Academic standards list

Eighth Grade — Mathematics


Academic standards define the expectations for knowledge and skills that students are to learn in a subject by a certain age or at the end of a school grade level. This page contains a list of standards for a specific content area, grade level, and/or course. The list of standards may be structured using categories and sub-categories.

The Number System

Know that there are numbers that are not rational, and approximate them by rational numbers.
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show  
Use rational approximations of irrational numbers to compare the size of irrational numbers locating them approximately on a number line diagram. Estimate  

Expressions and Equations

Work with radicals and integer exponents.
Know and apply the properties of integer exponents to generate equivalent numerical expressions.
Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Evaluate
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
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific
Understand the connections between proportional relationships, lines, and linear equations.
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in
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; know and derive
Analyze and solve linear equations and systems of two linear equations.
Solve linear equations in one variable.
     There are 2 components within this standard.
Analyze and solve systems of two linear equations.
     There are 3 components within this standard.


Define, evaluate, and compare functions.
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
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
Know and 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.
Use functions to model relationships between quantities.
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
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear


Understand and describe the effects of transformations on twodimensional figures and use informal arguments to establish facts about angles.
Verify experimentally the properties of rotations, reflections, and translations:  
     There are 3 components within this standard.
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.  
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  
Understand and apply the Pythagorean Theorem.
Explain a proof of the Pythagorean Theorem and its converse.
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
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.
Know and understand the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems.  

Statistics and Probability

Investigate patterns of association in bivariate data.
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such  
Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association,  
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  
Investigate chance processes and develop, use, and evaluate probability models.
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the  
♦  Academic Standards marked with a diamond are "Supporting Content" within the grade level or course.
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