Arkansas

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. Supporting standards: 6.ALG.5, 7.ALG.1, 8.NCC.3

    • Model polynomials with algebra tiles (A1-W.2)
    • Add and subtract polynomials using algebra tiles (A1-W.3)
    • Add and subtract polynomials (A1-W.4)
    • Add polynomials to find perimeter (A1-W.5)
    • Multiply a polynomial by a monomial (A1-W.6)
    • Multiply two binomials using algebra tiles (A1-W.7)
    • Multiply two binomials (A1-W.8)
    • Multiply two binomials: special cases (A1-W.9)
    • Multiply polynomials using area models (A1-W.10)
    • Multiply polynomials (A1-W.11)

  • A1.EX.2 Simplify and perform operations with radical expressions without variables; rationalizing denominators should not include conjugates. Supporting standards: 6.NCC.11, 8.NCC.8

    • Simplify radical expressions (A1-EE.1)
    • Add and subtract radical expressions (A1-EE.5)
    • Simplify radical expressions using the distributive property (A1-EE.6)
    • Simplify radicals with fractions (A1)
    • Multiply radicals (A1)

  • A1.EX.3 Simplify algebraic expressions using the laws of exponents. Supporting standards: 6.ALG.3, 7.NCC.7, 7.NCC.8, 8.NCC.3

    • Simplify variable expressions involving like terms and the distributive property (A1-B.9)
    • Multiplication rule for exponents (A1-R.4)
    • Division rule for exponents (A1-R.5)
    • Power rule for exponents (A1-R.6)
    • Simplify exponential expressions using the multiplication rule (A1-R.7)
    • Simplify exponential expressions using the division rule (A1-R.8)
    • Simplify exponential expressions using the multiplication and division rules (A1-R.9)
    • Simplify exponential expressions using the power rule (A1-R.10)
    • Evaluate expressions using exponent rules (A1-R.12)
    • Identify equivalent exponential expressions I (A1-R.13)
    • Identify equivalent exponential expressions II (A1-R.14)
    • Evaluate integers raised to positive rational exponents (A1-S.1)
    • Evaluate integers raised to rational exponents (A1-S.2)
    • Multiplication with rational exponents (A1-S.3)
    • Division with rational exponents (A1-S.4)
    • Power rule with rational exponents (A1-S.5)
    • Simplify expressions involving rational exponents (A1-S.6)
    • Factor out a monomial (A1-X.3)

  • A1.EX.4 Interpret the parts of expressions such as terms, factors, and coefficients in terms of a real-world context. Supporting standards: 5.CAR.13, 6.ALG.1, 6.ALG.2

    • Sort factors of variable expressions (A1-B.8)
    • Polynomial vocabulary (A1-W.1)
    • Interpret parts of quadratic expressions: word problems (A1-Y.13)

  • Checkpoint opportunity

    • Checkpoint: Exponents and radicals (A1)

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. Supporting standards: 7.ALG.5, 8.FN.3

    • Domain and range of relations (A1-M.2)
    • Identify independent and dependent variables (A1-M.3)
    • Identify functions (A1-M.4)
    • Identify functions: vertical line test (A1-M.5)

  • 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. Supporting standards: 7.ALG.5, 8.FN.3

    • Find values using function graphs (A1-M.6)
    • Complete a function table from a graph (A1-M.9)
    • Complete a function table from an equation (A1-M.10)

  • A1.FN.3 Graph functions given in function notation, understanding that the graph contains the points (x, f(x)). Supporting standards: 5.CAR.12, 6.ALG.3, 6.ALG.6, 7.NCC.9

    • Complete a table and graph a linear function (A1-N.3)

  • 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. Supporting standards: 7.ALG.5, 8.FN.3

    • Find values using function graphs (A1-M.6)
    • Evaluate a function (A1-M.7)
    • Evaluate a function: plug in an expression (A1-M.8)
    • Complete a function table from a graph (A1-M.9)
    • Complete a function table from an equation (A1-M.10)
    • Interpret functions using everyday language (A1-M.13)
    • Evaluate piecewise-defined functions (A1-Q.1)
    • Evaluate an exponential function (A1-V.1)
    • Complete a function table: quadratic functions (A1-Y.3)
    • Complete a function table: absolute value functions (A1-BB.1)

  • Checkpoint opportunity

    • Checkpoint: Function concepts (A1)

• 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. Supporting standards: 7.PR.1, 7.PR.4, 7.PR.5, 7.PR.6, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9

    • Exponential growth and decay: word problems (A1-V.9)
    • Write linear and exponential functions: word problems (A1-AA.5)
    • Linear functions over unit intervals (A1-AA.8)
    • Exponential functions over unit intervals (A1-AA.9)
    • Describe linear and exponential growth and decay (A1-AA.10)

  • 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. Supporting standards: 7.PR.1, 7.PR.4, 7.PR.5, 7.PR.6, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9

    • Identify linear and exponential functions from graphs (A1-AA.1)
    • Identify linear, quadratic, and exponential functions from graphs (A1-AA.2)
    • Identify linear and exponential functions from tables (A1-AA.3)
    • Identify linear, quadratic, and exponential functions from tables (A1-AA.4)
    • Write linear and exponential functions from tables (A1-AA.6)
    • Write linear, quadratic, and exponential functions from tables (A1-AA.7)
    • Compare linear and exponential growth (A1-AA.11)
    • Compare linear, exponential, and quadratic growth (A1-AA.12)

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. Supporting standards: 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2

    • Solve one-step and two-step linear equations: word problems (A1-C.9)
    • Consecutive integer problems (A1-C.11)
    • Solve linear equations with variables on both sides: word problems (A1-C.17)
    • Weighted averages: word problems (A1-E.7)

  • A1.LFE.2 Construct linear functions from arithmetic sequences with and without context. Supporting standards: 7.PR.1, 7.PR.4, 7.PR.6, 8.FN.6, 8.FN.7

    • Arithmetic sequences (A1-U.2)
    • Write variable expressions for arithmetic sequences (A1-U.7)
    • Write formulas for arithmetic sequences: function notation (A1)

  • A1.LFE.3 Solve linear formulas for a specified variable. Supporting standards: 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2

    • Rearrange multi-variable equations (A1-C.18)

  • 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. Supporting standards: 6.NCC.4, 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2

    • Write and solve linear equations that represent diagrams (A1)
    • Properties of equality (A1-C.4)
    • Identify equivalent equations (A1-C.5)
    • Model and solve linear equations using algebra tiles (A1-C.6)
    • Solve one-step linear equations (A1-C.7)
    • Solve two-step linear equations (A1-C.8)
    • Solve one-step and two-step linear equations: word problems (A1-C.9)
    • Solve linear equations with variables on one side (A1-C.10)
    • Solve linear equations with variables on both sides (A1-C.12)
    • Solve linear equations: mixed review (A1-C.13)
    • Solve linear equations: complete the solution (A1-C.14)
    • Solve linear equations with variables on both sides: word problems (A1-C.17)
    • Identify solutions to inequalities (A1-F.3)
    • Solve one-step linear inequalities: addition and subtraction (A1-F.4)
    • Solve one-step linear inequalities: multiplication and division (A1-F.5)
    • Solve one-step linear inequalities (A1-F.6)
    • Solve two-step linear inequalities (A1-F.8)
    • Solve advanced linear inequalities (A1-F.10)
    • Solve compound inequalities (A1-F.14)
    • Solve absolute value equations (A1-H.1)

  • Checkpoint opportunity

    • Checkpoint: Solve linear equations and inequalities (A1-F.16)
    • Checkpoint: Problem solving with linear equations and inequalities (A1)

• 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. Supporting standards: 7.ALG.4, 8.FN.3, 8.FN.8

    • Domain and range of linear functions: graphs (A1-N.9)

  • 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. Supporting standards: 7.ALG.4, 8.FN.3, 8.FN.8

    • Domain and range of linear functions: word problems (A1-N.10)

  • 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. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9

    • Find the slope of a graph (A1-K.1)
    • Find the slope from a table (A1-K.3)
    • Slope-intercept form: find the slope and y-intercept (A1-L.3)
    • Standard form: find x- and y-intercepts (A1-L.10)
    • Find the slope and intercepts from an equation (A1-L.17)
    • Identify linear functions from graphs and equations (A1-N.1)
    • Identify linear functions from tables (A1-N.2)
    • Evaluate a linear function from its graph: word problems (A1-N.4)
    • Complete a function table: absolute value functions (A1-BB.1)

  • A1.LFE.8 Flexibly use different representations of a linear function, including graphs, tables, and equations. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9

    • Relate the graph of a linear equation to its solutions (A1-L.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)
    • Equations of horizontal and vertical lines (A1-L.12)
    • Graph a horizontal or vertical line (A1-L.13)
    • 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)
    • Complete a table and graph a linear function (A1-N.3)
    • Write a linear function: word problems (A1-N.8)

  • 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. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9

    • Find the slope of a graph (A1-K.1)
    • Find the slope from two points (A1-K.2)
    • Find the slope from a table (A1-K.3)
    • Slope-intercept form: find the slope and y-intercept (A1-L.3)
    • Interpret the slope and y-intercept of a linear function (A1-N.7)

  • 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. Supporting standards: 6.ALG.4, 7.NCC.9, 7.ALG.1

    • Linear equations: solve for y (A1-L.8)
    • Write linear equations in standard form (A1-L.9)

• 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. Supporting standards: 6.ALG.1, 6.ALG.2, 6.ALG.3, 6.ALG.4, 6.ALG.5, 7.ALG.1, 7.ALG.2, 8.ALG.1, 8.ALG.3

    • Is (x, y) a solution to the system of equations? (A1-O.1)
    • Solve a system of equations by graphing (A1-O.2)
    • Solve a system of equations by graphing: word problems (A1-O.3)
    • Find the number of solutions to a system of equations by graphing (A1-O.4)
    • Find the number of solutions to a system of equations (A1-O.5)
    • Classify a system of equations by graphing (A1-O.6)
    • Solve a system of equations using substitution (A1-O.8)
    • Solve a system of equations using substitution: word problems (A1-O.9)
    • Solve a system of equations using elimination (A1-O.10)
    • Solve a system of equations using elimination: word problems (A1-O.11)
    • Solve a system of equations using any method (A1-O.14)
    • Solve a system of equations using any method: word problems (A1-O.15)

  • 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. Supporting standards: 6.ALG.1, 6.ALG.2, 6.ALG.3, 6.ALG.4, 6.ALG.5, 7.ALG.1, 7.ALG.2, 8.ALG.1, 8.ALG.3

    • Solve a system of linear and quadratic equations by graphing (A1-Z.9)

  • 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. Supporting standards: 6.ALG.1, 6.ALG.2, 6.ALG.3, 6.ALG.4, 6.ALG.5, 7.ALG.1, 7.ALG.2, 8.ALG.1, 8.ALG.3

    • Find solutions using a table (A1-M.11)
    • Approximate solutions using a table (A1-M.12)
    • Solve a system of equations by graphing (A1-O.2)
    • Solve a system of equations by graphing: word problems (A1-O.3)
    • Find the number of solutions to a system of equations by graphing (A1-O.4)

  • A1.LFE.14 Solve linear inequalities and systems of linear inequalities in two variables by graphing. Supporting standards: 6.ALG.1, 6.ALG.2, 6.ALG.3, 6.ALG.4, 6.ALG.5, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 8.ALG.1, 8.ALG.2, 8.ALG.3

    • 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 compound inequalities (A1-F.12)
    • Graph solutions to compound inequalities (A1-F.15)
    • Does (x, y) satisfy the inequality? (A1-P.1)
    • Graph a two-variable linear inequality (A1-P.3)
    • Is (x, y) a solution to the system of linear inequalities? (A1-P.6)
    • Solve systems of linear inequalities by graphing (A1-P.7)

  • Checkpoint opportunity

    • Checkpoint: Solve equations using graphs and tables (A1-M.19)
    • Checkpoint: Systems of equations and inequalities (A1-P.8)

• 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. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 6.ALG.1, 6.ALG.2, 6.ALG.3, 7.ALG.2, 7.ALG.4, 7.PR.6, 8.ALG.1, 8.ALG.2, 8.FN.9

    • 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)
    • Write a linear function: word problems (A1-N.8)

  • A1.LFE.16 Graph linear functions expressed as an equation and show intercepts of the graph without technology.Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7

    • Slope-intercept form: graph an equation (A1-L.4)
    • Standard form: graph a line from an equation (A1-L.11)
    • Graph a horizontal or vertical line (A1-L.13)
    • Point-slope form: graph an equation (A1-L.14)

  • A1.LFE.17 Graph absolute value functions expressed as an equation with and without technology, showing intercepts and end behavior. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 6.NCC.4, 7.NCC.3, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7

    • Graph an absolute value function (A1-BB.2)

  • A1.LFE.18 Graph and generalize the effect of transformations on linear and absolute value functions. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 6.NCC.4, 7.NCC.3, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7

    • Transformations of linear functions (A1-N.13)
    • Transformations of absolute value functions: translations and reflections (A1-BB.5)
    • Transformations of absolute value functions: translations, reflections, and dilations (A1-BB.6)

  • A1.LFE.19 Given the graph of a linear function, explain the effects of the transformation from the parent function, y = x. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7

  • Checkpoint opportunity

    • Checkpoint: Write linear functions (A1)
    • Checkpoint: Graph linear functions (A1)

• 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. Supporting standards: 8.SP.1, 8.SP.2

    • Write equations for lines of best fit (A1-JJ.5)
    • Find the equation of a regression line (A1-JJ.7)
    • Interpret regression lines (A1-JJ.8)
    • Analyze a regression line of a data set (A1-JJ.9)

  • 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. Supporting standards: 8.SP.1, 8.SP.2

    • Match correlation coefficients to scatter plots (A1-JJ.3)
    • Calculate correlation coefficients (A1-JJ.4)

  • A1.LFE.22 Compare and contrast correlation and causation in real-world problems. Supporting standards: 8.SP.1, 8.SP.2

    • Correlation and causation (A1-JJ.11)

  • Checkpoint opportunity

    • Checkpoint: Linear modeling (A1-JJ.12)

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. Supporting standards: 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.NCC.7, 8.NCC.8, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2

    • Interpret parts of quadratic expressions: word problems (A1-Y.13)
    • Solve quadratic equations: word problems (A1-Z.7)

  • A1.QFE.2 Write quadratic equations with real number solutions that model the relationship between two quantities and produce a graph of the equation. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 6.ALG.1, 6.ALG.2, 6.ALG.3, 7.ALG.2, 7.ALG.4, 7.PR.6, 8.ALG.1, 8.ALG.2, 8.FN.9

    • Graph quadratic functions in vertex form (A1-Y.5)
    • Write a quadratic function in vertex form (A1-Y.6)
    • Graph quadratic functions in standard form (A1-Y.7)
    • Match quadratic functions and graphs (A1-Y.8)
    • Write a quadratic function in vertex form from its vertex and another point (A1-Y.11)

  • 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. Supporting standards: 6.ALG.1, 6.ALG.2, 6.ALG.3, 6.ALG.4, 6.ALG.5, 7.ALG.1, 7.ALG.2, 7.NCC.9, 8.ALG.1, 8.ALG.2, 8.NCC.7, 8.NCC.8

    • Solve a quadratic equation using square roots (A1-Z.1)
    • Solve a quadratic equation using the zero product property (A1-Z.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)
    • Solve a quadratic equation using the quadratic formula (A1-Z.6)
    • Using the discriminant (A1-Z.8)

  • Checkpoint opportunity

    • Checkpoint: Solve quadratic equations (A1)

• 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. Supporting standards: 7.ALG.4, 8.FN.3, 8.FN.8

    • Domain and range of quadratic functions: graphs (A1-Y.9)
    • Domain and range of quadratic functions: equations (A1-Y.10)

  • 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. Supporting standards: 7.ALG.4, 8.FN.3, 8.FN.8

  • A1.QFE.6 Interpret the key features of a quadratic function that models a relationship between two quantities in a given context. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9

    • Characteristics of quadratic functions: graphs (A1-Y.1)
    • Characteristics of quadratic functions: equations (A1-Y.2)

  • A1.QFE.7 Flexibly use different representations of a quadratic function, including graphs, tables, and equations. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9

    • Complete a function table: quadratic functions (A1-Y.3)
    • Graph quadratic functions in vertex form (A1-Y.5)
    • Write a quadratic function in vertex form (A1-Y.6)
    • Graph quadratic functions in standard form (A1-Y.7)
    • Match quadratic functions and graphs (A1-Y.8)
    • Write a quadratic function in vertex form from its vertex and another point (A1-Y.11)

  • 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. Supporting standards: 6.ALG.4, 7.NCC.9, 7.ALG.1, 8.NCC.3, 8.NCC.7, 8.NCC.8, 8.FN.5

    • Interpret parts of quadratic expressions: word problems (A1-Y.13)

  • A1.QFE.9 Use factoring and completing the square to create equivalent forms of quadratic functions to reveal key attributes. Supporting standards: 6.ALG.1, 6.ALG.2, 6.ALG.3, 6.ALG.4, 6.ALG.5, 7.ALG.1, 7.ALG.2, 7.NCC.9, 8.ALG.1, 8.ALG.2, 8.NCC.3, 8.NCC.7, 8.NCC.8, 8.FN.5

    • Factor quadratics with leading coefficient 1 (A1-X.5)
    • Factor quadratics with other leading coefficients (A1-X.6)
    • Factor quadratics: special cases (A1-X.7)
    • Factor by grouping (A1-X.8)
    • Factor using a quadratic pattern (A1-X.9)
    • Complete the square (A1-Z.4)

• 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. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7

    • Graph quadratic functions in vertex form (A1-Y.5)
    • Graph quadratic functions in standard form (A1-Y.7)
    • Match quadratic functions and graphs (A1-Y.8)

  • A1.QFE.11 Graph and describe the effect of transformations on quadratic functions. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7

    • Transformations of quadratic functions (A1-Y.4)

  • A1.QFE.12 Given the graph of a quadratic function, explain the effects of the transformation from the parent function, y = x². Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7

  • Checkpoint opportunity

    • Checkpoint: Write and interpret equivalent expressions (A1)

• 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. Supporting standards: 8.SP.1, 8.SP.2

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. Supporting standards: 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2

    • Write exponential functions: word problems (A1-V.8)

  • A1.EFE.2 Represent real-world problems (growth, decay, and compound interest), using exponential equations. Supporting standards: 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2

    • Exponential growth and decay: word problems (A1-V.9)
    • Compound interest: word problems (A1-V.10)

  • A1.EFE.3 Construct exponential equations from geometric sequences with and without context. Supporting standards: 6.ALG.3, 6.ALG.4, 6.ALG.7, 6.ALG.8, 7.ALG.1, 7.ALG.2, 7.ALG.3, 7.NCC.9, 7.PR.6, 8.FN.6, 8.FN.7, 8.ALG.1, 8.ALG.2

    • Geometric sequences (A1-U.3)
    • Write variable expressions for geometric sequences (A1-U.8)
    • Write formulas for geometric sequences: function notation (A1)

• 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. Supporting standards: 7.ALG.4, 8.FN.3, 8.FN.8

    • Domain and range of exponential functions: graphs (A1-V.5)
    • Domain and range of exponential functions: equations (A1-V.6)

  • 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. Supporting standards: 7.ALG.4, 8.FN.3, 8.FN.8

  • A1.EFE.6 Interpret the key features of an exponential function that models a relationship between two quantities in a given context. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9

    • Match exponential functions and graphs I (A1-V.3)
    • Match exponential functions and graphs II (A1-V.4)

  • A1.EFE.7 Flexibly use different representations of an exponential function, including graphs, tables, and equations. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9

    • Graph exponential functions (A1-V.2)
    • Match exponential functions and graphs I (A1-V.3)
    • Match exponential functions and graphs II (A1-V.4)

  • A1.EFE.8 Interpret the quantities in an exponential equation in the context of a real-world problem, including growth, decay, and compound interest. Supporting standards: 5.GM.8, 6.NCC.4, 6.PR.2, 7.PR.1, 7.NCC.3, 7.PR.7, 7.ALG.5, 8.FN.4, 8.FN.5, 8.FN.6, 8.FN.7, 8.FN.8, 8.FN.9

    • Write exponential functions: word problems (A1-V.8)
    • Exponential growth and decay: word problems (A1-V.9)
    • Compound interest: word problems (A1-V.10)

  • Checkpoint opportunity

    • Checkpoint: Compare linear and exponential functions (A1-AA.13)
    • Checkpoint: Write linear, exponential, and quadratic functions (A1)

• Graphing: Students graph exponential functions.

  • A1.EFE.9 Graph exponential functions that model real-world problems (growth, decay, and compound interest), showing key attributes. Supporting standards: 5.GM.7, 5.GM.8, 6.GM.4, 7.ALG.1, 7.PR.4, 8.FN.1, 8.FN.5, 8.FN.6, 8.FN.7

    • Graph exponential functions (A1-V.2)
    • Match exponential functions and graphs I (A1-V.3)
    • Match exponential functions and graphs II (A1-V.4)

  • Checkpoint opportunity

    • Checkpoint: Exponential functions (A1)

• 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. Supporting standards: 8.SP.1, 8.SP.2

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. Supporting standards: 6.SP.2, 6.SP.3, 6.SP.4, 6.SP.5, 6.SP.6, 6.SP.7, 6.SP.8, 7.SP.1, 7.SP.3, 7.SP.4

    • Create histograms (A1-HH.3)
    • Interpret histograms (A1-HH.4)
    • Create bar graphs, line graphs, and histograms (A1-HH.5)
    • Box plots (A1-HH.9)
    • Mean, median, mode, and range (A1-II.2)
    • Calculate quartiles and interquartile range (A1-II.3)
    • Variance and standard deviation (A1-II.6)
    • Choose appropriate measures of center and variation (A1-II.7)

  • 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. Supporting standards: 6.SP.4, 6.SP.5, 6.SP.7

    • Box plots (A1-HH.9)
    • Identify an outlier and describe the effect of removing it (A1-II.5)

  • Checkpoint opportunity

    • Checkpoint: Compare data sets (A1-II.8)
    • Checkpoint: Histograms and box plots (A1)

• 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. Supporting standards: 6.SP.8, 7.SP.1, 8.SP.3

    • Find probabilities using two-way frequency tables (A1-KK.3)
    • Find conditional probabilities using two-way frequency tables (A1-KK.4)

  • Checkpoint opportunity

    • Checkpoint: Two-way frequency tables (A1-KK.11)

CAR Critical Algebra I Supporting Standards

• Fifth Grade

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

    • Evaluate numerical expressions (5-H.3)
    • Evaluate numerical expressions with parentheses and brackets (5-H.5)
    • Identify mistakes involving the order of operations (5-H.6)
    • Evaluate numerical expressions with parentheses in different places (5-H.7)

  • 5.CAR.13 Write simple expressions that record calculations with numbers, interpreting numerical expressions without evaluating them.

    • Write numerical expressions: one operation (5-H.1)
    • Write numerical expressions: two operations (5-H.2)
    • Comparison statements with numerical expressions (5-H.10)
    • Write numerical expressions for word problems (5-I.1)
    • Use numerical expressions to solve multi-step word problems (5-I.2)

  • 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.

    • Describe the coordinate plane (5-LL.1)
    • Objects on a coordinate plane (5-LL.2)

  • 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.

    • Graph points on a coordinate plane (5-LL.3)
    • Graph triangles and quadrilaterals (5-LL.4)
    • Graph points from a table (5-LL.5)
    • Analyze graphed relationships (5-LL.7)
    • Coordinate planes as maps (5-LL.8)
    • Follow directions on a coordinate plane (5-LL.9)

• Sixth Grade

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

    • Understanding absolute value (6-O.5)
    • Absolute value (6-O.6)
    • Absolute value and integers: word problems (6-O.10)
    • Absolute value of rational numbers (6-Q.8)

  • 6.NCC.11 Solve real-world and mathematical problems with the greatest common factor of two whole numbers less than or equal to 100.

    • Identify factors (6-F.2)
    • Find all the factor pairs of a number (6-F.3)
    • Greatest common factor (6-F.6)

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

    • Unit rates (6-S.11)
    • Calculate speed, distance, or time: word problems (6-S.13)
    • Compare rates: word problems (6-S.17)
    • Ratios and rates: word problems (6-S.18)
    • Unit prices (6-X.2)

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

    • Write variable expressions: one operation (6-Y.1)
    • Write variable expressions: two operations (6-Y.2)
    • Write variable expressions: word problems (6-Y.3)

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

    • Identify terms and coefficients (6-Y.8)
    • Sort factors of variable expressions (6-Y.9)

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

    • Evaluate numerical expressions one step at a time (6-E.6)
    • Evaluate numerical expressions involving whole numbers (6-E.7)
    • Identify mistakes involving the order of operations (6-E.8)
    • Evaluate numerical expressions involving decimals (6-J.3)
    • Evaluate numerical expressions involving fractions (6-N.3)
    • Convert between Celsius and Fahrenheit (6-W.11)
    • Evaluate variable expressions with whole numbers (6-Y.4)
    • Evaluate multi-variable expressions (6-Y.5)
    • Evaluate variable expressions with decimals, fractions, and mixed numbers (6-Y.6)
    • Evaluate variable expressions: word problems (6-Y.7)

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

    • Multiply using the distributive property: area models (6-Z.4)
    • Multiply using the distributive property (6-Z.5)
    • Factor variable expressions: area models (6-Z.7)
    • Factor variable expressions using the distributive property (6-Z.8)
    • Write equivalent expressions using properties (6-Z.10)
    • Add and subtract like terms (6-Z.11)

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

    • Identify equivalent expressions using strip models (6-Z.1)
    • Identify equivalent expressions I (6-Z.12)
    • Identify equivalent expressions II (6-Z.13)

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

    • Does x satisfy an equation? (6-AA.1)
    • Which x satisfies an equation? (6-AA.2)
    • Solutions to inequalities (6-BB.1)

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

    • Write an equation from words (6-AA.3)
    • Model and solve equations using algebra tiles (6-AA.5)
    • Model and solve equations using diagrams (6-AA.6)
    • Write and solve equations that represent diagrams (6-AA.7)
    • Solve one-step addition and subtraction equations with whole numbers (6-AA.8)
    • Solve one-step multiplication and division equations with whole numbers (6-AA.9)
    • Solve one-step equations with whole numbers (6-AA.10)
    • Solve one-step addition and subtraction equations with decimals and fractions (6-AA.11)
    • Solve one-step multiplication and division equations with decimals and fractions (6-AA.12)
    • Solve one-step equations with decimals and fractions (6-AA.13)
    • Solve one-step addition and subtraction equations: word problems (6-AA.14)
    • Solve one-step multiplication and division equations: word problems (6-AA.15)
    • Write a one-step equation: word problems (6-AA.16)
    • Solve one-step equations: word problems (6-AA.17)

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

    • Solve one-step inequalities (6-BB.5)
    • Graph solutions to one-step inequalities (6-BB.6)
    • One-step inequalities: word problems (6-BB.7)

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

    • Describe the coordinate plane (6-R.1)
    • Objects on a coordinate plane (6-R.2)
    • Graph points on a coordinate plane (6-R.3)
    • Quadrants (6-R.4)

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

    • Calculate mean, median, and mode (6)
    • Mean, median, and mode: find the missing number (6)

  • 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.

    • Identify an outlier (6-JJ.8)
    • Identify an outlier and describe the effect of removing it (6-JJ.9)

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

    • Calculate range and interquartile range (6)

  • 6.SP.6 Determine which measure of variation (range or interquartile range) is more appropriate to describe the shape; justify the choice.

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

    • Create line plots (6-II.1)
    • Create histograms (6-II.12)
    • Box plots (6-II.21)

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

    • Create relative frequency tables (6-II.6)
    • Interpret histograms (6-II.13)

• Seventh Grade

  • 7.NCC.3 Demonstrate in real-world contexts the distance between two rational numbers on the number line as the absolute value of their differences.

    • Understanding absolute value (7-A.4)

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

    • Complete addition and subtraction equations with integers (7-B.13)
    • Add and subtract integers: word problems (7-B.14)
    • Add and subtract decimals: word problems (7-D.2)
    • Add and subtract fractions: word problems (7-G.2)
    • Add and subtract mixed numbers: word problems (7-G.4)
    • Price lists (7-P.2)
    • Add and subtract fractions and mixed numbers: word problems (7)

  • 7.NCC.8 Use multiplication and division with rational numbers in any form to solve multi-step problems in real-world and mathematical contexts.

    • Complete multiplication and division equations with integers (7-B.23)
    • Multiply decimals and whole numbers: word problems (7-D.4)
    • Divide decimals by whole numbers: word problems (7-D.6)
    • Multiply fractions and mixed numbers: word problems (7-G.10)
    • Divide fractions and mixed numbers: word problems (7-G.14)

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

    • Evaluate numerical expressions involving integers (7-B.25)
    • Evaluate numerical expressions involving decimals (7-D.12)
    • Evaluate numerical expressions involving fractions (7-G.18)
    • Evaluate numerical expressions involving exponents (7-J.7)

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

    • Find the constant of proportionality from a table (7-N.1)
    • Find the constant of proportionality from a graph (7-N.4)

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

    • Identify equivalent ratios (7-L.2)
    • Equivalent ratios: word problems (7-L.4)
    • Do the ratios form a proportion? (7-L.10)
    • Do the ratios form a proportion: word problems (7-L.11)
    • Identify proportional relationships by graphing (7-N.3)
    • Identify proportional relationships from graphs and equations (7-N.6)
    • Identify proportional relationships from tables (7-N.7)

  • 7.PR.5 Compare two different proportional relationships represented in different forms.

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

    • Solve proportions: word problems (7-L.13)
    • Estimate population size using proportions (7-L.14)
    • Write equations for proportional relationships from tables (7-N.2)
    • Write equations for proportional relationships from graphs (7-N.5)
    • Write and solve equations for proportional relationships (7-N.11)
    • Percents of numbers and money amounts (7-O.6)
    • Percents of numbers: word problems (7-O.7)
    • Solve percent equations (7-O.8)
    • Solve percent equations: word problems (7-O.9)

  • 7.PR.7 Given a graph with a proportional relationship, explain the meaning of a point (x, y) on the graph, including the origin (0, 0) and the unit rate (1, r).

    • Interpret graphs of proportional relationships (7-N.10)

  • 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.

    • Simplify expressions by combining like terms (7-S.3)
    • Multiply using the distributive property: area models (7-S.4)
    • Multiply using the distributive property (7-S.5)
    • Write equivalent expressions using properties (7-S.6)
    • Add and subtract linear expressions (7-S.7)
    • Factor linear expressions: area models (7-S.9)
    • Factors of linear expressions (7-S.10)
    • Identify equivalent linear expressions using algebra tiles (7-S.11)
    • Identify equivalent linear expressions I (7-S.12)
    • Identify equivalent linear expressions II (7-S.13)
    • Identify equivalent linear expressions: word problems (7-S.14)

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

    • Model and solve equations using algebra tiles (7-T.4)
    • Solve two-step equations without parentheses (7-T.8)
    • Solve two-step equations with parentheses (7-T.9)
    • Solve two-step equations (7-T.10)
    • Solve two-step equations with fractions (7-T.11)
    • Choose two-step equations: word problems (7-T.12)
    • Solve two-step equations: word problems (7-T.13)
    • Solve equations: complete the solution (7-T.15)

  • 7.ALG.3 Create, solve, and graph two-step inequalities in real-world and mathematical problems in the forms px ± q > r, px ± q < r, px ± q ≥ r, and px ± q ≤ r.

    • Solve one-step inequalities (7-U.4)
    • Graph solutions to one-step inequalities (7-U.5)
    • One-step inequalities: word problems (7-U.6)
    • Solve two-step inequalities (7-U.7)
    • Graph solutions to two-step inequalities (7-U.8)

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

    • Identify independent and dependent variables (7-X.1)
    • Write a two-variable equation (7-X.5)

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

    • Complete a table for a two-variable relationship (7-X.4)
    • Identify the graph of an equation (7-X.6)
    • Graph a two-variable equation (7-X.7)
    • Interpret a graph: word problems (7-X.8)
    • Write an equation from a graph using a table (7-X.9)

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

    • Interpret histograms (7-GG.9)
    • Box plots (7-GG.13)

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

    • Create line plots (7-GG.1)
    • Create stem-and-leaf plots (7-GG.4)
    • Create bar graphs (7-GG.6)
    • Create histograms (7-GG.8)
    • Interpret charts and graphs to find mean, median, mode, and range (7-HH.2)
    • Calculate mean absolute deviation (7-HH.5)
    • Calculate range, quartiles, and interquartile range (7)
    • Identify an outlier (7-HH.7)

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

    • Compare populations using measures of center and spread (7-HH.11)

• Eighth Grade

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

    • Powers with negative bases (8-C.4)
    • Understanding negative exponents (8-C.6)
    • Evaluate powers with negative exponents (8-C.7)
    • Evaluate powers with negative or zero exponents (8-C.8)
    • Multiply powers: integer bases (8-C.9)
    • Divide powers: integer bases (8-C.10)
    • Multiply and divide powers: integer bases (8-C.11)
    • Power of a power: integer bases (8-C.12)
    • Evaluate expressions using properties of exponents (8-C.13)
    • Identify equivalent expressions involving exponents I (8-C.14)
    • Identify equivalent expressions involving exponents II (8-C.15)

  • Checkpoint opportunity

    • Checkpoint: Properties of exponents (8-C.20)

  • 8.NCC.7 Solve equations in the form of x² = p or x³ = p where p is a positive rational number.

    • Solve equations using square roots (8-E.6)
    • Solve equations using cube roots (8-E.9)

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

    • Square roots of perfect squares (8-E.1)
    • Relationship between squares and square roots (8-E.5)
    • Cube roots of positive perfect cubes (8-E.7)

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

    • Find the constant of proportionality from a graph (8-X.4)
    • Graph proportional relationships and find the slope (8-X.9)
    • Graph proportional relationships from equations (8)

  • 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.

    • Identify functions (8)
    • Identify functions: graphs (8-BB.2)
    • Identify functions: tables (8)
    • Identify functions: graphs and mapping diagrams (8)

  • 8.FN.4 Compare the rate of change (slope) and y-intercept (initial value) of two linear functions each represented in different forms.

    • Compare linear functions: graphs and equations (8-CC.9)
    • Compare linear functions: tables, graphs, and equations (8-CC.10)

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

    • Identify linear and nonlinear functions: graphs and equations (8-DD.1)

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

    • Find the slope from a graph (8-Z.1)
    • Find the slope from two points (8-Z.2)
    • Find the slope from a table (8-Z.3)
    • Slope-intercept form: find the slope and y-intercept (8-AA.3)
    • Rate of change of a linear function: graphs (8-CC.6)

  • 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.

    • Interpret graphs of proportional relationships (8-X.10)
    • Interpret the slope and y-intercept of a linear function (8-CC.7)

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

    • Write equations for proportional relationships from tables (8-X.2)
    • Write equations for proportional relationships from graphs (8-X.5)
    • Write a linear equation from a slope and y-intercept (8-AA.6)
    • Write a linear equation from a graph (8-AA.7)
    • Write a linear equation from a slope and a point (8-AA.8)
    • Write a linear equation from two points (8-AA.9)
    • Interpret the slope and y-intercept of a linear function (8-CC.7)
    • Write a linear function from a table (8-CC.8)
    • Write linear functions: word problems (8-CC.11)

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

    • Identify graphs: word problems (8-EE.3)

  • Checkpoint opportunity

    • Checkpoint: Compare linear functions (8-CC.14)
    • Checkpoint: Sketch and describe graphs (8-EE.4)
    • Checkpoint: Understand functions (8)
    • Checkpoint: Interpret slopes and y-intercepts (8)

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

    • Which x satisfies an equation? (8-M.1)
    • Solve equations involving like terms (8-M.11)
    • Solve equations with variables on both sides (8-M.12)
    • Solve equations with variables on both sides: fractional coefficients (8-M.13)
    • Solve equations with variables on both sides: word problems (8-M.14)
    • Solve equations using the distributive property (8-M.15)
    • Solve multi-step equations (8-M.16)
    • Solve multi-step equations with fractional coefficients (8-M.17)
    • Solve equations: mixed review (8-M.18)
    • Solve multi-step equations: complete the solution (8-M.19)
    • Find the number of solutions (8-M.20)
    • Create equations with no solutions or infinitely many solutions (8-M.21)

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

    • Solve multi-step inequalities (8-N.8)
    • Graph solutions to multi-step inequalities (8-N.9)
    • Solve inequalities with integers: variables on both sides (8-N.10)
    • Solve inequalities with decimals: variables on both sides (8-N.11)
    • Solve two-step inequalities: rational coefficients (8)

  • Checkpoint opportunity

    • Checkpoint: Solve linear equations (8-M.22)

  • 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.

    • Is (x, y) a solution to the system of equations? (8-GG.1)
    • Solve a system of equations by graphing: word problems (8-GG.3)
    • Solve a system of equations using substitution: word problems (8-GG.9)
    • Find the number of solutions to a system of equations by graphing (8)
    • Solve a system of equations by graphing (8)
    • Solve a system of equations in slope-intercept form (8)

  • Checkpoint opportunity

    • Checkpoint: Systems of equations (8)

  • 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.

    • Create scatter plots (8-II.4)
    • Identify trends with scatter plots (8-II.5)

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

    • Identify lines of best fit (8-II.8)
    • Write equations for lines of best fit (8-II.9)

  • 8.SP.3 Construct and interpret a relative frequency table, using data from two categorical variables collected from the same subject.

    • Find probabilities using two-way frequency tables (8-JJ.4)

  • Checkpoint opportunity

    • Checkpoint: Lines of best fit (8-II.13)
    • Checkpoint: Two-way frequency tables (8-JJ.11)