Arkansas Mathematics Standards (adopted in 2023): Algebra I
Skills available for Arkansas Algebra I standards
Standard
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EX
Expressions
Polynomials, Roots, & Exponent Laws: Students simplify algebraic and numerical expressions.
A1.EX.1 Add, subtract, and multiply polynomials; compare the system of polynomials to the system of integers when performing operations.
Understand polynomials
Addition and subtraction
Multiplication
A1.EX.1 Add, subtract, and multiply polynomials; compare the system of polynomials to the system of integers when performing operations.
Understand polynomials
Addition and subtraction
Multiplication
A1.EX.2 Simplify and perform operations with radical expressions without variables; rationalizing denominators should not include conjugates.
A1.EX.2 Simplify and perform operations with radical expressions without variables; rationalizing denominators should not include conjugates.
A1.EX.3 Simplify algebraic expressions using the laws of exponents.
Integer exponents
Rational exponents
Polynomial expressions
A1.EX.3 Simplify algebraic expressions using the laws of exponents.
Integer exponents
Rational exponents
Polynomial expressions
A1.EX.4 Interpret the parts of expressions such as terms, factors, and coefficients in terms of a real-world context.
A1.EX.4 Interpret the parts of expressions such as terms, factors, and coefficients in terms of a real-world context.
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FN
Functions
Domain & Range, Function Notation: Students understand the concept of a function, domain and range, and use function notation; students use function notation to solve problems.
A1.FN.1 Explain that a function assigns each element in the domain to exactly one element in the range.
Independent and dependent variables
Identify functions
Domain and range of relations
A1.FN.1 Explain that a function assigns each element in the domain to exactly one element in the range.
Independent and dependent variables
Identify functions
Domain and range of relations
A1.FN.2 Use function notation to represent functions, understanding that if f is a function and x is an element of its domain, then f(x) represents the output of f corresponding to the input x.
A1.FN.2 Use function notation to represent functions, understanding that if f is a function and x is an element of its domain, then f(x) represents the output of f corresponding to the input x.
A1.FN.3 Graph functions given in function notation, understanding that the graph contains the points (x, f(x)).
A1.FN.3 Graph functions given in function notation, understanding that the graph contains the points (x, f(x)).
A1.FN.4 Evaluate functions expressed in function notation for one or more elements in their domains (inputs); use function notation to describe a contextual situation.
Evaluate a function
Interpret function notation
Tables and graphs
A1.FN.4 Evaluate functions expressed in function notation for one or more elements in their domains (inputs); use function notation to describe a contextual situation.
Evaluate a function
Interpret function notation
Tables and graphs
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Construct & Compare: Students construct and compare linear, quadratic, and exponential models and solve problems.
A1.FN.5 Differentiate between real-world scenarios that can be modeled by exponential or linear functions by determining whether the relationship has a common difference or a common ratio.
A1.FN.5 Differentiate between real-world scenarios that can be modeled by exponential or linear functions by determining whether the relationship has a common difference or a common ratio.
A1.FN.6 Compare the growth pattern of exponential to linear or quadratic functions using graphs and tables and recognize how exponential growth exceeds other functions.
Linear and exponential functions
Linear, quadratic, and exponential functions
A1.FN.6 Compare the growth pattern of exponential to linear or quadratic functions using graphs and tables and recognize how exponential growth exceeds other functions.
Linear and exponential functions
Linear, quadratic, and exponential functions
LFE
Linear Functions, Equations, & Inequalities
Create & Solve: Students create and solve equations that model linear relationships.
A1.LFE.1 Represent and solve real-world problems, using linear expressions, equations, and inequalities in one variable.
A1.LFE.1 Represent and solve real-world problems, using linear expressions, equations, and inequalities in one variable.
A1.LFE.2 Construct linear functions from arithmetic sequences with and without context.
A1.LFE.2 Construct linear functions from arithmetic sequences with and without context.
A1.LFE.3 Solve linear formulas for a specified variable.
A1.LFE.3 Solve linear formulas for a specified variable.
A1.LFE.4 Solve linear equations, linear inequalities, and absolute value equations in one variable, including those with rational number coefficients, and variables on both sides of the equal or inequality sign; solve them fluently, explaining the process used.
Properties of equality
Equations with models
Linear equations
Absolute value equations
Linear inequalities
Compound inequalities
A1.LFE.4 Solve linear equations, linear inequalities, and absolute value equations in one variable, including those with rational number coefficients, and variables on both sides of the equal or inequality sign; solve them fluently, explaining the process used.
Properties of equality
Equations with models
Linear equations
Absolute value equations
Linear inequalities
Compound inequalities
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Interpret Key Features: Students interpret key features of equations that model linear relationships.
A1.LFE.5 Determine the domain and range of linear functions in mathematical problems.
A1.LFE.5 Determine the domain and range of linear functions in mathematical problems.
A1.LFE.6 Determine reasonable domain and range values of linear functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context.
A1.LFE.6 Determine reasonable domain and range values of linear functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context.
A1.LFE.7 Interpret the key features of a linear and absolute value functions that models a relationship between two quantities in a given context.
Linear functions
Absolute value functions
A1.LFE.7 Interpret the key features of a linear and absolute value functions that models a relationship between two quantities in a given context.
Linear functions
Absolute value functions
A1.LFE.8 Flexibly use different representations of a linear function, including graphs, tables, and equations.
Equations, tables, and graphs
Slope-intercept form
Standard form
Point-slope form
Horizontal and vertical lines
A1.LFE.8 Flexibly use different representations of a linear function, including graphs, tables, and equations.
Equations, tables, and graphs
Slope-intercept form
Standard form
Point-slope form
Horizontal and vertical lines
A1.LFE.9 Calculate and interpret the rate of change of a linear function represented in a table, graph, or as an equation in context of real-world and mathematical problems.
A1.LFE.9 Calculate and interpret the rate of change of a linear function represented in a table, graph, or as an equation in context of real-world and mathematical problems.
A1.LFE.10 Translate among equivalent forms of equations for linear functions, including standard, point-slope, and slope-intercept forms; recognize that each form reveals key features in a given context.
A1.LFE.10 Translate among equivalent forms of equations for linear functions, including standard, point-slope, and slope-intercept forms; recognize that each form reveals key features in a given context.
Systems of Equations & Inequalities: Students solve systems of equations and inequalities.
A1.LFE.11 Solve systems of linear equations by substitution, elimination, and graphing with and without a real-world context; understand that the solutions will be the same regardless of the method for solving.
Understand solutions
Graphing
Substitution
Elimination
Any method
A1.LFE.11 Solve systems of linear equations by substitution, elimination, and graphing with and without a real-world context; understand that the solutions will be the same regardless of the method for solving.
Understand solutions
Graphing
Substitution
Elimination
Any method
A1.LFE.12 Solve a system of equations consisting of a linear equation and a quadratic equation in two variables graphically with the assistance of technology.
A1.LFE.12 Solve a system of equations consisting of a linear equation and a quadratic equation in two variables graphically with the assistance of technology.
A1.LFE.13 Explain why a solution to the equation f(x) = g(x) is the x-coordinate where the y-coordinate of f(x) and g(x) are the same using graphs, tables, or approximations. Include cases where f(x) and/or g(x) are linear, quadratic, absolute value, and exponential.
Tables
Graphs
A1.LFE.13 Explain why a solution to the equation f(x) = g(x) is the x-coordinate where the y-coordinate of f(x) and g(x) are the same using graphs, tables, or approximations. Include cases where f(x) and/or g(x) are linear, quadratic, absolute value, and exponential.
Tables
Graphs
A1.LFE.14 Solve linear inequalities and systems of linear inequalities in two variables by graphing.
One-variable inequalities
Two-variable inequalities
A1.LFE.14 Solve linear inequalities and systems of linear inequalities in two variables by graphing.
One-variable inequalities
Two-variable inequalities
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Graphing & Transformations: Students graph linear functions, equations, and inequalities.
A1.LFE.15 Write linear equations that model the relationship between two quantities and produce a graph of the equation.
Slope-intercept form
Standard form
Point-slope form
A1.LFE.15 Write linear equations that model the relationship between two quantities and produce a graph of the equation.
Slope-intercept form
Standard form
Point-slope form
A1.LFE.16 Graph linear functions expressed as an equation and show intercepts of the graph without technology.
A1.LFE.16 Graph linear functions expressed as an equation and show intercepts of the graph without technology.
A1.LFE.17 Graph absolute value functions expressed as an equation with and without technology, showing intercepts and end behavior.
A1.LFE.17 Graph absolute value functions expressed as an equation with and without technology, showing intercepts and end behavior.
A1.LFE.18 Graph and generalize the effect of transformations on linear and absolute value functions.
A1.LFE.18 Graph and generalize the effect of transformations on linear and absolute value functions.
A1.LFE.19 Given the graph of a linear function, explain the effects of the transformation from the parent function, y = x.
A1.LFE.19 Given the graph of a linear function, explain the effects of the transformation from the parent function, y = x.
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Statistical Relationships: Students explore linear statistical relationships.
A1.LFE.20 Write linear functions that provide a reasonable fit to data and use them to make predictions, with and without technology; interpret the slope and y-intercept in context.
A1.LFE.20 Write linear functions that provide a reasonable fit to data and use them to make predictions, with and without technology; interpret the slope and y-intercept in context.
A1.LFE.21 Calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association.
A1.LFE.21 Calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association.
A1.LFE.22 Compare and contrast correlation and causation in real-world problems.
A1.LFE.22 Compare and contrast correlation and causation in real-world problems.
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QFE
Quadratic Functions & Equations
Create & Solve: Students create and solve equations that model quadratic relationships.
A1.QFE.1 Represent and solve real-world problems using quadratic expressions and equations in one variable.
A1.QFE.1 Represent and solve real-world problems using quadratic expressions and equations in one variable.
A1.QFE.2 Write quadratic equations with real number solutions that model the relationship between two quantities and produce a graph of the equation.
Write quadratic functions
Graph quadratic functions
A1.QFE.2 Write quadratic equations with real number solutions that model the relationship between two quantities and produce a graph of the equation.
Write quadratic functions
Graph quadratic functions
A1.QFE.3 Solve quadratic equations with real number solutions, containing one variable, including those with variables on both sides of the equal sign. Equations should be solved by: graphing, factoring (including perfect square trinomials and difference of squares binomials), using the quadratic formula, completing the square, or taking the square root.
Square roots
Factor
Complete the square
Quadratic formula
A1.QFE.3 Solve quadratic equations with real number solutions, containing one variable, including those with variables on both sides of the equal sign. Equations should be solved by: graphing, factoring (including perfect square trinomials and difference of squares binomials), using the quadratic formula, completing the square, or taking the square root.
Square roots
Factor
Complete the square
Quadratic formula
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Interpret Key Features: Students interpret key features of equations that model quadratic relationships.
A1.QFE.4 Determine the domain and range of quadratic functions in mathematical problems.
A1.QFE.4 Determine the domain and range of quadratic functions in mathematical problems.
A1.QFE.5 Determine reasonable domain and range values of quadratic functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context.
A1.QFE.5 Determine reasonable domain and range values of quadratic functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context.
A1.QFE.6 Interpret the key features of a quadratic function that models a relationship between two quantities in a given context.
A1.QFE.6 Interpret the key features of a quadratic function that models a relationship between two quantities in a given context.
A1.QFE.7 Flexibly use different representations of a quadratic function, including graphs, tables, and equations.
Tables
Graphs
Equations
A1.QFE.7 Flexibly use different representations of a quadratic function, including graphs, tables, and equations.
Tables
Graphs
Equations
A1.QFE.8 Explain how each form of a quadratic expression (standard, factored, and vertex form) identifies different key attributes, using the different forms to interpret quantities in context.
A1.QFE.8 Explain how each form of a quadratic expression (standard, factored, and vertex form) identifies different key attributes, using the different forms to interpret quantities in context.
A1.QFE.9 Use factoring and completing the square to create equivalent forms of quadratic functions to reveal key attributes.
Factor quadratics
Complete the square
A1.QFE.9 Use factoring and completing the square to create equivalent forms of quadratic functions to reveal key attributes.
Factor quadratics
Complete the square
Graphing & Transformations: Students graph quadratic functions and explore different transformations of f(x) = x2.
A1.QFE.10 Graph quadratic functions given as an equation or in function notation, labeling key attributes, without technology.
A1.QFE.10 Graph quadratic functions given as an equation or in function notation, labeling key attributes, without technology.
A1.QFE.11 Graph and describe the effect of transformations on quadratic functions.
A1.QFE.11 Graph and describe the effect of transformations on quadratic functions.
A1.QFE.12 Given the graph of a quadratic function, explain the effects of the transformation from the parent function, y = x2.
A1.QFE.12 Given the graph of a quadratic function, explain the effects of the transformation from the parent function, y = x2.
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Statistical Relationships: Students explore quadratic statistical relationships.
A1.QFE.13 Write quadratic functions that provide a reasonable fit to data and use them to make predictions with technology.
A1.QFE.13 Write quadratic functions that provide a reasonable fit to data and use them to make predictions with technology.
EFE
Exponential Functions & Equations
Create & Solve: Students create and solve problems that model exponential relationships.
A1.EFE.1 Represent and solve real-world problems, using exponential equations in one variable.
A1.EFE.1 Represent and solve real-world problems, using exponential equations in one variable.
A1.EFE.2 Represent real-world problems (growth, decay, and compound interest), using exponential equations.
A1.EFE.2 Represent real-world problems (growth, decay, and compound interest), using exponential equations.
A1.EFE.3 Construct exponential equations from geometric sequences with and without context.
A1.EFE.3 Construct exponential equations from geometric sequences with and without context.
Interpret Key Features: Students interpret key features of equations that model exponential relationships.
A1.EFE.4 Determine the domain and range of exponential functions in mathematical problems.
A1.EFE.4 Determine the domain and range of exponential functions in mathematical problems.
A1.EFE.5 Determine reasonable domain and range values of exponential functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context.
A1.EFE.5 Determine reasonable domain and range values of exponential functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context.
A1.EFE.6 Interpret the key features of an exponential function that models a relationship between two quantities in a given context.
A1.EFE.6 Interpret the key features of an exponential function that models a relationship between two quantities in a given context.
A1.EFE.7 Flexibly use different representations of an exponential function, including graphs, tables, and equations.
A1.EFE.7 Flexibly use different representations of an exponential function, including graphs, tables, and equations.
A1.EFE.8 Interpret the quantities in an exponential equation in the context of a real-world problem, including growth, decay, and compound interest.
A1.EFE.8 Interpret the quantities in an exponential equation in the context of a real-world problem, including growth, decay, and compound interest.
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Graphing: Students graph exponential functions.
A1.EFE.9 Graph exponential functions that model real-world problems (growth, decay, and compound interest), showing key attributes.
A1.EFE.9 Graph exponential functions that model real-world problems (growth, decay, and compound interest), showing key attributes.
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Statistical Relationships: Students explore exponential statistical relationships.
A1.EFE.10 Write exponential functions that provide a reasonable fit to data and use them to make predictions with technology.
A1.EFE.10 Write exponential functions that provide a reasonable fit to data and use them to make predictions with technology.
SP
Statistics & Probability
Numerical Data: Students summarize and describe distributions.
A1.SP.1 Use box plots and histograms to determine the statistics appropriate to the shape of the data distribution; compare the center and spread of two or more data sets.
Histograms
Bar graphs, line graphs, and histograms
Box plots
Center and spread
A1.SP.1 Use box plots and histograms to determine the statistics appropriate to the shape of the data distribution; compare the center and spread of two or more data sets.
Histograms
Bar graphs, line graphs, and histograms
Box plots
Center and spread
A1.SP.2 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points.
A1.SP.2 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points.
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Bivariate Data: Students will investigate patterns of association in bivariate data.
A1.SP.3 Summarize data from two categorical variables in a frequency table; interpret relative frequencies in the context of the data, recognizing data trends and associations.
A1.SP.3 Summarize data from two categorical variables in a frequency table; interpret relative frequencies in the context of the data, recognizing data trends and associations.
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