South Carolina: Grade 8 Math Standards
104 standards · 5 domains
DATA ANALYSIS, STATISTICS, AND PROBABILITY
- 8.DSP.1 Investigate bivariate data.
- 8.DSP.1a Collect bivariate data.
- 8.DSP.1b Graph the bivariate data on a scatter plot.
- 8.DSP.1c Describe patterns observed on a scatter plot, including clustering, outliers, and association (positive, negative, no correlation, linear, nonlinear).
- 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.
- 8.DSP.3 Apply concepts of an approximate line of best fit in real-world situations.
- 8.DSP.3a Find an approximate equation for the line of best fit using two appropriate data points.
- 8.DSP.3b Interpret the slope and intercept.
- 8.DSP.3c Solve problems using the equation.
- 8.DSP.4 Investigate bivariate categorical data in two-way tables.
- 8.DSP.4a Organize bivariate categorical data in a two-way table.
- 8.DSP.4b Interpret data in two-way tables using relative frequencies.
- 8.DSP.4c 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.5a Understand that a matrix is a way to organize data.
- 8.DSP.5b Recognize that a m x n matrix has m rows and n columns.
- 8.DSP.5c Add and subtract matrices of the same size.
- 8.DSP.5d Multiply a matrix by a scalar.
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.
- 8.EEI.2 Investigate concepts of square and cube roots.
- 8.EEI.2a Find the exact and approximate solutions to equations of the form x^2=p and x^3=p where p is a positive rational number.
- 8.EEI.2b Evaluate square roots of perfect squares.
- 8.EEI.2c Evaluate cube roots of perfect cubes.
- 8.EEI.2d Recognize that square roots of non-perfect squares are irrational.
- 8.EEI.3 Explore the relationship between quantities in decimal and scientific notation.
- 8.EEI.3a Express very large and very small quantities in scientific notation in the form a x 10^b = p where 1≤a<10 and b is an integer.
- 8.EEI.3b Translate between decimal notation and scientific notation.
- 8.EEI.3c Estimate and compare the relative size of two quantities in scientific notation.
- 8.EEI.4 Apply the concepts of decimal and scientific notation to solve real-world and mathematical problems.
- 8.EEI.4a Multiply and divide numbers expressed in both decimal and scientific notation.
- 8.EEI.4b Select appropriate units of measure when representing answers in scientific notation.
- 8.EEI.4c 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.5a Graph proportional relationships.
- 8.EEI.5b Interpret unit rate as the slope of the graph.
- 8.EEI.5c Compare two different proportional relationships given multiple representations, including tables, graphs, equations, diagrams, and verbal descriptions.
- 8.EEI.6 Apply concepts of slope and y-intercept to graphs, equations, and proportional relationships.
- 8.EEI.6a Explain why the slope, m, is the same between any two distinct points on a non-vertical line using similar triangles.
- 8.EEI.6b Derive the slope-intercept form (y=mx+b) for a non-vertical line.
- 8.EEI.6c Relate equations for proportional relationships (y=kx) with the slope-intercept form (y=mx+b) where b=0.
- 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.7a 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.
- 8.EEI.7b Recognize the three types of solutions to linear equations: one solution (x=a), infinitely many solutions (a=a), or no solutions (a=b).
- 8.EEI.7c Generate linear equations with the three types of solutions.
- 8.EEI.7d Justify why linear equations have a specific type of solution.
- 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.8a Graph systems of linear equations and estimate their point of intersection.
- 8.EEI.8b 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.
- 8.EEI.8c Solve systems of linear equations algebraically, including methods of substitution and elimination, or through inspection.
- 8.EEI.8d Understand that systems of linear equations can have one solution, no solution, or infinitely many solutions.
FUNCTIONS
- 8.F.1 Explore the concept of functions.
- 8.F.1a Understand that a function assigns to each input exactly one output.
- 8.F.1b Relate inputs (x-values or domain) and outputs (y-values or range) to independent and dependent variables.
- 8.F.1c Translate among the multiple representations of a function, including mappings, tables, graphs, equations, and verbal descriptions.
- 8.F.1d Determine if a relation is a function using multiple representations, including mappings, tables, graphs, equations, and verbal descriptions.
- 8.F.1e Graph a function from a table of values. Understand that the graph and table both represent a set of ordered pairs of that function.
- 8.F.2 Compare multiple representations of two functions, including mappings, tables, graphs, equations, and verbal descriptions, in order to draw conclusions.
- 8.F.3 Investigate the differences between linear and nonlinear functions using multiple representations (i.e. tables, graphs, equations, and verbal descriptions).
- 8.F.3a Define an equation in slope-intercept form (y=mx+b) as being a linear function.
- 8.F.3b Recognize that the graph of a linear function has a constant rate of change.
- 8.F.3c Provide examples of nonlinear functions.
- 8.F.4 Apply the concepts of linear functions to real-world and mathematical situations.
- 8.F.4a Understand that the slope is the constant rate of change and the y-intercept is the point where x = 0.
- 8.F.4b Determine the slope and the y-intercept of a linear function given multiple representations, including two points, tables, graphs, equations, and verbal descriptions.
- 8.F.4c Construct a function in slope-intercept form that models a linear relationship between two quantities.
- 8.F.4d Interpret the meaning of the slope and the y-intercept of a linear function in the context of the situation.
- 8.F.4e Explore the relationship between linear functions and arithmetic sequences.
- 8.F.5 Apply the concepts of linear and nonlinear functions to graphs in real-world and mathematical situations.
- 8.F.5a Analyze and describe attributes of graphs of functions (e.g., constant, increasing/decreasing, linear/nonlinear, maximum/minimum, discrete/continuous).
- 8.F.5b Sketch the graph of a function from a verbal description.
- 8.F.5c Write a verbal description from the graph of a function with and without scales.
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.1a Verify that lines are mapped to lines, including parallel lines.
- 8.GM.1b Verify that corresponding angles are congruent.
- 8.GM.1c Verify that corresponding line segments are congruent.
- 8.GM.2 Apply the properties of rigid transformations (rotations, reflections, translations).
- 8.GM.2a Rotate geometric figures 90, 180, and 270 degrees, both clockwise and counterclockwise, about the origin.
- 8.GM.2b Reflect geometric figures with respect to the x-axis and/or y-axis.
- 8.GM.2c Translate geometric figures vertically and/or horizontally.
- 8.GM.2d 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.
- 8.GM.2e 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.3a Use coordinate geometry to describe the effect of transformations on two-dimensional figures.
- 8.GM.3b Relate scale drawings to dilations of geometric figures.
- 8.GM.4 Apply the properties of transformations (rotations, reflections, translations, dilations).
- 8.GM.4a Dilate geometric figures using scale factors that are positive rational numbers.
- 8.GM.4b Recognize that two-dimensional figures are only similar if a series of transformations can be performed to map the pre-image to the image.
- 8.GM.4c Given two similar figures, describe the series of transformations that justifies this similarity.
- 8.GM.4d Use proportional reasoning to find the missing side lengths of two similar figures.
- 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.5a Discover that the sum of the three angles in a triangle is 180 degrees.
- 8.GM.5b Discover and use the relationship between interior and exterior angles of a triangle.
- 8.GM.5c Identify congruent and supplementary pairs of angles when two parallel lines are cut by a transversal.
- 8.GM.5d Recognize that two similar figures have congruent corresponding angles.
- 8.GM.6 Use models to demonstrate a proof of the Pythagorean Theorem and its converse.
- 8.GM.7 Apply the Pythagorean Theorem to model and solve real-world and mathematical problems in two and three dimensions involving right triangles.
- 8.GM.8 Find the distance between any two points in the coordinate plane using the Pythagorean Theorem.
- 8.GM.9 Solve real-world and mathematical problems involving volumes of cones, cylinders, and spheres and the surface area of cylinders.
THE NUMBER SYSTEM
- 8.NS.1 Explore the real number system and its appropriate usage in real-world situations.
- 8.NS.1a Recognize the differences between rational and irrational numbers.
- 8.NS.1b Understand that all real numbers have a decimal expansion.
- 8.NS.1c Model the hierarchy of the real number system, including natural, whole, integer, rational, and irrational numbers.
- 8.NS.2 Estimate and compare the value of irrational numbers by plotting them on a number line.
- 8.NS.3 Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers, and percentages). Include the conversion of repeating decimal numbers to fractions.