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Arkansas Mathematics Standards (adopted in 2023): Advanced Topics & Modeling Arkansas Mathematics Standards (adopted in 2023): Advanced Topics & Modeling
Arkansas Mathematics Standards (adopted in 2023): Algebra I Arkansas Mathematics Standards (adopted in 2023): Algebra I
Arkansas Mathematics Standards (adopted in 2023): Algebra II Arkansas Mathematics Standards (adopted in 2023): Algebra II
Arkansas Mathematics Standards (adopted in 2023): Algebra III Arkansas Mathematics Standards (adopted in 2023): Algebra III
Arkansas Mathematics Standards (adopted in 2023): Calculus Arkansas Mathematics Standards (adopted in 2023): Calculus
Arkansas Mathematics Standards (adopted in 2023): Critical Algebra I Arkansas Mathematics Standards (adopted in 2023): Critical Algebra I
Arkansas Mathematics Standards (adopted in 2023): Geometry Arkansas Mathematics Standards (adopted in 2023): Geometry
Arkansas Mathematics Standards (adopted in 2023): Mathematical Practices Arkansas Mathematics Standards (adopted in 2023): Mathematical Practices
Arkansas Mathematics Standards (adopted in 2023): Pre-Calculus Arkansas Mathematics Standards (adopted in 2023): Pre-Calculus
Arkansas Mathematics Standards (adopted in 2023): Statistics Arkansas Mathematics Standards (adopted in 2023): Statistics
Arkansas Mathematics Standards (adopted in 2023): Technical Math Arkansas Mathematics Standards (adopted in 2023): Technical Math
Arkansas Curriculum Framework: Advanced Topics and Modeling in Mathematics Arkansas Curriculum Framework: Advanced Topics and Modeling in Mathematics
Arkansas Curriculum Framework: Algebra I Arkansas Curriculum Framework: Algebra I
Arkansas Curriculum Framework: Algebra I Part A Arkansas Curriculum Framework: Algebra I Part A
Arkansas Curriculum Framework: Algebra I Part B Arkansas Curriculum Framework: Algebra I Part B
Arkansas Curriculum Framework: Algebra II/Advanced Algebra Arkansas Curriculum Framework: Algebra II/Advanced Algebra
Arkansas Curriculum Framework: Algebra III Arkansas Curriculum Framework: Algebra III
Arkansas Curriculum Framework: Bridge to Algebra II Arkansas Curriculum Framework: Bridge to Algebra II
Arkansas Curriculum Framework: Calculus Arkansas Curriculum Framework: Calculus
Arkansas Curriculum Framework: Computer Science and Mathematics Arkansas Curriculum Framework: Computer Science and Mathematics
Arkansas Curriculum Framework: Geometry Arkansas Curriculum Framework: Geometry
Arkansas Curriculum Framework: Geometry A Arkansas Curriculum Framework: Geometry A
Arkansas Curriculum Framework: Geometry B Arkansas Curriculum Framework: Geometry B
Arkansas Curriculum Framework: Mathematical Applications and Algorithms Arkansas Curriculum Framework: Mathematical Applications and Algorithms
Arkansas Curriculum Framework: Precalculus Arkansas Curriculum Framework: Precalculus
Arkansas Curriculum Framework: Statistics Arkansas Curriculum Framework: Statistics

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FR Functional Relationships

FR.1.BTAII Interpret the structure of expressions, write expressions in equivalent forms to solve problems, perform arithmetic operations on functions, and understand the relationship between zeros and factors of polynomials
- FR.1.BTAII.1 Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression using appropriate vocabulary, such as terms, factors, and coefficients. Interpret complicated expressions by viewing one or more of their parts as a single entity.
  - Polynomial vocabulary (A1-W.1)
- FR.1.BTAII.2 Use the structure of an expression to identify ways to rewrite it.
- FR.1.BTAII.3 Add, subtract, and multiply polynomials. Understand that polynomials, like the integers, are closed under addition, subtraction, and multiplication.
- FR.1.BTAII.4 Use various methods to factor quadratic polynomials; understand the relationship between the factored form of a quadratic polynomial and the zeros of a function.
- FR.1.BTAII.5 Identify zeros of polynomials (linear, quadratic) when suitable factorizations are available. Use the zeros to construct a rough graph of the function defined by the polynomial.
  - Solve a quadratic equation using the zero product property (A1-Z.2)
- FR.1.BTAII.6 Solve linear equations, inequalities and absolute value equations in one variable, including equations with coefficients represented by letters.
- FR.1.BTAII.7 Solve systems of equations in two variables using substitution and elimination. Understand that the solution to a system of equations will be the same when using substitution and elimination.
- FR.1.BTAII.8 In terms of a context, interpret the parameters (rates of growth or decay, domain and range restrictions where applicable, etc.) in a function.
  - Solve one-step and two-step linear equations: word problems (A1-C.9)
  - Exponential growth and decay: word problems (A1-V.9)

RF Representing Functions

RF.2.BTAII Represent and solve equations and inequalities graphically and analyze functions using different representations
- RF.2.BTAII.1 Explain why the x-coordinates 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 by using technology to graph the functions, making tables of values, finding successive approximations. Include cases (but not limited to) where f(x) and/or g(x) are linear, polynomial, absolute value, exponential.
- RF.2.BTAII.2 Graph functions expressed algebraically and show key features of the graph, with and without technology. Graph linear and quadratic functions and, when applicable, show intercepts, maxima, and minima. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph exponential functions, showing intercepts and end behavior.
- RF.2.BTAII.3 Explain how extending the properties of integer exponents to rational exponents provides an alternative notation for radicals.
  - Evaluate integers raised to rational exponents (A1-S.2)
- RF.2.BTAII.4 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
- RF.2.BTAII.5 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or any polynomial function.
- RF.2.BTAII.6 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Factor a quadratic expression to reveal the zeros of the function it defines. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
- RF.2.BTAII.7 Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)² = q that has the same solutions. Solve quadratic equations (as appropriate to the initial form of the equation) by: inspection of a graph, taking square roots, completing the square, using the quadratic formula, factoring.
- RF.2.BTAII.8 Solve systems of equations consisting of linear equations and nonlinear equations in two variables algebraically and graphically.
  - Solve a system of linear and quadratic equations (A1-Z.10)

FM Function Modeling

FM.3.BTAII Create equations that describe numbers or relationships, interpret functions that arise in applications in terms of a context, analyze functions using different representations, build a function that models a relationship between two quantities, and build new functions from existing functions
- FM.3.BTAII.1 Create equations and inequalities in one variable and use them to solve problems.
  - Write and solve linear equations that represent diagrams (A1)
  - Write variable equations (A1-C.1)
  - Model and solve linear equations using algebra tiles (A1-C.6)
  - Solve one-step and two-step linear equations: word problems (A1-C.9)
  - Consecutive integer problems (A1-C.11)
  - Weighted averages: word problems (A1-E.7)
  - Write inequalities from graphs (A1-F.2)
  - Write compound inequalities from graphs (A1-F.13)
- FM.3.BTAII.2 Create equations in two or more variables to represent relationships between quantities. Graph equations, in two variables, on a coordinate plane.
  - Write direct variation equations (A1-J.2)
  - Slope-intercept form: graph an equation (A1-L.4)
  - Slope-intercept form: write an equation from a graph (A1-L.5)
  - Slope-intercept form: write an equation (A1-L.6)
  - Slope-intercept form: write an equation from a table (A1-L.7)
  - Write linear equations in standard form (A1-L.9)
  - Standard form: graph a line from an equation (A1-L.11)
  - Point-slope form: graph an equation (A1-L.14)
  - Point-slope form: write an equation (A1-L.15)
  - Point-slope form: write an equation from a graph (A1-L.16)
  - Write a linear function: word problems (A1-N.8)
  - Graph quadratic functions in vertex form (A1-Y.5)
  - Write a quadratic function in vertex form from its vertex and another point (A1-Y.11)
  - Write linear, quadratic, and exponential functions from tables (A1-AA.7)
  - Graph an absolute value function (A1-BB.2)
- FM.3.BTAII.3 Represent and interpret constraints by equations or inequalities, and by systems of equations and/or inequalities. Interpret solutions as viable or nonviable options in a modeling and/or real-world context.
  - Solve a system of equations by graphing: word problems (A1-O.3)
  - Solve a system of equations using substitution: word problems (A1-O.9)
  - Solve a system of equations using elimination: word problems (A1-O.11)
  - Solve a system of equations using any method: word problems (A1-O.15)
  - Write two-variable inequalities: word problems (A1-P.5)
  - Solve systems of linear inequalities by graphing (A1-P.7)
- FM.3.BTAII.4 Rearrange literal equations using the properties of equality.
  - Rearrange multi-variable equations (A1-C.18)
  - Linear equations: solve for y (A1-L.8)
  - Write linear equations in standard form (A1-L.9)
- FM.3.BTAII.5 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.
  - Find the constant of variation (A1-J.1)
  - Find the slope of a graph (A1-K.1)
  - Slope-intercept form: find the slope and y-intercept (A1-L.3)
  - Slope-intercept form: graph an equation (A1-L.4)
  - Standard form: find x- and y-intercepts (A1-L.10)
  - Standard form: graph a line from an equation (A1-L.11)
  - Point-slope form: graph an equation (A1-L.14)
  - Slopes of parallel and perpendicular lines (A1-L.18)
  - Identify linear functions from graphs and equations (A1-N.1)
  - Identify linear functions from tables (A1-N.2)
  - Complete a table and graph a linear function (A1-N.3)
  - Match exponential functions and graphs II (A1-V.4)
  - Characteristics of quadratic functions: graphs (A1-Y.1)
  - Characteristics of quadratic functions: equations (A1-Y.2)
  - Graph quadratic functions in vertex form (A1-Y.5)
  - Identify linear, quadratic, and exponential functions from graphs (A1-AA.2)
  - Identify linear, quadratic, and exponential functions from tables (A1-AA.4)
  - Graph an absolute value function (A1-BB.2)
  - Identify proportional relationships (A1)
  - Graph a proportional relationship (A1)
- FM.3.BTAII.6 Relate the domain of a function to its graph. Relate the domain of a function to the quantitative relationship it describes.
  - Domain and range of exponential functions: graphs (A1-V.5)
  - Domain and range of exponential functions: equations (A1-V.6)
  - Domain and range of absolute value functions: graphs (A1-BB.3)
  - Domain and range of absolute value functions: equations (A1-BB.4)
- FM.3.BTAII.7 Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified interval. Estimate the rate of change from a graph.
  - Find the constant of variation (A1-J.1)
  - Find the slope of a graph (A1-K.1)
  - Find the slope from two points (A1-K.2)
  - Slope-intercept form: find the slope and y-intercept (A1-L.3)
  - Rate of change: tables (A1-M.15)
- FM.3.BTAII.8 Graph functions expressed algebraically and show key features of the graph, with and without technology. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph exponential functions, showing intercepts and end behavior.
  - Match exponential functions and graphs II (A1-V.4)
  - Graph an absolute value function (A1-BB.2)
- FM.3.BTAII.9 Write expressions for functions in different but equivalent forms to reveal key features of the function. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values (vertex), and symmetry of the graph, and interpret these in terms of a context.
  - Characteristics of quadratic functions: graphs (A1-Y.1)
  - Characteristics of quadratic functions: equations (A1-Y.2)
  - Solve a quadratic equation by factoring (A1-Z.3)
  - Complete the square (A1-Z.4)
  - Solve a quadratic equation by completing the square (A1-Z.5)
- FM.3.BTAII.10 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
  - Compare linear functions: graphs and equations (A1-N.11)
  - Compare linear functions: tables, graphs, and equations (A1-N.12)
- FM.3.BTAII.11 Write a function that describes a relationship between two quantities. From a context, determine an explicit expression, a recursive process, or steps for calculation.
  - Write variable expressions for arithmetic sequences (A1-U.7)
  - Write variable expressions for geometric sequences (A1-U.8)
  - Write linear, quadratic, and exponential functions from tables (A1-AA.7)
- FM.3.BTAII.12 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 of the transformed functions. Experiment with multiple transformations and illustrate an explanation of the effects on the graph with or without technology. Include recognizing even and odd functions from their graphs and algebraic representations for them.
  - Transformations of linear functions (A1-N.13)
  - Transformations of quadratic functions (A1-Y.4)
  - Transformations of absolute value functions: translations and reflections (A1-BB.5)
- FM.3.BTAII.13 Solve an equation of the form y = f(x) for a simple function f that has an inverse and write an expression for the inverse.
  - Find the inverse of a linear function (A1-CC.3)
- FM.3.BTAII.14 Define appropriate quantities for the purpose of descriptive modeling (I.E., Use units appropriate to the problem being solved.)
  - Solve one-step and two-step linear equations: word problems (A1-C.9)
  - Multi-step problems with unit conversions (A1-E.5)
  - Solve a system of equations using any method: word problems (A1-O.15)
  - Exponential growth and decay: word problems (A1-V.9)
- FM.3.BTAII.15 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
  - Precision (A1-D.4)
  - Greatest possible error (A1-D.5)
  - Minimum and maximum area and volume (A1-D.6)
  - Percent error (A1-D.7)
  - Percent error: area and volume (A1-D.8)
- FM.3.BTAII.16 Solve linear inequalities and systems of linear inequalities in two variables by graphing.
  - Graph solutions to one-step linear inequalities (A1-F.7)
  - Graph solutions to two-step linear inequalities (A1-F.9)
  - Graph solutions to advanced linear inequalities (A1-F.11)
  - Graph a two-variable linear inequality (A1-P.3)
  - Solve systems of linear inequalities by graphing (A1-P.7)
- FM.3.BTAII.17 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [e.g. The Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.]
  - Identify arithmetic and geometric sequences (A1-U.1)
  - Arithmetic sequences (A1-U.2)
  - Geometric sequences (A1-U.3)
  - Evaluate variable expressions for number sequences (A1-U.4)
  - Evaluate recursive formulas for sequences (A1-U.5)
  - Write variable expressions for arithmetic sequences (A1-U.7)
  - Write variable expressions for geometric sequences (A1-U.8)
  - Write a formula for a recursive sequence (A1-U.9)
  - Sequences: mixed review (A1-U.12)
- FM.3.BTAII.18 Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
  - Exponential growth and decay: word problems (A1-V.9)
- FM.3.BTAII.19 Construct linear and exponential equations, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
  - Slope-intercept form: write an equation from a graph (A1-L.5)
  - Slope-intercept form: write an equation (A1-L.6)
  - Slope-intercept form: write an equation from a table (A1-L.7)
  - Write a linear function: word problems (A1-N.8)
  - Write variable expressions for arithmetic sequences (A1-U.7)
  - Write variable expressions for geometric sequences (A1-U.8)
- FM.3.BTAII.20 Use the properties of exponents to transform expressions for exponential functions.
  - Evaluate expressions using exponent rules (A1-R.12)
  - Evaluate an exponential function (A1-V.1)

SP Statistics and Probability

SP.4.BTAII Summarize, represent, and interpret data on a single count or a measurement variable and use probability to evaluate outcomes of decisions
- SP.4.BTAII.1 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.
- SP.4.BTAII.2 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
- SP.4.BTAII.3 Compute (using technology) and interpret the correlation coefficient of a linear fit.
  - Match correlation coefficients to scatter plots (A1-JJ.3)
  - Calculate correlation coefficients (A1-JJ.4)

Arkansas

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FR Functional Relationships

FR.1.BTAII Interpret the structure of expressions, write expressions in equivalent forms to solve problems, perform arithmetic operations on functions, and understand the relationship between zeros and factors of polynomials

FR.1.BTAII.1 Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression using appropriate vocabulary, such as terms, factors, and coefficients. Interpret complicated expressions by viewing one or more of their parts as a single entity.

FR.1.BTAII.2 Use the structure of an expression to identify ways to rewrite it.

FR.1.BTAII.3 Add, subtract, and multiply polynomials. Understand that polynomials, like the integers, are closed under addition, subtraction, and multiplication.

FR.1.BTAII.4 Use various methods to factor quadratic polynomials; understand the relationship between the factored form of a quadratic polynomial and the zeros of a function.

FR.1.BTAII.5 Identify zeros of polynomials (linear, quadratic) when suitable factorizations are available. Use the zeros to construct a rough graph of the function defined by the polynomial.

FR.1.BTAII.6 Solve linear equations, inequalities and absolute value equations in one variable, including equations with coefficients represented by letters.

FR.1.BTAII.7 Solve systems of equations in two variables using substitution and elimination. Understand that the solution to a system of equations will be the same when using substitution and elimination.

FR.1.BTAII.8 In terms of a context, interpret the parameters (rates of growth or decay, domain and range restrictions where applicable, etc.) in a function.

RF Representing Functions

RF.2.BTAII Represent and solve equations and inequalities graphically and analyze functions using different representations

RF.2.BTAII.3 Explain how extending the properties of integer exponents to rational exponents provides an alternative notation for radicals.

RF.2.BTAII.4 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

RF.2.BTAII.5 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or any polynomial function.

RF.2.BTAII.8 Solve systems of equations consisting of linear equations and nonlinear equations in two variables algebraically and graphically.

FM Function Modeling

FM.3.BTAII.1 Create equations and inequalities in one variable and use them to solve problems.

FM.3.BTAII.2 Create equations in two or more variables to represent relationships between quantities. Graph equations, in two variables, on a coordinate plane.

FM.3.BTAII.3 Represent and interpret constraints by equations or inequalities, and by systems of equations and/or inequalities. Interpret solutions as viable or nonviable options in a modeling and/or real-world context.

FM.3.BTAII.4 Rearrange literal equations using the properties of equality.

FM.3.BTAII.5 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.

FM.3.BTAII.6 Relate the domain of a function to its graph. Relate the domain of a function to the quantitative relationship it describes.

FM.3.BTAII.7 Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified interval. Estimate the rate of change from a graph.

FM.3.BTAII.10 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

FM.3.BTAII.11 Write a function that describes a relationship between two quantities. From a context, determine an explicit expression, a recursive process, or steps for calculation.

FM.3.BTAII.13 Solve an equation of the form y = f(x) for a simple function f that has an inverse and write an expression for the inverse.

FM.3.BTAII.14 Define appropriate quantities for the purpose of descriptive modeling (I.E., Use units appropriate to the problem being solved.)

FM.3.BTAII.15 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

FM.3.BTAII.16 Solve linear inequalities and systems of linear inequalities in two variables by graphing.

FM.3.BTAII.17 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [e.g. The Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.]

FM.3.BTAII.18 Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

FM.3.BTAII.19 Construct linear and exponential equations, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

FM.3.BTAII.20 Use the properties of exponents to transform expressions for exponential functions.

SP Statistics and Probability

SP.4.BTAII Summarize, represent, and interpret data on a single count or a measurement variable and use probability to evaluate outcomes of decisions

SP.4.BTAII.1 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.

SP.4.BTAII.2 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

SP.4.BTAII.3 Compute (using technology) and interpret the correlation coefficient of a linear fit.