Gizmos for South Carolina - Mathematics: 8th Grade (SC--College- and Career-Ready Standards adopted 2015)

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

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.

8.NS.1.b: : Understand that all real numbers have a decimal expansion.

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, percentages). Include the conversion of repeating decimal numbers to fractions.

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.

8.F.1.c: : Translate among the multiple representations of a function, including mappings, tables, graphs, equations, and verbal descriptions.

8.F.1.d: : Determine if a relation is a function using multiple representations, including mappings, tables, graphs, equations, and verbal descriptions.

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.

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.3.a: : Define an equation in slope-intercept form (y = mx + b) as being a linear function.

8.F.3.b: : Recognize that the graph of a linear function has a constant rate of change.

8.F.3.c: : Provide examples of nonlinear functions.

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.

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.

8.F.4.c: : Construct a function in slope-intercept form that models a linear relationship between two quantities.

8.F.4.d: : Interpret the meaning of the slope and the y - intercept of a linear function in the context of the situation.

8.F.4.e: : 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.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.

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.

8.EEI.2.b: : Evaluate square roots of perfect squares.

8.EEI.2.d: : 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.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 ≤ a < 10 and b is an integer.

8.EEI.3.b: : Translate between decimal notation and scientific notation.

8.EEI.3.c: : 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.4.a: : Multiply and divide numbers expressed in both decimal and scientific notation.

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.

8.EEI.5.b: : Interpret unit rate as the slope of the graph.

8.EEI.5.c: : 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.6.a: : Explain why the slope, m, is the same between any two distinct points on a non-vertical line using similar triangles.

8.EEI.6.b: : Derive the slope-intercept form (y = mx + b) for a non-vertical line.

8.EEI.6.c: : 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.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.

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).

8.EEI.7.c: : Generate linear equations with the three types of solutions.

8.EEI.7.d: : 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.8.a: : Graph systems of linear equations and estimate their point of intersection.

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.

8.EEI.8.c: : Solve systems of linear equations algebraically, including methods of substitution and elimination, or through inspection.

8.EEI.8.d: : Understand that systems of linear equations can have one solution, no solution, or infinitely many solutions.

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.

8.GM.1.b: : Verify that corresponding angles are congruent.

8.GM.1.c: : Verify that corresponding line segments are congruent.

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.

8.GM.2.b: : Reflect geometric figures with respect to the x - axis and/or y - axis.

8.GM.2.c: : Translate geometric figures vertically and/or horizontally.

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.

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.

8.GM.3.b: : Relate scale drawings to dilations of geometric figures.

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.

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.

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.

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.

8.GM.5.b: : Discover and use the relationship between interior and exterior angles of a triangle.

8.GM.5.c: : Identify congruent and supplementary pairs of angles when two parallel lines are cut by a transversal.

8.GM.5.d: : 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.

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).

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.3.a: : Find an approximate equation for the line of best fit using two appropriate data points.

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.c: : Add and subtract matrices of the same size.

Correlation last revised: 9/16/2020

South Carolina - Mathematics: 8th Grade

SC--College- and Career-Ready Standards | Adopted: 2015

8.NS: : The Number System

8.F: : Functions

8.EEI: : Expressions, Equations, and Inequalities

8.GM: : Geometry and Measurement

8.DSP: : Data Analysis, Statistics, and Probability