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Tennessee Standards

Tennessee 8th Grade Math Standards

All 26 Tennessee math standards for 8th grade, each explained in plain English. The official wording is one click away under each one.

26 standards

The Number System

2 standards
Know that there are numbers that are not rational, and approximate them by rational numbers.
8.NS.A.1
Know that numbers like pi are irrational, show that rational numbers have decimals that end or repeat, and change such decimals into fractions.
Official wording
Know that real numbers that are not rational are called irrational (e.g., π, √2, etc.). Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually or terminates, and convert a decimal expansion which repeats eventually or terminates into a rational number.
8.NS.A.2
Estimate irrational numbers with nearby rationals to compare them and place them on a number line, like √3 being between 1.7 and 1.8, and estimate expressions like π².
Official wording
Use rational approximations of irrational numbers to compare the size of irrational numbers by locating them approximately on a number line diagram. Estimate the value of irrational expressions (such as 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 and Equations

9 standards
Work with radicals and integer exponents.
8.EE.A.1
Use the rules of integer exponents to rewrite numerical expressions, like 2⁴ × 2⁻⁶ = 2⁻² = 1/4.
Official wording
Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² x 3⁻⁵ = 3⁻³ = 1/3³ = 1/27.
8.EE.A.2
Use square and cube root symbols for solutions of x² = p and x³ = p with positive rational p, and find roots of small perfect squares and cubes, like √49 = 7.
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.
8.EE.A.3
Estimate very large or very small amounts as a single digit times a power of 10, and compare them, like 4 × 10⁶ being 200 times 2 × 10⁴.
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 x 10⁸ and the population of the world as 7 x 10⁹, and determine that the world population is more than 20 times larger.
8.EE.A.4
Solve real-world problems with decimals and scientific notation using technology, and pick sensible units for very big or very small measures, like light-years.
Official wording
Using technology, solve real-world problems with numbers expressed in decimal and scientific notation. 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).
Understand the connections between proportional relationships, lines, and linear equations.
8.EE.B.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.
Common Core 8.EE.5
8.EE.B.6
Use similar triangles to show a line has the same slope between any two points, and use y = mx for lines through the origin and y = mx + b otherwise.
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; know and apply 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, linear inequalities, and systems of two linear equations.
8.EE.C.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 combining like terms.
Common Core 8.EE.7
8.EE.C.8
Solve systems of two linear equations by graphing, knowing the point where the lines cross is the solution that works for both equations.
Official wording
Analyze and solve systems of two linear equations graphically.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.bEstimate solutions by graphing a system of two linear equations in two variables. Identify solutions by inspecting graphs of a system of linear equations in two variables.
8.EE.C.9
Graph a linear inequality with one or two variables, or study a graph already given, to find every value that works, like the shaded side of y > 2x + 1.
Official wording
By graphing on the coordinate plane or by analyzing a given graph, determine the solution set of a linear inequality in one or two variables.

Functions

5 standards
Define, evaluate, and compare functions.
8.F.A.1
Explain that a function gives exactly one output for each input, and that its graph is the set of input-output pairs, without function notation.
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. (Function notation is not required in 8th grade.)
8.F.A.2
Compare features of two functions shown in different ways, like a table and an equation, to decide 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 another linear function represented by an algebraic expression, determine which function has the greater rate of change.
8.F.A.3
Recognize y = mx + b as a linear function with a straight-line graph, and give examples of functions that are not linear, like y = x³.
Official wording
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. 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.B.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.
Common Core 8.F.4
8.F.B.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.
Common Core 8.F.5

Geometry

6 standards
Understand and describe the effects of transformations on two-dimensional figures and use informal arguments to establish facts about angles.
8.G.A.1
Use coordinates to describe how translations, rotations, reflections and dilations change a figure, checking what stays the same and how dilations match scale factors.
Official wording
Describe the effect of translations, rotations, reflections, and dilations on two-dimensional figures using coordinates.aVerify informally that lines are taken to lines, and determine when line segments are taken to line segments of the same length.bVerify informally that angles are taken to angles of the same measure.cVerify informally that parallel lines are taken to parallel lines.dMake connections between dilations and scale factors.
8.G.A.2
Give informal arguments about a triangle's angle sum and exterior angle, angles formed by a transversal across parallel lines, and the angle-angle test for similar triangles.
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.
Understand and apply the Pythagorean Theorem.
8.G.B.3
Explain a model, like squares built on a triangle's sides, that shows why the Pythagorean Theorem and its converse work.
Official wording
Explain a model of the Pythagorean Theorem and its converse.
8.G.B.4
Use the Pythagorean Theorem to find missing sides of right triangles in real-world and math problems, in flat figures and in 3D, like a box's diagonal.
Official wording
Know and 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.B.5
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.
Common Core 8.G.8
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
8.G.C.6
Use the volume formulas for cones, cylinders and spheres to solve real-world and math problems, like how much a cone-shaped cup holds.
Official wording
Apply the formulas for the volumes of cones, cylinders, and spheres to solve real-world and mathematical problems.

Statistics and Probability

4 standards
Investigate patterns of association in bivariate data.
8.SP.A.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.
Common Core 8.SP.1
8.SP.A.2
Know straight lines often model linear relationships, and for scatter plots that look linear, fit a line by eye and judge how close the points fall to it.
Official wording
Know that straight lines are widely used to model linear 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.A.3
Use the equation of a line fitted to two-variable data to solve problems, explaining what the slope and intercept mean, like each extra hour of study adding 3 test points.
Official wording
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercepts. 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.
Investigate chance processes and develop, use, and evaluate probability models
8.SP.B.4
Find probabilities of compound events as the share of outcomes in the sample space, listing those outcomes with lists, tables, tree diagrams or simulation, like rolling two sixes.
Official wording
Find probabilities of and represent sample spaces for compound events using organized lists, tables, tree diagrams, and simulation.aUnderstand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.bRepresent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.

The official Tennessee documents

Tennessee Academic Standards for Mathematics, Tennessee Department of Education, tn.gov/education.

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

The plain-English lines are EMStudio's own explanations, shown beside the official wording. They are not part of the standards.