation spreadsheet. This standard does not exist.NAEP 2005 M1hSolve mathematical or real-world problems involving perimeter or area of plane figures such as triangles, rectangles, circles, or composite figures.NAEP 2005 M1jSolve problems involving volume or surface area of rectangular solids, cylinders, prisms, or composite shapes.NAEP 2005 M1kSolve problems involving indirect measurement such as finding the height of a building by comparing its shadow with the height and shadow of a known object.NAEP 2005 M2aSelect or use appropriate type of unit for the attribute being measured such as length, area, angle, time, or volume.NAEP 2005 M2bSolve problems involving conversions within the same measurement system such as conversions involving square inches and square feet.NAEP 2005 M2dDetermine appropriate size of unit of measurement in problem situations involving such attributes as length, area, or volume.NAEP 2005 M2fConstruct or solve problems involving scale drawings.NAEP 2005 N1aUse place value to model and describe integers and decimals.NAEP 2005 N1bModel or describe rational numbers or numerical relationships using number lines and diagrams.NAEP 2005 N1dWrite or rename rational numbers.NAEP 2005 N1eRecognize, translate between, or apply multiple representations of rational numbers (fractions, decimals, and percents) in meaningful contexts.NAEP 2005 N1fExpress or interpret numbers using scientific notation from real life contexts.NAEP 2005 N1gFind or model absolute value or apply to problem situations.NAEP 2005 N1iOrder or compare rational numbers (fractions, decimals, percents, or integers) using various models and representations.NAEP 2005 N2aEstablish or apply benchmarks for rational numbers and common irrational numbers in contexts.NAEP 2005 N2bMake estimates appropriate to a given situation by: identifying when estimation is appropriate, determining the level of accuracy needed, selecting the appropriate method of estimation, or analyzing the effect of an estimation method on the accuracy of results.NAEP 2005 N2cVerify solutions or determine the reasonableness of results in a variety of situations including calculator and computer results.NAEP 2005 N2dEstimate square or cube roots of numbers less than 1,000 between two whole numbers.NAEP 2005 N3aPerform computations with rational numbers.NAEP 2005 N3dDescribe the effect of multiplying and dividing by numbers including the effect of multiplying or dividing a rational number by: zero, a number less than zero, a number between zero and one, one, or a number greater than one.NAEP 2005 N3gSolve application problems involving rational numbers and operations using exact answers or estimates as appropriate.NAEP 2005 N4aUse ratios to describe problem situations.NAEP 2005 N4bUse fractions to represent and express ratios and proportions.NAEP 2005 N4cUse proportional reasoning to model and solve problems (including rates, scaling, and similarity).NAEP 2005 N4dSolve problems involving percentages (including percent increase and decrease, interest rates, tax, discount, tips, or part/whole relationships).NAEP 2005 N5bRecognize, find, or use factors, multiples, or prime factorization.NAEP 2005 N5cRecognize or use prime and composite numbers to solve problems.NAEP 2005 N5eApply basic properties of operations.8NE 8.1.1By the end of eighth grade, students will recognize natural numbers, whole numbers, integers, and rational numbers.8NE 8.1.2By the end of eighth grade, students will determine equivalences among fractions, decimals, and percents.  Example indicators:  Find the equivalencies among fractions, decimals, and percents; solve problems with appropriate equivalencies.8NE 8.1.3By the end of eighth grade, students will write and use numbers in expanded exponential form and scientific notation.  Example indicators:  Write numbers in expanded form using exponential notation; express small and large numbers using scientific notation.8NE 8.1.4By the end of eighth grade, students will identify and display numbers including prime and composite, factors and multiples, divisibility, powers, and properties.  Example indicator:  Properties of numbers may include, but not be limited to, order of operations, commutative, associative, distributive, identity, and inverse.8NE 8.2.1By the end of eighth grade, students will add, subtract, multiply, and divide decimals and proper, improper, and mixed fractions with uncommon and common denominators with and without the use of technology.8NE 8.2.2By the end of eighth grade, students will identify the appropriate operation and do the correct calculations when solving word problems.8NE 8.2.3By the end of eighth grade, students will solve problems involving whole numbers, integers, and rational numbers (fractions, decimals, ratios, proportions, and percents) with and without the use of technology.  Example indicators:  Use proportions to solve scale-model problems with fractions and decimals; problems should be of increasing level of difficulty and solve real-life situations.8NE 8.2.4By the end of eighth grade, students will apply the order of operations to solve problems with and without the use of technology.  Example indicator:  Evaluate all types of numerical expressions, including grouping symbols and exponents.8NE 8.2.5By the end of eighth grade, students will apply strategies of estimation when solving problems with and without the use of technology.  Example indicators:  Properly round to an appropriate place value if context permits; perform estimation prior to calculation; without a calculator, estimate square roots of whole numbers up to one hundred to the nearest whole number; use compatible numbers to perform mental math; use estimation to check reasonableness of an answer.8NE 8.3.1By the end of eighth grade, students will select measurement tools and measure quantities for temperature, time, money, distance, angles, area, perimeter, volume, capacity, and weight/mass in standard and metric units at the designated level of precision.8NE 8.3.2By the end of eighth grade, students will convert units within measurement systems using standard and metric, given conversion factors.  Example indicators:  Convert between various units of area and various units of volume (square foot to square yards and cubic decimeters to liters, etc.); check solutions to problems using unit analysis (feet/second to miles/hour).8NE 8.4.1By the end of eighth grade, students will identify, describe, compare, and classify two- and three-dimensional geometric figures -- plane figures like polygons and circles; solid figures like prisms, pyramids, cones, spheres, and cylinders; lines, line segments, rays, angles, parallel and perpendicular lines.8NE 8.4.2By the end of eighth grade, students will use geometric properties, the Pythagorean theorem, and the relationship of congruence, similarity, and symmetry.8NE 8.4.3By the end of eighth grade, students will use formulas to solve problems involving perimeter and area of a square, rectangle, parallelogram, trapezoid and triangle, as well as the area and circumference of circles.8NE 8.4.4By the end of eighth grade, students will solve problems given formulas for volume and surface area of rectangular prisms, cylinders, and cones.8NE 8.4.5By the end of eighth grade, students will apply transformations to two- and three-dimensional geometric figures.  Example indicator: Draw geometric figures using translations or slides, rotations or turns, reflections or flips, and scale.8NE 8.4.6By the end of eighth grade, students will use geometric terms and representations to describe the physical world.8NE 8.5.1By the end of eighth grade, students will collect, construct, and interpret data displays and compute mean, median, and mode.  Example indicator:  Select appropriate representations of data when constructing data displays (graphs, tables, or charts).8NE 8.5.2By the end of eighth grade, students will read and interpret tables, charts, and graphs to make comparisons and predictions.8NE 8.5.3By the end of eighth grade, students will conduct experiments or simulations to demonstrate theoretical probability and relative frequency.  Example indicator:  Compare the results of a simulation (relative frequency) to the theoretical probability (a three-color spinner or a coin).8NE 8.5.4By the end of eighth grade, students will identify statistical methods and probability for making decisions.  Example indicators:  Identify the use of appropriate sampling techniques; identify the use of appropriate charts and graphs; identify the use of measures of central tendency (mean, median, and mode) appropriately.8NE 8.6.1By the end of eighth grade, students will demonstrate knowledge and use of the one- and two-dimensional coordinate systems.  Example indicators:  Order numbers on a number line; graph ordered pairs on a coordinate plane; generate a table of ordered pairs to graph an equation in two variables.8NE 8.6.2By the end of eighth grade, students will apply algebraic concepts and operations to solve linear equations and word problems.  Example indicators:  Solve multi-step equations with one variable; use order of operations to evaluate algebraic expressions for given replacement values of the variables; recognize and apply commutative, associative, distributive, inverse, and identity properties, and the properties of zero.8NE 8.6.3By the end of eighth grade, students will describe and represent relations, using tables, graphs, and rules.  Example indicator:  Use variables to recognize and describe patterns.8NJ 4.1.8.A.1aExtend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 8 pertain to these sets of numbers as well): Rational numbers.8NJ 4.1.8.A.1bExtend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 8 pertain to these sets of numbers as well): Percents.8NJ 4.1.8.A.1cExtend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 8 pertain to these sets of numbers as well): Exponents.8NJ 4.1.8.A.1dExtend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 8 pertain to these sets of numbers as well): Roots.8NJ 4.1.8.A.1eExtend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 8 pertain to these sets of numbers as well): Absolute values.8NJ 4.1.8.A.1fExtend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 8 pertain to these sets of numbers as well): Numbers represented in scientific notation.8NJ 4.1.8.A.2Demonstrate a sense of the relative magnitudes of numbers.8NJ 4.1.8.A.3Understand and use ratios, proportions, and percents (including percents greater than 100 and less than 1) in a variety of situations.8NJ 4.1.8.A.4Compare and order numbers of all named types.8NJ 4.1.8.A.5Use whole numbers, fractions, decimals, and percents to represent equivalent forms of the same number.8NJ 4.1.8.A.6 Recognize that repeating decimals correspond to fractions and determine their fractional equivalents.8NJ 4.1.8.A.7 Construct meanings for common irrational numbers, such as (pi) and the square root of 2.8NJ 4.1.8.B.1a Use and explain procedures for performing calculations involving addition, subtraction, multiplication, division, and exponentiation with integers and all number types named above with: Pencil-and-paper.8NJ 4.1.8.B.1b Use and explain procedures for performing calculations involving addition, subtraction, multiplication, division, and exponentiation with integers and all number types named above with: Mental math.8NJ 4.1.8.B.1c Use and explain procedures for performing calculations involving addition, subtraction, multiplication, division, and exponentiation with integers and all number types named above with: Calculator.8NJ 4.1.8.B.2Use exponentiation to find whole number powers of numbers.8NJ 4.1.8.B.3Find square and cube roots of numbers and understand the inverse nature of powers and roots.8NJ 4.1.8.B.4Solve problems involving proportions and percents.8NJ 4.1.8.B.5Understand and apply the standard algebraic order of operations, including appropriate use of parentheses.8NJ 4.1.8.C.1Estimate square and cube roots of numbers.8NJ 4.1.8.C.2Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation.8NJ 4.1.8.C.3Recognize the limitations of estimation and assess the amount of error resulting from estimation.8NJ 4.2.8.A.1a Understand and apply concepts involving lines, angles, and planes: Complementary and supplementary angles.8NJ 4.2.8.A.1b Understand and apply concepts involving lines, angles, and planes: Vertical angles.8NJ 4.2.8.A.1c Understand and apply concepts involving lines, angles, and planes: Bisectors and perpendicular bisectors.8NJ 4.2.8.A.2Understand and apply the Pythagorean theorem.8NJ 4.2.8.A.3aUnderstand and apply properties of polygons: Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi.8NJ 4.2.8.A.3bUnderstand and apply properties of polygons: Regular polygons.8NJ 4.2.8.A.3cUnderstand and apply properties of polygons: Sum of measures of interior angles of a polygon.8NJ 4.2.8.A.3dUnderstand and apply properties of polygons: Which polygons can be used alone to generate a tessellation and why.8NJ 4.2.8.A.4aUnderstand and apply the concept of similarity: Using proportions to find missing measures.8NJ 4.2.8.A.4bUnderstand and apply the concept of similarity: Scale drawings.8NJ 4.2.8.A.4cUnderstand and apply the concept of similarity: Models of 3D objects.8NJ 4.2.8.A.5Use logic and reasoning to make and support conjectures about geometric objects.8NJ 4.2.8.B.1aUnderstand and apply transformations: Finding the image, given the pre-image, and vice-versa.8NJ 4.2.8.B.1bUnderstand and apply transformations: Sequence of transformations needed to map one figure onto another.8NJ 4.2.8.B.1cUnderstand and apply transformations: Reflections, rotations, and translations result in images congruent to the pre-image.8NJ 4.2.8.C.1Use coordinates in four quadrants to represent geometric concepts.8NJ 4.2.8.C.2Use a coordinate grid to model and quantify transformations.8NJ 4.2.8.D.1Solve problems requiring calculations that involve different units of measurement within a measurement system.8NJ 4.2.8.D.2 Use approximate equivalents between standard and metric systems to estimate measurements.8NJ 4.2.8.D.3Recognize that the degree of precision needed in calculations depends on how the results will be used and the instruments used to generate the measurements.8NJ 4.2.8.D.4Select and use appropriate units and tools to measure quantities to the degree of precision needed in a particular problem-solving situation.8NJ 4.2.8.D.5Recognize that all measurements of continuous quantities are approximations.8NJ 4.2.8.D.6Solve problems that involve compound measurement units, such as speed (miles per hour), air pressure (pounds per square inch), and population density (persons per square mile).8NJ 4.2.8.E.1aDevelop and apply strategies for finding perimeter and area: Geometric figures made by combining triangles, rectangles and circles or parts of circles.8NJ 4.2.8.E.1bDevelop and apply strategies for finding perimeter and area: Estimation of area using grids of various sizes.8NJ 4.2.8.E.2Recognize that the volume of a pyramid or cone is one-third of the volume of the prism or cylinder with the same base and height.8NJ 4.2.8.E.3aDevelop and apply strategies and formulas for finding the surface area and volume of a three-dimensional figure: Volume � prism, cone, pyramid.8NJ 4.2.8.E.3bDevelop and apply strategies and formulas for finding the surface area and volume of a three-dimensional figure: Surface area � prism (triangular or rectangular base), pyramid (triangular or rectangular base).8NJ 4.2.8.E.3cDevelop and apply strategies and formulas for finding the surface area and volume of a three-dimensional figure: Impact of a dilation on the surface area and volume of a three-dimensional figure.8NJ 4.2.8.E.4Use formulas to find the volume and surface area of a sphere.8NJ 4.3.8.A.1aRecognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers: Descriptions using tables, verbal and symbolic rules, graphs, simple equations or expressions.8NJ 4.3.8.A.1bRecognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers: Finite and infinite sequences.8NJ 4.3.8.A.1cRecognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers: Arithmetic sequences.8NJ 4.3.8.A.1dRecognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers: Geometric sequences.8NJ 4.3.8.B.1a Graph functions, and understand and describe their general behavior: Equations involving two variables.8NJ 4.3.8.B.1b Graph functions, and understand and describe their general behavior: Rates of change (informal notion of slope).8NJ 4.3.8.B.2 Recognize and describe the difference between linear and exponential growth, using tables, graphs, and equations.8NJ 4.3.8.C.1Analyze functional relationships to explain how a change in one quantity can result in a change in another, using pictures, graphs, charts, and equations.8NJ 4.3.8.C.2aUse patterns, relations, symbolic algebra, and linear functions to model situations: Using concrete materials (manipulatives), tables, graphs, verbal rules, algebraic expressions/equations/inequalities.8NJ 4.3.8.C.2bUse patterns, relations, symbolic algebra, and linear functions to model situations: Growth situations, such as population growth and compound interest, using recursive formulas.8NJ 4.3.8.D.1aUse graphing techniques on a number line: Absolute value.8NJ 4.3.8.D.1bUse graphing techniques on a number line: Arithmetic operations represented by vectors (arrows).8NJ 4.3.8.D.2aSolve simple linear equations informally, graphically, and using formal algebraic methods: Multi-step, integer coefficients only (although answers may not be integers).8NJ 4.3.8.D.2bSolve simple linear equations informally, graphically, and using formal algebraic methods: Using paper-and-pencil, calculators, graphing calculators, spreadsheets, and other technology.8NJ 4.3.8.D.3Solve simple linear inequalities.8NJ 4.3.8.D.4aCreate, evaluate, and simplify algebraic expressions involving variables: Order of operations, including appropriate use of parentheses.8NJ 4.3.8.D.4bCreate, evaluate, and simplify algebraic expressions involving variables: Distributive property.8NJ 4.3.8.D.4cCreate, evaluate, and simplify algebraic expressions involving variables: Substitution of a number for a variable.8NJ 4.3.8.D.4dCreate, evaluate, and simplify algebraic expressions involving variables: Translation of a verbal phrase or sentence into an algebraic expression, equation, or inequality, and vice versa.8NJ 4.3.8.D.5aUnderstand and apply the properties of operations, numbers, equations, and inequalities: Additive inverse.8NJ 4.3.8.D.5bUnderstand and apply the properties of operations, numbers, equations, and inequalities: Multiplicative inverse.8NJ 4.3.8.D.5cUnderstand and apply the properties of operations, numbers, equations, and inequalities: Addition and multiplication properties of equality.8NJ 4.3.8.D.5dUnderstand and apply the properties of operations, numbers, equations, and inequalities: Addition and multiplication properties of inequalities.8NJ 4.4.8.A.1aSelect and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode): Type of display most appropriate for given data.8NJ 4.4.8.A.1bSelect and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode): Box-and-whisker plot, upper quartile, lower quartile.8NJ 4.4.8.A.1cSelect and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode): Scatter plot.8NJ 4.4.8.A.1eSelect and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode): Finding the median and mean (weighted average) using frequency data.8NJ 4.4.8.A.1fSelect and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode): Effect of additional data on measures of central tendency.8NJ 4.4.8.A.2Make inferences and formulate and evaluate arguments based on displays and analysis of data.8NJ 4.4.8.A.3Estimate lines of best fit and use them to interpolate within the range of the data.8NJ 4.4.8.A.4Use surveys and sampling techniques to generate data and draw conclusions about large groups.8NJ 4.4.8.B.1Interpret probabilities as ratios, percents, and decimals.8NJ 4.4.8.B.2Determine probabilities of compound events.8NJ 4.4.8.B.3Explore the probabilities of conditional events.8NJ 4.4.8.B.4Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models: Frequency, relative frequency.8NJ 4.4.8.B.5Estimate probabilities and make predictions based on experimental and theoretical probabilities.8NJ 4.4.8.B.6Play and analyze probability-based games, and discuss the concepts of fairness and expected value.8NJ 4.4.8.C.1aApply the multiplication principle of counting: Permutations: ordered situations with replacement vs. ordered situations without replacement.8NJ 4.4.8.C.1cApply the multiplication principle of counting: Concept of combinations.8NJ 4.4.8.C.3Apply techniques of systematic listing, counting, and reasoning in a variety of different contexts.8NM A.A.1To come8NM A.A.2aTo come8NM A.A.2bTo come8NM A.B.1To come8NM A.B.2To come8NM A.B.3To come8NM A.B.4To come8NM A.B.5To come8NM A.B.6To come8NM A.B.7To come8NM A.C.1To come8NM A.D.1To come8NM A.D.2To come8NM A.D.3To come8NM A.D.4To come8NM A.D.5To come8NM A.D.6To come8NM A.D.7To come8NM D.A.1To come8NM D.A.2To come8NM D.A.3aTo come8NM D.A.3bTo come8NM D.A.3cTo come8NM D.A.3dTo come8NM D.A.3eTo come8NM D.A.3fTo come8NM D.A.4To come8NM D.A.5To come8NM D.A.6To come8NM D.B.1To come8NM D.B.2To come8NM D.B.3aTo come8NM D.B.3cTo come8NM D.B.3dTo come8NM D.B.3eTo come8NM D.B.3fTo come8NM D.B.3gTo come8NM D.B.4To come8NM D.B.5To come8NM D.B.6To come8NM D.B.7To come8NM D.B.8To come8NM D.C.1To come8NM D.C.2To come8NM D.C.3To come8NM D.C.4To come8NM D.D.1To come8NM D.D.2To come8NM D.D.4To come8NM D.D.5To come8NM D.D.6To come8NM G.A.1To come8NM G.A.2To come8NM G.A.3To come8NM G.B.1To come8NM G.C.2To come8NM G.D.1To come8NM G.D.2To come8NM G.D.3To come8NM G.D.4To come8NM G.D.5To come8NM M.A.1To come8NM M.A.2To come8NM M.B.1To come8NM M.B.2To come8NM M.B.3To come8NM M.B.4To come8NM M.B.6To come8NM M.B.7To come8NM N.A.1To come8NM N.A.2To come8NM N.B.1To come8NM N.B.2To come8NM N.B.3To come8NM N.C.1To come8NM N.C.2To come8NM N.C.3To come8NM N.C.4To come8NM N.C.5To come8NM N.C.6To come8NM N.C.7To come8NM N.C.9To come8NV 1.8.1Read, write, add, subtract, multiply, and divide real numbers in various forms including radicals, exponential, and scientific notation.8NV 1.8.2Compute with rational and irrational numbers to solve a variety of problems including  rates, recipes, unit costs, and percents (e.g., discounts, interest, sale, prices, commissions, taxes).8NV 1.8.3Explain and apply number theory and the properties of real numbers to solve problems.8NV 1.8.6Compare and order rational numbers.8NV 1.8.7Estimate in problem-solving situations and in practical applications; determine the reasonableness of the answer and verify the results.8NV 1.8.9Explain the relationship among fractions, decimals, and percents; translate among various representations of equal numbers (e.g., from fractions to decimals to percents, various forms of 1 such as 3/3 or 16/16) to solve problems efficiently.8NV 2.8.1Use inductive reasoning to find the missing term in number and geometric patterns and to generalize basic patterns to the nth term, with and without calculators; use written, oral, and symbolic language to identify and describe patterns, sequences, and functions.8NV 2.8.2Translate among verbal descriptions, graphic, tabular, and algebraic representations of mathematical situations.8NV 2.8.3Identify, model, describe, and evaluate relationships, including functions, using a variety of methods with and without technology.8NV 2.8.4Add and subtract binomials; describe the connection between the algebraic process and the arithmetic process.8NV 2.8.6Model, identify, and solve linear equations and inequalities; relate this process to the order of operations.8NV 2.8.7Solve simple linear equations and connect that process to the order of operations.8NV 3.8.2Demonstrate an understanding of precision, error, and tolerance in measurement using the appropriate measurement tool to the required degree of accuracy.8NV 3.8.3Select and apply appropriate formulas to solve problems; identify the relationship between changes in area and volume and changes in linear measures of figures.8NV 3.8.5Apply ratios and proportions to calculate rates and as a method of indirect measure (e.g., miles per hour, cost per unit).8NV 4.8.2Apply the properties of equality and proportionality to solve problems involving congruent or similar shapes.8NV 4.8.5Use coordinate geometry to represent and interpret relationships defined by equations and formulas (including distance, midpoint, and slope), with and without technology.8NV 4.8.6Form generalizations and validate conclusions about properties of  geometric shapes including parallel lines, perpendicular lines, bisectors, triangles, and quadrilaterals.8NV 4.8.7Verify and explain the Pythagorean Theorem using various methods (e.g., using grid paper, applying it to a missing side of a right triangle); determine missing sides and angles of triangles based on properties of their sides and angles.8NV 4.8.8Use hand tools, technology, and models to construct figures and bisect angles and line segments; distinguish among constructions, sketches and drawings.8NV 5.8.1Organize, display, read, and analyze data, with and without technology, using a variety of displays including box-and-whisker plots.8NV 5.8.2Find the theoretical probability of an event using different counting methods (e.g., tree diagrams, sample spaces, and organized lists) and compare those results with actual (experimental) results, differentiating between the probability of an event and the odds of an event.8NV 5.8.3Find the number of combinations possible in given situations using a variety of counting methods.8NV 5.8.5Evaluate arguments that are based on data analysis for accuracy and validity; analyze the effect a change of scale or a change of format will have on statistical charts and graphs.8NV 5.8.6Formulate reasonable inferences and projections based on interpolations and extrapolations of data to solve problems.8NV 6.1Select, modify, develop, and apply strategies to solve a variety of mathematical and practical problems and to investigate and understand mathematical concepts.8NV 6.2Apply previous experience and knowledge to new problem-solving situations.8NV 6.7Apply multi-step, integrated, mathematical problem-solving strategies, persisting until a solution is found or until it is clear that no solution exists.8NV 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.8NV 6.11Apply combinations of proven strategies and previous knowledge to solve non-routine problems.8NV 6.13Use technology, including calculators, to solve problems and verify solutions.8NV 6.14Use technology, including calculators, to investigate, define, and describe quantitative relationships such as patterns and functions.8NV 7.2Use inquiry techniques (e.g., discussion, questioning, research, data gathering) to solve mathematical problems.8NV 7.6Interpret and solve word problems without the necessity of key words or phrases.8NV 7.9Model and explain mathematical relationships using oral, written, graphical, and algebraic methods.8NV 7.15Use everyday language to explain thinking about strategies and solutions to mathematical problems.8NV 7.17Use mathematical notation to communicate and explain mathematical situations.8NV 8.3Construct, justify, and defend mathematical conclusions using logical arguments, in situations related to mathematics, science, and technology.8NV 8.4Use patterns and relationships to analyze mathematical situations; draw logical conclusions about mathematical problems.8NV 8.7Recognize and apply deductive and inductive reasoning in both concrete and abstract contexts.8NV 8.11Determine relevant, irrelevant, and/or sufficient information to solve mathematical problems.8NV 9.1Link new concepts to prior knowledge.8NV 9.2Use mathematical ideas from one area of mathematics to explain an idea from another area of mathematics.8NV 9.3Use models to explain the relationship of concepts to procedures.8NV 9.8Identify, explain, and use mathematics in everyday life.8OH D1Use, create and interpret scatterplots and other types of graphs as appropriate.8OH D2Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose.8OH D5Explain the mean�s sensitivity to extremes and its use in comparison with the median and mode.8OH D7Identify different ways of selecting samples, such as survey response, random sample, representative sample and convenience sample.8OH D10Calculate the number of possible outcomes for a situation, recognizing and accounting for when items may occur more than once or when order is important.8OH D11Demonstrate an understanding that the probability of either of two disjoint events occurring can be found by adding the probabilities for each and that the probability of one independent event following another can be found by multiplying the probabilities.8OH G2Recognize the angles formed and the relationship between the angles when two lines intersect and when parallel lines are cut by a transversal.8OH G3Use proportions in several forms to solve problems involving similar figures (part-to-part, part-to-whole, corresponding sides between figures).8OH G4Represent and analyze shapes using coordinate geometry.8OH G5Draw the results of translations, reflections, rotations and dilations of objects in the coordinate plane, and determine properties that remain fixed.8OH G6Draw nets for a variety of prisms, pyramids, cylinders, and cones.8OH M1Compare and order the relative size of common U.S. customary units and metric units.8OH M2Use proportional relationships and formulas to convert units from one measurement system to another.8OH M4Derive formulas for surface area and volume and justify them using geometric models and common materials.8OH M4aFind the surface area of a cylinder as a function of its height and radius.8OH M4bFind that the volume of a pyramid (or cone) is one-third of the volume of a prism (or cylinder) with the same base area and height.8OH M5Determine surface area for pyramids by analyzing their parts.8OH M6Solve and determine the reasonableness of the results for problems involving rates and derived measurements, such as velocity and density, using formulas, models, and graphs.8OH M7Apply proportional reasoning to solve problems involving indirect measurements or rates.8OH M8Find the sum of the interior and exterior angles of regular convex polygons with and without measuring the angles with a protractor.8OH M9Demonstrate understanding of the concepts of perimeter, circumference and area by using established formulas for triangles, quadrilaterals, and circles to determine the surface area and volume of prisms, pyramids, cylinders, spheres, and cones.8OH M10Use conventional formulas to find the surface area and volume of prisms, pyramids and cylinders and the volume of spheres and cones to a specified level of precision.8OH N1Use scientific notation to express large numbers and small numbers between 0 and 1.8OH N3Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals.8OH N4Explain and use the inverse and identity properties and use inverse relationships (addition/subtraction, multiplication/division, squaring/square roots) in problem solving situations.8OH N5Determine when an estimate is sufficient and when an exact answer is needed in problem situations, and evaluate estimates in relation to actual answers.8OH N6Estimate, compute, and solve problems involving rational numbers, including ratio, proportion, and percent, and judge the reasonableness of solutions.8OH N7Find the square root of perfect squares, and approximate the square root of non-perfect squares as consecutive integers between which the root lies.8OH N8Add, subtract, multiply, divide and compare numbers written in scientific notation.8OH P1Relate the various representations of a relationship.8OH P2Generalize patterns and sequences by describing how to find the nth term.8OH P4Extend the uses of variables to include covariants where y depends on x.8OH P5Use physical models to add and subtract monomials and polynomials, and to multiply a polynomial by a monomial.8OH P6Describe the relationship between the graph of a line and its equation, including being able to explain the meaning of slope as a constant rate of change and y-intercept in real-world problems.8OH P7Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems.8OH P8Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems.8OH P9Solve linear equations and inequalities graphically, symbolically and using technology.8OH P10Solve 2 by 2 systems of linear equations graphically and by simple substitution.8OH P12Solve simple quadratic equations graphically.8OH P13Compute and interpret slope, midpoint and distance given a set of ordered pairs.8OH P14Differentiate and explain types of changes in mathematical relationships, such as linear vs. nonlinear, continuous vs. noncontinuous, direct variation vs. inverse variation.8PA 2.1.8.ARepresent and use numbers in equivalent forms.8PA 2.1.8.BSimplify numerical expressions involving exponents, scientific notation and using order of operations.8PA 2.1.8.CDistinguish between and order rational and irrational numbers.8PA 2.1.8.DApply ratio and proportion to mathematical problem situations involving distance, rate, time and similar triangles.8PA 2.1.8.ESimplify and expand algebraic expressions using exponential forms.8PA 2.1.8.FUse the number line model to demonstrate integers and their applications.8PA 2.1.8.GUse the inverse relationships between addition, subtraction, multiplication, division, exponentiation and root extraction to determine unknown quantities in equations.8PA 2.2.8.AComplete calculations by applying the order of operations.8PA 2.2.8.BAdd, subtract, multiply and divide different kinds and forms of rational numbers including integers, decimal fractions, percents and proper and improper fractions.8PA 2.2.8.CEstimate the value of irrational numbers.8PA 2.2.8.DEstimate amount of tips and discounts using ratios, proportions and percents.8PA 2.3.8.ADevelop formulas and procedures for determining measurements.8PA 2.4.8.AMake conjectures based on logical reasoning and test conjectures by using counter-examples.8PA 2.4.8.BCombine numeric relationships to arrive at a conclusion.8PA 2.4.8.EDistinguish between inductive and deductive reasoning.8PA 2.5.8.AInvent, select, use and justify the appropriate methods, materials and strategies to solve problems.8PA 2.5.8.BVerify and interpret results using precise mathematical language, notation and representations, including numerical tables and equations, simple algebraic equations and formulas, charts, graphs and diagrams.8PA 2.5.8.CJustify strategies and defend approaches used and conclusions reached.8PA 2.6.8.ACompare and contrast different plots of data using values of mean, median, mode, quartiles and range.8PA 2.6.8.CFit a line to the scatter plot of two quantities and describe any correlation of the variables.8PA 2.6.8.DDesign and carry out a random sampling procedure.8PA 2.6.8.EAnalyze and display data in stem-and-leaf and box-and-whisker plots.8PA 2.7.8.ADetermine the number of combinations and permutations for an event.8PA 2.7.8.BPresent the results of an experiment using visual representations.8PA 2.7.8.CAnalyze predictions.8PA 2.7.8.EMake valid inferences, predictions and arguments based on probability.8PA 2.8.8.AApply simple algebraic patterns to basic number theory and to spatial relations.8PA 2.8.8.BDiscover, describe and generalize patterns, including linear, exponential and simple quadratic relationships.8PA 2.8.8.CCreate and interpret expressions, equations, or inequalities that model problem situations.8PA 2.8.8.DUse concrete objects to model algebraic concepts.8PA 2.8.8.ESelect and use a strategy to solve an equation or inequality, explain the solution and check the solution for accuracy.8PA 2.8.8.FSolve and graph equations and inequalities using scientific and graphing calculators and computer spreadsheets.8PA 2.8.8.GRepresent relationships with tables or graphs in the coordinate plane and verbal or symbolic rules.8PA 2.8.8.HGraph a linear function from a rule or table.8PA 2.8.8.IGenerate a table or graph from a function and use graphing calculators and computer spreadsheets to graph and analyze functions.8PA 2.9.8.AConstruct figures incorporating perpendicular and parallel lines, the perpendicular bisector of a line segment and an angle bisector using computer software.8PA 2.9.8.BDraw, label, measure and list the properties of complementary, supplementary and vertical angles.8PA 2.9.8.DIdentify, name, draw and list all properties of squares, cubes, pyramids, parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, spheres, triangles, prisms and cylinders.8PA 2.9.8.EConstruct parallel lines, draw a transversal and measure and compare angles formed.8PA 2.9.8.GApproximate the value of ? (pi) through experimentation.8PA 2.9.8.HUse simple geometric figures to create, through rotation, transformational figures in three dimensions.8PA 2.9.8.JAnalyze geometric patterns and develop descriptions of the patterns.8PA 2.9.8.KAnalyze objects to determine whether they illustrate tessellations, symmetry, congruence, similarity and scale.8PA 2.10.8.ACompute measures of sides and angles using proportions, the Pythagorean Theorem and right triangle relationships.8PA 2.10.8.BSolve problems requiring indirect measurement for lengths of sides of triangles.8PA 2.11.8.BDescribe the concept of unit rate, ratio and slope in the context of rate of change.8PA 2.11.8.CContinue a pattern of numbers or objects that could be extended infinitely.8PA M8.A.1Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers and number systems.8PA M8.A.1.1Represent numbers in equivalent forms.8PA M8.A.1.1.1Represent numbers using scientific notation and/or exponential forms.8PA M8.A.1.1.2Find the square or cube of a whole number (single digit) and/or the square root of a perfect square (without a calculator).8PA M8.A.2.1.1Simplify numeric expressions involving integers, using the order of operations.  (May include all types of grouping symbols. No combining negatives with exponents or compound exponents.)8PA M8.A.2.2Represent or solve problems using rates, ratios, proportions and/or percents.8PA M8.A.2.2.1Solve problems involving percents (e.g., tax, discounts, etc) Do not include percent increase or decrease.8PA M8.A.2.2.2Represent or solve rate problems  (e.g., unit rates, simple interest, distance, etc.)  Students may be asked to solve for any term.8PA M8.A.3Compute accurately and fluently and make reasonable estimates.8PA M8.A.3.1.1Identify, use and/or explain when it is appropriate to round up or round down.8PA M8.A.3.1.2Identify, apply and/or explain when an exact answer is needed or when estimation is appropriate.8PA M8.A.3.2Use estimation strategies in problem-solving situations.8PA M8.A.3.3.1Add, subtract, multiply and/or divide integers, fractions and/or decimals with and without a calculator (straight computation or word problems).8PA M8.B.1.1.1Convert among metric measurements (milli, centi, kilo using meter, liter and gram).8PA M8.B.1.1.2Convert customary measurements up to 2 units above or below the given unit (e.g., inches to yards, pints to gallons).8PA M8.B.1.1.3Convert time up to 2 units above or below given unit (e.g., seconds to hours).8PA M8.B.1.1.4Convert from Fahrenheit to Celsius or Celsius to Fahrenheit.8PA M8.B.2Apply appropriate techniques, tools and formulas to determine measurements.8PA M8.B.2.1..3Determine the number of sides of a polygon given the total number of degrees in the interior angles (3-8 sided polygons).8PA M8.B.2.1.1Determine the total number of degrees in the interior angles of a polygon in 3 - 8 sided figures.8PA M8.B.2.1.2Determine the measurement of one interior angle of a regular polygon (3-8 sided polygons).8PA M8.B.2.3Use, describe and/or develop procedures to determine measures of perimeter, circumference, area, surface area and/or volume.8PA M8.B.2.3.1Calculate the surface area of cubes and rectangular prisms.8PA M8.B.2.3.2Calculate the volume of cubes and rectangular prisms.8PA M8.C.1.1.1Match the three-dimensional figure with its net (cube, cylinder, cone, prism, pyramid).  Any measurements used should be consistent in the stem and answer choices.8PA M8.C.1.1.2Define, identify and/or use properties of angles formed by intersecting lines (complementary, supplementary, adjacent and/or vertical angles).8PA M8.C.1.1.3Define, identify and/or use properties of angles formed when two parallel lines are cut by a transversal (alternate interior, alternate exterior, vertical corresponding).8PA M8.C.1.2.1Use the Pythagorean Theorem to find the measure of a missing side of a right triangle (whole numbers only).8PA M8.C.2.1.1Plot, locate or identify ordered pairs on a coordinate plane (the point may be a vertex of a polygon).8PA M8.D.1Demonstrate an understanding of patterns, relations and functions.8PA M8.D.1.1.1Continue a numeric or algebraic pattern (pattern must show 3 repetitions � may include up to 2 operations, squares and square roots).8PA M8.D.1.1.2Find missing elements in numeric or geometric patterns and/or functions (may be given a table or rule � pattern must show 3 repetitions).8PA M8.D.1.1.3Determine the rule of a function (given elements in an input-output table, chart or list � limit to linear functions).8PA M8.D.2Represent and/or analyze mathematical situations using numbers, symbols, words, tables and/or graphs.8PA M8.D.2.1Select and/or use a strategy to simplify an expression, solve an equation or inequality and/or check the solution for accuracy.8PA M8.D.2.1.1Solve one- or two-step equations and inequalities (should not include absolute values � one variable only).8PA M8.D.2.1.2Use substitution to check the accuracy of a given value for an equation or inequality (simple inequalities with one variable).8PA M8.D.2.1.3Determine the value of an algebraic expression by simplifying and/or substituting a number for the variable.8PA M8.D.2.2.1Match a written situation to its numeric and/or algebraic expression, equation or inequality (up to two variables in equations or expressions � one variable with inequalities).8PA M8.D.2.2.2Write and/or solve an equation for a given problem situation (one variable only).8PA M8.D.3.1Represent relationships with tables or graphs on the coordinate plane.8PA M8.D.3.1.1Graph a linear function based on an x/y table (integers only).8PA M8.E.1Formulate or answer questions that can be addressed with data and/or organize, display, interpret or analyze data.8PA M8.E.1.1.2Analyze data and/or answer questions pertaining to data shown in multiple line graphs, circle graphs or histograms.8PA M8.E.1.1.3Interpret data shown in stem-and-leaf or box-and-whisker plots.8PA M8.E.2.1Calculate the probability of an event.8PA M8.E.2.1.1Find the probability for a mutually exclusive or an independent event (written as a fraction in simplest form).8PA M8.E.3Understand and/or apply basic concepts of probability or outcomes.8PA M8.E.3.1.1Determine/show the number of combinations and/or permutations for an event using up to four choices (e.g., organized list, etc.).8PA M8.E.4Develop and/or evaluate inferences and predictions or draw conclusions based on data or data displays.8PA M8.E.4.1.1Fit a line to a scatter plot and/or describe any correlation between the two variables (positive, negative, strong, weak or none).8PA M8.E.4.1.2Make predictions based on survey results or graphs (bar, line, circle, scatter plots, etc.).TX TEKS 8.1Acompare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimalsTX TEKS 8.1Bselect and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationshipsTX TEKS 8.1Capproximate (mentally and with calculators) the value of irrational numbers as they arise from problem situationsTX TEKS 8.1Dexpress numbers in scientific notation, including negative exponents, in appropriate problem situations.TX TEKS 8.2Aselect appropriate operations to solve problems involving rational numbers and justify the selectionsTX TEKS 8.2Buse appropriate operations to solve problems involving rational numbers in problem situationsTX TEKS 8.2Cevaluate a solution for reasonablenessTX TEKS 8.2Duse multiplication by a constant factor (unit rate) to represent proportional relationships.TX TEKS 8.3Acompare and contrast proportional and non-proportional linear relationshipsTX TEKS 8.3Bestimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates.TX TEKS 8.4The student makes connections among various representations of a numerical relationship.TX TEKS 8.5Apredict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equationsTX TEKS 8.5Bfind and evaluate an algebraic expression to determine any term in an arithmetic sequence (with a constant rate of change).TX TEKS 8.6Bgraph dilations, reflections, and translations on a coordinate plane.TX TEKS 8.7Adraw three-dimensional figures from different perspectivesTX TEKS 8.7Buse geometric concepts and properties to solve problems in fields such as art and architectureTX TEKS 8.7Dlocate and name points on a coordinate plane using ordered pairs of rational numbers.TX TEKS 8.8Afind lateral and total surface area of prisms, pyramids, and cylinders using concrete models and nets (two-dimensional models)TX TEKS 8.8Bconnect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objectsTX TEKS 8.8Cestimate measurements and use formulas to solve application problems involving lateral and total surface area and volume.TX TEKS 8.9Ause the Pythagorean Theorem to solve real-life problemsTX TEKS 8.9Buse proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements.TX TEKS 8.11Afind the probabilities of dependent and independent eventsTX TEKS 8.11Buse theoretical probabilities and experimental results to make predictions and decisionsTX TEKS 8.11Cselect and use different models to simulate an event.TX TEKS 8.12Aselect the appropriate measure of central tendency or range to describe a set of data and justify the choice for a particular situationTX TEKS 8.12Bdraw conclusions and make predictions by analyzing trends in scatterplotsTX TEKS 8.12Cselect and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line graphs, stem and leaf plots, circle graphs, bar graphs, box and whisker plots, histograms, and Venn diagrams, with and without the use of technology.TX TEKS 8.13Aevaluate methods of sampling to determine validity of an inference made from a set of dataTX TEKS 8.13Brecognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis.TX TEKS 8.14Aidentify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topicsTX TEKS 8.14Buse a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonablenessTX TEKS 8.14Cselect or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problemTX TEKS 8.14Dselect tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.TX TEKS 8.15Acommunicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical modelsTX TEKS 8.15Bevaluate the effectiveness of different representations to communicate ideasTX TEKS 8.16Amake conjectures from patterns or sets of examples and nonexamplesTX TEKS 8.16Bvalidate his/her conclusions using mathematical properties and relationshipsTX TEKS 8.7Cuse pictures or models to demonstrate the Pythagorean Theorem.8UT PA 1.1.1Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator.8UT PA 1.1.2Add, subtract, multiply, and divide integers.8UT PA 1.1.3Check the reasonableness of results using estimation.8UT PA 1.1.4Justify the steps used in solving problems using correct notation.8UT PA 1.2Represent rational numbers in a variety of ways.8UT PA 1.2.1Recognize and create equivalent forms of a rational number.8UT PA 1.2.2Find an approximate location of a rational number on a number line.8UT PA 1.2.3Find a rational number between any two rational numbers8UT PA 1.2.5Represent very large and very small numbers using scientific notation.8UT PA 1.3.1Compare and order rational numbers.8UT PA 1.3.3Recognize and use the special multiplication properties of zero.8UT PA 1.3.5Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares.8UT PA 1.3.6Add or multiply numbers using the Commutative and Associative Properties of Addition or Multiplication8UT PA 1.4Solve problems involving rational numbers using addition, subtraction, multiplication, and division.8UT PA 1.4.1Recognize absolute value of a rational number as the value of its distance from zero. 28UT PA 1.4.2Evaluate numerical and algebraic expressions containing absolute value.8UT PA 1.4.3Compute with percents, including those greater than 100% and less than 1%.8UT PA 1.4.4Solve problems using simple proportions.8UT PA 2.1.1Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules.8UT PA 2.1.2Describe simple patterns using a mathematical rule or algebraic expression.8UT PA 2.1.3Create and extend simple numeric and visual patterns, including those that have a recursive nature (e.g., Fibonacci numbers, triangular and square numbers).8UT PA 2.2Represent, solve, and analyze mathematical situations and properties using algebraic symbols.8UT PA 2.2.1Evaluate algebraic expressions when given values for the variable(s).8UT PA 2.2.2Identify the horizontal and vertical intercepts of a linear relation from a graph or table.8UT PA 2.2.3Determine the slope of a linear relation from a graph or ordered pairs.8UT PA 2.2.4Solve one- and two-step single-variable equations and inequalities.8UT PA 2.3Represent quantitative relationships using mathematical models and symbols.8UT PA 2.3.1Create a table, graph, or algebraic expression to represent the relationship between two variables.8UT PA 2.3.2Graph ordered pairs of rational numbers on a rectangular coordinate system.8UT PA 2.3.3Identify approximate rational coordinates when given the graph of a point on a rectangular coordinate system.8UT PA 2.3.4Model real-world problems using various representations, such as graphs, tables, equations, manipulatives, and pictures.8UT PA 3.1Analyze characteristics and properties of two- and three-dimensional shapes and develop mathematical arguments about geometric relationships.8UT PA 3.1.1Identify congruent and similar shapes.8UT PA 3.1.2Find missing lengths of similar plane figures using proportions.8UT PA 3.1.3Classify two- and three-dimensional objects according to the defining characteristics.8UT PA 3.2.1Create and interpret scale drawings.8UT PA 3.2.2Represent and explain numerical and algebraic relationships using geometric models, e.g., rectangular models for multiplication.8UT PA 3.3Apply transformations and use symmetry to analyze mathematical situations.8UT PA 3.3.1Reflect a geometric shape across a line in a coordinate plane and identify the coordinates of the vertices.8UT PA 3.3.2Translate a geometric shape a given distance on a coordinate plane and identify the vertices.8UT PA 4.1Understand measurable attributes of objects and the units, systems, and processes of measurement.8UT PA 4.1.1Estimate measurable quantities in both standard and metric units, e.g., a vase holds a little less than a quart or about a liter; a 10K run is about 6 miles.8UT PA 4.1.2Convert from one unit of measure to an equivalent unit of measure using a given conversion factor, e.g., 60 miles/hour � 1 hour/3600 sec � 5280 ft/1mile = 88 ft/sec.8UT PA 4.1.3Measure angles, perimeter, area, and volume using the correct size and type of units.8UT PA 4.2Determine measurements using appropriate techniques, tools, and formulas.8UT PA 4.2.1Determine an approximate distance between two points using map scales.8UT PA 4.2.2Solve problems involving scale factors using ratios and proportions.8UT PA 4.2.3Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet.8UT PA 4.2.4Measure inaccessible heights or distances using similar triangles8UT PA 4.2.5Calculate surface area and volume of right prisms and cylinders using appropriate units.8UT PA 4.2.6Develop formulas for calculating the circumference of circles and the areas of triangles, parallelograms, and trapezoids.8UT PA 4.2.7Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas.8UT PA 5.1Formulate and answer questions by collecting, organizing, and analyzing data.8UT PA 5.1.1Conduct a survey or experiment to collect data.8UT PA 5.1.2Organize and display data using graphical representations such as line plots, bar graphs, stem-and-leaf plots, histograms, scatter plots, circle graphs, box plots (box-and-whisker plots), and pictographs.8UT PA 5.1.3Make conjectures from a graphical representation.8UT PA 5.1.4Calculate the mean, median, mode, and range for a data set.8UT PA 5.1.5Choose a measure of central tendency most appropriate to analyze a particular set of data.8UT PA 5.1.6Describe how an individual data point may affect the measures of central tendency.8UT PA 5.1.7Interpret and describe the spread of a set of data, e.g., range, box plot (box-and-whisker).8UT PA 5.1.8Make predictions and describe the limitations of the predictions when using data samples.8UT PA 5.1.9Evaluate reported inferences or predictions based on a data set.8UT PA 5.2Apply basic concepts of probability.8UT PA 5.2.1Conduct experiments to approximate the probability of simple events.8UT PA 5.2.2Recognize that results of an experiment more closely approximate the actual or theoretical probability of an event as the number of trials increases.8UT PA 5.2.3Derive the probability of an event mathematically, e.g., building a table or tree diagram, creating an area model, making a list, or using the basic counting principle.8UT PA 5.2.4Represent the probability of an event as a fraction, percent, ratio, or decimal.8UT PA 5.2.6Recognize that the sum of the probability of an event and the probability of its complement is equal to one.UT PA 1.2.3Find a rational number between any two rational numbers