8th Grade Math (West Virginia CCR Standards)

The Number System – Irrational numbers and rational approximations

• M.8.1 Know what irrational numbers are, explain decimal expansions and convert repeating decimals to fractions.
• M.8.2 Use rational approximations and properties of rational and irrational numbers.
  • a. Compare irrational numbers, place them on a number line and estimate the value of expressions.
  • b. Explain why sums and products of rational and irrational numbers are rational or irrational.

Expressions and Equations – Radicals and integer exponents

• M.8.3 Apply the properties of integer exponents to write equivalent numerical expressions.
• M.8.4 Use root symbols for solutions of x² = p and x³ = p, evaluate small roots and know √2 is irrational.
• M.8.5 Use a single digit times a power of 10 to estimate very large or very small quantities and compare them.
• M.8.6 Compute with scientific notation, choose suitable units and read scientific notation produced by technology.

Expressions and Equations – Proportional relationships, lines and linear equations

• M.8.7 Graph proportional relationships, read the unit rate as slope and compare relationships shown in different ways.
• M.8.8 Use similar triangles to explain why slope is constant and derive y = mx and y = mx + b.

Expressions and Equations – Linear equations, systems and one-variable inequalities

• M.8.9 Solve real-world and math problems with linear equations in one variable.
  • a. Classify equations as having one, infinitely many or no solutions by transforming them.
  • b. Solve equations with rational coefficients, including distributing and combining like terms.
• M.8.10 Solve pairs of linear equations by graphing (integer solutions) and link the intersection to the shared solution.
• M.8.11 Justify each step in solving and build a sound argument for the solution method.
• M.8.12 Solve real-world and math problems with linear inequalities in one variable.
• M.8.13 Rearrange formulas to solve for a given variable, focusing on linear formulas.

Functions – Define, evaluate and compare functions

• M.8.14 Understand a function as a rule giving exactly one output for each input, with a graph of ordered pairs (notation not required).
• M.8.15 Compare properties of two functions represented in different ways, such as their rates of change.
• M.8.16 Interpret y = mx + b as a linear function with a straight-line graph and give examples of nonlinear functions.

Functions – Model relationships with functions

• M.8.17 Build a linear function model and find its rate of change and initial value from a description, table or graph.
• M.8.18 Describe a functional relationship qualitatively from a graph and sketch a graph from a verbal description.

Geometry – Congruence and similarity

• M.8.19 Verify by experiment that rotations, reflections and translations keep key properties of figures.
  • a. Lines go to lines and segments to segments of the same length.
  • b. Angles go to angles of the same measure.
  • c. Parallel lines go to parallel lines.
• M.8.20 Show two plane figures are congruent by a sequence of rigid motions and describe the sequence.
• M.8.21 Describe the effect of dilations, translations, rotations and reflections on figures using coordinates.
• M.8.22 Show two figures are similar by a sequence of transformations including dilations and describe the sequence.
• M.8.23 Argue informally about triangle angle sums, exterior angles, parallel lines cut by a transversal and AA similarity.

Geometry – The Pythagorean theorem

• M.8.24 Explain a proof of the Pythagorean theorem and its converse.
• M.8.25 Apply the Pythagorean theorem to find unknown side lengths of right triangles in two and three dimensions.
• M.8.26 Apply the Pythagorean theorem to find the distance between two points on a coordinate grid.

Geometry – Volume of cylinders, cones and spheres

• M.8.27 Know the volume formulas for cones, cylinders and spheres and use them to solve problems.

Statistics and Probability – Patterns of association in bivariate data

• M.8.28 Make and interpret scatter plots and describe clustering, outliers and linear or nonlinear association.
• M.8.29 Fit a straight line informally to scatter plots with linear association and judge the fit by how close the points are.
• M.8.30 Use the equation of a linear model to solve problems, interpreting slope and intercept in context.
• M.8.31 Use two-way tables of frequencies and relative frequencies to describe association between categorical variables.