8.A8.N Number and Quantity

8.A8.N.NS The Real Number System

8 Extend the properties of exponents to rational exponents.

8.A8.N.NS.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

8.A8.N.NS.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
 Simplify radical expressions (Algebra 1 – EE.1)
 Simplify radical expressions involving fractions (Algebra 1 – EE.2)
 Multiply radical expressions (Algebra 1 – EE.3)
 Add and subtract radical expressions (Algebra 1 – EE.4)
 Simplify radical expressions using the distributive property (Algebra 1 – EE.5)
 Simplify radical expressions: mixed review (Algebra 1 – EE.7)
 Simplify radical expressions (Geometry – A.4)
 Roots of integers (Algebra 2 – L.1)
 Roots of rational numbers (Algebra 2 – L.2)
 Nth roots (Algebra 2 – L.4)
 Simplify radical expressions with variables I (Algebra 2 – L.5)
 Simplify radical expressions with variables II (Algebra 2 – L.6)
 Multiply radical expressions (Algebra 2 – L.7)
 Divide radical expressions (Algebra 2 – L.8)
 Add and subtract radical expressions (Algebra 2 – L.9)
 Simplify radical expressions using the distributive property (Algebra 2 – L.10)
 Simplify radical expressions using conjugates (Algebra 2 – L.11)
 Multiplication with rational exponents (Algebra 2 – M.2)
 Division with rational exponents (Algebra 2 – M.3)
 Power rule (Algebra 2 – M.4)
 Simplify expressions involving rational exponents I (Algebra 2 – M.5)
 Simplify expressions involving rational exponents II (Algebra 2 – M.6)


8 Use properties of rational and irrational numbers.

8.A8.N.NS.3 Understand informally that the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.



8.A8.N.Q Quantities

8.A8.N.Q.4 Define appropriate quantities for the purpose of descriptive modeling.
 Interpret bar graphs, line graphs, and histograms (Algebra 1 – N.1)
 Create bar graphs, line graphs, and histograms (Algebra 1 – N.2)
 Interpret stemandleaf plots (Algebra 1 – N.4)
 Interpret boxandwhisker plots (Algebra 1 – N.5)
 Interpret a scatter plot (Algebra 1 – N.6)
 Scatter plots: line of best fit (Algebra 1 – N.7)

8.A8.A Algebra

8.A8.A.EE Expressions and Equations

8 Work with radicals and integer exponents.

8.A8.A.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.
 Understanding exponents (Eighth grade – F.1)
 Evaluate exponents (Eighth grade – F.2)
 Solve equations with variable exponents (Eighth grade – F.3)
 Exponents with negative bases (Eighth grade – F.4)
 Exponents with decimal and fractional bases (Eighth grade – F.5)
 Understanding negative exponents (Eighth grade – F.6)
 Evaluate negative exponents (Eighth grade – F.7)
 Multiplication with exponents (Eighth grade – F.8)
 Division with exponents (Eighth grade – F.9)
 Multiplication and division with exponents (Eighth grade – F.10)
 Power rule (Eighth grade – F.11)
 Evaluate expressions involving exponents (Eighth grade – F.12)
 Multiply monomials (Eighth grade – Z.6)
 Divide monomials (Eighth grade – Z.7)
 Multiply and divide monomials (Eighth grade – Z.8)
 Powers of monomials (Eighth grade – Z.9)

8.A8.A.EE.2 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.


8 Understand the connections between proportional relationships, lines, and linear equations.

8.A8.A.EE.3 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
 Unit rates (Eighth grade – H.5)
 Do the ratios form a proportion? (Eighth grade – H.6)
 Do the ratios form a proportion: word problems (Eighth grade – H.7)
 Solve proportions (Eighth grade – H.8)
 Solve proportions: word problems (Eighth grade – H.9)
 Find the constant of proportionality from a graph (Eighth grade – I.3)
 Graph proportional relationships (Eighth grade – I.5)
 Solve problems involving proportional relationships (Eighth grade – I.8)

8.A8.A.EE.4 Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
 Write equations for proportional relationships (Eighth grade – I.4)
 Find the slope of a graph (Eighth grade – W.1)
 Find the slope from two points (Eighth grade – W.2)
 Find the slope of an equation (Eighth grade – W.4)
 Graph a line using slope (Eighth grade – W.5)
 Graph a line from an equation (Eighth grade – X.9)


8 Analyze and solve linear equations and pairs of simultaneous linear equations.

8.A8.A.EE.5 Solve linear equations in one variable.

8.A8.A.EE.5.a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

8.A8.A.EE.5.b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
 Solve equations involving squares and square roots (Eighth grade – F.18)
 Properties of addition and multiplication (Eighth grade – T.1)
 Distributive property (Eighth grade – T.2)
 Write equivalent expressions using properties (Eighth grade – T.3)
 Model and solve equations using algebra tiles (Eighth grade – U.3)
 Write and solve equations that represent diagrams (Eighth grade – U.4)
 Solve onestep equations (Eighth grade – U.5)
 Solve twostep equations (Eighth grade – U.6)
 Solve multistep equations (Eighth grade – U.7)
 Solve equations involving like terms (Eighth grade – U.8)


8.A8.A.EE.6 Analyze and solve pairs of simultaneous linear equations.

8.A8.A.EE.6.a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

8.A8.A.EE.6.b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.
 Find the number of solutions to a system of equations (Eighth grade – Y.5)
 Classify a system of equations by graphing (Eighth grade – Y.6)
 Classify a system of equations (Eighth grade – Y.7)
 Solve a system of equations using substitution (Eighth grade – Y.8)
 Solve a system of equations using elimination (Eighth grade – Y.10)

8.A8.A.EE.6.c Solve realworld and mathematical problems leading to two linear equations in two variables.




8.A8.A.SS Seeing Structure in Expressions

8 Interpret the structure of expressions

8.A8.A.SS.7 Interpret expressions that represent a quantity in terms of its context.

8.A8.A.SS.7.a Interpret parts of an expression, such as terms, factors, and coefficients.

8.A8.A.SS.7.b Interpret complicated expressions by viewing one or more of their parts as a single entity.


8.A8.A.SS.8 Use the structure of an expression to identify ways to rewrite it.

8.A8.A.SS.8.a Use the distributive property to express a sum of terms with a common factor as a multiple of a sum of terms with no common factor.

8.A8.A.SS.8.b Use the properties of operations to express a product of a sum of terms as a sum of products.



8 Write expressions in equivalent forms to solve problems

8.A8.A.SS.9 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

8.A8.A.SS.9.a Factor a quadratic expression to reveal the zeros of the function it defines.
 Factor quadratics with leading coefficient 1 (Algebra 1 – AA.3)
 Factor quadratics with other leading coefficients (Algebra 1 – AA.4)
 Factor quadratics: special cases (Algebra 1 – AA.5)
 Solve a quadratic equation by factoring (Algebra 1 – BB.6)
 Factor quadratics (Algebra 2 – I.2)
 Solve a quadratic equation by factoring (Algebra 2 – J.8)

8.A8.A.SS.9.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.




8.A8.A.AP Arithmetic with Polynomials and Rational Expressions

8 Perform arithmetic operations on polynomials

8.A8.A.AP.10 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials, and divide polynomials by monomials. Solve problems in and out of context.
 Model polynomials with algebra tiles (Algebra 1 – Z.2)
 Add and subtract polynomials using algebra tiles (Algebra 1 – Z.3)
 Add and subtract polynomials (Algebra 1 – Z.4)
 Add polynomials to find perimeter (Algebra 1 – Z.5)
 Multiply a polynomial by a monomial (Algebra 1 – Z.6)
 Multiply two polynomials using algebra tiles (Algebra 1 – Z.7)
 Multiply two binomials (Algebra 1 – Z.8)
 Multiply two binomials: special cases (Algebra 1 – Z.9)
 Multiply polynomials (Algebra 1 – Z.10)
 Add and subtract polynomials (Algebra 2 – K.2)
 Multiply polynomials (Algebra 2 – K.3)



8.A8.A.CE Creating Equations

8 Create equations that describe numbers or relationships

8.A8.A.CE.11 Create equations and inequalities in one variable including ones with absolute value and use them to solve problems in and out of context, including equations arising from linear functions.
 Write variable equations (Algebra 1 – I.4)
 Model and solve equations using algebra tiles (Algebra 1 – J.1)
 Write and solve equations that represent diagrams (Algebra 1 – J.2)
 Solve linear equations: word problems (Algebra 1 – J.8)
 Write inequalities from graphs (Algebra 1 – K.2)
 Write compound inequalities from graphs (Algebra 1 – K.13)
 Weighted averages: word problems (Algebra 1 – O.5)
 Write variable expressions (Geometry – A.5)
 Solve linear equations (Geometry – A.6)
 Solve linear inequalities (Geometry – A.7)
 Solve linear equations (Algebra 2 – B.1)
 Solve linear equations: word problems (Algebra 2 – B.2)
 Write inequalities from graphs (Algebra 2 – C.3)
 Solve linear inequalities (Algebra 2 – C.5)

8.A8.A.CE.12 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales (limit to linear and quadratic).
 Graph a function (Algebra 1 – Q.9)
 Write a function rule: word problems (Algebra 1 – Q.10)
 Write a rule for a function table (Algebra 1 – Q.12)
 Write direct variation equations (Algebra 1 – R.4)
 Write inverse variation equations (Algebra 1 – R.7)
 Write and solve inverse variation equations (Algebra 1 – R.8)
 Slopeintercept form: graph an equation (Algebra 1 – S.6)
 Slopeintercept form: write an equation from a graph (Algebra 1 – S.7)
 Slopeintercept form: write an equation (Algebra 1 – S.8)
 Linear function word problems (Algebra 1 – S.11)
 Write equations in standard form (Algebra 1 – S.12)
 Standard form: graph an equation (Algebra 1 – S.14)
 Pointslope form: graph an equation (Algebra 1 – S.17)
 Pointslope form: write an equation (Algebra 1 – S.19)
 Write linear, quadratic, and exponential functions (Algebra 1 – CC.3)
 Graph an absolute value function (Algebra 1 – DD.3)
 Graph a linear equation (Geometry – E.3)
 Equations of lines (Geometry – E.4)
 Graph a linear inequality in the coordinate plane (Algebra 2 – C.2)
 Graph a quadratic function (Algebra 2 – J.4)
 Write and solve direct variation equations (Algebra 2 – Q.1)
 Write and solve inverse variation equations (Algebra 2 – Q.2)
 Write joint and combined variation equations I (Algebra 2 – Q.4)
 Write joint and combined variation equations II (Algebra 2 – Q.6)
 Solve variation equations (Algebra 2 – Q.7)
 Graph parabolas (Algebra 2 – T.9)
 Graph circles (Algebra 2 – U.7)

8.A8.A.CE.13 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
 Solve a system of equations by graphing: word problems (Algebra 1 – U.3)
 Solve a system of equations using substitution: word problems (Algebra 1 – U.9)
 Solve a system of equations using elimination: word problems (Algebra 1 – U.11)
 Solve a system of equations using augmented matrices: word problems (Algebra 1 – U.13)
 Solve a system of equations using any method: word problems (Algebra 1 – U.15)
 Solve systems of linear equations (Geometry – A.8)
 Solve a system of equations by graphing: word problems (Algebra 2 – E.3)
 Solve a system of equations using substitution: word problems (Algebra 2 – E.7)
 Solve a system of equations using elimination: word problems (Algebra 2 – E.9)
 Solve a system of equations using any method: word problems (Algebra 2 – E.11)
 Find the vertices of a solution set (Algebra 2 – F.4)
 Linear programming (Algebra 2 – F.5)

8.A8.A.CE.14 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.



8.A8.A.RE Reasoning with Equations and Inequalities

8 Solve equations and inequalities in one variable

8.A8.A.RE.15 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
 Model and solve equations using algebra tiles (Algebra 1 – J.1)
 Write and solve equations that represent diagrams (Algebra 1 – J.2)
 Solve onestep linear equations (Algebra 1 – J.3)
 Solve twostep linear equations (Algebra 1 – J.4)
 Solve advanced linear equations (Algebra 1 – J.5)
 Solve equations with variables on both sides (Algebra 1 – J.6)
 Identities and equations with no solutions (Algebra 1 – J.7)
 Solve linear equations: word problems (Algebra 1 – J.8)
 Solve linear equations: mixed review (Algebra 1 – J.9)
 Identify solutions to inequalities (Algebra 1 – K.3)
 Solve onestep linear inequalities: addition and subtraction (Algebra 1 – K.4)
 Solve onestep linear inequalities: multiplication and division (Algebra 1 – K.5)
 Solve onestep linear inequalities (Algebra 1 – K.6)
 Graph solutions to onestep linear inequalities (Algebra 1 – K.7)
 Solve twostep linear inequalities (Algebra 1 – K.8)
 Graph solutions to twostep linear inequalities (Algebra 1 – K.9)
 Solve advanced linear inequalities (Algebra 1 – K.10)
 Graph solutions to advanced linear inequalities (Algebra 1 – K.11)
 Graph compound inequalities (Algebra 1 – K.12)
 Write compound inequalities from graphs (Algebra 1 – K.13)
 Solve compound inequalities (Algebra 1 – K.14)
 Graph solutions to compound inequalities (Algebra 1 – K.15)
 Linear equations: solve for y (Algebra 1 – S.9)
 Solve linear equations (Geometry – A.6)
 Solve linear inequalities (Geometry – A.7)
 Solve linear equations (Algebra 2 – B.1)
 Solve linear equations: word problems (Algebra 2 – B.2)
 Solve linear inequalities (Algebra 2 – C.5)
 Graph solutions to linear inequalities (Algebra 2 – C.6)

8.A8.A.RE.16 Solve quadratic equations in one variable.

8.A8.A.RE.16.a 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. Derive the quadratic formula from this form.

8.A8.A.RE.16.b Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
 Solve a quadratic equation using square roots (Algebra 1 – BB.4)
 Solve an equation using the zero product property (Algebra 1 – BB.5)
 Solve a quadratic equation by factoring (Algebra 1 – BB.6)
 Complete the square (Algebra 1 – BB.7)
 Solve a quadratic equation by completing the square (Algebra 1 – BB.8)
 Solve a quadratic equation using the quadratic formula (Algebra 1 – BB.9)
 Using the discriminant (Algebra 1 – BB.10)
 Solve quadratic equations (Geometry – A.9)
 Solve a quadratic equation using square roots (Algebra 2 – J.6)
 Solve a quadratic equation using the zero product property (Algebra 2 – J.7)
 Solve a quadratic equation by factoring (Algebra 2 – J.8)
 Solve a quadratic equation using the quadratic formula (Algebra 2 – J.11)
 Using the discriminant (Algebra 2 – J.12)



8 Solve systems of equations

8.A8.A.RE.17 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
 Is (x, y) a solution to the system of equations? (Algebra 1 – U.1)
 Solve a system of equations by graphing (Algebra 1 – U.2)
 Solve a system of equations by graphing: word problems (Algebra 1 – U.3)
 Find the number of solutions to a system of equations by graphing (Algebra 1 – U.4)
 Find the number of solutions to a system of equations (Algebra 1 – U.5)
 Classify a system of equations by graphing (Algebra 1 – U.6)
 Classify a system of equations (Algebra 1 – U.7)
 Solve a system of equations using substitution (Algebra 1 – U.8)
 Solve a system of equations using substitution: word problems (Algebra 1 – U.9)
 Solve a system of equations using elimination (Algebra 1 – U.10)
 Solve a system of equations using elimination: word problems (Algebra 1 – U.11)
 Solve a system of equations using augmented matrices (Algebra 1 – U.12)
 Solve a system of equations using augmented matrices: word problems (Algebra 1 – U.13)
 Solve a system of equations using any method (Algebra 1 – U.14)
 Solve a system of equations using any method: word problems (Algebra 1 – U.15)
 Solve systems of linear equations (Geometry – A.8)
 Is (x, y) a solution to the system of equations? (Algebra 2 – E.1)
 Solve a system of equations by graphing (Algebra 2 – E.2)
 Solve a system of equations by graphing: word problems (Algebra 2 – E.3)
 Find the number of solutions to a system of equations (Algebra 2 – E.4)
 Classify a system of equations (Algebra 2 – E.5)
 Solve a system of equations using substitution (Algebra 2 – E.6)
 Solve a system of equations using substitution: word problems (Algebra 2 – E.7)
 Solve a system of equations using elimination (Algebra 2 – E.8)
 Solve a system of equations using elimination: word problems (Algebra 2 – E.9)
 Solve a system of equations using any method (Algebra 2 – E.10)
 Solve a system of equations using any method: word problems (Algebra 2 – E.11)


8 Represent and solve equations and inequalities graphically

8.A8.A.RE.18 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

8.A8.A.RE.19 Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding halfplanes.


8.A8.F Functions

8.A8.F.F Functions

8 Define, evaluate, and compare functions.

8.A8.F.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

8.A8.F.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

8.A8.F.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.


8 Use functions to model relationships between quantities.

8.A8.F.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
 Find the constant of proportionality from a graph (Eighth grade – I.3)
 Write equations for proportional relationships (Eighth grade – I.4)
 Find the constant of proportionality: word problems (Eighth grade – I.7)
 Solve problems involving proportional relationships (Eighth grade – I.8)
 Find the slope of a graph (Eighth grade – W.1)
 Find the slope from two points (Eighth grade – W.2)
 Rate of change (Eighth grade – X.4)
 Constant rate of change (Eighth grade – X.5)
 Write a linear function from a table (Eighth grade – X.11)
 Write linear functions: word problems (Eighth grade – X.13)

8.A8.F.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.



8.A8.F.IF Interpreting Functions

8 Interpret functions that arise in applications in terms of the context

8.A8.F.IF.6 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
 Identify proportional relationships (Algebra 1 – R.1)
 Find the constant of variation (Algebra 1 – R.2)
 Graph a proportional relationship (Algebra 1 – R.3)
 Identify direct variation and inverse variation (Algebra 1 – R.6)
 Slopeintercept form: find the slope and yintercept (Algebra 1 – S.5)
 Standard form: find x and yintercepts (Algebra 1 – S.13)
 Slopes of parallel and perpendicular lines (Algebra 1 – S.20)
 Characteristics of quadratic functions (Algebra 1 – BB.1)
 Identify linear, quadratic, and exponential functions from graphs (Algebra 1 – CC.1)
 Identify linear, quadratic, and exponential functions from tables (Algebra 1 – CC.2)
 Graph an absolute value function (Algebra 1 – DD.3)
 Rational functions: asymptotes and excluded values (Algebra 1 – GG.1)
 Slopes of lines (Geometry – E.2)
 Characteristics of quadratic functions (Algebra 2 – J.1)
 Graph a quadratic function (Algebra 2 – J.4)
 Rational functions: asymptotes and excluded values (Algebra 2 – N.1)
 Classify variation (Algebra 2 – Q.3)
 Find the constant of variation (Algebra 2 – Q.5)
 Match exponential functions and graphs (Algebra 2 – S.3)

8.A8.F.IF.7 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.


8 Analyze functions using different representations

8.A8.F.IF.8 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

8.A8.F.IF.8.a Graph linear and quadratic functions and show intercepts, maxima, and minima.
 Slopeintercept form: graph an equation (Algebra 1 – S.6)
 Standard form: graph an equation (Algebra 1 – S.14)
 Pointslope form: graph an equation (Algebra 1 – S.17)
 Characteristics of quadratic functions (Algebra 1 – BB.1)
 Graph a linear equation (Geometry – E.3)
 Graph a linear function (Algebra 2 – D.7)
 Graph a quadratic function (Algebra 2 – J.4)


8.A8.F.IF.9 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

8.A8.F.IF.9.a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
 Characteristics of quadratic functions (Algebra 1 – BB.1)
 Solve a quadratic equation by factoring (Algebra 1 – BB.6)
 Complete the square (Algebra 1 – BB.7)
 Solve a quadratic equation by completing the square (Algebra 1 – BB.8)
 Characteristics of quadratic functions (Algebra 2 – J.1)
 Solve a quadratic equation by factoring (Algebra 2 – J.8)
 Complete the square (Algebra 2 – J.9)
 Convert equations of parabolas from general to vertex form (Algebra 2 – T.7)
 Find properties of a parabola from equations in general form (Algebra 2 – T.8)




8.A8.F.BF Building Functions

8 Build a function that models a relationship between two quantities

8.A8.F.BF.10 Write a function that describes a relationship between two quantities.

8.A8.F.BF.10.a Determine an explicit expression, a recursive process, or steps for calculation from a context.
 Write variable expressions for arithmetic sequences (Algebra 1 – P.5)
 Write variable expressions for geometric sequences (Algebra 1 – P.6)
 Write inverse variation equations (Algebra 1 – R.7)
 Write and solve inverse variation equations (Algebra 1 – R.8)
 Write linear, quadratic, and exponential functions (Algebra 1 – CC.3)
 Write a formula for an arithmetic sequence (Algebra 2 – BB.6)
 Write a formula for a geometric sequence (Algebra 2 – BB.7)



8 Build new functions from existing functions

8.A8.F.BF.11 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.



8.A8.F.LQ Linear, Quadratic, and Exponential Models

8 Interpret expressions for functions in terms of the situation they model

8.A8.F.LQ.12 Interpret the parameters in a linear or exponential function in terms of a context.
 Solve linear equations: word problems (Algebra 1 – J.8)
 Exponential growth and decay: word problems (Algebra 1 – X.3)
 Solve linear equations: word problems (Algebra 2 – B.2)
 Exponential growth and decay: word problems (Algebra 2 – S.12)
 Compound interest: word problems (Algebra 2 – S.13)
 Continuously compounded interest: word problems (Algebra 2 – S.14)

8.A8.F.LQ.13 Apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.


8.A8.G Geometry

8.A8.G.G Geometry

8 Understand congruence and similarity using physical models, transparencies, or geometry software.

8.A8.G.G.1 Verify experimentally the properties of rotations, reflections, and translations:

8.A8.G.G.1.a Lines are taken to lines, and line segments to line segments of the same length.

8.A8.G.G.1.b Angles are taken to angles of the same measure.

8.A8.G.G.1.c Parallel lines are taken to parallel lines.


8.A8.G.G.2 Understand that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

8.A8.G.G.3 Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates.

8.A8.G.G.4 Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them.

8.A8.G.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angleangle criterion for similarity of triangles.
 Identify complementary, supplementary, vertical, adjacent, and congruent angles (Eighth grade – N.1)
 Find measures of complementary, supplementary, vertical, and adjacent angles (Eighth grade – N.2)
 Transversal of parallel lines (Eighth grade – N.3)
 Find missing angles in triangles and quadrilaterals (Eighth grade – N.6)
 Interior angles of polygons (Eighth grade – N.9)
 Congruent triangles: SSS, SAS, and ASA (Eighth grade – N.14)


8 Understand and apply the Pythagorean Theorem.

8.A8.G.G.6 Explain a proof of the Pythagorean Theorem and its converse.

8.A8.G.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions.

8.A8.G.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.



8.A8.G.EG Expressing Geometric Properties with Equations

8 Use coordinates to prove simple geometric theorems algebraically

8.A8.G.EG.9 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).


8.A8.SP Statistics and Probability

8.A8.SP.SP Statistics and Probability

8 Investigate patterns of association in bivariate data.

8.A8.SP.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

8.A8.SP.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

8.A8.SP.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

8.A8.SP.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.


8.A8.VA Constructing Viable Arguments

8.A8.VA.VA Constructing Viable Arguments

8.A8.VA.VA.1 Use and know simple aspects of a logical argument.

8.A8.VA.VA.1.a Use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion.


8.A8.VA.VA.2 Use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements:

8.A8.VA.VA.2.a Use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions.

8.A8.VA.VA.2.b Judge the validity of an argument according to whether the properties of the real number system and the order of operations have been applied correctly at each step.

8.A8.VA.VA.2.c Given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities, determine whether the statement is true sometimes, always, or never.

