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ThisWorkbook=lx 7 as a statement that 3 is located to the right of 7 on a number line oriented from left to right.AR includes irrationals.`AR.912.SEI.AI.2.4 (SEI.2.AI.4) Solve and graph simple absolute value equations and inequalitiesAR.912.TF.AIII.5.2 (TF.5.AIII.2) Develop and use, with and without appropriate technology, the Law of Sines and the Law of Cosines to solve oblique trianglesSRT.11CC.912.G.SRT.11 (+) Apply trigonometry to general triangles. Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces).C.1^CC.912.G.C.1 Understand and apply theorems about circles. Prove that all circles are similar.AR.912.R.G.4.5 (R.4.G.5) Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circlesAR.912.CGT.G.5.6 (CGT.5.G.6) Write, in standard form, the equation of a circle given a graph on a coordinate plane or the center and radius of a circleC.2AR.912.DA.TDM.5.1 (DA.5.TDM.1) Read, interpret, and analyze graphical representations of data used in various contexts (e.g., science reasoning, newspaper graphs)aAR.912.DA.TDM.5.3 (DA.5.TDM.3) Collect, analyze, and compare data sets using fivenumber summaryAR.912.S.TFM.4.2 (S.4.TFM.2) Calculate and interpret statistical problems using measures of central tendencies and graphs:
 histograms,
 normal curverAR.912.S.TFM.4.3 (S.4.TFM.3) Analyze and compare data sets using fivenumber summary, graphically and numericallyID.2CC.912.S.ID.2 Summarize, represent, and interpret data on a single count or measurement variable. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.* AR.912.DS.S.5.2 (DS.1.S.2) Compute and use mean, mode, weighted mean, geometric mean, harmonic mean, range, quartiles, variance, and standard deviation{AR.912.DAP.AII.6.5 (DAP.6.AII.5) Compute and explain measures of spread (range, percentiles, variance, standard deviation)tAR.912.DIP.AI.5.4 (DIP.5.AI.4) Determine the effects of changes in the data set on the measures of central tendencyAR.912.PS.TM.4.2 (PS.4.TM.2) Describe and summarize data numerically using central tendency variation, position statistics, and distributionsAR.912.DA.TDM.5.5 (DA.5.TDM.5) Determine and interpret the measures of spread of a data set (e.g., standard deviation, range, percentiles, variance)lAR.912.S.TFM.4.4 (S.4.TFM.4) Investigate and analyze the characteristics of normal and skewed distributionsAR.912.S.TFM.4.5 (S.4.TFM.5) Determine and interpret measures of variation of a data set, with or without technology:
 standard deviation,
 range,
 percentiles,
 varianceID.3CC.912.S.ID.3 Summarize, represent, and interpret data on a single count or measurement variable. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).* AR.912.DA.S.4.1 (DA.4.S.1) Summarize distributions of univariate data by determining and interpreting measures of center, spread, position, boxplot, and effects of changing units on summary measures.FAR standard DS.2.S.1 should be added to list, but not found in system.nAR.912.DA.TDM.5.4 (DA.5.TDM.4) Investigate and analyze the characteristics of normal and skewed distributionsID.4NO. 3.6.1 (remove division), No. 3.4.3 (bullets 1 and 3); No. 3.6.1 (remove division), No. 3.3. (just multiplication) Grade 3 added no.3.3.3 and commentedAR had only up to 2digits times 1digit.dAR.912.ELF.AII.5.7 (ELF.5.AII.7) Use properties of logarithms to manipulate logarithmic expressionsLE.1CC.912.F.LE.1 Construct and compare linear, quadratic, and exponential models and solve problems. Distinguish between situations that can be modeled with linear functions and with exponential functions.*PAR.912.EF.TM.2.3 (EF.2.TM.3) Compare and contrast linear and exponential models8AR.912.EF.TM.2.2 (EF.2.TM.2) Compare exponential modelsLE.1aCC.912.F.LE.1a Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.*LE.1b~CC.912.F.LE.1b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.*vAR.912.LF.TM.1.1 (LF.1.TM.1) Identify a linear relationship represented by a table, by a graph, and by symbolic formsLE.1cCC.912.F.LE.1c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative< to another.*vAR.912.EF.TM.2.1 (EF.2.TM.1) Identify exponential growth or decay by creating tables, graphs, and mathematical modelsLE.2CC.8.EE.8 Analyze and solve linear equations and pairs of simultaneous linear equations. Analyze and solve pairs of simultaneous linear equations.0Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. CC.K12.MP.4 Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, twoway tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. The standards for mathematical practice are an integral part of the Common Core State Standards for grades K8. Although there were no Arkansas mathematics standards matched to the eight Standards of Mathematical Practice, it is safe to say that many of these practices are already being used to facilitate learning in the mathematics classroom at all grade levels (K12). Teachers are strongly encouraged to make every effort to incorporate all eight of these practice standards in their regular classroom instruction. As you review the document that analyzes the Common Core State Standards, be aware of places where these very important standards for mathematical practice can be combined with the teaching of mathematical content. !No matches in Arkansas FrameworksSSE.1a]CC.912.S.ID.6c Fit a linear function for a scatter plot that suggests a linear association.*ID.7CC.912.S.ID.7 Interpret linear models. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.*ID.8~CC.912.S.ID.8 Interpret linear models. Compute (using technology) and interpret the correlation coefficient of a linear fit.*ZAR.912.DA.S.5.4 (DA.5.S.4) Identify possible correlations between variables in a data setbAR.912.SI.S.11.4 (SI.11.S.4) Calculate and interpret the correlation coefficient of a set of dataAR.912.DAP.AII.6.2 (DAP.6.AII.2) Interpret and use the correlation coefficient to assess the strength of the linear relationship between two variablesID.9WCC.912.S.ID.9 Interpret linear models. Distinguish between correlation and causation.*AR.912.PS.AC.1.3 (PS.1.AC.3) Compute and display theoretical and experimental probability including the use of Venn diagrams:
 simple,
 complementary,
 compound (mutually exclusive, inclusive, independent and dependent events)FAR.912.ST.TFM.2.1 (ST.2.TFM.1) Define sets using setbuilder notation~AR.912.CT.TFM.3.5 (CT.3.TFM.5) Calculate probabilities of mutually exclusive events, independent events, and dependent eventsxAR.912.ST.TFM.2.3 (ST.2.TFM.3) Perform set operations such as union and intersection, complement, and Cartesian productCP.22CC.912.S.CP.2 Understand independence and conditional probability and use them to interpret data. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.*CP.3CC.912.A.APR.3 Understand the relationship between zeros and factors of polynomials. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.AR.912.DA.S.5.6 (DA.5.S.6) Use data from samples to make inferences about a population and determine whether claims are reasonable or unreasonablelAR.912.DIP.AI.5.12 (DIP.5.AI.12) *Recognize when arguments based on data confuse correlation with causationIC.1CC.912.S.IC.1 Understand and evaluate random processes underlying statistical experiments. Understand statistics as a process for making inferences about population parameters based on a random sample from that population.*AR.912.DIP.AI.5.11 (DIP.5.AI.11) *Explain how sampling methods, bias, and phrasing of questions in data collection impact the conclusionsMD.3CC.912.S.MD.3 (+) Calculate expected values and use them to solve problems. Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiplechoice test where each question has four choices, and find the expected grade under various grading schemes.*MD.4 eCC.912.S.CP.5 Understand independence and conditional probability and use them to interpret data. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.*CP.6CC.912.G.CO.11 Prove geometric theorems. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.AR.912.CGT.G.5.5 (CGT.5.G.5) Determine, given a set of points, the type of figure based on its properties (parallelogram, isosceles triangle, trapezoid)CO.12CC.912.G.CO.12 Make geometric constructions. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.CO.13ECC.8.SP.1 Investigate patterns of association in bivariate data. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.VCC.8.SP.2 Investigate patterns of association in bivariate data. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.CC.8.SP.3 Investigate patterns of association in bivariate data. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.CC.8.SP.4 Investigate patterns of association in bivariate data. Understand that patterns of as< sociation can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?AR.912.DIP.AI.5 Data Interpretation and Probability: Content Standard 5. Students will compare various methods of reporting data to make inferences or predictions.NRN.1CC.912.N.RN.1 Extend the properties of exponents to rational exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want [5^(1/3)]^3 = 5^[(1/3) x 3] to hold, so [5^(1/3)]^3 must equal 5.AR.912.PRF.AII.4.7 (PRF.4.AII.7) Establish the relationship between radical expressions and expressions containing rational exponentsyAR.912.PRF.AII.4.8 (PRF.4.AII.8) Simplify variable expressions containing rational exponents using the laws of exponentsAR.912.QEF.AII.3.1 (QEF.3.AII.1) Perform computations with radicals:
 simplify radicals with different indices,
 add, subtract, multiply and divide radicals,
 rationalize denominators,
 solve equations that contain radicals or radical expressionsAR.912.PC.PCT.8.1 (PC.8.PCT.1) Convert polar coordinates to rectangular coordinates and rectangular coordinates to polar coordinatesCC.912.F.TF.6 (+) Model periodic phenomena with trigonometric functions. Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.TF.7CC.912.F.TF.7 (+) Model periodic phenomena with trigonometric functions. Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.*CC.912.G.CO.13 Make geometric constructions. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.SRT.1AR.912.QEF.AII.3.5 (QEF.3.AII.5) Develop and analyze, with and without appropriate technology, quadratic relations:
 graph a parabolic relationship when given its equation
 write an equation when given its roots (zeros or solutions) or graph
 determine the nature of the solutions graphically and by evaluating the discriminan
 determine the maximum or minimum values and the axis of symmetry both graphically and algebraicallyAR.912.F.TFM.5.2 (F.5.TFM.2) Apply properties of logarithms to convert and solve logarithmic (common and natural) and exponential equationsSSE.3a_CC.912.A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines.*SSE.3bCC.912.A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.*SSE.3cCC.912.A.SSE.3c Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15^t can be rewritten as [1.15^(1/12)]^(12t) H" 1.012^(12t) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.*SSE.4CC.912.A.SSE.4 Write expressions in equivalent forms to solve problems. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.*AR.912.SS.PCT.4.2 (SS.4.PCT.2) Define and discriminate between arithmetic and geometric sequences and series and use appropriate technology when neededAR.912.SS.PCT.4.3 (SS.4.PCT.3) Solve, with and without appropriate technology, problems involving the sum (including Sigma notation) of finite and infinite sequences and seriesAR.912.F.TFM.5.3 (F.5.TFM.3) Solve realworld problems involving:
 compound interest,
 amortization,
 annuities,
 appreciation,
 depreciation,
 investmentsAPR.1CC.912.A.APR.1 Perform arithmetic operations on polynomials. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.AR.912.LA.AI.1.5 (LA.1.AI.5) Perform polynomial operations (addition, subtraction, multiplication) with and without manipulativesAR.912.RF.AII.1.2 (RF.1.AII.2) Evaluate, add, subtract, multiply, and divide functions and give appropriate domain and range restrictionsAPR.2CC.912.A.APR.2 Understand the relationship between zeros and factors of polynomial. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x a is p(a), so p(a) = 0 if and only if (x a) is a factor of p(x).AR.912.PRF.PCT.1.2 (PRF.1.PCT.2) Solve, with and without appropriate technology, polynomial equations utilizing techniques such as Descartes' Rule of Signs, upper and lower bounds, Intermediate Value Theorem and Rational Root TheoremAPR.3oKindergarten Common Core State Standards Comparison with Arkansas Student Learning Expectations for MathematicsjGrade 1 Common Core State Standards Comparison with Arkansas Student Learning Expectations for MathematicsjGrade 2 Common Core State Standards Comparison with Arkansas Student Learning Expectations for MathematicsjGrade 3 Common Core State Standards Comparison with Arkansas Student Learning Expectations for MathematicsjGrade 4 Common Core State Standards Comparison with Arkansas Student Learning Expectations for MathematicsjGrade 5 Common Core State Standards Comparison with Arkansas Student Learning Expectations for MathematicsjGrade 6 Common Core State Standards Comparison with Arkansas Student Learning Expectations for MathematicsjGrade 7 Common Core State Standards Comparison with Arkansas Student Learning Expectations for MathematicsjGrade 8 Common Core State Standards Comparison with Arkansas Student Learning Expectations for MathematicsnHigh School Common Core State Standards Comparison with Arkansas Student Learning Expectations for MathematicsAR.2.G.8.2 (G.8.2.2)Characteristics and PropertiesThree Dimensional:Match threedimensional objects to their twodimensional faces ,CCSS Coding Chart for MathematicsGrades K8CCSS Coding Chart for MathematicsHigh SchoolAR.912.ELF.AIII.3.3 (ELF.3.AIII.3) Solve, with and without appropriate technology, equations and real world problems involving exponential and logarithmic expressions graphically, algebraically and numericallyREI.12ZCC.912.A.REI.12 Represent and solve equations and inequalities graphically. Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding halfplanes.AR.912.LSM.TFM.1.3 (LSM.1.TFM.3) Graph systems of linear inequalities with multiple constraints and identify vertices of the feasible regionIF.1JAR.912.PI.CM.3.4 (PI.3.CM.4) Create constraints to validate cell entries.IF.3Mathematically proficient students check their answers to problems using a different method< , and they continually ask themselves, Does this make sense? They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. CC.K12.MP.1 Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. `Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. CC.K12.MP.3 Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and if there is a flaw in an argument explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. CC.K12.MP.5 Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. AR.912.ELF.AII.5.3 (ELF.5.AII.3) Identify the effect that changes in the parameters of the base have on the graph of the exponential functionAR.912.EF.TDM.4.3 (EF.4.TDM.3) Use the change of base formula to simplify and evaluate logarithmic expressions, using technologyIF.9YCC.912.F.IF.9 Analyze functions using different representations. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.AR.912.LF.TM.1.3 (LF.1.TM.3) Make inferences and predictions using:
 recursion on the table,
 inspection on the graph,
 algebraic manipulation on the modelAR.912.EF.TM.2.4 (EF.2.TM.4) Make inferences and predictions using:
 recursion on the table,
 inspection of the graph,
 algebraic manipulation on the modelAR.912.MM.TM.3.3 (MM.3.TM.3) Make inferences and predictions using:
 recursion on the table,
 inspection of the graph, 
 algebraic manipulation on the modelAR.912.PS.TM.4.4 (PS.4.TM.4) Make inferences and predictions using:
 recursion on the table,
 inspection of the graph,
 algebraic manipulation on the modelBF.1CC.912.F.BF.1 Build a function that models a relationship between two quantities. Write a function that describes a relationship between two quantities.* AR not descriptiveuAR.912.LA.AI.1.1 (LA.1.AI.1) Evaluate algebraic expressions, including radicals, by applying the order of operationsCC.8.EE.1 Work with radicals and integer exponents. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 3^( 5) = 3^( 3) = 1/(3^3) = 1/27.OAR.912.LA.AI.1.3 (LA.1.AI.3) Apply the laws of (integral) exponents and roots.$AR not explicit; NO.1.7.6 soft matchsAR.8.NO.3.4 (NO.3.8.4) Application of Computation: Apply factorization to find LCM and GCF of algebraic expressions7CC.8.EE.2 Work with radicals and integer exponents. Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that "2 is irrational.AR does not address "solutions"CC.8.EE.3 Work with radicals and integer exponents. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 10^8 and the population of the world as 7 10^9, and dete< rmine that the world population is more than 20 times larger.sAR.912.LA.AI.1.4 (LA.1.AI.4) *Solve problems involving scientific notation, including multiplication and division.AR.8.NO.1.1 (NO.1.8.1) Rational Numbers: Read, write, compare and solve problems, with and without appropriate technology, including numbers less than 1 in scientific notationAR.8.NO.1.2 (NO.1.8.2) Rational Numbers: Convert between scientific notation and standard notation, including numbers from zero to one.CC.8.EE.4 Work with radicals and integer exponents. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.9AR does NOT address "choose units of appropriate size..."CC.8.EE.5 Understand the connections between proportional relationships, lines, and linear equations. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distancetime graph to a distancetime equation to determine which of two moving objects has greater speed.AR.8.A.4.3 (A.4.8.3) Patterns, Relations and Functions: Interpret and represent a two operation function as an algebraic equationAR.912.LF.AI.3.9 (LF.3.AI.9) Describe the effects of parameter changes, slope and/or yintercept, on graphs of linear functions and vice versavCC.8.EE.6 Understand the connections between proportional relationships, lines, and linear equations. Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane; derive the equation y =mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.}AR.912.LF.AI.3.6 (LF.3.AI.6) Calculate the slope given:
 two points,
 the graph of a line,
 the equation of a linevAR.912.LF.AI.3.7 (LF.3.AI.7) Determine by using slope whether a pair of lines are parallel, perpendicular, or neitherAR.912.TF.PCT.5.9 (TF.5.PCT.9) Identify and graph, with and without appropriate technology, the inverse of trigonometric functions including the restrictions on the domainBF.5
CC.912.S.CP.6 Use the rules of probability to compute probabilities of compound events in a uniform probability model. Find the conditional probability of A given B as the fraction of B s outcomes that also belong to A, and interpret the answer in terms of the model.*CP.7CC.912.S.CP.7 Use the rules of probability to compute probabilities of compound events in a uniform probability model. Apply the Addition Rule, P(A or B) = P(A) + P(B) P(A and B), and interpret the answer in terms of the model.*CC.912.F.IF.1 Understand the concept of a function and use function notation. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).AR.912.LF.AI.3.3 (LF.3.AI.3) Know and/or use function notation, including evaluating functions for given values in their domainAR.912.RF.AII.1.1 (RF.1.AII.1) Determine, with or without technology, the domain and range of a relation defined by a graph, a table of values, or a symbolic equation including those with restricted domains and whether a relation is a functionIF.2CC.912.F.IF.2 Understand the concept of a function and use function notation. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.InterpretationKAR.912.PS.CM.1.4 (PS.1.CM.4) Write an algorithm from a mathematical model."Look at transitions and algebra I.BF.1bCC.912.F.BF.1b Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. BF.1cCC.912.F.BF.1c (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.BF.2CC.912.F.BF.2 Build a function that models a relationship between two quantities. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*AR.912.SS.AIII.4.1 (SS.4.AIII.1) Develop, with and without appropriate technology, a representation of sequences recursively and explicitlyAR.912.SS.AIII.4.2 (SS.4.AIII.2) Define and discriminate, with and without appropriate technology, between arithmetic and geometric sequences and seriesAR.912.SS.AIII.4.5 (SS.4.AIII.5) Use, with and without appropriate technology, sequences and series to solve real world problemsBF.3CC.912.F.BF.3 Build new functions from existing functions. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.AR.912.NF.AC.4.6 (NF.4.AC.6) Recognize function families including vertical shifts, horizontal shifts and reflections over the xaxisAR.912.EF.TDM.4.2 (EF.4.TDM.2) Apply properties of logarithms to convert and solve logarithmic (common and natural) and exponential equationsBF.4a"CC.912.N.Q.1 Reason quantitatively and use units to solve problems. Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.*AR.912.DIP.AI.5.5 (DIP.5.AI.5) Use two or more graphs (i.e., boxand whisker, histograms, scatter plots) to compare data setspAR.912.DIP.AI.5.6 (DIP.5.AI.6) Construct and interpret a cumulative frequency histogram in real life situationsAR.912.DIP.AI.5.1 (DIP.5.AI.1) Construct and use scatter plots and line of best fit to make inferences in real life situationswAR.912.SEI.AI.2.5 (SEI.2.AI.5) Solve real world problems that involve a combination of rates, proportions and percentsAR.912.SEI.AI.2.6 (SEI.2.AI.6) Solve problems involving direct variation and indirect (inverse) variation to model rates of changeAR.912.PS.AC.1.5 (PS.1.AC.5) Interpret and evaluate, with and without appropriate technology, graphical and tabular data displays for:
 consistency with the data,
 appropriateness of type of graph or data display,
 scale,
 overall messageAR.912.ME.TDM.3.1 (ME.3.TDM.1) Solve problems using dimensional analysis (factorlabel method) (e.g., construction, medical, metric, standard to metric, rate conversions)Q.2CC.912.N.Q.2 Reason quantitatively and use units to solve problems. Define appropriate quantities for the purpose of descriptive modeling.*CC.K12.MP.6 Attend to precision. Mathematically proficient students try to communicate< precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.0CC.K12.MP.7 Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 8 equals the well remembered 7 5 + 7 3, in preparation for learning about the distributive property. In the expression x^2 + 9x + 14, older students can see the 14 as 2 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 3(x y)^2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. CC.912.S.ID.4 Summarize, represent, and interpret data on a single count or measurement variable. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.*}AR.912.SI.S.10.1 (SI.10.S.1) Explore the characteristics and applications of the normal distribution and standardized scores`AR.912.DAP.AII.6.6 (DAP.6.AII.6) Describe the characteristics of a Gaussian normal distributionID.5gCC.912.S.ID.5 Summarize, represent, and interpret data on two categorical and quantitative variables. Summarize categorical data for two categories in twoway frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.*AR.912.PS.AC.1.2 (PS.1.AC.2) Conduct and interpret simple probability experiments using:
 manipulatives (spinners, dice, cards, coins),
 simulations (using random number tables, graphing calculators, or computer software)ID.6aCC.912.S.ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.*AR.912.T.G.2.2 (T.2.G.2) Investigate the measures of segments to determine the existence of triangles (triangle inequality theorem)AR.6.M.13.6 (M.13.6.6) Applications: Use estimation to check the reasonableness of measurements obtained from use of various instruments (including angle measures)CC.7.G.3 Draw, construct, and describe geometrical figures and describe the relationships between them. Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. ,AR does not have a SLE about slicing shapes.AR.8.G.8.2 (G.8.8.2) Characteristics of Geometric Shapes: Make, with and without appropriate technology, and test conjectures about characteristics and properties between twodimensional figures and threedimensional objectsAR.8.G.8.1 (G.8.8.1) Characteristics of Geometric Shapes: Form generalizations and validate conclusions about properties of geometric shapesCC.K.CC.2 Know number names and the count sequence. Count forward beginning from a given number within the known sequence (instead of having to begin at 1).gAR.912.TF.AIII.5.1 (TF.5.AIII.1) Define sine, cosine, and tangent as ratios of sides of right triangleSRT.7CC.912.G.SRT.7 Define trigonometric ratios and solve problems involving right triangles. Explain and use the relationship between the sine and cosine of complementary angles.AR.912.T.G.2.7 (T.2.G.7) Use similarity of right triangles to express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given lengths of sidesSRT.8CC.912.G.SRT.8 Define trigonometric ratios and solve problems involving right triangles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.vAR.912.T.G.2.5 (T.2.G.5) Use the special right triangle relationships (306090 and 454590) to solve problemsAR.912.SEI.AI.2.7 (SEI.2.AI.7) Use coordinate geometry to represent and/or solve problems (midpoint, length of a line segment, and Pythagorean Theorem)AR.912.SEI.AC.3.4 (SEI.3.AC.4) Use, with and without appropriate technology, coordinate geometry to represent and solve problems including midpoint, length of a line segment and Pythagorean TheoremSRT.9CC.912.G.SRT.9 (+) Apply trigonometry to general triangles. Derive the formula A = (1/2)ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.AR.912.OT.PCT.6.3 (OT.6.PCT.3) Determine the area of an oblique triangle by using an appropriate formula and appropriate technology when neededAR.912.TF.AIII.5.3 (TF.5.AIII.3) Determine (by using an appropriate formula), with and without technology, the area of an oblique triangleSRT.10CC.912.G.SRT.10 (+) Apply trigonometry to general triangles. Prove the Laws of Sines and Cosines and use them to solve problems.AR.912.ME.TDM.3.3 (ME.3.TDM.3) Use laws of sine and cosine to determine lengths of sides, measures of angles, and area of triangles for real world problems (e.g., Heron's formula)AR.912.OT.PCT.6.1 (OT.6.PCT.1) Develop and use the Law of Sines and the Law of Cosines to solve oblique triangles and use appropriate technology when neededAR.912.OT.PCT.6.2 (OT.6.PCT.2) Solve real world problems applying the Law of Sines and the Law of Cosines and appropriate technology when neededCC.912.G.CO.4 Experiment with transformations in the plane. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.CO.5/CC.912.G.CO.5 Experiment with transformations in the plane. Given a geometric figure and a rotation, reflection, or translation, draw the transform< ed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.CO.64CC.912.G.CO.6 Understand congruence in terms of rigid motions. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.CO.7CC.912.G.CO.7 Understand congruence in terms of rigid motions. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.AR.912.T.G.2.1 (T.2.G.1) Apply congruence (SSS ...) and similarity (AA ...) correspondences and properties of figures to find missing parts of geometric figures and provide logical justificationCO.8CC.912.G.CO.8 Understand congruence in terms of rigid motions. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.eAR.912.LG.G.1.3 (LG.1.G.3) Describe relationships derived from geometric figures or figural patternsCO.9lCC.912.G.CO.9 Prove geometric theorems. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment s endpoints.AR.8.G.8.3 (G.8.8.3) Characteristics of Geometric Shapes: Determine appropriate application of geometric ideas and relationships, such as congruence, similarity, and the Pythagorean theorem, with and without appropriate technologyCC.8.G.7 Understand and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions.CC.8.G.8 Understand and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.AR.8.M.13.4 (M.13.8.4) Applications: Find the distance between two points on a coordinate plane using with the Pythagorean theoremCC.8.G.9 Solve realworld and mathematical problems involving volume of cylinders, cones and spheres. Know the formulas for the volume of cones, cylinders, and spheres and use them to solve realworld and mathematical problems.+AR.912.M.G.3.2 (M.3.G.2) Apply, using appropriate units, appropriate formulas (area, perimeter, surface area, volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders, spheres as well as composite figures, expressing solutions in both exact and approximate formsCC.2.MD.6 Relate addition and subtraction to length. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, & , and represent wholenumber sums and differences within 100 on a number line diagram. (CC.2.MD.9 Represent and interpret data. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in wholenumber units.CC.3.MD.7 Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Relate area to the operations of multiplication and addition.CC.3.MD.7d Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve real world problems. CC.5.NF.5 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret multiplication as scaling (resizing) by:
 a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
 b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (na) / (nb) to the effect of multiplying a/b by 1.CC.912.F.IF.7d (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.* IF.7eCC.912.F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.*AR.912.ELF.AIII.3.5 (ELF.3.AIII.5) Draw and analyze, with and without appropriate technology, graphs of logarithmic and exponential functionsAR.912.EF.TDM.4.1 (EF.4.TDM.1) Draw and recognize the graphs of logarithmic and exponential functions, with and without appropriate technologyAR.912.ELF.PCT.2.5 (ELF.2.PCT.5) Draw and analyze, with and without appropriate technology, graphs of logarithmic and exponential functionAR.912.TF.PCT.5.7 (TF.5.PCT.7) Graph the six trigonometric functions, identify domain, range, intercepts, period, amplitude, and asymptotes as applicable and use symmetry to determine whether the function is even or odd through appropriate technology when neededAR.912.TF.PCT.5.8 (TF.5.PCT.8) Determine, with and without appropriate technology, the amplitude, period, phase shift, and vertical shift, and sketch the graph of transformations of the trigonometric functionsIF.8CC.912.F.IF.8 Analyze functions using different representations. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. yAR.912.PS.CM.1.2 (PS.1.CM.2) Write an algorithm to solve mathematical problems using formulas, equations, and functions.5Look at Algebra II/III/PCT...multiple representationsAR.912.ELF.PCT.2.2 (ELF.2.PCT.2) Develop and apply the laws of logarithms and the changeofbase formula to simplify and evaluate expressionsIF.8aCC.912.F.IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. AR.912.DAP.AII.6.1 (DAP.6.AII.1) Find regression line for scatter plot, using appropriate technology, and interpret the correlation coefficientcAR.912.DAP.AII.6.3 (DAP.6.AII.3) Find the quadratic curve of best fit using appropriate technologyoAR.912.DIP.AI.5.7 (DIP.5.AI.7) Recognize linear functions and nonlinear functions by using a table or a graphuAR.912.DAP.AII.6.4 (DAP.6.AII.4) Identify strengths and weaknesses of using regression equations to approximate dataID.6b_CC.912.S.ID.6b Informally assess the fit of a function by plotting and analyzing residuals.* AR.912.DA.S.5.5 (DA.5.S.5) Develop, use, and explain application and limitations of linear models and line of best fit (linear regression) in a variety of contextsID.6cCC.6.NS.6b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, th< e locations of the points are related by reflections across one or both axes. AR.7.G.9.2 (G.9.7.2) Symmetry and Transformations: Perform translations and reflections of twodimensional figures using a variety of methods (paper folding, tracing, graph paper)S3 collectively, 2 individually. g.9.7.2 w/o translations. AR includes translations.AR.8.G.9.2 (G.9.8.2) Symmetry and Transformations: Draw the results of translations and reflections about the x and yaxis and rotations of objects about the origin6cCC.6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.Collectively a 3.CC.6.NS.7 Apply and extend previous understandings of numbers to the system of rational numbers. Understand ordering and absolute value of rational numbers. 83 collectively, 2 individually. no.1.8.4 not irrationalsAR.7.NO.3.5 (NO.3.7.5) Application of Computation: Represent and solve problem situations that can be modeled by and solved using concepts of absolute value, exponents and square roots (for perfect squares) with and without appropriate technologyfAR.6.NO.1.5 (NO.1.6.5) Rational Numbers: Recognize and identify perfect squares and their square rootsCC.912.F.BF.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2(x^3) or f(x) = (x+1)/(x1) for x `" 1 (x not equal to 1). AR.912.RF.AII.1.3 (RF.1.AII.3) Determine the inverse of a function (Graph, with and without appropriate technology, functions and their inverses)BF.4dlCC.912.F.BF.4d (+) Produce an invertible function from a noninvertible function by restricting the domain.uAR.912.MM.TM.3.2 (MM.3.TM.2) Apply, with appropriate technology, matrices to real world problems and decision makingAR.912.MA.TDM.1.1 (MA.1.TDM.1) Collect and interpret data in a matrix and perform operations to solve realworld problems, with and without technologyVM.7CC.912.N.VM.7 (+) Perform operations on matrices and use matrices in applications. Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. gAR.912.DIP.AI.5.2 (DIP.5.AI.2) Use simple matrices in addition, subtraction, and scalar multiplicationVM.8CC.912.N.VM.8 (+) Perform operations on matrices and use matrices in applications. Add, subtract, and multiply matrices of appropriate dimensions.VM.9CC.912.N.VM.9 (+) Perform operations on matrices and use matrices in applications. Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. VM.10PCC.912.N.VM.10 (+) Perform operations on matrices and use matrices in applications. Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. tAR.912.MA.TDM.1.3 (MA.1.TDM.3) Find and use the inverse of a matrix to solve realworld problems (e.g., cryptology)VM.11CC.912.N.VM.11 (+) Perform operations on matrices and use matrices in applications. Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.VM.12CC.912.N.VM.12 (+) Perform operations on matrices and use matrices in applications. Work with 2 X 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. SSE.1eCC.912.F.TF.3 (+) Extend the domain of trigonometric functions using the unit circle. Use special triangles to determine geometrically the values of sine, cosine, tangent for /3, /4 and /6, and use the unit circle to express the values of sine, cosine, and tangent for  x, + x, and 2  x in terms of their values for x, where x is any real number.AR.912.TF.PCT.5.4 (TF.5.PCT.4) Find the values of the trigonometric functions given the value of one trigonometric function and an additional piece of qualifying information or given the coordinates of a point on the terminal side of an angleAR.912.TF.PCT.5.5 (TF.5.PCT.5) Develop and become fluent in the recall of the exact values of the trigonometric functions for special anglesTF.4CC.912.F.TF.4 (+) Extend the domain of trigonometric functions using the unit circle. Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.TF.5CC.912.F.TF.5 Model periodic phenomena with trigonometric functions. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* AR.912.TF.AIII.5.4 (TF.5.AIII.4) Solve, with and without appropriate technology, real world problems involving applications of:
 trigonometric functions,
 law of Sines,
 law of Cosines,
 area of oblique trianglesTF.6AR.7.A.5.1 (A.5.7.1) Expressions, Equations and Inequalities: Solve and graph onestep linear equations and inequalities using a variety of methods (i.e., handson, inverse operations, symbolic) with real world application with and without technologyAR.6.NO.2.3 (NO.2.6.3) Number theory: Apply the addition, subtraction, multiplication and division properties of equality to onestep equations with whole numbers6CC.6.EE.6 Reason about and solve onevariable equations and inequalities. Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.,a.5.8.1 is rated a 3. no.2.7.2 rated as a 3.AR.7.NO.2.2 (NO.2.7.2) Number theory: Apply the addition, subtraction, multiplication and division properties of equality to onestep equations with integers, fractions, and decimalsCC.6.EE.7 Reason about and solve onevariable equations and inequalities. Solve realworld and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.sAR.8.A.5.2 (A.5.8.2) Expressions, Equations and Inequalities: Solve and graph linear equations (in the form y=mx+b)aCC.6.EE.8 Reason about and solve onevariable equations and inequalities. Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.a.5.7.1 is rated a 3CC.912.A.SSE.1 Interpret the structure of expressions. Interpret expressions that represent a quantity in terms of its context.*AR.912.LA.AI.1.2 (LA.1.AI.2) Translate word phrases and sentences into expressions, equations, and inequalities, and vice versaSSE.1bCC.912.A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and a factor not depending on P.*AR.912.RF.AII.1.4 (RF.1.AII.4) Analyze and report, with and without appropriate technology, the effect of changing coefficients, exponents, and other parameters on functions and their graphs (linear, quadratic, and higher degree polynomial)SSE.2
CC.912.A.SSE.2 Interpret the structure of express< ions. Use the structure of an expression to identify ways to rewrite it. For example, see x^4 y^4 as (x^2)^2 (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 y^2)(x^2 + y^2).AR.912.NLF.AI.4.1 (NLF.4.AI.1) Factoring polynomials:
 greatest common factor,
 binomials (difference of squares),
 trinomialsAR.912.NF.AC.4.1 (NF.4.AC.1) Factor polynomials:
 greatest common factor,
 binominals (difference of squares),
 trinomials,
 combinations of the aboveSSE.3CC.912.A.SSE.3 Write expressions in equivalent forms to solve problems. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*AR.912.NLF.AI.4.3 (NLF.4.AI.3) Solve quadratic equations using the appropriate methods with and without technology:
 factoring,
 quadratic formula with real number solutionsAR.912.NF.AC.4.3 (NF.4.AC.3) Solve, with and without appropriate technology, quadratic equations with real number solutions using factoring and the quadratic formulaAR.6.G.8.1 (G.8.6.1) Characteristics of Geometric Shapes: Identify threedimensional geometric figures using models (rectangular prisms, cylinders, cones, pyramids and spheres)CC.6.G.2 Solve realworld and mathematical problems involving area, surface area, and volume. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems.CC does not address cylindersyCC.6.G.3 Solve realworld and mathematical problems involving area, surface area, and volume. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving realworld and mathematical problems.AR.7.G.10.2 (G.10.7.2) Coordinate Geometry: Plot points that form the vertices of a geometric figure and draw, identify and classify the figure.UFirst 2 rate a 2 and last one rates a 3. First 2 do not focus on real world problems.AR.6.G.10.2 (G.10.6.2) Coordinate Geometry: Plot points that form the vertices of a geometric figure and draw, identify and classify the figure.AR.8.G.10.1 (G.10.8.1) Coordinate Geometry: Use coordinate geometry to explore the links between geometric and algebraic representations of problems (lengths of segments/distance between points, slope/perpendicularparallel lines)ECC.6.G.4 Solve realworld and mathematical problems involving area, surface area, and volume. Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems.CC.912.S.MD.4 (+) Calculate expected values and use them to solve problems. Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?*MD.5aCC.912.S.MD.5a (+) Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fastfood restaurant.*MD.5bCC.912.S.MD.5b (+) Evaluate and compare strategies on the basis of expected values. For example, compare a highdeductible versus a lowdeductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.*CC.K12.MP.2 Reason abstractly and quantitatively. Mathematically proficient students make sense of the quantities and their relationships in problem situations. Students bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. AIAIIPCTAIIIGeoACTDMFYTMAI/AIITFMCMGeo/AII lThe 4th bullet applies for Arkansas standard 2.4.2., and the 2nd bullet applies for Arkansas standard 2.3.2.tAR.912.LA.AI.1.9 (LA.1.AI.9) Add, subtract, and multiply simple radical expressions like 3"20 + 7"5 and (4"5)(2"3).Q.1AR.912.PRF.AIII.2.6 (PRF.2.AIII.6) Apply, with and without appropriate technology, the concepts of polynomial and rational functions to model real world situationsAPR.4CC.912.A.APR.4 Use polynomial identities to solve problems. Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^2 + y^2)^2 = (x^2 y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples.2Nothing here about proof of polynomial identities.APR.5CC.6.SP.3 Develop understanding of statistical variability. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.CC.6.SP.4 Summarize and describe distributions. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. AR includes more types of graphs. Dap.14.7.2 and dap.15.7.1 are rated a 3. DS.1.S.1 needs to be added, but not loaded in system.AR.7.DAP.14.2 (DAP.14.7.2) Collect, organize and display data: Explain which types of displ< ay are appropriate for various data sets (line graph for change over time, circle graph for parttowhole comparison, scatter plot for trends)CC.6.SP.5 Summarize and describe distributions. Summarize numerical data sets in relation to their context, such as by:
 a. Reporting the number of observations.
 b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
 c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data was gathered.
 d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered.2Collectively it is a 3, but individually it is a 2AR.8.DAP.16.1 (DAP.16.8.1) Inferences and Predictions: Use observations about differences between sets of data to make conjectures about the populations from which the data was takenAR.6.DAP.16.1 (DAP.16.6.1) Inferences and Predictions: Use observations about differences in data to make justifiable inferencesmAR.5.DAP.16.1 (DAP.16.5.1) Inferences and Predictions: Make predictions and justify conclusions based on data{AR.8.DAP.15.1 (DAP.15.8.1) Data Analysis: Compare and contrast the reliability of data sets with different size populationsAR.8.DAP.14.1 (DAP.14.8.1) Collect, organize and display data: Design and conduct investigations which include:
 adequate number of trials,
 unbiased sampling,
 accurate measurement,
 recordkeepingAR.8.DAP.14.2 (DAP.14.8.2) Collect, organize and display data: Explain which types of display are appropriate for various data sets (scatter plot for relationship between two variants and line of best fit)AR.6.DAP.14.2 (DAP.14.6.2) Collect, organize and display data: Collect data and select appropriate graphical representations to display the data including Venn diagramsrAR.912.PC.PCT.8.2 (PC.8.PCT.2) Represent equations given in rectangular coordinates in terms of polar coordinates`AR.912.PC.PCT.8.3 (PC.8.PCT.3) Graph polar equations and use appropriate technology when needed{AR.912.PC.PCT.8.4 (PC.8.PCT.4) Apply polar coordinates to real world situations and use appropriate technology when neededMAR.912.LA.AI.1.8 (LA.1.AI.8) Simplify radical expressions such as 3 / ("7).AR.912.PRF.AIII.2.5 (PRF.2.AIII.5) Establish the relationship between radical expressions and expressions containing rational exponents, and simplify variable expressions containing rational exponents using the laws of exponentsRN.2CC.912.N.RN.2 Extend the properties of exponents to rational exponents. Rewrite expressions involving radicals and rational exponents using the properties of exponents.6b/CC.912.S.MD.1 (+) Calculate expected values and use them to solve problems. Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.*YAR.912.P.S.7.1 (P.7.S.1) Compare and contrast independent and dependent random variablesCC.912.A.REI.5 Solve systems of equations. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.*AR frameworks do not ask students to proveAR.912.SEI.AC.3.2 (SEI.3.AC.2) SLE 2. Solve, with and without appropriate technology, systems of two linear equations and systems of two inequalities numerically, algebraically and graphicallyREI.6CC.912.A.REI.6 Solve systems of equations. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.REI.7CC.912.A.REI.7 Solve systems of equations. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = 3x and the circle x^2 + y^2 = 3.REI.8CC.912.A.REI.8 (+) Solve systems of equations. Represent a system of linear equations as a single matrix equation in a vector variable.Vector variableAR.912.MA.TDM.1.2 (MA.1.TDM.2) Solve realworld problems involving systems of linear equations using matrices (e.g., inverses, augmented, Cramer's rule)AR.912.LSM.TFM.1.1 (LSM.1.TFM.1) Use matrices (e.g., rowechelon form, GaussJordan method, inverses) to solve systems of linear equations, with or without technologyREI.9CC.912.S.CP.3 Understand independence and conditional probability and use them to interpret data. Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.*CP.4CC.912.S.CP.4 Understand independence and conditional probability and use them to interpret data. Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the twoway table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.*CP.5CC.912.A.REI.9 (+) Solve systems of equations. Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 3 or greater).vAR.912.LSM.TFM.1.2 (LSM.1.TFM.2) Find and use the inverse of a matrix to solve realworld problems (e.g., cryptology)REI.10CC.912.A.REI.10 Represent and solve equations and inequalities graphically. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).REI.11CC.912.A.REI.11 Represent and solve equations and inequalities graphically. Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.*AR.912.C.PCT.3.2 (C.3.PCT.2) Solve, with and without appropriate technology, systems of equations and inequalities involving conics and other types of equationsAR.912.LQF.AIII.1.1 (LQF.1.AIII.1) Evaluate, add, subtract, multiply, divide and compose functions and determine appropriate domain and range restrictionsAR.912.LQF.AIII.1.8 (LQF.1.AIII.8) Apply, with and without appropriate technology the concepts of functions to real world situations including linear programmingCED.4CC.912.A.CED.4 Create equations that describe numbers or relationship. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm s law V = IR< to highlight resistance R.*dAR.912.SEI.AI.2.3 (SEI.2.AI.3) Solve linear formulas and literal equations for a specified variablehConcerns about Arkansas SLEs being limited to linear...
Derive the quadratic formula could be included.kAR.912.SEI.AC.3.3 (SEI.3.AC.3) SLE 3. Solve linear formulas and literal equations for a specified variableREI.1\CC.912.A.REI.1 Understand solving equations as a process of reasoning and explain the reasoning. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.Understanding?AR.912.SEI.AC.3.1 (SEI.3.AC.1) SLE 1. Solve, with and without appropriate technology, multistep equations and inequalities with rational coefficients numerically, algebraically and graphicallyAR.912.PRF.PCT.1.3 (PRF.1.PCT.3) Describe, with and without appropriate technology, the fundamental characteristics of rational functions: zeros, discontinuities (including vertical asymptotes), and end behavior (including horizontal asymptotes)REI.2CC.7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.LAR does not address converting a rational number to decimal by long divisionRCC.7.NS.3 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Solve realworld and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
7AR includes "multistep," CC includes complex fractionsCC.7.EE.1 Use properties of operations to generate equivalent expressions. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.6AR does not include generating equivalent expressions.@CC.7.EE.2 Use properties of operations to generate equivalent expressions. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that increase by 5% is the same as multiply by 1.05. AR only deals operations.AR.5.DAP.14.2 (DAP.14.5.2) Collect, organize and display data: Collect numerical and categorical data using surveys, observations and experiments that would result in bar graphs, line graphs, line plots and stemandleaf plotsAR.5.G.8.3 (G.8.5.3) Characteristics of Geometric Shapes: Model and identify circle, radius, diameter, center, circumference and chordAR.6.G.8.4 (G.8.6.4) Characteristics of Geometric Shapes: Draw, label and determine relationships among the radius, diameter, center and circumference (e.g. radius is half the diameter) of a circlezCC.7.EE.3 Solve reallife and mathematical problems using numerical and algebraic expressions and equations. Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.,AR does not include real world or estimationAR.7.NO.3.1 (NO.3.7.1) Computational Fluency: Compute, with and without appropriate technology, with integers and positive rational numbers using real world situations to solve problems CC.7.EE.4 Solve reallife and mathematical problems using numerical and algebraic expressions and equations. Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.CC.7.EE.4a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?CC.7.EE.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example, As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.CC.7.G.1 Draw, construct, and describe geometrical figures and describe the relationships between them. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.AR.7.M.13.5 (M.13.7.5) Applications: Apply properties (scale factors, ratio, and proportion) of congruent or similar triangles to solve problems involving missing lengths and angle measuresAR.8.M.13.3 (M.13.8.3) Applications: Apply proportional reasoning to solve problems involving indirect measurements, scale drawings or ratesAR.7.G.8.1 (G.8.7.1) Characteristics of Geometric Shapes: Identify, draw, classify and compare geometric figures using models and real world examplesAR.7.G.8.6 (G.8.7.6) Characteristics of Geometric Shapes: Develop the properties of similar figures (ratio of sides and congruent angles)AR.912.M.G.3.4 (M.3.G.4) Use (given similar geometric objects) proportional reasoning to solve practical problems (including scale drawings)zCC.7.G.2 Draw, construct, and describe geometrical figures and describe the relationships between them. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.bAR.3.G.9.1 (G.9.3.1) Symmetry and Transformations: Draw one or more lines of symmetry in a polygonAR.6.G.9.1 (G.9.6.1) Symmetry and Transformations: Identify and describe line and rotational symmetry in twodimensional shapes, patterns and designs}AR.K.G.9.1 (G.9.K.1) Symmetry and Transformations: Identify figures with a line of symmetry as they appear in the environmentAR.1.G.9.1 (G.9.1.1) Symmetry and Transformations: Identify a line or lines of symmetry in two dimensional figures and justify by foldingCC.7.G.5 Solve reallife and mathematical problems involving angle measure, area, surface area, and volume. Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. 0CC.7.G.6 Solve reallife and mathematical problems involving angle measure, area, surface area, and volume. Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. {AR.912.SS.PCT.4.1 (SS.4.PCT.1) Develop, with and without appropriate technology, a rep< resentation of sequences recursivelyAR.912.SS.PCT.4.5 (SS.4.PCT.5) Use, with and without appropriate technology, sequences and series to solve real world problemsAR.912.SS.AIII.4.3 (SS.4.AIII.3) Solve, with and without appropriate technology, problems involving the sum (including Sigma notation) of finite and infinite sequences and seriesJAR.912.PI.CM.3.2 (PI.3.CM.2) Create functions using recursions and loops.AR.912.SS.PCT.4.4 (SS.4.PCT.4) Determine the nth term of a sequence given a rule or specific terms and use appropriate technology when neededAR.912.SS.AIII.4.4 (SS.4.AIII.4) Determine, with and without appropriate technology, the nth term of a sequence given a rule or specific termsIF.4AR.7.G.8.2 (G.8.7.2) Characteristics of Geometric Shapes: Investigate geometric properties and their relationships in one, two, and threedimensional models, including convex and concave polygons)CC.7.G.4 Solve reallife and mathematical problems involving angle measure, area, surface area, and volume. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.AR.7.G.8.5 (G.8.7.5) Characteristics of Geometric Shapes: Model and develop the concept that pi () is the ratio of the circumference to the diameter of any circleAR.8.M.12.1 (M.12.8.1) Attributes and Tools: Understand, select and use, with and without appropriate technology, the appropriate units and tools to measure angles, perimeter, area, surface area and volume to solve real world problemsAR.912.NF.AC.4.5 (NF.4.AC.5) Identify and apply nonlinear functions to real world situations such as acceleration, area, volume, population, bacteria, compound interest, percent depreciation and appreciation, amortization, geometric sequences, etc.RCC.912.F.IF.3 Understand the concept of a function and use function notation. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n1) for n e" 1 (n is greater than or equal to 1).tAR.912.DIP.AI.5.9 (DIP.5.AI.9) Recognize patterns using explicitly defined and recursively defined linear functionsAR.912.PD.CM.2.6 (PD.2.CM.6) Develop recursive relationships from mathematical models (e.g. arithmetic and geometric sequences).nAR.912.P.S.7.2 (P.7.S.2) Find the standard deviation for sums and differences of independent random variablesMD.5CC.912.S.MD.5 (+) Use probability to evaluate outcomes of decisions. Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.*MD.6CC.912.S.MD.6 (+) Use probability to evaluate outcomes of decisions. Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).* AR.912.PS.AC.1.3 (PS.1.AC.4) Apply probability to realworld situations such as weather prediction, game theory, fair division, insurance tables, and election theory.MD.7CC.912.S.MD.7 (+) Use probability to evaluate outcomes of decisions. Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).*`CC.K.CC.4c Understand that each successive number name refers to a quantity that is one larger. )CC.7.SP.7 Investigate chance processes and develop, use, and evaluate probability models. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. OAR.912.M.G.3.1 (M.3.G.1) Calculate probabilities arising in geometric contextsiAR.4.DAP.15.2 (DAP.15.4.2) Data Analysis: Match a set of data with a graphical representation of the data6CC.7.SP.7a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.tCC.7.SP.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land openend down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?dAR.6.DAP.17.1 (DAP.17.6.1) Probability: Distinguish between theoretical and experimental probabilityqAR.5.DAP.17.1 (DAP.17.5.1) Probability: Identify and predict the probability of events within a simple experimentCC.7.SP.8 Investigate chance processes and develop, use, and evaluate probability models. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.AR.3.DAP.17.3 (DAP.17.3.3) Probability: Use physical models, pictures, and organized lists to find combinations of two sets of objectsfAR.4.DAP.17.1 (DAP.17.4.3) Probability: Find all possible combinations of two or three sets of objects8aAR.912.NLF.AI.4.4 (NLF.4.AI.4) Recognize function families and their connections including vertical shift and reflection over the xaxis:
 quadratics (with rational coefficients),
 absolute value,
 exponential functionsIF.8b%CC.912.F.IF.8b Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as representing exponential growth and decay.CC.5.NF.2 Use equivalent fractions as a strategy to add and subtract fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by us
!"#$%&'()*+,./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdeghijklmnopqrstuvwxyz{}~ing visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 by observing that 3/7 < 1/2. For No.2.5.5, use real word situations through word problems along with the use of benchmark fractions to estimate reasonableness, for No.3.6.4, remove decimals, and for No. 3.7.3, remove decimalswAR.6.NO.3.4 (NO.3.6.4) Estimation: Estimate reasonable solutions to problem situations involving fractions and decimalsAR.7.NO.3.3 (NO.3.7.3) Estimation: Determine when an estimate is sufficient and use estimation to decide whether answers are reasonable in problems including fractions and decimalsCC.7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.AR.8.DAP.17.1 (DAP.17.8.1) Probability: Compute, with and without appropriate technology, probabilities of compound events, using organized lists, tree diagrams and logic grid8bCC.7.SP.8b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes ), identify the outcomes in the sample space which compose the event.< 8c2CC.7.SP.8c Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?CC.8.NS.1. Know that there are numbers that are not rational, and approximate them by rational numbers. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.#AR does NOT include "understanding"CC.8.NS.2 Know that there are numbers that are not rational, and approximate them by rational numbers. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., ^2). For example, by truncating the decimal expansion of "2 (square root of 2), show that "2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.AR.8.NO.3.5 (NO.3.8.5) Application of Computation: Calculate and find approximations of square roots with appropriate technology]CC.5.NF.4a Interpret the product (a/b) q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a q b. For example, use a visual fraction model to show (2/3) 4 = 8/3, and create a story context for this equation. Do the same with (2/3) (4/5) = 8/15. (In general, (a/b) (c/d) = ac/bd.) ,Exclude division, mixed numbers and decimals\CC.5.NF.4b Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas."Include fractional side in lengthsCC.5.NF.6 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.exclude decimals CC.5.NF.7 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.)exclude decimals and mixed numbers, specify fractions by whole numbers. they also need to specify whole numbers by fractions and specify use of word problems.DCC.5.NF.7a Interpret division of a unit fraction by a nonzero whole number, and compute such quotients. For example, create a story context for (1/3) 4 and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) 4 = 1/12 because (1/12) 4 = 1/3.Fexclude decimals and mixed numbers, specify whole numbers by fractions7CC.5.NF.7b Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 (1/5) and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 (1/5) = 20 because 20 (1/5) = 4.Nexclude decimals and mixed numbers; specify use of whole numbers by fractions tAR.912.CT.TFM.3.1 (CT.3.TFM.1) Use fundamental counting principles of addition and multiplication to solve problemsCP.8!CC.912.S.CP.8 (+) Use the rules of probability to compute probabilities of compound events in a uniform probability model. Apply the general Multiplication Rule in a uniform probability model, P(A and B) = [P(A)]x[P(BA)] =[P(B)]x[P(AB)], and interpret the answer in terms of the model.*CP.9CC.912.S.CP.9 (+) Use the rules of probability to compute probabilities of compound events in a uniform probability model. Use permutations and combinations to compute probabilities of compound events and solve problems.*yAR.912.P.S.6.1 (P.6.S.1) Understand the counting principle, permutations and combinations and use them to solve problemsLAR.912.P.S.6.2 (P.6.S.2) Compare and contrast permutations and combinations]AR.912.P.S.6.3 (P.6.S.3) Calculate the number of permutations of n objects taken r at a time]AR.912.P.S.6.4 (P.6.S.4) Calculate the number of combinations of n objects taken r at a timeAR.912.PS.AC.1.1 (PS.1.AC.1) Apply counting techniques to determine the number of outcomes:
 tree diagram,
 fundamental Counting Principle,
 permutations (with and without repetition),
 combinationsAR.912.PS.TM.4.3 (PS.4.TM.3) Use counting methods, permutations, and combinations to evaluate the likelihood of events occurringCC.912.F.BF.5 (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.jAR.912.ELF.AII.5.5 (ELF.5.AII.5) Establish the relationship between exponential and logarithmic functionsQAR.912.ELF.AII.5.6 (ELF.5.AII.6) Evaluate simple logarithms using the definitiontAR.912.ELF.AIII.3.1 (ELF.3.AIII.1) Establish the inverse relationship between exponential and logarithmic functionsrAR.912.ELF.PCT.2.1 (ELF.2.PCT.1) Establish the inverse relationship between exponential and logarithmic functionsAR.912.SEI.AI.2.1 (SEI.2.AI.1) Solve multistep equations and inequalities with rational coefficients:
 numerically (from a table or guess and check),
 algebraically (including the use of manipulatives),
 graphically,
 technologically\CC.8.EE.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).CC.8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.AR.8.NO.2.1 (NO.2.8.1) Number theory: Apply the addition, subtraction, multiplication and division properties of equality to twostep equationsCC.5.MD.5 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
@For 12.5.5, exclude surface area, for M.12.5.4, delete linear units for perimeter, for M.13.3.12, sqaure unit for area, for No. 2.5.2, only use volume, for 13,7.4 and No.2.5.2, delete surace area and cylinders for CC.5D.5b., and for M. 13.7.4, CC.5.MD.5c, add use 2 rectangular prisms take out surface area and cylinder.AR.7.M.13.4 (M.13.7.4) Applications: Derive and use formulas for surface area and volume of prisms and cylinders and justify them using geometric models and common materials5aCC.5.MD.5a Find the volume of a right rectangular prism with wholenumber side lengths by packing it with unit cubes, and show t< hat the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication.u For M.12.5.4, delete linear units for perimeter, M.13.3.12, sqaure units for area, and for No.2.52, use only volume.5bCC.5.MD.5b Apply the formulas V =(l)(w)(h) and V = (b)(h) for rectangular prisms to find volumes of right rectangular prisms with wholenumber edge lengths in the context of solving real world and mathematical problems. !Delete surface area and cylinders5cCC.5.MD.5c Recognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real world problems.DAdd use 2 rectangular prisms and take out surface area and cylinder.CC.5.G.1 Graph points on the coordinate plane to solve realworld and mathematical problems. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate).
AR.912.SEI.AI.2.2 (SEI.2.AI.2) Solve systems of two linear equations:
 numerically (from a table or guess and check),
 algebraically (including the use of manipulatives),
 graphically,
 technologically]CC.912.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.*coCC.912.F.BF.1a Determine an explicit expression, a recursive process, or steps for calculation from a context.BF.1aAR.912.SS.PCT.4.1 > AR.912.SS.PCT.4.1 (SS.4.PCT.1) Develop, with and without appropriate technology, a representation of sequences recursively [Grade Level 912]AR.912.PS.CM.1.2 > AR.912.PS.CM.1.2 (PS.1.CM.2) Write an algorithm to solve mathematical problems using formulas, equations, and functions. [Grade Level 912]AR.912.SS.AIII.4.3 > AR.912.SS.AIII.4.3 (SS.4.AIII.3) Solve, with and without appropriate technology, problems involving the sum (including Sigma notation) of finite and infinite sequences and series [Grade Level 912]qAR.912.PI.CM.3.2 > AR.912.PI.CM.3.2 (PI.3.CM.2) Create functions using recursions and loops. [Grade Level 912]DomainAbbreviationKindergartenCounting and CardinalityHSNumber and Quantitiy!Operations and Algebraic ThinkingThe Real Number SystemRN!Number and Operations in Base Ten
QuantitiesQMeasurement and DataThe Complex Number SystemCNGeometryVector and Matrix QuantitiesVMFirstAlgebraSeeing Structure in ExpressionsSSE2Arithmetic with Polynomials and Rational FunctionsAPRCreating EquationsCEDSecond)Reasoning with Equations and InequalitiesREI FunctionsInterpreting FunctionsIFBuilding FunctionsBFThird)Linear, Quadratic, and Exponential ModelsLETrigonometric FunctionsTF"Number and Operations in Fractions
CongruenceCOSimilarity, Right Triangles, and TrigonometrySRTFourthCirclesC.Expressing Geometric Properties with EquationsGPE#Geometric Measurement and DimensionGMDModeling with GeometryMGStatistics and ProbabilityFifth.Interpreting Categorical and Quantitative DataID,Making Inferences and Justifying ConclusionsIC4Conditional Probability and the Rules of ProbabilityCP#Using Probability to Make DecisionsSixth$Ratio and Proportional RelationshipsThe Number SystemExpressions and EquationsHigh School Courses Algebra ISeventhAlgebraic Connections
Algebra IIAlgebra IIIPreCalculus with Trigonometry
StatisticsEighthTopics in Finite MathTopics in Discrete Math
Computer MathTransition to College MathTCMyAR.912.CT.TFM.3.2 (CT.3.TFM.2) Evaluate expressions indicating permutations or combinations, with and without technology[AR.912.CT.TFM.3.3 (CT.3.TFM.3) Evaluate expressions involving distinguishable permutationskAR.912.CT.TFM.3.4 (CT.3.TFM.4) Distinguish between and use permutations and combinations to solve problemsMD.1AR.912.LG.G.1.4 (LG.1.G.4) Apply, with and without appropriate technology, definitions, theorems, properties, and postulates related to such topics as complementary, supplementary, vertical angles, linear pairs, and angles formed by perpendicular linesAR.912.T.G.2.3 (T.2.G.3) Identify and use the special segments of triangles (altitude, median, angle bisector, perpendicular bisector, and midsegment) to solve problemsAR.912.M.G.3.5 (M.3.G.5) Identify and apply properties of and theorems about parallel and perpendicular lines to prove other theorems and perform basic Euclidean constructionsCO.10bCC.912.G.CO.10 Prove geometric theorems. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.MAR.912.R.G.4.4 (R.4.G.4) Identify the attributes of the five Platonic SolidsCO.11CC.8.G.5 Understand congruence and similarity using physical models, transparencies, or geometry software. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angleangle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the three angles appear to form a line, and give an argument in terms of transversals why this is so.AR.912.LG.G.1.5 (LG.1.G.5) Explore, with and without appropriate technology, the relationship between angles formed by two lines cut by a transversal to justify when lines are parallel[AR.912.LG.G.1.6 (LG.1.G.6) Give justification for conclusions reached by deductive reasoning. State and prove key basic theorems in geometry (i.e., the Pythagorean theorem, the sum of the measures of the angles of a triangle is 180, and the line joining the midpoints of two sides of a triangle is parallel to the third side and half it's lengthuCC.8.G.6 Understand and apply the Pythagorean Theorem. Explain a proof of the Pythagorean Theorem and its converse. fAR.912.T.G.2.4 (T.2.G.4) Apply the Pythagorean Theorem and its converse in solving practical problemsAR.6.A.6.1 (A.6.6.1) Algebraic Models and Relationships: Complete, with and without appropriate technology, and interpret tables and line graphs that represent the relationship between two variables in quadrant IAR.7.A.6.1 (A.6.7.1) Algebraic Models and Relationships: Use tables and graphs to represent linear equations by plotting, with and without appropriate technology, points in a coordinate planeZAR.6.G.10.1 (G.10.6.1) Coordinate Geometry: Use ordered pairs to plot points in Quadrant ICC.6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed. For example, If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?mAR.6.A.7.1 (A.7.6.1) Analyze Change: Identify and compare situations with constant or varying rates of changeGNO.3.8.3 has estimation which is embedded in the mathematical practice.AR.7.A.7.1 (A.7.7.1) Analyze Change: Use, with and without appropriate technology, tables and graphs to compare and identify situations with constant or varying rates of changeCC.6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whol< e given a part and the percent.,matched as 3 collectively, 2 by themselves. AR.6.NO.1.1 (NO.1.6.1) Rational Numbers: Demonstrate conceptual understanding to find a specific percent of a number, using models, real life examples, or explanationsAR.6.NO.3.7 (NO.3.6.7) Application of Computation: Determine the percent of a number and solve related problems in real world situationsrAR.7.NO.3.6 (NO.3.7.6) Application of Computation: Solve, with and without technology, real world percent problemsCC.6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.*matched as 3 collectively, 2 by thenselveshAR.7.M.12.2 (M.12.7.2) Attributes and Tools: Understand relationships among units within the same systemAR.8.M.12.2 (M.12.8.2) Attributes and Tools: Describe and apply equivalent measures using a variety of units within the same system of measurementNS!CC.6.NS.1 Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?!3 collectively, 2 by themselves
AR.8.NO.2.5 (NO.2.8.5) Understand Operations: Model and develop addition, subtraction, multiplication and division of rational numbersCC.6.NS.2 Compute fluently with multidigit numbers and find common factors and multiples. Fluently divide multidigit numbers using the standard algorithm. 3 collectively, 2 individuallyCC.6.NS.3 Compute fluently with multidigit numbers and find common factors and multiples. Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation.AR.7.NO.3.4 (NO.3.7.4) Application of Computation: Apply factorization, LCM, and GCF to solve problems using more than two numbers and explain the solutionCC.6.NS.4 Compute fluently with multidigit numbers and find common factors and multiples. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1 100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).CC.6.NS.5 Apply and extend previous understandings of numbers to the system of rational numbers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in realworld contexts, explaining the meaning of 0 in each situation.AR contains Irrational numbersAR.7.NO.1.6 (NO.1.7.6) Rational Numbers: Recognize subsets of the real number system (natural, whole, integers, rational, and irrational numbers)dAR.2.M.12.5 (M.12.2.5) Temperature: Compare temperatures using the Fahrenheit scale on a thermometerAR.3.M.12.3 (M.12.3.3) Temperature: Distinguish the temperature in contextual problems using the Fahrenheit scale on a thermometerVAR.4.M.13.6 (M.13.4.6) Temperature: Read temperatures on Fahrenheit and Celsius scales>CC.6.NS.6 Apply and extend previous understandings of numbers to the system of rational numbers. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. R3 collectively, 2 individually. no.1.8.3 w/o irrationals. no.1.7.6 w/o irrationalsAR.8.NO.1.3 (NO.1.8.3) Rational Numbers: Compare and order real numbers including irrational numbers and find their approximate location on a number line (Use technology when appropriate)tAR.8.NO.1.4 (NO.1.8.4) Rational Numbers: Understand and justify classifications of numbers in the real number system6aCC.6.NS.6a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., ( 3) = 3, and that 0 is its own opposite.?3 collectively, 2 individually, AR includes irrational numbers.#change strategies to multiplication7bCC.3.MD.8 Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different area or with the same area and different perimeter.YAR.4.M.13.9 (M.13.4.9) Perimeter: Use strategies for finding the perimeter of a rectangleDdelete triangle, rectangle, parallelgram. m13.6.4 includes polygonsAR.6.G.8.2 (G.8.6.2) Characteristics of Geometric Shapes: Investigate with manipulatives or grid paper what happens to the perimeter and area of a twodimensional shape when the dimensions are changedAR.6.M.12.3 (M.12.6.3) Attributes and Tools: Compare and contrast the differences among linear units, square units, and cubic unitsgAR.3.M.13.10 (M.13.3.10) Perimeter: Find the perimeter of a figure by measuring the length of the sidesCC.3.G.1 Reason with shapes and their attributes. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.}AR.5.G.8.1 (G.8.5.1) Characteristics of Geometric Shapes: Identify and model regular and irregular polygons including decagon~AR.4.G.8.2 (G.8.4.2) Characteristics and PropertiesTwo Dimensional: Identify regular and irregular polygons including octagon912MAR.912.R.G.4.1 (R.4.G.1) Explore and verify the properties of quadrilateralshCC.912.G.C.2 Understand and apply theorems about circles. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.RAR.912.R.G.4.6 (R.4.G.6) Solve problems using inscribed and circumscribed figuresC.3CC.912.G.C.3 Understand and apply theorems about circles. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.C.4CC.912.G.C.4 (+) Understand and apply theorems about circles. Con< struct a tangent line from a point outside a given circle to the circle.C.5.CC.912.G.C.5 Find arc lengths and areas of sectors of circles. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.GPE.1CC.912.G.GPE.1 Translate between the geometric description and the equation for a conic section. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.GPE.2CC.912.G.GPE.2 Translate between the geometric description and the equation for a conic section. Derive the equation of a parabola given a focus and directrix.GPE.3CC.912.G.GPE.3 (+) Translate between the geometric description and the equation for a conic section. Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.GPE.47CC.912.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, "3) lies on the circle centered at the origin and containing the point (0, 2).AR.912.CGT.G.5.1 (CGT.5.G.1) Use coordinate geometry to find the distance between two points, the midpoint of a segment, and the slopes of parallel, perpendicular, horizontal, and vertical linesGPE.5)CC.912.G.GPE.5 Use coordinates to prove simple geometric theorems algebraically. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).uAR.912.LF.AC.2.6 (LF.2.AC.6) Determine, using slope, whether a pair of lines are parallel, perpendicular, or neitherGPE.6CC.912.G.GPE.6 Use coordinates to prove simple geometric theorems algebraically. Find the point on a directed line segment between two given points that partitions the segment in a given ratio.GPE.7CC.912.G.GPE.7 Use coordinates to prove simple geometric theorems algebraically. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*xAR.912.M.G.3.3 (M.3.G.3) Relate changes in the measurement of one attribute of an object to changes in other attributesGMD.1CC.912.G.GMD.1 Explain volume formulas and use them to solve problems. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri s principle, and informal limit arguments.GMD.2CC.912.G.GMD.2 (+) Explain volume formulas and use them to solve problems. Give an informal argument using Cavalieri s principle for the formulas for the volume of a sphere and other solid figures.GMD.3CC.912.G.GMD.3 Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*GMD.4CC.912.G.GMD.4 Visualize relationships between twodimensional and threedimensional objects. Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects.aAR.912.R.G.4.8 (R.4.G.8) Draw, examine, and classify crosssections of threedimensional objectsMG.1CC.912.G.MG.1 Apply geometric concepts in modeling situations. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*AR.912.MM.TM.3.1 (MM.3.TM.1) Establish connections between tables and graphs and the symbolic form using geometric and algebraic models (quadratic, rational, etc.)MG.2CC.912.G.MG.2 Apply geometric concepts in modeling situations. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).*MG.3CC.912.G.MG.3 Apply geometric concepts in modeling situations. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).*AR.8.G.11.1 (G.11.8.1) Spatial Visualization and Models: Using isometric dot paper interpret and draw different views of buildingsAR.7.G.11.2 (G.11.7.2) Spatial Visualization and Models: Construct a building out of cubes from a set of views (front, top, side)SID.1CC.912.S.ID.1 Summarize, represent, and interpret data on a single count or measurement variable. Represent data with plots on the real number line (dot plots, histograms, and box plots).* UAr standard DS.1.S.1 needs to be added to the match as a 1, but not loaded in system.AR.1.A.4.5 (A.4.1.5) Recognize, describe and develop patterns: Identify a number that is one more or one less than any whole number less than 100CC.4.NBT.2 Generalize place value understanding for multidigit whole numbers. Read and write multidigit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)ONO. 1.4.2 (with comparing piece) and NO. 1.4.3 (remove ordering and technology)AR.4.NO.1.3 (NO.1.4.3) Whole Numbers: Use mathematical language and symbols to compare and order any whole numbers with and without appropriate technology (<, >, =)CC.4.NBT.3 Generalize place value understanding for multidigit whole numbers. Use place value understanding to round multidigit whole numbers to any place. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)yAR.4.NO.3.5 (NO.3.4.5) Estimation: Use estimation strategies to solve problems and judge the reasonableness of the answer7Change estimation to rounding for No.3.4.5 and No.3.3.5yAR.3.NO.3.5 (NO.3.3.5) Estimation: Use estimation strategies to solve problems and judge the reasonableness of the answerBCC.4.NBT.4 Use place value understanding and properties of operations to perform multidigit arithmetic. Fluently add and subtract multidigit whole numbers using the standard algorithm. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.)bNo. 3.5.1 (without multiplication) and No. 3.6.1 (without multiplication); this is very close to 3XAR.5.NO.3.1 (NO.3.5.1) Computational Fluency: Develop and use a variety of algorithms with computational fluency to perform whole number operations using addition and subtraction (up to fivedigit numbers), multiplication (up to threedigit x twodigit), division (up to twodigit divisor) interpreting remainders, including real world problemsAR.6.NO.3.1 (NO.3.6.1) Computational Fluency: Apply, with and without appropriate technology, algorithms with computational fluency to perform whole number operations (+, , x, /)CC.6.EE.9 Represent and analyz< e quantitative relationships between dependent and independent variables. Use variables to represent two quantities in a realworld problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.AR.8.A.4.4 (A.4.8.4) Patterns, Relations and Functions: Use tables, graphs, and equations to identify independent/dependent variables (input/output)AR.912.LF.AC.2.2 (LF.2.AC.2) Create, given a situation, a graph that models the relationship between the independent and dependent variablesAR.912.LF.AC.2.3 (LF.2.AC.3) Determine the independent and dependent variables, domain and range of a relation from an algebraic expression, graph, set of ordered pairs, or table of dataCC.4.NF.1 Extend understanding of fraction equivalence and ordering. Explain why a fraction a/b is equivalent to a fraction (n a)/(n b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)MFor No. 1.5.5 remove 3rd bullet and For No. 1.5.1, remove ratios and percentsHCC.4.NF.2 Extend understanding of fraction equivalence and ordering. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)AR.4.A.5.2 (A.5.4.2) Expressions, Equations and Inequalities: Express mathematical relationships using simple equations and inequalities (>, <, =, `")*Leave off decimal and percent for No.1.6.44CC.4.NF.3 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)For No.2.5.5, remove mult., for No. 1.6.4 remove decimals and percents, for No. 1.5.5, the third bullet, both use vocab of mixed numbers and improper fractions, but no mention of adding. Even though 3d was not mentioned, the group rated it is a no match.AR.6.G.11.1 (G.11.6.1) Spatial Visualization and Models: Identify twodimensional patterns (nets) for threedimensional solids, such as prisms, pyramids, cylinders, and conesVLast one is a rating of 3. The grade 5 SLE that matches this standard is a weak match.AR.7.G.11.1 (G.11.7.1) Spatial Visualization and Models: Build threedimensional solids from twodimensional patterns (nets)AR.8.M.13.2 (M.13.8.2) Applications: Solve problems involving volume and surface area of pyramids, cones and composite figures, with and without appropriate technologyAR.5.G.11.1 (G.11.5.1) Spatial Visualization and Models: Using grid paper, draw and identify twodimensional patterns (nets) for cubesSPCC.6.SP.1 Develop understanding of statistical variability. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, How old am I? is not a statistical question, but How old are the students in my school? is a statistical question because one anticipates variability in students ages.AR.6.DAP.14.1 (DAP.14.6.1) Collect, organize and display data: Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population&Lacking clarity on variability in SLEsAR.7.DAP.14.1 (DAP.14.7.1) Collect, organize and display data: Identify different ways of selecting samples and compose appropriate questionshAR.5.DAP.14.1 (DAP.14.5.1) Collect, organize and display data: Develop appropriate questions for surveysAR.912.PRF.AII.4.2 (PRF.4.AII.2) Analyze and sketch, with and without appropriate technology, the graph of a given polynomial function, determining the characteristics of domain and range, maximum and minimum points, end behavior, zeros, multiplicity of zeros, yintercept, and symmetry^AR.912.NLF.AI.4.2 (NLF.4.AI.2) Determine minimum, maximum, vertex, and zeros, given the graphAR.6.DAP.14.3 (DAP.14.6.3) Collect, organize and display data: Construct and interpret graphs, using correct scale, including line graphs and doublebar graphsAR.7.DAP.14.3 (DAP.14.7.3) Collect, organize and display data: Construct and interpret circle graphs, boxandwhisker plots, histograms, scatter plots and double line graphs with and without appropriate technologyAR.8.DAP.14.3 (DAP.14.8.3) Collect, organize and display data: Interpret or solve real world problems using data from charts, line plots, stemand leaf plots, doublebar graphs, line graphs, boxand whisker plots, scatter plots, frequency tables or double line graphsgAR.6.DAP.15.1 (DAP.15.6.1) Data Analysis: Interpret graphs such as double line graphs and circle graphskAR.7.DAP.15.1 (DAP.15.7.1) Data Analysis: Analyze data displays, including ways that they can be misleadingFor No.1.5.1 (remove rations and percentages), for no 1.5.5, exclude bullets 1and 2, keep bullet 3, add mult. of fractions and whole numbers, for 3.6.2 remove decimals, for No. 2.55, omit addition, subtraction and decimals, and for No. 1.5.1 no buleets and add word units fractions time a whole number for 4b, for No. 1.4.4 keep only part about the number line, and for No. 1.5.5 add multiply fractions and whole numbers, need contextual situationsCC.4.NF.4a Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 (1/4), recording the conclusion by the equation 5/4 = 5 (1/4). For No.1.5.1 remove ratios and percentages, for No. 1.5.5 exclude bullets and and 2, keep bullet 3, add multiplications of fractions and whole numbers)iAR.5.NO.1.3 (NO.1.5.3) Rational Numbers: Identify decimal and percent equivalents for benchmark fractionsCC.4.NF.4b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 (2/5) as 6 (1/5), recognizing this product as 6/5. (In general, n (a/b) = (n a)/b.)For 3.6.2, remove decimals, for No. 2.5.5, omit subtraction and decimals, and for No. 1.5.1 no bullets and add words unit fractions time a whole number4cCC.4.NF.4c Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? For 1.4.4 keep onl< y the part about a number line, and for No. 1.5.5 add multiply fractions and whole numbers,and it needs contextual situationsCC.4.NF.5 Understand decimal notation for fractions, and compare decimal fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100 and add 3/10 + 4/100 = 34/100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)*For No. 1.5.3 and NO. 1.6.2 remove percentAR.4.NO.1.6 (NO.1.4.6) Rational Numbers: Use the place value structure of the base ten number system and be able to represent and compare decimals to hundredths (using models, illustrations, symbols, expanded notation and problem solving)AR.912.DC.S.3.5 (DC.3.S.5) Use simulations to develop an understanding of the Central Limit Theorem and its importance in confidence intervals and tests of significanceIC.6CC.912.S.IC.6 Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Evaluate reports based on data.*mAR.912.DC.S.3.3 (DC.3.S.3) Apply statistical principles and methods in sample surveys; identify difficultiesCP.1vCC.912.A.APR.5 (+) Use polynomial identities to solve problems. Know and apply that the Binomial Theorem gives the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal s Triangle. (The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.)GAR.912.CT.TFM.3.6 (CT.3.TFM.6) Construct and examine Pascal's triangleDAR.912.CT.TFM.3.7 (CT.3.TFM.7) Develop and use the binomial theoremaAR.912.CT.TFM.3.8 (CT.3.TFM.8) Use combinations to find a specified term in a binomial expansionAPR.6]CC.912.A.APR.6 Rewrite rational expressions. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.kAR.912.PRF.AIII.2.3 (PRF.2.AIII.3) Simplify, add, subtract, multiply, and divide with rational expressionsAPR.7$CC.912.A.APR.7 (+) Rewrite rational expressions. Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.iAR.912.PRF.AII.4.6 (PRF.4.AII.6) Simplify, add, subtract, multiply, and divide with rational expressionsLAR does not reach the level of understanding required to meet this standard.GAR.912.LA.AI.1.6 (LA.1.AI.6) Simplify algebraic fractions by factoringGAR.912.LA.AI.1.7 (LA.1.AI.7) Recognize when an expression is undefinedCED.1CC.912.A.CED.1 Create equations that describe numbers or relationship. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.*[Arkansas Standards LF.1.AIII.2 and LF.1.AIII.3 need to be matched, but not found in system.AR.912.LEI.AII.2.1 (LEI.2.AII.1) Solve, with and without appropriate technology, absolute value equations and inequalities written in one or two variables, and graph solutions.AR.912.QEF.AII.3.6 (QEF.3.AII.6) Apply the concepts of quadratic equations and functions to model real world situations by using appropriate technology when needednAR.912.ELF.AII.5.4 (ELF.5.AII.4) Recognize and solve problems that can be modeled using exponential functionsAR.912.LF.AC.2.1 (LF.2.AC.1) Create, given a graph without an explicit formula, a written or oral interpretation of the relationship between the independent and dependent variablesAR.912.ELF.PCT.2.3 (ELF.2.PCT.3) Solve graphically, algebraically and numerically, with and without appropriate technology, equations and real world problems involving exponential and logarithmic expressionsCC.912.G.SRT.1 Understand similarity in terms of similarity transformations. Verify experimentally the properties of dilations given by a center and a scale factor:
 a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
 b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.SRT.2CC.7.NS.2 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. ~AR.7.NO.2.4 (NO.2.7.4) Understand Operations: Model and develop addition, subtraction, multiplication and division of integersAR.8.NO.3.1 (NO.3.8.1) Computational Fluency: Compute, with and without appropriate technology, with rational numbers in multistep problems)CC.7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with nonzero divisor) is a rational number. If p and q are integers then (p/q) = ( p)/q = p/( q). Interpret quotients of rational numbers by describing realworld contexts.`CC.7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers.CC.4.MD.2 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.\AR.4.M.13.2 (M.13.4.2) Clock: Solve problems involving conversions between minutes and hoursoAR.4.M.13.3 (M.13.4.3) Clock: Restate the time in multiple ways given an analog clock to the nearest oneminutebAR.1.M.13.3 (M.13.1.3) Elapsed Time: Determine elapsed time (to the hour) in contextual situationsAR.2.M.13.3 (M.13.2.3) Elapsed Time: Determine elapsed time in contextual situations in hour increments regardless of starting timeAR.4.M.13.4 (M.13.4.4) Elapsed Time: Determine elapsed time in contextual situations to fiveminute intervals with beginning time unknownAR.3.M.13.12 (M.13.3.12) Volume: Develop strategies for finding the volume (cubic units) of rectangular prisms and cubes using modelspAR.4.M.13.11 (M.13.4.11) Volume: Use strategies to find the volume (cubic units) of rectangular prisms and cubesAR.7.M.13.1 (M.13.7.1) Attributes and Tools: Solve real world problems involving two or more elapsed times, counting forward and backward (calendar and clock)CC.4.MD.3 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Apply the area and perimeter formulas for rectangles < in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.area and perimeterAR.7.M.12.3 (M.12.7.3) Attributes and Tools: Find different areas for a given perimeter and find a different perimeter for a given areaCC.4.MD.4 Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.line plots piececAR.5.DAP.17.2 (DAP.17.5.2) Probability: List and explain all possible outcomes in a given situationAR.5.DAP.15.2 (DAP.15.5.2) Data Analysis: Determine, with and without appropriate technology, the range, mean, median and mode (whole number data sets) and explain what each indicates about the set of dataAR.5.G.9.1 (G.9.5.1) Symmetry and Transformations: Predict and describe the results of translation (slide), reflection (flip), rotation (turn), showing that the transformed shape remains unchangedAR.6.G.9.2 (G.9.6.2) Symmetry and Transformations: Describe positions and orientations of shapes under transformation (translation, reflection and rotation) recognizing the size and shape do not changeAR.5.G.8.2 (G.8.5.2) Characteristics of Geometric Shapes: Identify and draw congruent, adjacent, obtuse, acute, right and straight angles (Label parts of an angle: vertex, rays, interior and exterior)CC.4.MD.6 Geometric measurement: understand concepts of angle and measure angles. Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure.say to use protactorCC.4.MD.7 Geometric measurement: understand concepts of angle and measure angles. Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.FAR.7.G.8.3 (G.8.7.3) Characteristics of Geometric Shapes: Recognize the pairs of angles formed and the relationship between the angles including two intersecting lines and parallel lines cut by a transversal (vertical, supplementary, complementary, corresponding, alternate interior, alternate exterior angles and linear pair)using modelsAR.7.G.8.4 (G.8.7.4) Characteristics of Geometric Shapes: Use paper or physical models to determine the sum of the measures of interior angles of triangles and quadrilateralsCC.4.G.1 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.AR.4.G.8.3 (G.8.4.3) Characteristics and PropertiesOne Dimensional: Identify, draw, and describe a line, line segment, a ray, an angle, intersecting, perpendicular, and parallel linesCollectively taken as a 3AR.4.G.8.4 (G.8.4.4) Geometrical Relationships: Identify and describe intersecting, perpendicular and parallel lines in problem solving contextsAR.4.G.8.5 (G.8.4.5) Geometrical Relationships: Classify angles relative to 90 as more than, less than or equal toaAR.3.G.8.4 (G.8.3.4) Geometrical Relationships: Identify and draw intersecting and parallel linesAR.3.G.8.3 (G.8.3.3) Characteristics and PropertiesOne Dimensional: Identify and draw line, line segment and ray using appropriate labelsPCC.4.G.2 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.bAR standards do not specifically state "presence or absence of parallel, perpendicular, and anglesBCC.4.G.3 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry.AR.2.G.9.1 (G.9.2.1) Symmetry and Transformations: Use lines of symmetry to demonstrate and describe congruent figures within a twodimensional figureSNot a strong match. Note for g.9.8.1: rate as 2 because cc did not include compare.AR.6.G.8.3 (G.8.6.3) Characteristics of Geometric Shapes: Identify, describe, draw, and classify triangles as equilateral, isosceles, scalene, right, acute, obtuse, and equiangularAR.4.M.13.8 (M.13.4.8) Applications: Estimate and measure length, capacity/volume and mass using appropriate customary and metric units:
 Length: 1/2 inch, 1 cm;
 Perimeter: inches, feet, centimeters, meters;
 Area: square inches, square feet, square centimeters, square meters;
 Weight: pounds/ounces;
 Mass: kilograms/grams;
 Capacity: cups, pints, quarts, gallons;
 Volume: liters.CC.2.MD.4 Measure and estimate lengths in standard units. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.?AR second grade says to use nonstandard; CC says standard unitsAR.5.M.13.5 (M.13.5.5) Applications: Count the distance between two points on a horizontal or vertical line and compare the lengths of the paths on a grid)CC.2.MD.5 Relate addition and subtraction to length. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.EAR does not include length problems involving adding and subtracting.CC.2.MD.7 Work with time and money. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. KAR.2.M.13.2 (M.13.2.2) Clock: Tell time to the nearest fiveminute interval<Grade 2  AR left out words a.m. p.m.; Grade 3 rated it a 1.xAR.3.M.12.2 (M.12.3.2) Time: Clock: Recognize that 60 minutes equals 1 hour and that a day is divided into A.M. and P.M.NAR.2.M.12.2 (M.12.2.2) Time: Clock: Recognize that there are 24 hours in a daywAR.1.M.12.3 (M.12.1.3) Time: Clock: Recognize that an hour is longer than a minute and a minute is longer than a secondCC.912.F.IF.4 Interpret functions that arise in applications in terms of the context. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*AR.912.RF.AII.1.6 (RF.1.AII.6) Recognize periodic phenomena (sine or cosine functions such as sound waves, length of daylight, circular motion)AR.912.RF.AII.1.7 (RF.1.AII.7) Investigate and identify key characteristics of period functions and their graphs (period, amplitude, maximum, and minimum)aAR.912.RF.AII.1.8 (RF.1.AII.8) Use basic properties of frequency and amplitude to solve problemsKAR.912.PRF.AIII.2.2 (PRF.2.AIII.2) Investigate and sketch the graphs of polynomial and rational functions using the characteristics of domain and range, upper and lower bounds, maximum and minimum points, asymptotes and end behavior, zeros, multiplicity of zeros, yintercepts, and symmetry with and without appropriate technologyXAR.912.RF.AII.1.9 (RF.1.AII.9) Apply the concepts of functions to real world situations2AR.912.PRF.AII.4.5 (PRF.4.AII.5) < Identify the characteristics of graphs of power functions of the form f(x) = ax^n, for negative integral values of n, including domain, range, end behavior, and behavior at x = 0, and compare these characteristics to the graphs of related positive integral power functionswAR.912.ELF.AII.5.1 (ELF.5.AII.1) Recognize the graphs of exponential functions distinguishing between growth and decaymAR.912.OP.TDM.2.4 (OP.2.TDM.4) Model and solve realworld problems involving optimization of area and volumeCC.7.SP.4 Draw informal comparative inferences about two populations. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventhgrade science book are generally longer than the words in a chapter of a fourthgrade science book.KAR.912.PRF.PCT.1.1 (PRF.1.PCT.1) Investigate and sketch, with and without appropriate technology, the graphs of polynomial and rational functions using the characteristics of domain and range, upper and lower bounds, maximum and minimum points, asymptotes and end behavior, zeros, multiplicity of zeros, yintercepts, and symmetryAR.912.PRF.PCT.1.4 (PRF.1.PCT.4) Apply the concepts of polynomial and rational functions to model real world situations using appropriate technology when neededIF.5CC.912.F.IF.5 Interpret functions that arise in applications in terms of the context. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of personhours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*contextual domain?uAR.912.LF.AC.2.4 (LF.2.AC.4) Interpret the rate of change (slope) and intercepts within the context of everyday lifeIF.6CC.912.F.IF.6 Interpret functions that arise in applications in terms of the context. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*Only linear in AR frameworksAR.912.LF.TM.1.2 (LF.1.TM.2) Determine the initial condition and the rate of change in realworld situations described by y = mx + bIF.7CC.912.F.IF.7 Analyze functions using different representations. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*AR.912.LF.TM.1.4 (LF.1.TM.4) Explain, conjecture, summarize, and defend results orally, in writing and through the use of appropriate technologyAR.912.EF.TM.2.6 (EF.2.TM.6) Explain, conjecture, summarize, and defend results orally, in writing, and through the use of appropriate technologyAR.912.MM.TM.3.4 (MM.3.TM.4) Explain, conjecture, summarize, and defend results orally, in writing, and through the use of appropriate technologyIF.7a^CC.912.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.*hNothing about linear functions included. Review for AR SLEs related to graphing lines.
Algebra II 3.5
IF.7bCC.912.F.IF.7b Graph square root, cube root, and piecewisedefined functions, including step functions and absolute value functions.* AR.912.LQF.AIII.1.6 (LQF.1.AIII.6) Graph, with and without appropriate technology, functions defined as piecewise and stepvAR.912.LF.AC.2.8 (LF.2.AC.8) Graph, with and without appropriate technology, functions defined as piecewise and stepIF.7cCC.912.F.IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.* IF.7dXAR.4.DAP.17.1 (DAP.17.4.1) Probability: Use fractions to predict probability of an event_AR.4.DAP.16.1 (DAP.16.4.1) Inferences and Predictions: Make predictions for a given set of data_AR.3.DAP.16.1 (DAP.16.3.1) Inferences and Predictions: Make predictions for a given set of dataCC.5.NF.1 Use equivalent fractions as a strategy to add and subtract fractions. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) LTake out multiplication of fractions and decimals and include mixed numbers.kCC.5.NBT.4 Understand the place value system. Use place value understanding to round decimals to any place.CC.5.NBT.5 Perform operations with multidigit whole numbers and with decimals to hundredths. Fluently multiply multidigit whole numbers using the standard algorithm. (Limited to only multiplication for 3.5.1CC.5.NBT.6 Perform operations with multidigit whole numbers and with decimals to hundredths. Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. AR.4.NO.2.4 (NO.2.4.4) Whole Number Operations: Represent and explain division as measurement and partitive division including equal groups, related rates, price, rectangular arrays (area model), combinations and multiplicative comparison?CC.3.OA.3 Represent and solve problems involving multiplication and division. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. jexcept remainders and multiplicative compare; specific language. For AR Standard NO.3.4.3 use bullet 1. AR.3.NO.3.3 (NO.3.3.3) Computational FluencyMultiplication and Division: Develop, with and without appropriate technology, computational fluency in multiplication and division up to twodigit by onedigit numbers using twodigit by onedigit number contextual problems using:
 strategies for multiplying and dividing numbers,
 performance of operations in more than one way,
 estimation of products and quotients in appropriate situations, and
 relationships between operationsDAR.4.NO.3.3 (NO.3.4.3) Computational FluencyMultiplication and Division: Attain, with and without appropriate technology, computational fluency in multiplication and division using contextual problems using:
 twodigit by twodigit multiplication (larger numbers with technology),
 up to threedigit by twodigit division (larger numbers with technology),
 strategies for multiplication and dividing numbers,
 performance of operations in more than one way,
 estimation of products and quotients in appropriate situations, and
 relationships between operationsCC.5.NF.3 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3 and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?ZFor, No.1.5.1, add to solve word problems and mixed numbers and delete ratio and percents.CC.5.NF.4 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. AR.6.NO.2.5 (NO.2.6.5) Understand Operations: Model multiplicati< on and division of fractions (including mixed numbers) and decimals using pictures and physical objectsStandards A and B combined together exclude division and mixed numbers and decimals and also include fractional sides in length AR.6.NO.2.2 (NO.2.6.2) Number theory: Apply the distributive property of multiplication over addition to simplify computations with whole numbersCC.3.OA.6 Understand properties of multiplication and the relationship between multiplication and division. Understand division as an unknownfactor problem. For example, divide 32 8 by finding the number that makes 32 when multiplied by 8. 6AR.4.NO.2.2 (NO.2.4.2) Number Theory: Apply number theory:
 determine if any number is even or odd,
 use the terms 'multiple,' 'factor,' and 'divisible by' in an appropriate context,
 generate and use divisibility rules for 2, 5, and 10,
 demonstrate various multiplication & division relationships^AR.8.NO.2.2 (NO.2.8.2) Number theory: Understand and apply the inverse and identity properties>CC.3.OA.7 Multiply and divide within 100. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 5 = 40, one knows 40 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of onedigit numbers.AR.3.NO.3.2 (NO.3.3.2) Computational FluencyMultiplication and Division: Develop, with and without appropriate technology, fluency with basic number combinations for multiplication and division facts (10 x 10)Exclude with technology bullet 2 and bullet 1{CC.5.NF.7c Solve realworld problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3cup servings are in 2 cups of raisins? @exclude decimals and mixed numbers; specify use of word problemsCC.5.MD.1 Convert like measurement units within a given measurement system. Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep real world problems.delete plot pointsAR.3.G.10.1 (G.10.3.1) Coordinate Geometry: Locate and identify points on a coordinate grid and name the ordered pair (quadrant one only) using common language and geometric vocabulary (horizontal and vertical)AR.4.G.10.1 ( G.10.4.1) Coordinate Geometry: Locate and identify points on a coordinate grid and name the ordered pair (quadrant one only) using common language and geometric vocabulary (horizontal and vertical)AR.912.LF.AI.3.8 (LF.3.AI.8) *Write an equation in slopeintercept, pointslope, and standard forms given:
 two points,
 a point and yintercept,
 xintercept and yintercept,
 a point and slope,
 a table of data,
 the graph of a lineAR.912.LF.AC.2.5 (LF.2.AC.5) Calculate the slope given:
 two points,
 a graph of a line,
 an equation of a lineCC.8.EE.7 Analyze and solve linear equations and pairs of simultaneous linear equations. Solve linear equations in one variable.tAR.912.SEI.AI.2.8 (SEI.2.AI.8) Communicate real world problems graphically, algebraically, numerically and verballybAR not descriptive: note for SEI.2.a1.1, SEI.2.a1.8.
a.5.8.1 and SEI. 2.a1.1 are matched as a 3. CC.5.MD.3 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
 a. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume.
 b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.sAR.2.M.13.14 (M.13.2.14) Volume: Compare and order containers of various shapes and sizes according to their volumeAdd classify <'sCC.5.MD.4 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.AR.2.NO.3.5 (NO.3.2.5) Estimation: Use estimation strategies to solve addition and subtraction problems and judge the reasonableness of the answeryAR.2.A.4.2 (A.4.2.2) Recognize, describe and develop patterns: Describe repeating and growing patterns in the environmentCC.3.OA.9 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. AR.5.NO.2.1 (NO.2.5.1) Number theory: Use divisibility rules to determine if a number is a factor of another number (2, 3, 5, 10)}AR.6.NO.2.1 (NO.2.6.1) Number theory: Use divisibility rules to determine if a number is a factor of another number (4, 6, 9)AR.1.A.6.1 (A.6.1.1) Algebraic Models and Relationships: Explore the use of a chart or table to organize information and to understand relationshipsAR.2.A.6.1 (A.6.2.1) Algebraic Models and Relationships: Use a chart or table to organize information and to understand relationshipsbAR.5.NO.1.2 (NO.1.5.2) Rational Numbers: Develop understanding of decimal place value using models}AR.5.NO.1.4 (NO.1.5.4) Rational Numbers: Round and compare decimals to a given place value (whole number, tenths, hundredths)=CC.3.NBT.2 Use place value understanding and properties of operations to perform multidigit arithmetic. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. (A range of algorithms may be used.)remove technologyAR.4.NO.3.1 (NO.3.4.1) Computational FluencyAddition and Subtraction: Demonstrate, with and without appropriate technology, computational fluency in multidigit addition and subtraction in contextual problems/CC.3.NBT.3 Use place value understanding and properties of operations to perform multidigit arithmetic. Multiply onedigit whole numbers by multiples of 10 in the range 1090 (e.g., 9 80, 5 60) using strategies based on place value and properties of operations. (A range of algorithms may be used.)NFQCC.3.NF.1 Develop understanding of fractions as numbers. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)~Delete plot points for G.10.5.1, and Grade 5 rated the fifth grade standards as a 2, and grade 7 rated their standards as a 3.AR.7.A.6.2 (A.6.7.2) Algebraic Models and Relationships: Represent, with and without appropriate technology, linear equations by plotting and graphing points in the coordinate plane using all four quadrants given data in a table from a real world situationCC.8.EE.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.CC.8.EE.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equ< ations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.CC.8.EE.8c Solve realworld and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.FCC.8.F.1 Define, evaluate, and compare functions. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.)AR.7.A.4.1 (A.4.7.1) Patterns, Relations and Functions: Create and complete a function table (input/output) using a given rule with two operationsFLAGA.6.3.1 and a.6.7.3 were rated as a 2, but all other matches are rated as a 3.
CC skill is necessary to complete AR skill.AR.912.LF.AI.3.1 (LF.3.AI.1) Distinguish between functions and nonfunctions/relations by inspecting graphs, ordered pairs, mapping diagrams and/or tables of dataAR.912.LF.AI.3.2 (LF.3.AI.2) Determine domain and range of a relation from an algebraic expression, graphs, set of ordered pairs, or table of datajAR.8.A.4.1 (A.4.8.1) Patterns, Relations and Functions: Find the nth term in a pattern or a function tableAR.8.A.4.2 (A.4.8.2) Patterns, Relations and Functions: Using real world situations, describe patterns in words, tables, pictures, and symbolic representationsCC.8.F.2 Define, evaluate, and compare functions. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. $AR SLE's are not descriptive enough.AR.8.A.6.4 (A.6.8.4) Algebraic Models and Relationships: Represent, with and without appropriate technology, simple exponential and/or quadratic functions using verbal descriptions, tables, graphs and formulas and translate among these representationsCC.8.F.3 Define, evaluate, and compare functions. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.AR is not descriptiveCC.8.F.4 Use functions to model relationships between quantities. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.sAR.912.LF.AI.3.5 (LF.3.AI.5) Interpret the rate of change/slope and intercepts within the context of everyday lifeAR.912.TEI.PCT.7.3 (TEI.7.PCT.3) Solve trigonometric equations algebraically and graphically and use appropriate technology when neededdAR.2.G.9.2 (G.9.2.2) Symmetry and Transformations: Demonstrate the motion of a single transformationAR.912.CGT.G.5.7 (CGT.5.G.7) Draw and interpret the results of transformations and successive transformations on figures in the coordinate plane:
 translations,
 reflections,
 rotations (90, 180, clockwise and counterclockwise about the origin),
 dilations (scale factor)AR.5.A.6.1 (A.6.5.1) Algebraic Models and Relationships: Draw conclusions and make predictions, with and without appropriate technology, from models, tables and line graphs+Matched as 3 collectively, 2 by themselves.jAR.5.A.7.1 (A.7.5.1) Analyze Change: Model and describe quantities that change using real world situationsCC.6.RP.3a Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.AR.8.A.7.1 (A.7.8.1) Analyze Change: Use, with and without technology, graphs of real life situations to describe the relationships and analyze change including graphs of change (cost per minute) and graphs of accumulation (total cost),matched as 3 collectively, 2 by themselves
OAR.7.G.10.1 (G.10.7.1) Coordinate Geometry: Plot points in the coordinate planeAR.5.M.13.1 (M.13.5.1) Attributes and Tools: Solve real world problems involving one elapsed time, counting forward (calendar and clock)?AR.K.M.13.3 (M.13.K.3) Elapsed Time: Order events based on time_AR.2.M.13.9 (M.13.2.9) Temperature: Read temperatures on a Fahrenheit scale in intervals of tenvAR.2.M.13.2 (M.13.2.1) Calendar: Use a calendar to determine elapsed time involving a time period within a given monthmAR.1.M.13.1 (M.13.1.1) Calendar: Use a calendar to determine elapsed time involving a time period of one weeksAR.3.M.13.7 (M.13.3.7) Temperature: Read temperatures on Fahrenheit and Celsius scales in intervals of two and five]AR.3.M.13.1 (M.13.3.1) Calendar: Use a calendar to determine elapsed time from month to monthAR.4.M.12.2 (M.12.4.2) Temperature: Distinguish the temperature in contextual problems using the Fahrenheit scale on a thermometer_AR.4.M.13.1 (M.13.4.1) Calendar: Using a calendar to determine elapsed time from month to monthAR.K.NO.3.1 (NO.3.K.1) Computational FluencyAddition and Subtraction: Develop strategies for basic addition facts:
 counting all,
 counting on,
 one more, two moreAR.K.NO.3.2 (NO.3.K.2) Computational FluencyAddition and Subtraction: Develop strategies for basic subtraction facts:
 counting back,
 one less, two lessAR.k.NO.2.2 (NO.2.K.2) Whole Number Operations: Use physical and pictorial models to demonstrate various meanings of addition and subtractionAR.1.NO.2.4 (NO.2.1.4) Whole Number Operations: Use physical, pictorial and symbolic models to demonstrate various meanings of addition and subtractionAR.K.A.5.1 (A.5.K.1) Expressions, Equations and Inequalities: Use drawings and labels to record solutions of addition and subtraction problems with answers less than or equal to 10CC.K.OA.2 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.AR.K.NO.3.3 (NO.3.K.3) Application of Computation: Solve problems by using a variety of methods and tools (e.g., objects, and/or illustrations, with and without appropriate technology and mental computations)AR.K.NO.2.3 (NO.2.K.3) Whole Number Operations: Demonstrate the relationship between addition and subtraction with informal language and models in contextual situations involving whole numbersAR.1.NO.2.5 (NO.2.1.5) Whole Number Operations: Identify and use relationships between addition and subtraction to solve problems in contextual situations involving whole numbersCC.3.MD.2 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to repre< sent the problem. (Excludes multiplicative comparison problems (problems involving notions of times as much. )AR.7.M.12.1 (M.12.7.1) Attributes and Tools: Understand, select and use the appropriate units and tools (metric and customary) to measure length, weight, mass and volume to the required degree of accuracy for real world problemsBnothing for volume. Grams, kilograms, and litersmass/volume onlyyAR.6.M.12.2 (M.12.6.1) Attributes and Tools: Identify and select appropriate units and tools from both systems to measure^CC.3.MD.3 Represent and interpret data. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep how many more and how many less problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.pictographs and bar graphs onlyiAR.3.DAP.15.2 (DAP.15.3.2) Data Analysis: Match a set of data with a graphical representation of the dataAR.5.DAP.14.3 (DAP.14.5.3) Collect, organize and display data: Construct and interpret frequency tables, charts, line plots, stemandleaf plots and bar graphsAR.4.DAP.15.1 (DAP.15.4.1) Data Analysis: Represent and interpret data using pictographs, bar graphs and line graphs in which symbols or intervals are greater than oneCC.3.MD.4 Represent and interpret data. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters..line plot only. Only to the 1/2 and 1/4 inch.nAR.5.M.13.3 (M.13.5.3) Attributes and Tools: Draw and measure distance to the nearest cm and inch accuratelyCC.3.MD.5 Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Recognize area as an attribute of plane figures and understand concepts of area measurement.
 a. A square with side length 1 unit, called a unit square, is said to have one square unit of area, and can be used to measure area.
 b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. AR.5.M.12.4 (M.12.5.4) Attributes and Tools: Understand when to use linear units to describe perimeter, square units to describe area or surface area, and cubic units to describe volume, in real world situationsxAR.5.NO.1.6 (NO.1.5.6) Rational Numbers: Use models to differentiate between perfect squares up to 100 and other numbersCC.3.MD.6 Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). 7aCC.3.MD.7a Find the area of a rectangle with wholenumber side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.CC.3.MD.7b Multiply side lengths to find areas of rectangles with wholenumber side lengths in the context of solving real world and mathematical problems, and represent wholenumber products as rectangular areas in mathematical reasoning. AR.5.M.13.4 (M.13.5.4) Attributes and Tools: Develop and use strategies to solve real world problems involving perimeter and area of rectangledelete perimeter7cCC.3.MD.7c Use tiling to show in a concrete case that the area of a rectangle with wholenumber side lengths a and b + c is the sum of a b and a c. Use area models to represent the distributive property in mathematical reasoning. CC.K.MD.3 Classify objects and count the number of objects in each category. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. (Limit category counts to be less than or equal to 10.)G<CC.K.G.1 Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.AR.K.G.8.3 (G.8.K.3) Characteristics and PropertiesTwo Dimensional: Sort, describe and make geometric figures (triangle, rectangle [including square] and circle) by investigating their physical characteristics independent of position or size:AR.1.g.10.1 AR uses near, far, close to, left, and right.CC.6.NS.7b Write, interpret, and explain statements of order for rational numbers in realworld contexts. For example, write 3C > 7C to express the fact that 3C is warmer than 7C.no.1.8.3 w/o irrationals?CC.6.NS.7c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a realworld situation. For example, for an account balance of 30 dollars, write  30 = 30 to describe the size of the debt in dollars.7d{AR.912.SEI.AC.3.6 (SEI.3.AC.6) SLE 6. Apply linear, piecewise and step functions to real world situations that involve a combination of rates, proportions and percents such as sales tax, simple interest, social security, constant depreciation and appreciation, arithmetic sequences, constant rate of change, income taxes, postage, utility bills, commission, and traffic ticketsQ.3CC.912.N.Q.3 Reason quantitatively and use units to solve problems. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.*#Confusion about intent of standard.CN.1CC.912.N.CN.1 Perform arithmetic operations with complex numbers. Know there is a complex number i such that i^2 = "1, and every complex number has the form a + bi with a and b real. AR.912.QEF.AII.3.2 (QEF.3.AII.2) Extend the number system to include the complex numbers:
 define the set of complex numbers,
 add, subtract, multiply, and divide complex numbers,
 rationalize denominatorsCN.2CC.912.N.CN.2 Perform arithmetic operations with complex numbers. Use the relation i^2 = 1 and th< e commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.CN.3CC.912.N.CN.3 (+) Perform arithmetic operations with complex numbers. Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.CN.41CC.912.N.CN.4 (+) Represent complex numbers and their operations on the complex plane. Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.CN.7CC.912.N.CN.7 Use complex numbers in polynomial identities and equations. Solve quadratic equations with real coefficients that have complex solutions.=CC.6.EE.2b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. AR.7.A.5.3 (A.5.7.3) Expressions, Equations and Inequalities: Translate phrases and sentences into algebraic expressions and equations including parentheses and positive and rational numbers and simplify algebraic expressions by combining like terms2cAR.912.QEF.AII.3.3 (QEF.3.AII.3) Analyze and solve quadratic equations with and without appropriate technology by:
 factoring,
 graphing,
 extracting the square root,
 completing the square,
 using the quadratic formulaCN.8CC.912.N.CN.8 (+) Use complex numbers in polynomial identities and equations. Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x 2i).CN.9CC.912.N.CN.9 (+) Use complex numbers in polynomial identities and equations. Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.AR.912.PRF.AII.4.1 (PRF.4.AII.1) Determine the factors of polynomials by:
 using factoring techniques including grouping and the sum or difference of two cubes,
 using long division,
 using synthetic division!Does not explicitly state the FTAAR.912.PRF.AIII.2.1 (PRF.2.AIII.1) Determine the factors of polynomials by:
 using factoring techniques including grouping, the difference of two squares, and the sum or difference of two cubes,
 using synthetic divisionVM.1 CC.912.N.VM.1 (+) Represent and model with vector quantities. Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v(bold), v, v, v(not bold)).AR.912.OT.PCT.6.4 (OT.6.PCT.4) Use vectors to solve problems and describe addition of vectors and multiplication of a vector by a scalar, both symbolically and geometricallyAR.912.OT.PCT.6.5 (OT.6.PCT.5) Use vectors to model situations defined by magnitude and direction and analyze and solve real world problems by using appropriate technology when neededVM.2CC.912.N.VM.2 (+) Represent and model with vector quantities. Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.VM.3CC.912.N.VM.3 (+) Represent and model with vector quantities. Solve problems involving velocity and other quantities that can be represented by vectors.VM.4LCC.912.N.VM.4 (+) Perform operations on vectors. Add and subtract vectors.
VM.4aCC.912.N.VM.4a (+) Add vectors endtoend, componentwise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.VM.4b{CC.912.N.VM.4b (+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. VM.4c;CC.912.N.VM.4c (+) Understand vector subtraction v w as v + ( w), where ( w) is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction componentwise.VM.5PCC.912.N.VM.5 (+) Perform operations on vectors. Multiply a vector by a scalar.VM.5aCC.912.N.VM.5a (+) Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication componentwise, e.g., as c(v(sub x), v(sub y)) = (cv(sub x), cv(sub y)).VM.5bCC.912.N.VM.5b (+) Compute the magnitude of a scalar multiple cv using cv = cv. Compute the direction of cv knowing that when cv =8 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).VM.6CC.912.N.VM.6 (+) Perform operations on matrices and use matrices in applications. Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. AR.912.LEI.AII.2.3 (LEI.2.AII.3) Develop and apply, with and without appropriate technology, the basic operations and properties of matrices (associative, commutative, identity, and inverse)RAR.912.DIP.AI.5.3 (DIP.5.A1.3) Construct simple matrices for real life situationsCC.K.OA.1 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Represent addition and subtraction with objects, fingers, mental images, drawings (drawings need not show details, but should show the mathematics in the problem), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. AR.5.NO.1.1 (NO.1.5.1) Rational Numbers: Use models and visual representations to develop the concepts of the following:
Fractions: parts of unit wholes, parts of a collection, locations on number lines, locations on ruler (benchmark fractions), divisions of whole numbers;
Ratios: parttopart (2 boys to 3 girls), parttowhole (2 boys to 5 people);
Percents: partto1002ayCC.3.NF.2a Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.).Specify just creating a fractional number line2b:CC.3.NF.2b Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)RSpecify locate a specific fraction by using an endpoint on the created number line
CC.4.NBT.5 Use place value understanding and properties of operations to perform multidigit arithmetic. Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.)NO. 3.6.1 (remove division), No. 3.4.3 (bullets 1 and 3); No. 3.6.1 (remove division), No. 3.3. (just multipl< ication)Grade 3 added no.3.3.3 and commentedAR had only up to 2digits times 1digit.UCC.6.G.1 Solve realworld and mathematical problems involving area, surface area, and volume. Find area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems."3 collectively, but 2 individuallyAR.7.M.13.3 (M.13.7.3) Attributes and Tools: Develop and use strategies to solve problems involving area of a trapezoid and circumference and area of a circlefAR.8.M.13.5 (M.13.8.5) Applications: Estimate and compute the area of irregular twodimensional shapesAR.7.M.13.7 (M.13.7.7) Applications: Estimate and compute the area of more complex or irregular twodimensional shapes by dividing them into more basic shapes:CC.4.NBT.6 Use place value understanding and properties of operations to perform multidigit arithmetic. Find wholenumber quotients and remainders with up to fourdigit dividends and onedigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.)`MUST be careful with explaining calculation wiht equations, rectangular arrays and/or area modelAR.4.NO.3.2 (NO.3.4.2) Computational FluencyMultiplication and Division: Demonstrate fluency with combinations for multiplication and division facts (12 x 12) and use these combinations to mentally compute related problems (30 x 50)AR.2.NO.2.6 (NO.2.2.6) Whole Number Operations: Demonstrate various addition and subtraction relationships (property) to solve problems in contextual situations involving whole numbersAR.1.A.5.3 (A.5.1.3) Expressions, Equations and Inequalities: Recognize that symbols such as , and % in an addition or subtraction equation, represent a missing value that will make the statement trueAR.2.A.5.3 (A.5.2.3) Expressions, Equations and Inequalities: Recognize that symbols such as , and % in an addition or subtraction equation, represent a missing value that will make the statement trueAR.1.NO.3.3 (NO.3.1.3) Application of Computation: Solve problems by using a variety of methods and tools (e.g., objects, mental computations, paper and pencil and with and without appropriate technology)"CC.1.OA.2 Represent and solve problems involving addition and subtraction. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.AR.5.NO.2.5 (NO.2.5.5) Understand Operations: Model addition, subtraction, and multiplication of fractions with like and unlike denominators and decimals2AR.5.NO.3.2 (NO.3.5.2) Computational Fluency: Develop and use algorithms:
 to add and subtract numbers containing decimals (up to thousandths place),
 to multiply decimals (hundredths x tenths),
 to divide decimals by whole number divisors,
 to add and subtract fractions with like denominatorsxCC.4.NF.3a Understand addition and subtraction of fractions as joining and
separating parts referring to the same whole.remove mult./CC.4.NF.3b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.CC.4.NF.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.AR.7.DAP.15.2 (DAP.15.7.2) Data Analysis: Analyze, with and without appropriate technology, a set of data by using and comparing measures of central tendencies (mean, median, mode) and measures of spread (range, quartile, interquartile range)AR.8.DAP.15.2 (DAP.15.8.2) Data Analysis: Analyze, with and without appropriate technology, graphs by comparing measures of central tendencies and measures of spreadrAR.8.DAP.15.3 (DAP.15.8.3) Data Analysis: Given at least one of the measures of central tendency create a data setgAR.8.DAP.15.4 (DAP.15.8.4) Data Analysis: Describe how the inclusion of outliers affects those measuresAR.6.NO.3.2 (NO.3.6.2) Computational Fluency: Develop and analyze algorithms for computing with fractions (including mixed numbers) and decimals and demonstrate, with and without technology, computational fluency in their use and justify the solutionAR.1.DAP.15.1 (DAP.15.1.1) Data Analysis: Analyze and interpret concrete and pictorial graphs (i.e. bar graphs, pictographs, Venn diagrams, Tchart)AR.1.DAP.15.2 (DAP.15.1.2) Data Analysis: Make a true statement about the data displayed on a graph or chart (i.e. 5 people ride the bus)pAR.1.DAP.16.1 (DAP.16.1.1) Inferences and Predictions: Explore making simple predictions for a given set of data#CC.1.G.1 Reason with shapes and their attributes. Distinguish between defining attributes (e.g., triangles are closed and threesided) versus nondefining attributes (e.g., color, orientation, overall size); for a wide variety of shapes; build and draw shapes to possess defining attributes.AR.2.G.8.3 (G.8.2.3) Characteristics and PropertiesTwo Dimensional: Identify, classify and describe twodimensional geometric figures (rectangle [including square], triangle and circle) using concrete objects drawings, and computer graphicsoAR.1.A.4.1 (A.4.1.1) Sort and Classify: Sort and classify objects by one or two attributes in more than one wayAR.1.G.8.1 (G.8.1.1) Characteristics and PropertiesThree Dimensional: Compare threedimensional solids (sphere, cube, rectangular prism, cone, and cylinder) by investigating their physical characteristicszAR.2.A.4.1 (A.4.2.1) Sort and Classify: Sort, classify, and label objects by three or more attributes in more than one wayCC.1.G.2 Reason with shapes and their attributes. Compose twodimensional shapes (rectangles, squares, trapezoids, triangles, halfcircles, and quartercircles) or threedimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as right rectangular prism. )_Language not specific; Grade 3 added G.11.3.1 and G.11.3.2 and thought it should be rated a 3. AR.2.G.11.1 (G.11.2.1) Spatial Visualization and Models: Replicate a simple geometric design from a briefly displayed example or from a descriptionAR.4.G.11.1 (G.11.4.1) Spatial Visualization and Models: Construct a threedimensional model composed of cubes when given an illustrationAR.3.G.11.1 (G.11.3.1) Spatial Visualization and Models: Replicate a threedimensional model composed of cubes when given a physical modelAR.3.G.11.2 (G.11.3.2) Spatial Visualization and Models: Determine which new figure will be formed< by combining and subdividing models of existing figuresCC.1.G.3 Reason with shapes and their attributes. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. %specific language needs to be clearerCC.7.RP.1 Analyze proportional relationships and use them to solve realworld and mathematical problems. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour.AR.7.NO.1.1 (NO.1.7.1) Rational Numbers: Relate, with and without models and pictures, concepts of ratio, proportion, and percent, including percents less than 1 and greater than 100AR includes "percent"CC.7.RP.2 Analyze proportional relationships and use them to solve realworld and mathematical problems. Recognize and represent proportional relationships between quantities.`CC does not include yintercept,AR includes varying rates of change, AR includes tables & graphs.AR.8.A.6.1 (A.6.8.1) Algebraic Models and Relationships: Describe, with and without appropriate technology, 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 (rise/run) and yintercept in real world problemsAR.8.A.6.2 (A.6.8.2) Algebraic Models and Relationships: Represent, with and without appropriate technology, linear relationships concretely, using tables, graphs and equations.AR.8.A.6.3 (A.6.8.3) Algebraic Models and Relationships: Differentiate between independent/dependent variables given a linear relationship in contextCC.7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.CC.7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.@CC does not include yint., AR includes varying rates of change.AR.912.PRF.AIII.2.4 (PRF.2.AIII.4) Describe, with and without appropriate technology, the fundamental characteristics of rational functions: zeros, discontinuities (including vertical asymptotes), and end behavior (including horizontal asymptotes)CED.2CC.912.A.CED.2 Create equations that describe numbers or relationship. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*sAR.912.CGT.G.5.2 (CGT.5.G.2) Write the equation of a line parallel to a line through a given point not on the linehAR.912.CGT.G.5.3 (CGT.5.G.3) Write the equation of a line perpendicular to a line through a given point`AR.912.CGT.G.5.4 (CGT.5.G.4) Write the equation of the perpendicular bisector of a line segment]AR.912.PRF.AII.4.3 (PRF.4.AII.3) Write the equation of a polynomial function given its rootsiAR.912.PRF.AII.4.4 (PRF.4.AII.4) Identify the equation of a polynomial function given its graph or tableAR.912.ELF.AII.5.2 (ELF.5.AII.2) Graph exponential functions and identify key characteristics: domain, range, intercepts, asymptotes, and end behaviorAR.912.LQF.AIII.1.2 (LQF.1.AIII.2) Develop, write, and graph, with and without appropriate technology, equations of lines in slopeintercept, pointslope, and standard forms given:
 a point and the slope,
 two points,
 real world data/CC.912.S.CP.1 Understand independence and conditional probability and use them to interpret data. Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ( or, and, not ).*rAR.912.P.S.6.6 (P.6.S.6) Find conditional probabilities for dependent, independent, and mutually exclusive eventsAR.912.OP.TDM.2.1 (OP.2.TDM.1) Graph systems of linear inequalities with multiple constraints and identify vertices of the feasible regionrAR.7.M.13.6 (M.13.7.6) Applications: Find the distance between two points on a number line and locate the midpoint1d^CC.7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers. 1CC.7.NS.1b Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing realworld contexts.ZAR.6.M.13.5 (M.13.6.5) Applications: Find the distance between two points on a number line1c
CC.7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p q = p + ( q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in realworld contexts.does not include absolute valueCC.7.RP.2d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.=CC.7.RP.3 Analyze proportional relationships and use them to solve realworld and mathematical problems. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.AR.8.NO.3.6 (NO.3.8.6) Application of Computation: Solve, with and without technology, real world percent problems including percent of increase or decreaseAR.8.NO.3.3 (NO.3.8.3) Estimation: Use estimation to solve problems involving rational numbers; including ratio, proportion, percent (increase or decrease) then judge the reasonableness of solutionsHCC.7.NS.1 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.AR.8.NO.2.3 (NO.2.8.3) Number theory: Use inverse relationships (addition and subtraction, multiplication and division, squaring and square roots) in problem solving situations1aCC.7.NS.1a Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. 1b}AR.5.M.12.2 (M.12.5.2) Attributes and Tools: Make conversions within the customary measurement system in real world problems.wAR.6.M.12.2 (M.12.6.2) Attributes and Tools: Make conversions within the same measurement system in real world problemsAR.6.NO.3.5 (NO.3.6.5) Application of Computation: Find and use factorization (tree diagram) including prime factorization of composite numbers (expanded and exponential notation) to determine the greatest common factor (GCF) and least common multiple (LCM)CC.4.OA.5 Generate and analyze patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in t< he rule itself. For example, given the rule Add 3 and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. AR.3.A.4.4 (A.4.3.4) Recognize, describe and develop patterns: Use repeating and growing numeric or geometric patterns to solve problems~wording; needs to use function tables, input/output; a.4.3.5, commented select the rule to generate a rule, and rated it a 1.AR.4.A.4.2 (A.4.4.2) Recognize, describe and develop patterns: Use repeating and growing numeric and geometric patterns to make predictions and solve problemsAR.4.A.4.3 (A.4.4.3) Patterns, Relations and Functions: Determine the relationship between sets of numbers by selecting the ruleAR.2.A.4.6 (A.4.2.6) Recognize, describe and develop patterns: Recognize, describe, extend, and create repeating and growing patterns using a wide variety of materials to solve problemsAR.3.A.6.1 (A.6.3.1) Algebraic Models and Relationships: Complete a chart or table to organize given information and to understand relationships and explain the resultsAR.4.A.6.1 (A.6.4.1) Algebraic Models and Relationships: Create a chart or table to organize given information and to understand relationships and explain the resultsuAR.5.A.4.2 (A.4.5.2) Patterns, Relations and Functions: Interpret and write a rule for a one operation function tableAR.6.DAP.15.2 (DAP.15.6.2) Data Analysis: Compare and interpret information provided by measures of central tendencies (mean, median and mode) and measures of spread (range)
CC.2.NBT.7 Use place value understanding and properties of operations to add and subtract. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting threedigit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.<cc adds numbers to 1000. no.1.2.2 increase decomposing 100'sAR.4.NO.1.1 (NO.1.4.1) Whole Numbers: Recognize equivalent representations for the same whole number and generate them by composing and decomposing numbersCC.2.NBT.8 Use place value understanding and properties of operations to add and subtract. Mentally add 10 or 100 to a given number 100900, and mentally subtract 10 or 100 from a given number 100900.AR left out mentally9CC.2.NBT.9 Use place value understanding and properties of operations to add and subtract. Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.) 1AR demonstrates only; cc must explain and justifyCC.2.MD.1 Measure and estimate lengths in standard units. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. AR.2.M.13.10 (M.13.2.10) Applications: Select appropriate customary measurement tools (rulers, balance scale, cup and thermometer) for situations involving length, capacity, and massAR says nonstandard; AR picks up in 3rd. 3rd grade added m.13.3.8, commented that length onlyno capacity or mass and rated it a 1. m.13.8.1 rated as 3.$AR.3.M.13.9 (M.13.3.9) Applications: Estimate and measure length, capacity/volume and mass using appropriate customary units:
 Length: 1 inch;
 Perimeter: inches, feet, etc;
 Area: square inches (use models);
 Weight: pounds/ounces;
 Capacity: cups, pints, quarts, gallons.nAR.3.M.13.8 (M.13.3.8) Applications: Use appropriate customary measurement tools for length, capacity and massmAR.K.M.13.4 (M.13.K.4) Applications: Name common tools for measurement (balance scale, ruler and thermometer)~AR.8.M.13.1 (M.13.8.1) Attributes and Tools: Draw and apply measurement skills with fluency to appropriate levels of precisiongAR.5.M.12.1 (M.12.5.1) Attributes and Tools: Identify and select appropriate units and tools to measureAR.5.M.13.2 (M.13.5.2) Attributes and Tools: Determine which unit of measure or measurement tool matches the context for a problem situationAR.6.M.13.2 (M.13.6.2) Attributes and Tools: Determine which unit of measure or measurement tool matches the context for a problem situationpAR.6.M.13.3 (M.13.6.3) Attributes and Tools: Draw and measure distance to the nearest mm and 1/8 inch accuratelyGCC.K.G.4 Analyze, compare, create, and compose shapes. Analyze and compare two and threedimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/ corners ) and other attributes (e.g., having sides of equal length).AR.3.G.8.1 (G.8.3.1) Characteristics and PropertiesThree Dimensional: Compare, contrast and build threedimensional solids by investigating the number of faces, edges, and vertices on modelsAR.K.G.11.1 (G.11.K.1) Spatial Visualization and Models: Arrange physical materials (toothpicks, pretzel sticks, modeling clay, etc...) to form twodimensional figuresCC.K.G.5 Analyze, compare, create, and compose shapes. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.AR.1.G.11.1 (G.11.1.1) Spatial Visualization and Models: Replicate a simple twodimensional figure from a briefly displayed example or from a descriptionCC.2.MD.2 Measure and estimate lengths in standard units. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. Ssays to use relationships, AR only makes simple comparisons and CC goes much deeper
AR.3.M.12.4 (M.12.3.4) Tools and Attributes: Demonstrate the relationship among different standard units:
 Length: 12 in = 1 ft, 3 ft = 1 yd, 36 in = 1 yd,
 Capacity: 2 cups = 1 pint, 2 pints = 1 quart, 4 quarts = 1 gallon,
 Weight: 16 ounces = 1 lb.AR.4.M.12.3 (M.12.4.3) Tools and Attributes: Use the relationship among units of measurement:
Length: 12 in = 1 ft, 3 ft = 1 yd, 36 in = 1 yd, 100 cm = 1 m;
Capacity: 2 cups = 1 pint, 2 pints = 1 quart, 4 quarts = 1 gallon;
Weight: 16 ounces = 1 lbCC.2.MD.3 Measure and estimate lengths in standard units. Estimate lengths using units of inches, feet, centimeters, and meters.[AR.5.M.13.6 (M.13.5.6) Applications: Use benchmark angles to estimate the measure of anglesKAR.4.M.13.5 (M.13.4.5) Money: Apply money concepts in contextual situationsCC.7.SP.1 Use random sampling to draw inferences about a population. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences..ADE introduces topics and cc is more specific.CC.7.SP.2 Use random sampling to draw inferences about a population. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a b< ook by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.ADE introduces topic, cc goes deep with topic>CC.7.SP.3 Draw informal comparative inferences about two populations. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.AR.7.DAP.16.1 (DAP.16.7.1) Inferences and Predictions: Make, with and without appropriate technology, conjectures of possible relationships in a scatter plot and approximate the line of best fit (trend line)AR.8.G.9.1 (G.9.8.1) Symmetry and Transformations: Determine a transformation's line of symmetry and compare the properties of the figure and its transformationAR.7.G.9.1 (G.9.7.1) Symmetry and Transformations: Examine the congruence, similarity, and line or rotational symmetry of objects using transformationsCC.5.OA.1 Write and interpret numerical expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.AR.5.NO.2.4 (NO.2.5.4) Number theory: Apply rules (conventions) for order of operations to whole numbers where the left to right computations are modified only by the use of parenthesesCC.7.SP.5 Investigate chance processes and develop, use, and evaluate probability models. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.AR.7.DAP.17.1 (DAP.17.7.1) Probability: Understand that probability can take any value between 0 and 1 (events that are not going to occur have probability 0, events certain to occur have probability 1)XAR.3.DAP.17.1 (DAP.17.3.1) Probability: Use fractions to predict probability of an event~AR.2.DAP.17.1 (DAP.17.2.1) Probability: Describe the probability of an event as being more, less, and equally likely to occur AR.1.DAP.17.1 (DAP.17.1.1) Probability: Describe the probability of an event as being more, less, or equally likely to occurnAR.K.DAP.17.1 (DAP.17.K.1) Probability: Describe the probability of an event as being possible or not possibleWAR.912.DIP.AI.5.8 (DIP.5.AI.8) Compute simple probability with and without replacementvAR.912.DIP.AI.5.10 (DIP.5.AI.10) Communicate real world problems graphically, algebraically, numerically and verballyAR.4.DAP.17.1 (DAP.17.4.2) Probability: Conduct simple probability experiments, record the data and draw conclusions about the likelihood of possible outcome (roll number cubes, pull tiles from a bag, spin spinner, or determine the fairness of the game)CC.7.SP.6 Investigate chance processes and develop, use, and evaluate probability models. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.AR.8.DAP.17.2 (DAP.17.8.2) Probability: Make predictions based on theoretical probabilities, design and conduct an experiment to test the predictions, compare actual results to predict results, and explain differencesADE no relative frequencyAR.73.DAP.17.2 (DAP.17.7.2) Probability: Design, with and without appropriate technology, an experiment to test a theoretical probability and explain how the results may varyAR.3.DAP.17.2 (DAP.17.3.2) Probability: Conduct simple probability experiments, record the data and draw conclusions about the likelihood of possible outcomes (roll number cubes, pull tiles from a bag, spin a spinner, or determine the fairness of games)TNeeds to include up tp 4 digit dividends and 2digit divisors; just division phrase.}CC.5.NBT.7 Perform operations with multidigit whole numbers and with decimals to hundredths. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.?Needs to exclude add and subt fractions with like denominators.CC.5.NBT.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.Grade 3 originally added SLE No.1.3.6 and rated it as a 1 because it was using money, but it was not to the thousandths, and it was taken out.tCC.1.OA.5 Add and subtract within 20. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).AR.2.NO.1.1 (NO.1.2.1) Whole Numbers: Use efficient strategies to count a given set of objects in groups of 2s and 5s to 100 and in groups of 3s to 30yUse efficient strategies to count a set of objects/CCrelate strategies to addition/subtraction. (need specific language)YCC.4.NF.4 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and
!"#$%&'()*+,./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefgijklmnopqrstuvwxyz{}~ 100.)CC.3.NF.3 Develop understanding of fractions as numbers. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)delete decimals and percentswAR.3.NO.1.7 (NO.1.3.7) Rational Numbers: Write a fraction that is equivalent to a given fraction with the use of modelswAR.4.NO.1.8 (NO.1.4.8) Rational Numbers: Write a fraction that is equivalent to a given fraction with the use of modelsAR.5.NO.1.5 (NO.1.5.5) Rational Numbers: Use models of benchmark fractions and their equivalent forms:
 to analyze the size of fractions,
 to determine that simplification does not change the value of the fraction,
 to convert between mixed numbers and improper fractionsAR.6.NO.1.4 (NO.1.6.4) Rational Numbers: Convert, compare and order fractions (mixed numbers and improper fractions) decimals and percents and find their approximate locations on a number linekAR.4.NO.1.7 (NO.1.4.7) Rational Numbers: Write an equivalent decimal for a given fraction relating to money3aCC.3.NF.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)delete ratio and percent3bCC.3.NF.3b Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3), Explain why the fractions are equivalent, e.g., by using a visual fraction model. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)3c Match*Strand CodeCommon Core State StandardMatched Arkansas StandardCC.3.G.2 Reason with shapes and their attributes. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part is 1/4 of the area of the shape.AR.4.G.11.2 (G.11.4.2) Spatial Visualization and Models: Create new figures by combining and subdividing models of existing figures in multiple ways and record results in a table7CC.4.OA.1< Use the four operations with whole numbers to solve problems. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.$ just commutative part for No. 2.5.2AR.5.A.5.1 (A.5.5.1) Expressions, Equations and Inequalities: Model and solve simple equations by informal methods using manipulatives and appropriate technologyAR.3.G.8.2 (G.8.3.2) Characteristics and PropertiesTwo Dimensional: Identify regular polygons with at least 4 sides (square, pentagon, hexagon and octagon)AR.2.G.8.1 (G.8.2.1) Characteristics and PropertiesThree Dimensional: Identify, name, sort and describe threedimensional solids (cube, sphere, rectangular prism, cone, and cylinder) according to the shapes of facesAR.2.G.8.2 (G.8.2.2) Characteristics and PropertiesThree Dimensional: Match threedimensional objects to their twodimensional facesCC.2.G.2 Reason with shapes and their attributes. Partition a rectangle into rows and columns of samesize squares and count to find the total number of them. VAR.2.M.13.13 (M.13.2.13) Area: Find the area of a region by counting squares on a gridNeeds to address partitioning a rectangle; Grade 3 added g.8.3.2, commentedadd octagon, and rated it a 2. Grade 2 took g.8.3.2 back out.\AR.3.M.13.11 (M.13.3.11) Area: Find the area of any region counting squares and halfsquaresQAR.4.M.13.10 (M.13.4.10) Area: Use strategies for finding the area of a rectanglefAR.K.M.13.7 (M.13.K.7) Area: Cover a figure with one type of shape and tell how many it takes to coverUAR.1.M.13.10 (M.13.1.10) Area: Cover a figure with squares and tell how many it takesYCC.2.G.3 Reason with shapes and their attributes. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. qVocabulary such as partition, describe, and include equal shares of identical wholes need not have the same shapecCC.3.OA.8 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Solve twostep word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).)AR.4.A.5.1 (A.5.4.1) Expressions, Equations and Inequalities: Select and/or write number sentences (equations) to find the unknown in problemsolving contexts involving twodigit by onedigit division using appropriate labelsAR.6.A.5.2 (A.5.6.2) Expressions, Equations and Inequalities: Write simple algebraic expressions using appropriate operations (+, , x, /) with one variableAR.6.A.5.3 (A.5.6.3) Expressions, Equations and Inequalities: Evaluate algebraic expressions with one variable using appropriate properties and operations (+, , x, /)AR.6.NO.2.4 (NO.2.6.4) Number theory: Apply rules (conventions) for order of operations to whole numbers with and without parenthesesGrade
Matched GradeNotesCC1VCC.K.CC.1 Know number names and the count sequence. Count to 100 by ones and by tens. KAR.K.A.4.4 (A.4.K.4) Recognize, describe and develop patterns: Use patterns to rote count up to 100 and count backward from 20 to 0AAR.K.A.4.5 (A.4.K.5) Recognize, describe and develop patterns: Identify, describe and extend skipcounting patterns by 5s and 10sAR.5.G.10.1 (G.10.5.1) Coordinate Geometry: Use geometric vocabulary (horizontal/xaxis, vertical/ yaxis, ordered pairs) to describe the location and plot points in Quadrant ICC.5.MD.2 Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.PInclude the unit as being fractions in line plots only. m.13.7.2 matced as a 3.AR.2.A.4.4 (A.4.2.4) Recognize, describe and develop patterns: Identify, describe and extend skip counting patterns from any given number1cc. adds to 1000, AR picks up in a.4.3.1, a.4.3.2AR.3.A.4.1 (A.4.3.1) Recognize, describe and develop patterns: Count forward and backward when given a number less than or equal to 1000 ____, 399, ___, ____nAR.3.A.4.2 (A.4.3.2) Recognize, describe and develop patterns: Relate skipcounting patterns to multiplicationAR.2.A.4.3 (A.4.2.3) Recognize, describe and develop patterns: Use patterns to count forward and backward when given a number less than or equal to 100 ___, 69, ___, ___{CC.2.NBT.3 Understand place value. Read and write numbers to 1000 using baseten numerals, number names, and expanded form.Fcc to 1000, AR to only 100; Grade 3 included no.1.3.1 and rated it a 3AR.3.NO.1.1 (NO.1.3.1) Whole Numbers: Recognize equivalent representations for the same whole number and generate them by composing and decomposing numbersCC.2.NBT.4 Understand place value. Compare two threedigit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.cc says compare 2 3digit numbers, AR 3rd grade jumps to 4 digit; Doeasn't include thousands, models, illistrates, problemsolvingAR.3.NO.1.3 (NO.1.3.3) Whole Numbers: Use mathematical language and symbols to compare and order fourdigit numbers with and without appropriate technologyCC.2.NBT.5 Use place value understanding and properties of operations to add and subtract. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. no.3.2.2  3rd gradeCC.2.NBT.6 Use place value understanding and properties of operations to add and subtract. Add up to four twodigit numbers using strategies based on place value and properties of operations.yAR.3.NO.3.1 (NO.3.3.1) Computational FluencyAddition and Subtraction: Develop, with and without appropriate technology, computational fluency, in multidigit addition and subtraction through 999 using contextual problems:
 strategies for adding and subtracting numbers,
 estimation of sums and differences in appropriate situations,
 relationships between operationsb3rd grade; Grade 3 added no.3.3.4 and rated it a 3.; Grade 2 rated it a 2 due to specific languageAR.3.NO.3.4 (NO.3.3.4) Application of Computation: Solve simple problems using one operation involving addition and subtraction using a variety of methods and tools (e.g., objects, mental computation, paper and pencil and with and without appropriate technology)CC.2.MD.8 Work with time and money. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ (dollars) and (cents) symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? \AR.2.M.13.4 (M.13.2.4) Money: Determine the value of a combination of coins up to the dollari3rd grade added values to $10 add rated it a 2. Grade 1 added money problems. Grade 1  actual measuring.qAR.2.M.13.5 (M.13.2.5) Money: Demonstrate a given value of money up to $1.00 using a variety of coin combinationslAR.2.M.13.6 (M.13.2.6) Money: Demonstrate a given value of money up to $1.00 using the fewest coins possibleAR.7.A.6.3 (A.6.7.3) Algebraic Models and Relationships: Create and complete a function table (input/output) using a given rule with two operations in real world situationsCC.5.G.2 Gra< ph points on the coordinate plane to solve realworld and mathematical problems. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. KCC.5.G.3 Classify twodimensional figures into categories based on their properties. Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.add classify anglesTF.8CC.912.F.TF.8 Prove and apply trigonometric identities. Prove the Pythagorean identity (sin A)^2 + (cos A)^2 = 1 and use it to find sin A, cos A, or tan A, given sin A, cos A, or tan A, and the quadrant of the angle.AR.912.TEI.PCT.7.1 (TEI.7.PCT.1) Develop the Pythagorean Identities and use to verify other identities and simplify expressionsTF.9CC.912.F.TF.9 (+) Prove and apply trigonometric identities. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.AR.912.TEI.PCT.7.2 (TEI.7.PCT.2) Develop and use trigonometric formulas including sum and difference formulas and multipleangle formulasCO.1CC.912.G.CO.1 Experiment with transformations in the plane. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.AR.912.LG.G.1.2 (LG.1.G.2) Represent points, lines, and planes pictorially with proper identification, as well as basic concepts derived from these undefined terms, such as segments, rays, and anglesCO.2CC.912.G.CO.2 Experiment with transformations in the plane. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).CO.3CC.912.G.CO.3 Experiment with transformations in the plane. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.EAR.912.R.G.4.3 (R.4.G.3) Identify and explain why figures tessellateCO.4pAR.5.G.8.4 (G.8.5.4) Characteristics of Geometric Shapes: Model and identify the properties of congruent figuresAR.4.G.9.1 (G.9.4.1) Symmetry and Transformations: Determine the result of a transformation of a twodimensional figure as a slide (translation), flip (reflection) or turn (rotation) and justify the answerCC.8.G.3 Understand congruence and similarity using physical models, transparencies, or geometry software. Describe the effect of dilations, translations, rotations and reflections on twodimensional figures using coordinates.KAR standard cgt.5.6.7 should also be matched, but not loaded into system. CC.8.G.4 Understand congruence and similarity using physical models, transparencies, or geometry software. Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them.)AR CGT.5.G.7 does not include similarity.AR.3.G.9.2 (G.9.3.2) Symmetry and Transformations: Describe the motion (transformation) of a twodimensional figure as a flip (reflection), slide (translation) or turn (rotation)BCC.1.NBT.4 Use place value understanding and properties of operations to add and subtract. Add within 100, including adding a twodigit number and a onedigit number, and adding a twodigit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding twodigit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. AR.2.NO.3.2 (NO.3.2.2) Computational FluencyAddition and Subtraction: Demonstrate multiple strategies for adding or subtracting twodigit whole numbers:
 Compatible Numbers,
 compensatory numbers,
 informal use of commutative and associative properties of additionNeeds more specific languageCC.1.NBT.5 Use place value understanding and properties of operations to add and subtract. Given a twodigit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.AR.2.A.4.5 (A.4.2.5) Recognize, describe and develop patterns: Identify a number that is more or less than any whole number less than 100 using multiples of tenAddressed in 2nd gradeCC.1.NBT.6 Use place value understanding and properties of operations to add and subtract. Subtract multiples of 10 in the range 1090 from multiples of 10 in the range 1090 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 1Does not address written method and strategy usedAR.3.A.4.3 (A.4.3.3) Recognize, describe and develop patterns: Identify a number that is more or less than any whole number up to 1000 using multiples of ten and/or 100AR.4.A.4.1 (A.4.4.1) Recognize, describe and develop patterns: Identify a number that is more or less than any whole number using multiples of 10, 100 and/or 1000CC.1.MD.1 Measure lengths indirectly and by iterating length units. Order three objects by length; compare the lengths of two objects indirectly by using a third object. rAR.1.M.13.8 (M.13.1.8) Applications: Estimate and measure length, capacity/volume and mass with nonstandard units"Language needs to be more specificAR.K.M.13.5 (M.13.K.5) Applications: Estimate and measure length, capacity/volume and mass of familiar objects using nonstandard unitsAR.2.M.13.11 (M.13.2.11) Applications: Estimate and measure length, capacity/volume and mass with nonstandard units to recognize the need for standard unitsWAR does not require the comparison of the algebraic solution to the arithmetic solutionNo Match to AR Standards!No Matches in Arkansas Frameworks;CC.3.OA.4 Represent and solve problems involving multiplication and division. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 ? = 48, 5 = __ 3, 6 6 = ?.AR.3.A.5.1 (A.5.3.1) Expressions, Equations and Inequalities: Select and/or write number sentences (equations) to find the unknown in problem solving contexts involving twodigit times onedigit multiplication using appropriate labelsAR.3.A.5.3 (A.5.3.3) Expressions, Equations and Inequalities: Use a symbol to represent an unknown quantity in a number sentence involving contextual situations and find the valueAR.4.A.5.3 (A.5.4.3) Expressions, Equations and Inequalities: Use a variable to represent an unknown quantity in a number sentence involving contextual situations and find the valueECC.K.OA.3 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). AR.K.NO.1.2 (NO.1.K.2) Whole Numbers: Group physical objects to represent a whole number less than 10 in at least two ways using composition and decomposition,CC.K.OA.4 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. For any number from 1 to 9, find the number that makes 10 when added to the g< iven number, e.g., by using objects or drawings, and record the answer with a drawing or equation.AR.1.NO.1.2 (NO.1.1.2) Whole Numbers: Represent a whole number less than 15 in all possible ways using composition and decompositionCC.K.OA.5 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Fluently add and subtract within 5.NBTCC.K.NBT.1 Work with numbers 1119 to gain foundations for place value. Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. sAR.2.NO.1.2 (NO.1.2.2) Whole Numbers: Represent a whole number in multiple ways using composition and decompositionMDCC.K.MD.1 Describe and compare measurable attributes. Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.AR.K.M.12.7 (M.12.K.7) Tools and Attributes: Explore the attributes of length, weight, capacity, and mass using relative terms (longer, shorter, bigger, smaller, heavier, lighter, more and less) some of AR are very weak matchesSAR.K.A.4.1 (A.4.K.1) Sort and Classify: Identify how objects are alike or differentAR.1.M.12.1 (M.12.1.1) Time: Calendar: Recognize the number of days in a week and the number of days in a month using a calendarMAR.1.M.12.2 (M.12.1.2) Time: Calendar: Orally sequence the months of the yearAR.2.M.12.1 (M.12.2.1) Time: Calendar: Recognize that there are 12 months in a year and that each month has a specific number of daysAR.3.M.12.1 (M.12.3.1) Time: Calendar: Determine the number of days in a month, days in a year and identify the number of weeks in a yearAR.K.M.12.1 (M.12.K.1) Time: Calendar: Recognize that a calendar is used to measure time and use it to identify units of time (day, week, month, season, year) and compare them5CC.K.MD.2 Describe and compare measurable attributes. Directly compare two objects with a measurable attribute in common, to see which object has more of / less of the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.CC.K.G.6 Analyze, compare, create, and compose shapes. Compose simple shapes to form larger shapes. For example, "can you join these two triangles with full sides touching to make a rectangle? AR.2.G.11.2 (G.11.2.2) Spatial Visualization and Models: Create new figures by combining and subdividing models of existing figuresAR.1.G.11.2 (G.11.1.2) Spatial Visualization and Models: Recognize that new figures can be created by combining and subdividing models of existing figureswCC.1.OA.1 Represent and solve problems involving addition and subtraction. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. gAR.2.NO.2.5 (NO.2.2.5) Whole Number Operations: Demonstrate various meaning of addition and subtractionNeed specific languageCC.4.NF.7 Understand decimal notation for fractions, and compare decimal fractions. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons comparisons are valid only when two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)remove percentfrom 1.6.4 and remove mixed numbers and integers from No. 1.7.5 and for No.1.5.3, NO. 1.6.2 and for 1.7.4 remove percentAR.7.NO.1.5 (NO.1.7.5) Rational Numbers: Compare and represent integers, fractions, decimals and mixed numbers and find their approximate location on a number lineCC.6.NS.7d Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than 30 dollars represents a debt greater than 30 dollars.ZCC.6.NS.8 Apply and extend previous understandings of numbers to the system of rational numbers. Solve realworld and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.EECC.6.EE.1 Apply and extend previous understandings of arithmetic to algebraic expressions. Write and evaluate numerical expressions involving wholenumber exponents.AR.5.A.5.3 (A.5.5.3) Expressions, Equations and Inequalities: Select, write and evaluate algebraic expressions with one variable by substitution43 collectively, 2 individually. no.3.7.5exponents.AR.7.A.5.4 (A.5.7.4) Expressions, Equations and Inequalities: Write and evaluate algebraic expressions using positive rational numbers}AR.8.A.5.4 (A.5.8.4) Expressions, Equations and Inequalities: Write and evaluate algebraic expressions using rational numbersAR.5.NO.3.5 (NO.3.5.5) Application of Computation: Use factors of numbers:
 to introduce exponents,
 to find common factors of two numbers,
 to simplify fractions to the lowest termsCC.6.EE.2 Apply and extend previous understandings of arithmetic to algebraic expressions. Write, read, and evaluate expressions in which letters stand for numbers.AR.5.A.5.2 (A.5.5.2) Expressions, Equations and Inequalities: Write expressions containing one variable (a letter representing an unknown quantity) using rules for addition and subtractionCC.6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5 y. #a.5.6.3 is rated at 3 instead of 2.AR.K.NO.1.11 (NO.1.K.11) Rational Numbers: Use physical models and drawings to represent commonly used fractions such as halves, thirds and fourths in relation to the wholeAR.2.NO.1.10 (NO.1.2.10) Rational Numbers: Utilize models to recognize that a fractional part can mean different amounts depending on the original quantityCC.2.OA.1 Represent and solve problems involving addition and subtraction. Use addition and subtraction within 100 to solve one and twostep word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. =in context situations model reps. AR add division as sharing.AR.2.NO.2.7 (NO.2.2.7) Whole Number Operations: Model, represent and explain division as sharing equally and repeated subtraction in contextual situationsAR.2.NO.3.4 (NO.3.2.4) Application of Computation: Solve problems using a variety of methods and tools (e.g., objects, mental computation, paper and pencil, and with and without appropriate technology)AR.2.A.5.1 (A.5.2.1) Expressions, Equations and Inequalities< : Select and/or write number sentences to find the unknown in problemsolving contexts involving twodigit addition and subtraction using appropriate labelsCC.2.OA.2 Add and subtract within 20. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two onedigit numbers. %CC.2.OA.3 Work with equal groups of objects to gain foundations for multiplication. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.CC.7.RP.2c Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.AR includes tables and graphs.2dCC.5.OA.2 Write and interpret numerical expressions. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation add 8 and 7, then multiply by 2 as 2 (8 + 7). Recognize that 3 (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.AR.5.NO.3.3 (NO.3.5.3) Computational Fluency: Solve, with and without appropriate technology, twostep problems using a variety of methods and tools (i.e. objects, mental computation, paper and pencil)AR.5.NO.3.4 (NO.3.5.4) Estimation: Develop and use strategies to estimate the results of whole number computations and to judge the reasonableness of such resultsAR.6.NO.3.3 (NO.3.6.3) Computational Fluency: Solve, with and without appropriate technology, multistep problems using a variety of methods and tools (i.e., objects, mental computation, paper and pencil)AR.7.NO.3.2 (NO.3.7.2) Computational Fluency: Solve with and without appropriate technology, multistep problems using a variety of methods and tools (i.e., objects, mental computation, paper and pencil)AR.8.NO.3.2 (NO.3.8.2) Computational Fluency: Solve, with and without appropriate technology, multistep problems using a variety of methods and tools (i.e. objects, mental computation, paper and pencil)HCC.5.OA.3 Analyze patterns and relationships. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. uAR.7.A.4.3 (A.4.7.3) Patterns, Relations and Functions: Interpret and write a rule for a two operation function tableAR.7.A.5.2 (A.5.7.2) Expressions, Equations and Inequalities: Solve simple linear equations using integers and graph on a coordinate planemAR.7.A.4.2 (A.4.7.2) Patterns, Relations and Functions: Identify and extend patterns in real world situationsCC.5.NBT.1 Understand the place value system. Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 7CC.5.NBT.2 Understand the place value system. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10.AR.7.NO.1.2 (NO.1.7.2) Rational Numbers: Demonstrate, with and without appropriate technology, an understanding of place value using powers of 10 and write numbers greater than one in scientific notationAR.7.NO.1.3 (NO.1.7.3) Rational Numbers: Convert between scientific notation and standard notation using numbers greater than one._CC.5.NBT.3 Understand the place value system. Read, write, and compare decimals to thousandths.2Only goes to hundrethsneed to go to thousandths.pAR.6.NO.1.3 (NO.1.6.3) Rational Numbers: Round and compare decimals to a given place value including thousandthsAR.3.NO.1.6 (NO.1.3.6) Rational Numbers: Use the place value structure of the base ten number system and be able to represent and compare decimals to hundredths in money (using models, illustrations, symbols, expanded notation and problem solving)CC.5.NBT.3a Read and write decimals to thousandths using baseten numerals, number names, and expanded form, e.g., 347.392 = 3 100 + 4 10 + 7 1 + 3 (1/10) + 9 (1/100) + 2 (1/1000). AR.2.M.13.7 (M.13.2.7) Money: Represent and write the value of money using the cent sign and in decimal form when using the dollar signXAR.3.M.13.6 (M.13.3.6) Money: Apply money concepts in contextual situations up to $10.00DAR.3.M.13.5 (M.13.3.5) Money: Determine the value of money up to $10MAR.K.M.12.5 (M.12.K.5) Money: State the values of coins (penny, nickel, dime)oAR.1.M.12.4 (M.12.1.4) Money: Recognize and identify attributes of penny, nickel, dime, quarter and dollar bill_AR.1.M.12.6 (M.12.1.6) Money: Compare the value of coins (pennies, nickels, dimes and quarters)AR.1.M.13.4 (M.13.1.4) Money: Determine the value of a small collection of coins (with a total value up to one dollar) using one or two different types of coins, including pennies, nickels, dimes and quartersXAR.1.M.13.5 (M.13.1.5) Money: Represent and write the value of money using the cent signAR.3.NO.1.4 (NO.1.3.4) Rational Numbers: Represent fractions (halves, thirds, fourths, sixths and eighths) using words, numerals and physical modelsNo sets or contiguous partsAR.3.NO.1.5 (NO.1.3.5) Rational Numbers: Utilize models to recognize that the size of the whole determines the size of the fraction depending on the original quantityAR.4.NO.1.5 (NO.1.4.5) Rational Numbers: Utilize models, benchmarks, and equivalent forms to recognize that the size of the whole determines the size of the fractionCC.3.NF.2 Develop understanding of fractions as numbers. Understand a fraction as a number on the number line; represent fractions on a number line diagram. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)AR.4.NO.1.4 (NO.1.4.4) Rational Numbers: Write a fraction to name part of a whole, part of a set, a location on a number line, and the division of whole numbers, using modelsSpecify just creating a fractional number line; specify locate a specific fraction by using an endpoint on the created number line for SLE NO1.5.1CC.5.G.4 Classify twodimensional figures into categories based on their properties. Classify twodimensional figures in a hierarchy based on properties.AR.912.R.G.4.2 (R.4.G.2) Solve problems using properties of polygons:
 sum of the measures of the interior angles of a polygon,
 interior and exterior angle measure of a regular polygon or irregular polygon,
<  number of sides or angles of a polygonRPSCC.8.F.5 Use functions to model relationships between quantities. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.AR is not at this high levelCC.8.G.1 Understand congruence and similarity using physical models, transparencies, or geometry software. Verify experimentally the properties of rotations, reflections, and translations:
 a. Lines are taken to lines, and line segments to line segments of the same length.
 b. Angles are taken to angles of the same measure.
 c. Parallel lines are taken to parallel lines. &Arkansas does not include "notations.:oAR.6.G.8.5 (G.8.6.5) Characteristics of Geometric Shapes: Identify similar figures and explore their properties^CC.4.MD.1 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. For example: Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), & . CThere are no AR SLE's that require students to add 3 whole numbers.CC.1.OA.3 Understand and apply properties of operations and the relationship between addition and subtraction. Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) (Students need not use formal terms for these properties.)AR.1.NO.2.2 (NO.2.1.2) Number Theory: Develop an understanding of the commutative (turn around facts) and identity (add 0) properties of addition using objectsYAR.2.NO.2.2 (NO.2.2.2) Number Theory: Model and use the commutative property for additiontAR.2.NO.2.3 (NO.2.2.3) Number Theory: Develop an understanding of the associative property of addition using objectsCC.1.OA.4 Understand and apply properties of operations and the relationship between addition and subtraction. Understand subtraction as an unknownaddend problem. For example, subtract 10 8 by finding the number that makes 10 when added to 8. #AR.1.NO.3.1 (NO.3.1.1) Computational FluencyAddition and Subtraction: Develop strategies for basic addition facts:
 counting all,
 counting on,
 one more, two more,
 doubles,
 doubles plus one or minus one,
 make ten,  using ten frames,
 Identity Property (add zero)Specific languageAR.1.NO.3.2 (NO.3.1.2) Computational FluencyAddition and Subtraction: Develop strategies for basic subtraction facts:
 relating to addition,
 one less, two less,
 all but one,
 using ten frames of the answers'AR.2.NO.3.1 (NO.3.2.1) Computational FluencyAddition and Subtraction: Develop strategies for basic addition facts:
 counting all
 counting on,
 one more, two more,
 doubles,
 doubles plus one or minus one,
 make ten,
 using ten frames,
 Identity Property (add zero)For the 3rd bullet and for 3.5.2 the 4th bulletboth use vocabulary of mixed numbers and improper fractions but no mention of adding and subtractionCC.4.NF.3d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. {For 2.5.5 add contextual situations and only addition and subtraction, and for 3.5.2, add contextual situations, 4th bulletCC.6.SP.2 Develop understanding of statistical variability. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.'Collectively a 3, but individually a 2.
CC.6.RP.3 Understand ratio concepts and use ratio reasoning to solve problems. Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.OCC.3.NF.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)Delete mixed numbers3dCC.3.NF.3d Compare two fractions with the same numerator or the same denominator, by reasoning about their size, Recognize that valid comparisons rely on the two fractions referring to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)Delete decimals and percents]CC.3.MD.1 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
&add in minute on a number line diagramMAR.4.M.12.1 (M.12.4.1) Time: Clock: Recognize that 60 seconds equals 1 minuteKAR.3.M.13.2 (M.13.3.2) Clock: Tell time to the nearest oneminute intervalsAR.6.M.13.1 (M.13.6.1) Attributes and Tools: Solve real world problems involving one elapsed time, counting forward and backward (calendar and clock)mAR.3.M.13.4 (M.13.3.4) Elapsed Time: Determine elapsed time in contextual situations to fiveminute intervalsbCommon Core State Standards Comparison with Arkansas Student Learning Expectations for Mathematics2AR.4.NO.2.2 (NO.2.4.2) Number Theory: Apply number theory:  determine if any number is even or odd,  use the terms 'multiple,' 'factor,' and 'divisible by' in an appropriate context,  generate and use divisibility rules for 2, 5, and 10,  demonstrate various multiplication & division relationshipsAR.3.NO.3.3 (NO.3.3.3) Computational FluencyMultiplication and Division: Develop, with and without appropriate technology, computational fluency in multiplication and division up to twodigit by onedigit numbers using twodigit by onedigit number contextual problems using:  strategies for multiplying and dividing numbers,  performance of operations in more than one way,  estimation of products and quotients in appropriate situations, and  relationships between operationsAR.3.NO.3.2 (NO.3.3.2) Computational FluencyMultiplication and Division: Develop, with and without appropriate technology, fluency with basic number combinations for multiplication and division facts (10 x 10) < ~AR.5.NO.1.1 (NO.1.5.1) Rational Numbers: Use models and visual representations to develop the concepts of the following: Fractions: parts of unit wholes, parts of a collection, locations on number lines, locations on ruler (benchmark fractions), divisions of whole numbers; Ratios: parttopart (2 boys to 3 girls), parttowhole (2 boys to 5 people); Percents: partto100AR.5.NO.1.5 (NO.1.5.5) Rational Numbers: Use models of benchmark fractions and their equivalent forms:  to analyze the size of fractions,  to determine that simplification does not change the value of the fraction,  to convert between mixed numbers and improper fractionsAR.5.M.13.4 (M.13.5.4) Attributes and Tools: Develop and use strategies to solve real world problems involving perimeter and area of rectangle [CAR does not explicitly state relate to multiplication and addition AR.1.NO.1.12 (NO.1.1.12) Rational Numbers: Represent commonly used fractions using words and physical models for halves, thirds and fourthsAR.2.NO.1.9 (NO.1.2.9) Rational Numbers: Represent fractions (halves, thirds, fourths, sixths and eighths) using words, numerals, and physical modelsAR.6.NO.1.2 (NO.1.6.2) Rational Numbers: Find decimal and percent equivalents for proper fractions and explain why they represent the same valueuCC.4.NF.6 Understand decimal notation for fractions, and compare decimal fractions. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)For No.1.6.2, remove percent, and for No.1.7.4, remove 20, for 1.5.3, remove percent, and for No. 1.7.5 remove mixed numbers and integersAR.7.NO.1.4 (NO.1.7.4) Rational Numbers: Find decimal and percent equivalents for mixed numbers and explain why they represent the same valueAR.912.LQF.AIII.1.3 (LQF.1.AIII.3) Develop, write, and graph, given a point and the slope, two points, or a point and a line, the equation of:
 a parallel line
 a perpendicular line
 the perpendicular bisector of a line segmentAR.912.LF.AC.2.7 (LF.2.AC.7) Write an equation given:
 two points,
 a point and yintercept,
 an xintercept and yintercept,
 a point and slope,
 a table of data,
 the graph of a lineAR.912.C.PCT.3.1 (C.3.PCT.1) Identify, graph, write, and analyze equations of conic sections, using properties such as symmetry, intercepts, foci, asymptotes, and eccentricity, and when appropriate, use technologyCED.3pCC.912.A.CED.3 Create equations that describe numbers or relationship. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.*AR.912.LQF.AIII.1.7 (LQF.1.AIII.7) Solve, with and without appropriate technology, systems of linear and quadratic equations and inequalities with two or more variablesAR.912.LEI.AII.2.2 (LEI.2.AII.2) Solve, with and without appropriate technology, systems of linear equations with two variables and graph the solution setAR.912.LEI.AII.2.4 (LEI.2.AII.4) Solve, with and without appropriate technology, systems of linear equations with *three variables using algebraic methods, including matricesAR.912.LEI.AII.2.5 (LEI.2.AII.5) Apply, with or without technology, the concepts of linear and absolute value equations and inequalities and systems of linear equations and inequalities to model real world situations including linear programmingxAR.912.RF.AII.1.5 (RF.1.AII.5) Graph, with and without appropriate technology, functions defined as piecewise and stepAR.3.M.12.5 (M.12.3.5) Tools and Attributes: Create and complete a conversion table (from larger unit to smaller unit) to show relationships between units of measurement in the same systemyAR.5.M.12.3 (M.12.5.3) Attributes and Tools: Establish through experience benchmark prefixes of milli, centi, and kiloAR.4.M.12.4 (M.12.4.4) Tools and Attributes: Create and complete a conversion table to show relationships between units of measurement in the same systemyAR.4.M.13.7 (M.13.4.7) Applications: Use appropriate customary and metric measurement tools for length, capacity and massyAR.1.A.4.4 (A.4.1.4) Recognize, describe and develop patterns: Identify, describe and extend skipcounting patterns by 2sCC.1.OA.6 Add and subtract within 20. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 4 = 13 3 1 = 10 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).AR.2.NO.3.3 (NO.3.2.3) Computational FluencyAddition and Subtraction: Demonstrate computational fluency (accuracy, efficiency and flexibility) in addition facts with addends through 9 and corresponding subtractions2CC.1.OA.7 Work with addition and subtraction equations. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.AR.1.A.5.2 (A.5.1.2) Expressions, Equations and Inequalities: Recognize that "=" indicates a relationship in which the quantities on each side of an equation are equalWNeeds to address determining if an equation involving add/subtraction is true or false.AR.2.A.5.2 (A.5.2.2) Expressions, Equations and Inequalities: Express mathematical relationships using equalities and inequalities (>, <, =, `")AR.3.A.5.2 (A.5.3.2) Expressions, Equations and Inequalities: Express mathematical relationships using equalities and inequalities (>, <, =, `")8#CC.1.OA.8 Work with addition and subtraction equations. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? 3, 6 + 6 = ?. AUses the word recognizes symbols verses determine unknown number.CC.1.NBT.1 Extend the counting sequence. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.< AR.1.A.4.3 (A.4.1.3) Recognize, describe and develop patterns: Use patterns to count forward and backward when given a number less than or equal to 50)Count up to 120 in CC but less than in ARAR.1.NO.2.1 (NO.2.1.1) Number Theory: Count on (forward) and back (backward) using physical models or a number line starting at any whole number up to fiftyAR.2.NO.2.1 (NO.2.2.1) Number Theory: Count on (forward) and back (backward) on a number line and a 100's chart starting at any whole number up to 100CC.1.NBT.2 Understand place value. Understand that the two digits of a twodigit number represent amounts of tens and ones. Understand the following as special cases:
 a. 10 can be thought of as a bundle of ten ones called a ten.
 b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
 c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).NAR.K.NO.1.4 (NO.1.K.4) Whole Numbers: Represent numbers to 10 in various formsaThis has a collective rating of a three for parts
A. and B., but part C. shows as a "No Match."NAR.1.NO.1.4 (NO.1.1.4) Whole Numbers: Represent numbers to 20 in various formszAR.1.NO.1.5 (NO.1.1.5) Whole Numbers: Use multiple models to develop understandings of place value including tens and onesCC.1.NBT.3 Understand place value. Compare two twodigit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. AR.2.NO.1.7 (NO.1.2.7) Whole Numbers: Compare 2 numbers, less than 100 using numerals and =, <, > with and without appropriate technologySymbols <,>,=, not addressed in first grade and excludes specific value language. In first grade and excludes specific place value languageAR.1.NO.1.10 (NO.1.1.10) Whole Numbers: Compare 2 numbers, less than 100 using mathematical language of greater than, equal to (same amount as), less thanAR.1.NO.1.11 (NO.1.1.11) Rational Numbers: Communicate the relative position of any number less than 20 (18 is less than 20 and greater than 12)AR.2.NO.1.8 (NO.1.2.8) Rational Numbers: Communicate the relative position of any number less than 100 (27 is greater than 25 and less than 30)dCC.3.OA.5 Understand properties of multiplication and the relationship between multiplication and division. Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication.) 3 5 2 can be found by 3 5 = 15 then 15 2 = 30, or by 5 2 = 10 then 3 10 = 30. (Associative property of multiplication.) Knowing that 8 5 = 40 and 8 2 = 16, one can find 8 7 as 8 (5 + 2) = (8 5) + (8 2) = 40 + 16 = 56. (Distributive property.) (Students need not use formal terms for these properties.)AR.4.NO.2.1 (NO.2.4.1) Number Theory: Develop an understanding of the associative and zero properties of multiplication using objectsUAR.5.NO.2.2 (NO.2.5.2) Number theory: Identify commutative and associative propertiesAR.5.NO.2.3 (NO.2.5.3) Number theory: Identify the distributive property by using physical models to solve computation and real world problemsAR.K.DAP.14.1 (DAP.14.K.1) Collect, Organize and display data: Explore and discuss data collection by collecting, organizing and displaying physical objectsMSpecific language; needs frequency tables, line plots, pictographs, bar graphAR.2.DAP.14.1 (DAP.14.2.1) Collect, Organize and display data: Identify the purpose for data collection and collect, organize, record and display the data using physical materials (pictographs, Venn diagrams and vertical and horizontal bar graphs)AR.3.DAP.14.1 (DAP.14.3.1) Collect, Organize and display data: Design a survey question after being given a topic and collect, organize, display and describe simple data using frequency tables or line plots, pictographs, and bar graphsAR.K.DAP.15.1 (DAP.15.K.1) Data Analysis: Analyze and interpret concrete and pictorial graphs (i.e. bar graphs, pictographs, Venn diagrams, Tchart)qAR.2.DAP.15.1 (DAP.15.2.1) Data Analysis: Analyze and make predictions from data represented in charts and graphsAR.1.DAP.14.1 (DAP.14.1.1) Collect, Organize and display data: Identify the purpose for data collection and collect, organize and display physical objects for describing the resultsAR.2.NO.2.4 (NO.2.2.4) Number Theory: Apply number theory:
 determine if a twodigit number is odd or even,
 use the terms sum, addends, and difference in an appropriate context (2 + 3 = 5, 2 and 3 are addends; 5 is a sum).Pcovers odd, even only; cc goes up to 20, AR.n.2.3.2 includes threedigit numbersAR.3.NO.2.2 (NO.2.3.2) Number Theory: Apply number theory:
 determine if a threedigit number is even or odd,
 use the terms multiple, factor, product and quotient in an appropriate contextAR.1.NO.2.3 (NO.2.1.3) Number Theory: Apply number theory:
 determine if a onedigit number is odd or even,
 use the terms sum and difference in appropriate context,
 use conventional symbols (+, , =) to represent the operations of addition and subtraction.CC.2.OA.4 Work with equal groups of objects to gain foundations for multiplication. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.AR.3.NO.2.4 (NO.2.3.4) Whole Number Operations: Model, represent and explain division as measurement and partitive division including equal groups, related rates, price, rectangular arrays (area model), combinations and multiplicative comparisonthird grade, not found in 2
kAR.2.G.10.1 (G.10.2.1) Coordinate Geometry: Extend the use of directional words to include rows and columnsCC.2.NBT.1 Understand place value. Understand that the three digits of a threedigit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
 a. 100 can be thought of as a bundle of ten tens called a hundred.
 b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).OAR.2.NO.1.4 (NO.1.2.4) Whole Numbers: Represent numbers to 100 in various formsAR.4.NO.1.2 (NO.1.4.2) Whole Numbers: Use the place value structure of the base ten number system and be able to represent and compare whole numbers to millions (using models, illustrations, symbols, expanded notation and problem solving)AR.3.NO.1.2 (NO.1.3.2) Whole Numbers: Use the place value structure of the base ten number system and be able to represent and compare whole numbers including thousands (using models, illustrations, symbols, expanded notation and problem solving)vAR.2.NO.1.5 (NO.1.2.5) Whole Numbers: Use multiple models to represent understanding of place value including hundredsVCC.2.NBT.2 Understand place value. Count within 1000; skipcount by 5s, 10s, and 100s.<AR.2.M.12.4 (M.12.2.4) Money: Compare the value of all coins< GAR.2.M.12.3 (M.12.2.3) Money: State the value of all coins and a dollardAR.1.M.12.5 (M.12.1.5) Money: State the values of a penny, nickel, dime, and quarter and dollar billZAR.1.M.13.6 (M.13.1.6) Money: Show different combination of coins that have the same valuecAR.K.M.12.4 (M.12.K.4) Money: Recognize and identify attributes of penny, nickel, dime, and quarter10CC.2.MD.10 Represent and interpret data. Draw a picture graph and a bar graph (with singleunit scale) to represent a data set with up to four categories. Solve simple puttogether, takeapart, and compare problems using information presented in a bar graph. add solve simple problems . . . put together, take apart, compare problems using info. from graph; Grade 3 added dap.15.3.1, commented increments greater than 1, and rated it a 2. Grade 2 added No prodicitons or inferences problem solving with data. AR.3.DAP.15.1 (DAP.15.3.1) Data Analysis: Read and interpret pictographs and bar graphs in which symbols or intervals are greater than onefAR.2.DAP.16.1 (DAP.16.2.1) Inferences and Predictions: Make simple predictions for a given set of datakAR.2.DAP.15.2 (DAP.15.2.2) Data Analysis: Make true statements comparing data displayed on a graph or chartCC.6.RP.1 Understand ratio concepts and use ratio reasoning to solve problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. For every vote candidate A received, candidate C received nearly three votes. AR.6.NO.3.6 (NO.3.6.6) Application of Computation: Use proportional reasoning and ratios to represent problem situations and determine the reasonableness of solutions with and without appropriate technology~AR.4.A.7.1 (A.7.4.1) Analyze Change: Identify, describe and generalize relationships in which quantities change proportionallyCC.6.RP.2 Understand ratio concepts and use ratio reasoning to solve problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b `" 0 (b not equal to zero), and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." (Expectations for unit rates in this grade are limited to noncomplex fractions.)CC.6.EE.2c Evaluate expressions at specific values for their variables. Include expressions that arise from formulas in realworld problems. Perform arithmetic operations, including those involving wholenumber exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s^3 and A = 6 s^2 to find the volume and surface area of a cube with sides of length s = 1/2. AR.7.NO.2.3 (NO.2.7.3) Number theory: Apply rules (conventions) for order of operations to integers and positive rational numbers including parentheses, brackets or exponentskAR.8.NO.2.4 (NO.2.8.4) Number theory: Apply rules (conventions) for order of operations to rational numbersAR.6.M.13.4 (M.13.6.4) Attributes and Tools: Establish and apply formulas to find area and perimeter of triangles, rectangles, and parallelogramsCC.6.EE.3 Apply and extend previous understandings of arithmetic to algebraic expressions. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.AR.7.NO.2.1 (NO.2.7.1) Number theory: Apply the distributive property of multiplication over addition or subtraction to simplify computations with integers, fractions and decimalsAR.8.A.5.3 (A.5.8.3) Expressions, Equations and Inequalities: Translate sentences into algebraic equations and inequalities and combine like terms within polynomialsyCC.6.EE.4 Apply and extend previous understandings of arithmetic to algebraic expressions. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.[CC.6.EE.5 Reason about and solve onevariable equations and inequalities. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.AR.8.A.5.1 (A.5.8.1) Expressions, Equations and Inequalities: Solve and graph twostep equations and inequalities with one variable and verify the reasonableness of the result with real world application with and without technologya.5.8.1 is rated a 3.<Grade 3 added no.1.3.3 and commentedonly through 4 digits.AR.K.NO.1.8 (NO.1.K.8) Whole Numbers: Compare 2 numbers, with less than 6 in each set, using objects and pictures, with and without appropriate technologyAR.K.NO.1.9 (NO.1.K.9) Whole Numbers: Compare and order numbers less than twenty using terms more than, same amount as, less thanAR.K.A.5.2 (A.5.K.2) Expressions, Equations and Inequalities: Identify, create, compare and describe sets of objects as more, less or equalbAR.1.M.12.7 (M.12.1.7) Temperature: Distinguish between hot and cold temperatures on a thermometerhAR.K.M.12.6 (M.12.K.6) Temperature: Differentiate and make connections between hot and cold temperatures7^CC.K.CC.7 Compare numbers. Compare two numbers between 1 and 10 presented as written numerals./Add language written numbers; specific languageOAAR.6.A.5.2 (A.5.6.2) Expressions, Equations and Inequalities: Write simple algebraic expressions using appropriate operations (+, , x, /) with one variableAR.6.A.5.3 (A.5.6.3) Expressions, Equations and Inequalities: Evaluate algebraic expressions with one variable using appropriate properties and operations (+, , x, /)AR.Geo.R.G.4.2 (R.4.G.2) Solve problems using properties of polygons:
 sum of the measures of the interior angles of a polygon,
 interior and exterior angle measure of a regular polygon or irregular polygon,
 number of sides or angles of a polygonCC.3.NBT.1 Use place value understanding and properties of operations to perform multidigit arithmetic. Use place value understanding to round whole numbers to the nearest 10 or 100AR.2.M.12.6 (M.12.2.6) Tools and Attributes: Make simple comparisons within units of like dimension (units of length, mass/weight and capacity)AR.K.A.4.2 (A.4.K.2) Sort and Classify: Sort objects into groups in one or more ways and identify which attribute was used to sortNAR.2.A.7.1 (A.7.2.1) Analyze Change: Interpret and compare quantitative changeBAR.3.A.7.1 (A.7.3.1) Analyze Change: Identify the change ove< r timeAR.4.DAP.14.1 (DAP.14.4.1) Collect, Organize and display data: Create a data collection plan after being given a topic and collect, organize, display, describe and interpret simple data using frequency tables or line plots, pictographs and bar graphstAR.5.DAP.15.1 (DAP.15.5.1) Data Analysis: Interpret graphs such as line graphs, double bar graphs, and circle graphs6CC.2.G.1 Reason with shapes and their attributes. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. (Sizes are compared directly or visually, not compared by measuring.)8Specific language to include specific shapes and drawingeAR says nonstandard for 2nd; CC says standard; Grade 3 commentedlength only,area, wieght, capacity CC.1.MD.2 Measure lengths indirectly and by iterating length units. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of samesize length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.AR.1.M.12.8 (M.12.1.8) Tools and Attributes: Recognize attributes of measurement (length, weight, capacity and mass) and identify appropriate tools used to measure each attributexAR.1.M.13.7 (M.13.1.7) Applications: Select the appropriate nonstandard measurement tools for length, capacity and masshAR.1.M.13.9 (M.13.1.9) Perimeter: Surround a figure with objects and tell how many it takes to go aroundAR.2.M.13.12 (M.13.2.12) Perimeter: Determine perimeter using physical materials (paper clips, craft sticks or grids) and by using measurement tools (rulers)kCC.1.MD.3 Tell and write time. Tell and write time in hours and halfhours using analog and digital clocks.8AR.1.M.13.2 (M.13.1.2) Clock: Tell time to the halfhourpAdd write in hours and halfhours; Grade 1 "only time found" CC does not include quarter till and quarter after AR.3.M.13.3 (M.13.3.3) Clock: Express time to the half hour and quarter hour using the terms half past, quarter after, quarteruntilOAR.K.M.12.3 (M.12.K.3) Time: Clock: Recognize that a clock is used to tell timecAR.K.M.13.2 (M.13.K.2) Clock: Tell time to the hour the nearest hour using analog and digital clockCC.1.MD.4 Represent and interpret data. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.AR.912.QEF.AII.3.3 (QEF.3.AII.3) Analyze and solve quadratic equations with and without appropriate technology by:  factoring,  graphing,  extracting the square root,  completing the square,  using the quadratic formulaAR.912.PRF.AII.4.1 (PRF.4.AII.1) Determine the factors of polynomials by:  using factoring techniques including grouping and the sum or difference of two cubes,  using long division,  using synthetic divisionzAR.912.LF.AI.3.6 (LF.3.AI.6) Calculate the slope given:  two points,  the graph of a line,  the equation of a line%CC.3.OA.1 Represent and solve problems involving multiplication and division. Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 7. AR.3.NO.2.3 (NO.2.3.3) Whole Number Operations: Use conventional mathematical symbols to write equations for contextual problems involving multiplication@For Arkansas standard NO.2.3.2, the second bullet is applicable.AR.3.NO.2.1 (NO.2.3.1) Number Theory: Develop an understanding of the commutative and identity properties of multiplication using objectsCC.3.OA.2 Represent and solve problems involving multiplication and division. Interpret wholenumber quotients of whole numbers, e.g., interpret 56 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 8.AR.K.NO.2.4 (NO.2.K.4) Whole Number Operations: Partition or share a small set of objects into groups of equal size e.g., sharing 6 pencils equally among 3 childrenxAR.1.NO.2.6 (NO.2.1.6) Whole Number Operations: Model and represent division as sharing equally in contextual situationsxAR.1.NO.1.1 (NO.1.1.1) Whole Numbers: Use efficient strategies to count a given set of objects in groups of 10 up to 1002CC.K.CC.2 Know number names and the count sequence. Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
AR.K.NO.2.1 (NO.2.K.1) Number Theory: Count on (forward) and count back (backward) using physical models or a number line starting at any whole number between zero and twenty3CC.K.CC.3 Know number names and the count sequence. Write numbers from 0 to 20. Represent a number of objects with a written numeral 020 (with 0 representing a count of no objects).AR.K.NO.1.3 (NO.1.K.3) Whole Numbers: Connect various physical models and representations to the quantities they represent using number names, numerals and number words up to 10 with and without appropriate technologyAR.1.NO.1.3 (NO.1.1.3) Whole Numbers: Connect various physical models and representations to the quantities they represent using number names, numerals and number words to 20 with and without appropriate technology4CC.K.CC.4 Count to tell the number of objects. Understand the relationship between numbers and quantities; connect counting to cardinality. AR.2.NO.1.3 (NO.1.2.3) Whole Numbers: Connect various physical models and representations to the quantities they represent using number names, numerals and number words to 100 with and without appropriate technologyAR.K.NO.1.1 (NO.1.K.1) Whole Numbers: Count with understanding, explaining that each object should be counted only once and that placement of objects does not change the total amountAR.K.NO.1.5 (NO.1.K.5) Whole Numbers: Recognize the number or quantity in sets up to 5 without counting, regardless of arrangementdAR.K.NO.1.10 (NO.1.K.10) Rational Numbers: Consecutively order sets of physical objects from 1 to 104aCC.K.CC.4a When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.4bCC.K.CC.4b Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.5CC.K.CC.5 Count to tell the number of objects. Count to answer how many? questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 120, count out that many objects.AR.1.NO.1.6 (NO.1.1.6) Whole Numbers: Recognize the number or quantity of sets up to 10 without counting, regardless of arrangementAR.K.NO.1.6 (NO.1.K.6) Whole Numbers: Estimate quantities fewer than or equal to 10 and judge the reasonableness of the estimate6CC.K.CC.6 Compare numbers. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. (Include groups with up to ten objects.)AR.1.NO.1.9 (NO.1.1.9) Whole Numbers: Compare 2 numbers, with less than 12 in each set, using objects and pictures with and without appro<priate technologyAR.3.A.4.5 (A.4.3.5) Patterns, Relations and Functions: Determine the relationship between sets of numbers by selecting the rule (1 step rule in words)AR.5.A.4.1 (A.4.5.1) Patterns, Relations and Functions: Solve problems by finding the next term or missing term in a pattern or function table using real world situationsAR.6.A.4.1 (A.4.6.1) Patterns, Relations and Functions: Solve problems by finding the next term or missing term in a pattern or function table using real world situationsCC.4.NBT.1 Generalize place value understanding for multidigit whole numbers. Recognize that in a multidigit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 70 = 10 by applying concepts of place value and division. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)AR.K.G.8.1 (G.8.K.1) Characteristics and PropertiesThree Dimensional: Sort and describe threedimensional solids (sphere, cube, cone, and cylinder) by investigating their physical characteristicsAR.K.G.8.2 (G.8.K.2) Characteristics and PropertiesThree Dimensional: Locate the presence of twodimensional figures within threedimensional objects in the environmentAR.1.G.8.3 (G.8.1.3) Characteristics and PropertiesTwo Dimensional: Compare and make geometric figures (triangle, rectangle [including square] and circle) by investigating their physical characteristics independent of position or sizeAR.K.G.10.1 (G.10.K.1) Coordinate Geometry: Demonstrate and describe the relative position of objects as follows: over, under, inside, outside, on, beside, between, above, below, on top of, upsidedown, behind, in back of and in front ofAR.1.G.8.2 (G.8.1.2) Characteristics and PropertiesThree Dimensional: Investigate the presence of threedimensional objects in the environmentAR.1.G.10.1 (G.10.1.1) Coordinate Geometry: Extend the use of location words to include distance (near, far, close to) and direction (left and right)pAR.1.A.4.2 (A.4.1.2) Recognize, describe and develop patterns: Identify and describe patterns in the environmentcAR.K.A.4.3 (A.4.K.3) Recognize, describe and develop patterns: Identify patterns in the environmentCC.K.G.2 Identify and describe shapes (such as squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Correctly name shapes regardless of their orientations or overall size.CC.K.G.3 Identify and describe shapes (such as squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Identify shapes as twodimensional (lying in a plane, flat ) or threedimensional ( solid ).AR.4.NO.3.4 (NO.3.4.4) Application of Computation: Solve simple problems using operations involving addition, subtraction, and multiplication using a variety of methods and tools (e.g., objects, mental computation, paper and pencil and with and without appropriate technology)?CC.4.OA.2 Use the four operations with whole numbers to solve problems. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. 6For AR standard 2.4.4, note divisionwithout remainderAR.4.NO.2.3 (NO.2.4.3) Whole Number Operations: Use conventional mathematical symbols to write equations for contextual problems involving multiplicationCC.4.OA.3 Use the four operations with whole numbers to solve problems. Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. 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