Common Core State Standards

8th Grade Math Standards

All 28 Common Core math standards for 8th grade, grouped into domains and written in plain English. The official wording is one click away.

28 standards

The Number System NS

2 standards

Know that there are numbers that are not rational, and approximate them by rational numbers.

8.NS.1

Tell rational numbers from irrational ones, show that a fraction's decimal ends or repeats, and turn a repeating decimal like 0.333... back into 1/3.

Official wording

Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

8.NS.2

Pin down an irrational number with decimals, like the square root of 2 is between 1.4 and 1.5, to compare such numbers and place them on a number line.

Official wording

Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Expressions & Equations EE

8 standards

Work with radicals and integer exponents.

8.EE.1

Use the exponent rules, like 2³ × 2² = 2⁵ or 3⁻² = 1/9, to rewrite expressions with whole-number and negative exponents.

Official wording

Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3⁻⁵ = 3⁻³ = 1/3³ = 1/27.

8.EE.2

Solve equations like x² = 25 or x³ = 8 with square and cube roots, find the roots of small perfect squares and cubes, and know that the square root of 2 is irrational.

Official wording

Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

8.EE.3

Estimate very large or very small amounts as a single digit times a power of 10, like 3 × 10⁸ people in the United States, and say how many times bigger one is.

Official wording

Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 10⁸ and the population of the world as 7 times 10⁹, and determine that the world population is more than 20 times larger.

8.EE.4

Add, subtract, multiply and divide numbers in scientific notation, mix them with ordinary decimals, and pick sensible units for very large or very small measurements.

Official wording

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

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

8.EE.5

Graph a proportional relationship, read its unit rate as the slope, and compare two such relationships shown in different ways, like a graph against an equation.

Official wording

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

8.EE.6

Explain with similar triangles why a line's slope is the same between any two of its points, and derive the equations y = mx and y = mx + b.

Official wording

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical 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.

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

8.EE.7

Solve one-variable linear equations with fractions, parentheses and like terms, and tell whether an equation has one solution, none or infinitely many.

Official wording

Solve linear equations in one variable.aGive 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).bSolve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

8.EE.8

Solve a pair of linear equations in two variables by graphing or algebra, knowing the solution is where the two lines cross, and use such pairs to solve word problems.

Official wording

Analyze and solve pairs of simultaneous linear equations.aUnderstand 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.bSolve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.cSolve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Functions F

5 standards

Define, evaluate, and compare functions.

8.F.1

Know that a function gives exactly one output for each input, and that its graph is the set of all its input-output pairs.

Official wording

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.F.2

Compare two functions given in different ways, like one as a table and one as an equation, to see which has the greater rate of change.

Official wording

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

8.F.3

Recognize y = mx + b as a linear function whose graph is a straight line, and give examples of nonlinear ones, like the area of a square A = s².

Official wording

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. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Use functions to model relationships between quantities.

8.F.4

Write a linear function for a real situation, find its rate of change and starting value from a description, table, graph or two points, and explain what they mean.

Official wording

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.

8.F.5

Describe what a graph shows about two quantities, like where it rises, falls or curves, and sketch a graph from a verbal description.

Official wording

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.

Geometry G

9 standards

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

8.G.1

Check with tracing paper or software that sliding, turning or flipping a figure keeps its side lengths, angles and parallel lines unchanged.

Official wording

Verify experimentally the properties of rotations, reflections, and translations:aLines are taken to lines, and line segments to line segments of the same length.bAngles are taken to angles of the same measure.cParallel lines are taken to parallel lines.

8.G.2

Know that two figures are congruent when one can be moved onto the other by slides, turns and flips, and describe the moves that do it.

Official wording

Understand that a two-dimensional 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.G.3

Describe what happens to a figure's coordinates when it is slid, turned, flipped or scaled up or down.

Official wording

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

8.G.4

Know that two figures are similar when slides, turns, flips and a resize can map one onto the other, and describe the sequence that does it.

Official wording

Understand that a two-dimensional 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 two-dimensional figures, describe a sequence that exhibits the similarity between them.

8.G.5

Argue informally why a triangle's angles add to 180 degrees, which angles match when a line crosses parallel lines, and why two equal angles make triangles similar.

Official wording

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 angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

Understand and apply the Pythagorean Theorem.

8.G.6

Explain a proof that a² + b² = c² in every right triangle, and that a triangle whose sides fit that rule must be a right triangle.

Official wording

Explain a proof of the Pythagorean Theorem and its converse.

8.G.7

Use the Pythagorean theorem to find a missing side of a right triangle in real problems, flat or in three dimensions, like the diagonal of a box.

Official wording

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

8.G.8

Find the distance between two points on a coordinate grid by treating it as the long side of a right triangle.

Official wording

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

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

8.G.9

Use the volume formulas for cylinders, cones and spheres to solve real problems, like how much a can or an ice cream cone holds.

Official wording

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Statistics & Probability SP

4 standards

Investigate patterns of association in bivariate data.

8.SP.1

Make a scatter plot of two measurements, like height and shoe size, and describe clusters, outliers and whether the points trend up, down, in a line or in a curve.

Official wording

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.SP.2

Draw a straight line of best fit by eye through a scatter plot that looks linear, and judge how well it fits by how close the points sit to it.

Official wording

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.SP.3

Use the equation of a fitted line to solve problems, explaining what its slope and intercept mean, like 1.5 cm of growth per extra hour of sunlight.

Official wording

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

8.SP.4

Organize yes-or-no data about two things, like curfews and chores, in a two-way table and use row or column percentages to see whether the two are linked.

Official wording

Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way 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. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?