Skills available for
South Carolina eighth-grade math standards
Standards
are in bold, followed by a list of the IXL math
skills that are aligned to that
standard.
Students can practice
these skills
online at www.ixl.com.
Standards: South Carolina College- and Career-Ready Standards
8.NS The Number System
8.NS.1 Explore the real number system and its appropriate usage in real-world situations.
8.NS.1.a Recognize the differences between rational and irrational numbers.
Identify rational and irrational numbers (8-D.5)
8.NS.1.b Understand that all real numbers have a decimal expansion.
Convert between decimals and fractions or mixed numbers (8-D.4)
8.NS.1.c Model the hierarchy of the real number system, including natural, whole, integer, rational, and irrational numbers.
Classify numbers (8-A.8)
8.NS.2 Estimate and compare the value of irrational numbers by plotting them on a number line.
Estimate positive and negative square roots (8-F.16)
8.NS.3 Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Include the conversion of repeating decimal numbers to fractions.
Convert between decimals and fractions or mixed numbers (8-D.4)
Convert between percents, fractions, and decimals (8-J.1)
8.F Functions
8.F.1 Explore the concept of functions.
8.F.1.a Understand that a function assigns to each input exactly one output.
Identify functions (A1-Q.4)
Identify functions: vertical line test (A1-Q.5)
8.F.1.b Relate inputs (x- values or domain) and outputs (y- values or range) to independent and dependent variables.
Complete a table for a linear function (8-Z.7)
Complete a table and graph a linear function (8-Z.8)
Interpret the graph of a linear function: word problems (8-Z.9)
8.F.1.c Translate among the multiple representations of a function, including mappings, tables, graphs, equations, and verbal descriptions.
Graph a line from an equation (8-Y.6)
Write a linear equation from a graph (8-Y.8)
Complete a table for a linear function (8-Z.7)
Complete a table and graph a linear function (8-Z.8)
Interpret the graph of a linear function: word problems (8-Z.9)
Write a linear function from a table (8-Z.10)
8.F.1.d Determine if a relation is a function using multiple representations, including mappings, tables, graphs, equations, and verbal descriptions.
Identify functions (A1-Q.4)
Identify functions: vertical line test (A1-Q.5)
8.F.1.e Graph a function from a table of values. Understand that the graph and table both represent a set of ordered pairs of that function.
Complete a table and graph a linear function (8-Z.8)
8.F.2 Compare multiple representations of two functions, including mappings, tables, graphs, equations, and verbal descriptions, in order to draw conclusions.
Graph a line from an equation (8-Y.6)
Complete a table and graph a linear function (8-Z.8)
Write a linear function from a table (8-Z.10)
Identify linear and nonlinear functions (8-Z.14)
8.F.3 Investigate the differences between linear and nonlinear functions using multiple representations (i.e. tables, graphs, equations, and verbal descriptions).
8.F.3.a Define an equation in slope-intercept form (y = mx + b) as being a linear function.
Graph a line from an equation (8-Y.6)
Write a linear equation from a slope and y-intercept (8-Y.7)
Write a linear equation from a graph (8-Y.8)
Write a linear equation from a slope and a point (8-Y.9)
Write a linear equation from two points (8-Y.10)
Identify linear and nonlinear functions (8-Z.14)
8.F.3.b Recognize that the graph of a linear function has a constant rate of change.
Find the constant of proportionality from a graph (8-I.3)
Constant rate of change (8-Z.5)
Identify linear and nonlinear functions (8-Z.14)
8.F.3.c Provide examples of nonlinear functions.
Evaluate a nonlinear function (8-Z.16)
8.F.4 Apply the concepts of linear functions to real-world and mathematical situations.
8.F.4.a Understand that the slope is the constant rate of change and the y- intercept is the point where x = 0.
Find the slope of a graph (8-Y.1)
Find the slope from two points (8-Y.2)
Find the slope of an equation (8-Y.4)
Slope-intercept form: find the slope and y-intercept (A1-S.5)
8.F.4.b Determine the slope and the y-intercept of a linear function given multiple representations, including two points, tables, graphs, equations, and verbal descriptions.
Find the slope of a graph (8-Y.1)
Find the slope from two points (8-Y.2)
Find the slope of an equation (8-Y.4)
Write a linear equation from a graph (8-Y.8)
Write a linear equation from two points (8-Y.10)
Slope-intercept form: find the slope and y-intercept (A1-S.5)
8.F.4.c Construct a function in slope-intercept form that models a linear relationship between two quantities.
Slope-intercept form: write an equation from a graph (A1-S.7)
Slope-intercept form: write an equation (A1-S.8)
8.F.4.d Interpret the meaning of the slope and the y - intercept of a linear function in the context of the situation.
Write linear functions: word problems (8-Z.12)
8.F.4.e Explore the relationship between linear functions and arithmetic sequences.
Arithmetic sequences (8-U.2)
Evaluate variable expressions for number sequences (8-U.6)
Write variable expressions for arithmetic sequences (8-U.7)
Evaluate a linear function (8-Z.6)
Complete a table for a linear function (8-Z.7)
Write a linear function from a table (8-Z.10)
8.F.5 Apply the concepts of linear and nonlinear functions to graphs in real-world and mathematical situations.
8.F.5.a Analyze and describe attributes of graphs of functions (e.g., constant, increasing/decreasing, linear/nonlinear, maximum/minimum, discrete/continuous).
8.F.5.b Sketch the graph of a function from a verbal description.
8.F.5.c Write a verbal description from the graph of a function with and without scales.
8.EEI Expressions, Equations, and Inequalities
8.EEI.1 Understand and apply the laws of exponents (i.e. product rule, quotient rule, power to a power, product to a power, quotient to a power, zero power property, negative exponents) to simplify numerical expressions that include integer exponents.
Understanding exponents (8-F.1)
Evaluate exponents (8-F.2)
Solve equations with variable exponents (8-F.3)
Exponents with negative bases (8-F.4)
Exponents with decimal and fractional bases (8-F.5)
Understanding negative exponents (8-F.6)
Evaluate negative exponents (8-F.7)
Multiplication with exponents (8-F.8)
Division with exponents (8-F.9)
Multiplication and division with exponents (8-F.10)
Power rule (8-F.11)
Evaluate expressions involving exponents (8-F.12)
8.EEI.2 Investigate concepts of square and cube roots.
8.EEI.2.a Find the exact and approximate solutions to equations of the form x² = p and x³ = p where p is a positive rational number.
Square roots of perfect squares (8-F.14)
Positive and negative square roots (8-F.15)
Estimate positive and negative square roots (8-F.16)
Relationship between squares and square roots (8-F.17)
Cube roots of perfect cubes (8-F.19)
Estimate cube roots (8-F.21)
Evaluate radical expressions (8-V.7)
8.EEI.2.b Evaluate square roots of perfect squares.
Square roots of perfect squares (8-F.14)
8.EEI.2.c Evaluate cube roots of perfect cubes.
Cube roots of perfect cubes (8-F.19)
8.EEI.2.d Recognize that square roots of non-perfect squares are irrational.
Estimate positive and negative square roots (8-F.16)
8.EEI.3 Explore the relationship between quantities in decimal and scientific notation.
8.EEI.3.a Express very large and very small quantities in scientific notation in the form a x 10 to the b power = p where 1 ² a < 10 and b is an integer.
Convert between standard and scientific notation (8-G.1)
8.EEI.3.b Translate between decimal notation and scientific notation.
Convert between standard and scientific notation (8-G.1)
8.EEI.3.c Estimate and compare the relative size of two quantities in scientific notation.
Compare numbers written in scientific notation (8-G.2)
8.EEI.4 Apply the concepts of decimal and scientific notation to solve real-world and mathematical problems.
8.EEI.4.a Multiply and divide numbers expressed in both decimal and scientific notation.
Multiply and divide rational numbers (8-E.5)
Multiply numbers written in scientific notation (8-G.3)
Divide numbers written in scientific notation (8-G.4)
8.EEI.4.b Select appropriate units of measure when representing answers in scientific notation.
8.EEI.4.c Translate how different technological devices display numbers in scientific notation.
8.EEI.5 Apply concepts of proportional relationships to real-world and mathematical situations.
8.EEI.5.a Graph proportional relationships.
Graph proportional relationships (8-I.5)
8.EEI.5.b Interpret unit rate as the slope of the graph.
Find the constant of proportionality from a graph (8-I.3)
Write equations for proportional relationships (8-I.4)
Find the constant of proportionality: word problems (8-I.7)
8.EEI.5.c Compare two different proportional relationships given multiple representations, including tables, graphs, equations, diagrams, and verbal descriptions.
Write equations for proportional relationships (8-I.4)
Graph proportional relationships (8-I.5)
8.EEI.6 Apply concepts of slope and y - intercept to graphs, equations, and proportional relationships.
8.EEI.6.a Explain why the slope, m, is the same between any two distinct points on a non-vertical line using similar triangles.
Write equations for proportional relationships (8-I.4)
Find the slope of a graph (8-Y.1)
Find the slope from two points (8-Y.2)
Find the slope of an equation (8-Y.4)
Graph a line using slope (8-Y.5)
Graph a line from an equation (8-Y.6)
8.EEI.6.b Derive the slope-intercept form (y = mx + b) for a non-vertical line.
Write a linear equation from a graph (8-Y.8)
Slope-intercept form: write an equation from a graph (A1-S.7)
Slope-intercept form: write an equation (A1-S.8)
8.EEI.6.c Relate equations for proportional relationships (y = kx) with the slope-intercept form (y = mx + b) where b = 0.
Write equations for proportional relationships (8-I.4)
8.EEI.7 Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations.
8.EEI.7.a Solve linear equations and inequalities with rational number coefficients that include the use of the distributive property, combining like terms, and variables on both sides.
Model and solve equations using algebra tiles (8-W.3)
Write and solve equations that represent diagrams (8-W.4)
Solve one-step equations (8-W.6)
Solve two-step equations (8-W.7)
Solve multi-step equations (8-W.8)
Solve equations involving like terms (8-W.9)
Solve equations with variables on both sides (8-W.10)
Solve equations: mixed review (8-W.11)
Solve one-step inequalities (8-X.4)
Graph solutions to one-step inequalities (8-X.5)
Solve two-step inequalities (8-X.6)
Graph solutions to two-step inequalities (8-X.7)
Solve multi-step inequalities (8-X.8)
Graph solutions to multi-step inequalities (8-X.9)
8.EEI.7.b Recognize the three types of solutions to linear equations: one solution (x = a), infinitely many solutions (a = a), or no solutions (a = b).
Find the number of solutions (8-W.13)
8.EEI.7.c Generate linear equations with the three types of solutions.
Find the number of solutions (8-W.13)
8.EEI.7.d Justify why linear equations have a specific type of solution.
Find the number of solutions (8-W.13)
8.EEI.8 Investigate and solve real-world and mathematical problems involving systems of linear equations in two variables with integer coefficients and solutions.
8.EEI.8.a Graph systems of linear equations and estimate their point of intersection.
Solve a system of equations by graphing (8-AA.2)
Solve a system of equations by graphing: word problems (8-AA.3)
8.EEI.8.b Understand and verify that a solution to a system of linear equations is represented on a graph as the point of intersection of the two lines.
Is (x, y) a solution to the system of equations? (8-AA.1)
Solve a system of equations by graphing (8-AA.2)
Solve a system of equations by graphing: word problems (8-AA.3)
8.EEI.8.c Solve systems of linear equations algebraically, including methods of substitution and elimination, or through inspection.
Solve a system of equations using substitution (8-AA.8)
Solve a system of equations using substitution: word problems (8-AA.9)
Solve a system of equations using elimination (8-AA.10)
Solve a system of equations using elimination: word problems (8-AA.11)
8.EEI.8.d Understand that systems of linear equations can have one solution, no solution, or infinitely many solutions.
Find the number of solutions to a system of equations by graphing (8-AA.4)
Find the number of solutions to a system of equations (8-AA.5)
Classify a system of equations by graphing (8-AA.6)
Classify a system of equations (8-AA.7)
8.GM Geometry and Measurement
8.GM.1 Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, technology).
8.GM.1.a Verify that lines are mapped to lines, including parallel lines.
Identify reflections, rotations, and translations (8-P.2)
Translations: graph the image (8-P.3)
Reflections: graph the image (8-P.5)
Rotations: graph the image (8-P.7)
8.GM.1.b Verify that corresponding angles are congruent.
Identify reflections, rotations, and translations (8-P.2)
Translations: graph the image (8-P.3)
Reflections: graph the image (8-P.5)
Rotations: graph the image (8-P.7)
8.GM.1.c Verify that corresponding line segments are congruent.
Identify reflections, rotations, and translations (8-P.2)
Translations: graph the image (8-P.3)
Reflections: graph the image (8-P.5)
Rotations: graph the image (8-P.7)
8.GM.2 Apply the properties of rigid transformations (rotations, reflections, translations).
8.GM.2.a Rotate geometric figures 90, 180, and 270 degrees, both clockwise and counterclockwise, about the origin.
Rotations: graph the image (8-P.7)
Rotations: find the coordinates (8-P.8)
8.GM.2.b Reflect geometric figures with respect to the x - axis and/or y - axis.
8.GM.2.d Recognize that two-dimensional figures are only congruent if a series of rigid transformations can be performed to map the pre-image to the image.
Side lengths and angle measures of congruent figures (8-P.9)
Congruence statements and corresponding parts (8-P.10)
Similar and congruent figures (8-Q.1)
8.GM.2.e Given two congruent figures, describe the series of rigid transformations that justifies this congruence.
8.GM.3 Investigate the properties of transformations (rotations, reflections, translations, dilations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, dynamic software).
8.GM.3.a Use coordinate geometry to describe the effect of transformations on two-dimensional figures.
Translations: find the coordinates (8-P.4)
Reflections: find the coordinates (8-P.6)
Rotations: find the coordinates (8-P.8)
Dilations: graph the image (8-Q.2)
Dilations: find the coordinates (8-Q.3)
8.GM.3.b Relate scale drawings to dilations of geometric figures.
Dilations: scale factor and classification (8-Q.4)
8.GM.4 Apply the properties of transformations (rotations, reflections, translations, dilations).
8.GM.4.a Dilate geometric figures using scale factors that are positive rational numbers.
Dilations: graph the image (8-Q.2)
Dilations: find the coordinates (8-Q.3)
8.GM.4.b Recognize that two-dimensional figures are only similar if a series of transformations can be performed to map the pre-image to the image.
Similar and congruent figures (8-Q.1)
Side lengths and angle measures of similar figures (8-Q.5)
Similar solids (8-S.5)
8.GM.4.c Given two similar figures, describe the series of transformations that justifies this similarity.
8.GM.4.d Use proportional reasoning to find the missing side lengths of two similar figures.
Side lengths and angle measures of similar figures (8-Q.5)
8.GM.5 Extend and apply previous knowledge of angles to properties of triangles, similar figures, and parallel lines cut by a transversal.
8.GM.5.a Discover that the sum of the three angles in a triangle is 180 degrees.
Find missing angles in triangles and quadrilaterals (8-O.4)
8.GM.5.b Discover and use the relationship between interior and exterior angles of a triangle.
Find missing angles in triangles and quadrilaterals (8-O.4)
Exterior Angle Theorem (8-O.5)
Interior angles of polygons (8-O.6)
8.GM.5.c Identify congruent and supplementary pairs of angles when two parallel lines are cut by a transversal.
Identify complementary, supplementary, vertical, adjacent, and congruent angles (8-O.7)
Find measures of complementary, supplementary, vertical, and adjacent angles (8-O.8)
Transversal of parallel lines (8-O.9)
8.GM.5.d Recognize that two similar figures have congruent corresponding angles.
Similar and congruent figures (8-Q.1)
Side lengths and angle measures of similar figures (8-Q.5)
8.GM.6 Use models to demonstrate a proof of the Pythagorean Theorem and its converse.
Converse of the Pythagorean theorem: is it a right triangle? (8-R.5)
8.GM.7 Apply the Pythagorean Theorem to model and solve real-world and mathematical problems in two and three dimensions involving right triangles.
Pythagorean theorem: find the length of the hypotenuse (8-R.1)
Pythagorean theorem: find the missing leg length (8-R.2)
Pythagorean theorem: find the perimeter (8-R.3)
Pythagorean theorem: word problems (8-R.4)
8.GM.8 Find the distance between any two points in the coordinate plane using the Pythagorean Theorem.
Find the distance between two points (8-N.4)
8.GM.9 Solve real-world and mathematical problems involving volumes of cones, cylinders, and spheres and the surface area of cylinders.
Volume of cubes, prisms, and pyramids (8-T.7)
Surface area of cubes, prisms, and pyramids (8-T.8)
Volume of cylinders and cones (8-T.9)
Surface area of cylinders and cones (8-T.10)
Surface area of spheres (8-T.12)
8.DSP Data Analysis, Statistics, and Probability
8.DSP.1 Investigate bivariate data.
8.DSP.1.a Collect bivariate data.
8.DSP.1.b Graph the bivariate data on a scatter plot.
8.DSP.1.c Describe patterns observed on a scatter plot, including clustering, outliers, and association (positive, negative, no correlation, linear, nonlinear).
Scatter plots (8-CC.14)
8.DSP.2 Draw an approximate line of best fit on a scatter plot that appears to have a linear association and informally assess the fit of the line to the data points.
Scatter plots: line of best fit (A1-KK.12)
8.DSP.3 Apply concepts of an approximate line of best fit in real-world situations.
8.DSP.3.a Find an approximate equation for the line of best fit using two appropriate data points.
Scatter plots: line of best fit (A1-KK.12)
8.DSP.3.b Interpret the slope and intercept.
8.DSP.3.c Solve problems using the equation.
8.DSP.4 Investigate bivariate categorical data in two-way tables.
8.DSP.4.a Organize bivariate categorical data in a two-way table.
8.DSP.4.b Interpret data in two-way tables using relative frequencies.
8.DSP.4.c Explore patterns of possible association between the two categorical variables.
8.DSP.5 Organize data in matrices with rational numbers and apply to real-world and mathematical situations.
8.DSP.5.a Understand that a matrix is a way to organize data.
8.DSP.5.b Recognize that a m x n matrix has m rows and n columns.
Matrix vocabulary (A1-M.1)
8.DSP.5.c Add and subtract matrices of the same size.