Gizmos for Arkansas - Mathematics: Critical Algebra I (Academic Standards adopted 2023)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

A1.EX: : Expressions

1.1: : Polynomials, Roots, & Exponent Laws

1.1.1: : 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.

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.

A1.EX.4: : Interpret the parts of expressions such as terms, factors, and coefficients in terms of a real-world context.

A1.FN: : Functions

2.1: : Domain & Range, Function Notation

2.1.1: : 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.

2.2: : Construct & Compare

2.2.1: : 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.6: : Compare the growth pattern of exponential to linear or quadratic functions using graphs and tables and recognize how exponential growth exceeds other functions.

A1.LFE: : Linear Functions, Equations, & Inequalities

3.1: : Create & Solve

3.1.1: : 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.2: : Construct linear functions from arithmetic sequences with and without context.

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.

3.2: : Interpret Key Features

3.2.1: : 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.7: : Interpret the key features of a linear and absolute value functions that models a relationship between two quantities in a given context.

A1.LFE.8: : Flexibly use different representations of a linear function, including graphs, tables, and equations.

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.

3.3: : Systems of Equations & Inequalities

3.3.1: : 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.

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.

A1.LFE.14: : Solve linear inequalities and systems of linear inequalities in two variables by graphing.

3.4: : Graphing & Transformations

3.4.1: : 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.

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.18: : Graph and generalize the effect of transformations on linear and absolute value functions.

3.5: : Statistical Relationships

3.5.1: : 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.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.QFE: : Quadratic Functions & Equations

4.1: : Create & Solve

4.1.1: : 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.2: : Write quadratic equations with real number solutions that model the relationship between two quantities and produce a graph of the equation.

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:

A1.QFE.3.1: : Graphing,

A1.QFE.3.2: : Factoring (including perfect square trinomials and difference of squares binomials),

A1.QFE.3.3: : Using the quadratic formula,

4.2: : Interpret Key Features

4.2.1: : Students interpret key features of equations that model quadratic relationships.

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.

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.

4.3: : Graphing & Transformations

4.3.1: : 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.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.EFE: : Exponential Functions & Equations

5.1: : Create & Solve

5.1.1: : Students create and solve problems that model exponential relationships.

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.

5.2: : Interpret Key Features

5.2.1: : 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.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.8: : Interpret the quantities in an exponential equation in the context of a real-world problem, including growth, decay, and compound interest.

5.3: : Graphing

5.3.1: : Students graph exponential functions.

A1.EFE.9: : Graph exponential functions that model real-world problems (growth, decay, and compound interest), showing key attributes.

A1.SP: : Statistics & Probability

6.1: : Numerical Data

6.1.1: : 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.

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.

7: : Critical Algebra I Supporting Standards:

5: : Fifth Grade

5.CAR.12: : Evaluate numerical expressions with parentheses or brackets and exponents with the base of ten, using the Order of Operations.

5.GM.7: : Graph points with whole number coordinates on a coordinate plane in the first quadrant, explaining how the coordinates relate to the horizontal and vertical axes to describe the location of points in the plane.

5.GM.8: : Represent real-world and mathematical problems by graphing points in the first quadrant on a coordinate plane, interpreting coordinate values of points in the context of the situation.

6: : Sixth Grade

6.NCC.4: : Interpret the absolute value of numbers for positive or negative quantities in a real-world context.

6.PR.2: : Calculate unit rates to include unit pricing and constant speed.

6.ALG.1: : Read and write expressions in real-world or mathematical problems in which letters stand for numbers.

6.ALG.2: : Use mathematical terms to identify parts of an expression, including the names of operations, terms, factors, coefficients, variables, and constants.

6.ALG.3: : Write and evaluate expressions for given values of variables, using order of operations, including expressions with whole number exponents.

6.ALG.4: : Generate equivalent expressions by applying the associative, commutative, distributive, and identity properties.

6.ALG.5: : Identify when two expressions are equivalent by using properties of operations including like terms.

6.ALG.6: : Use substitution to determine if a given value in a specified set makes an equation or inequality true.

6.ALG.7: : Write and solve one-step equations in real-world and mathematical problems, involving positive rational numbers and zero.

6.ALG.8: : Write, solve, and graph one-step inequalities in real-world and mathematical problems.

6.GM.4: : Find and graph pairs of rational numbers in all four quadrants of the coordinate plane in real-world and mathematical problems.

6.SP.2: : Calculate and interpret any measure of center (mean, median, and mode) of a numerical data set.

6.SP.3: : Determine which measure of center (mean or median) is more appropriate to describe the center of data and justify the choice.

6.SP.4: : Describe how the mean or median is affected by outliers of a numerical data set.

6.SP.5: : Calculate and interpret the measure of variation [range and interquartile range (IQR)] of a numerical data set.

6.SP.7: : Represent numerical data on a number line, histogram, and box plot.

6.SP.8: : Calculate the relative frequency of an interval of data values when given a histogram.

7: : Seventh Grade

7.NCC.7: : Use addition and subtraction with rational numbers in any form to solve multi-step problems in real-world and mathematical contexts.

7.NCC.9: : Apply operations with rational numbers involving the order of operations, involving nested grouping symbols.

7.PR.1: : Determine the unit rate (constant of proportionality) from tables, graphs, equations, diagrams, or verbal descriptions of proportional relationships.

7.PR.4: : Determine whether two quantities represent proportional relationships by using equivalent ratios in a table and by graphing on a coordinate plane.

7.PR.6: : Create equations in the form of y = mx from tables, verbal descriptions, or graphs.

7.ALG.1: : Generate and justify equivalent expressions, using properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients within mathematical and real-world problems.

7.ALG.2: : Model and solve fluently two-step equations in real-world or mathematical problems.

7.ALG.4: : Write an equation to express two quantities in terms of the dependent and independent variables.

7.ALG.5: : Describe the relationship between the dependent and independent variables in an equation using tables and graphs, relating these to the equation.

7.SP.1: : Interpret data displayed in a histogram and box plot to answer questions about the data.

7.SP.3: : Graph two numerical data sets and compare their variability.

7.SP.4: : Select an appropriate measure(s) of center or variability and draw valid comparative inferences for two data sets.

8: : Eighth Grade

8.NCC.3: : Know and apply the properties of integer exponents to generate equivalent numerical expressions.

8.NCC.8: : Evaluate square roots of perfect squares and cube roots of perfect cubes.

8.FN.1: : Graph proportional relationships, interpreting the unit rate as the slope of the graph.

8.FN.3: : Determine whether a relation is a function or not when given a function map, table, graph, equation, or set of ordered pairs.

8.FN.5: : Distinguish between linear and nonlinear functions by comparing graphs and equations.

8.FN.6: : Determine the rate of change (slope) and y-intercept (initial value) from tables, graphs, equations, and verbal descriptions of linear relationships.

8.FN.7: : Interpret and explain the meaning of the rate of change (slope) and y-intercept (initial value) of a linear relationship in a real-world context.

8.FN.8: : Analyze a graph by describing the functional relationships between two quantities.

8.FN.9: : Sketch a graph that exhibits qualitative features of a function described verbally.

8.ALG.1: : Analyze and solve one-variable linear equations with rational coefficients containing solutions with one, zero, or infinitely many solutions.

8.ALG.2: : Analyze and solve one-variable linear inequalities with rational coefficients.

8.ALG.3: : Analyze and solve systems of linear equations in the form y = mx + b in real-world or mathematical contexts, graphically and algebraically.

8.SP.1: : Construct scatter plots using bivariate data; determine if the data displays a linear or nonlinear pattern and positive, negative, or no association.

8.SP.2: : Construct straight lines to approximately fit data displaying a linear association when presented in scatter plots.

Correlation last revised: 10/8/2025

Arkansas - Mathematics: Critical Algebra I

Academic Standards | Adopted: 2023