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Washington Standards

Washington 8th Grade Math Standards

All 32 Washington math standards for 8th grade, each explained in plain English. The official wording is one click away under each one.

32 standards

Data Analysis

8 standards
M.8.DA.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.
Common Core 8.SP.1
M.8.DA.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.
Common Core 8.SP.2
M.8.DA.SP.3
Use the equation of a best-fit line to solve problems with two-variable data and explain what its slope and intercept mean, like 2 inches of growth per year.
Official wording
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
M.8.DA.SP.4
Make and read two-way tables of counts and relative frequencies for two categories from the same people to spot possible links, like owning a pet and liking science.
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.
Formulate statistical investigative questions.
M.8.DA.DS.1
Write statistical questions that look for links in two-way categorical data, knowing a topic can raise several, like whether athletes are likelier to eat breakfast.
Official wording
Formulate statistical investigative questions to articulate research topics and uncover patterns of association seen in bivariate categorical data, that multiple investigative questions may exist for a research topic and must take into account context.
Collect and consider data.
M.8.DA.DS.2
Question a data set by checking how and from whom it was collected, which variables it has, how they were measured and what values they can take.
Official wording
Understand how to interrogate the data to determine how the data were collected, from whom they were collected, what types of variables are in the data, how the variables were measured, and possible outcomes for the variables.
Analyze the data.
M.8.DA.DS.3
Build tables and scatter plots that present a data set clearly, adding context that tells a story and backs a claim about the data.
Official wording
Create data visualizations about a data set. Organize and present the data in appropriate ways, including in tables and scatter plots, and incorporate other relevant information that helps to tell a story and support a claim about the data.
Interpret results.
M.8.DA.DS.4
Draw conclusions about a larger group from a sample, backing them with statistical evidence, naming the sample's limits and judging whether results make sense.
Official wording
Generalize beyond the sample providing statistical evidence for the conclusion, being sure to address limitations of the sample, evidenced in the data. Consider the reasonableness of the results.

Quantity

6 standards
Know that there are numbers that are not rational and approximate them by rational numbers.
M.8.Q.NS.1
Explain that numbers that are not rational are irrational, show that rational numbers have decimals that repeat eventually, and turn repeating decimals into fractions.
Official wording
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers efficiently, flexibly, and accurately show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
M.8.Q.NS.2
Use decimal approximations of irrational numbers to compare them, place them on a number line and estimate values, like pi squared is close to 9.9.
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).
Work with radicals and integer exponents.
M.8.Q.EE.1
Use the rules of integer exponents to rewrite number expressions, like 3^2 x 3^-5 = 3^-3 = 1/27.
Official wording
Know and apply the properties of integer exponents to generate equivalent numerical expressions.
M.8.Q.EE.2
Use square and cube root symbols to solve equations like x^2 = 49 or x^3 = 8, evaluate roots of perfect squares and cubes, and know the square root of 2 is irrational.
Official wording
Use square roots and cube roots where p is a positive rational number. Use square root symbols to represent solutions to equations of the form x² = p. Evaluate square roots of perfect squares. Use cube root symbols to represent solutions to equations of the form x³ = p and evaluate cube roots of perfect cubes. Know that √2 is irrational.
M.8.Q.EE.3
Estimate very large or very small amounts as a single digit times a power of 10 and compare them, like 3 x 10^8 is 75 times 4 x 10^6.
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.
M.8.Q.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.
Common Core 8.EE.4

Relationships

9 standards
Understand the connections between proportional relationships, lines, and linear equations.
M.8.R.EE.5
Graph proportional relationships, read the unit rate as the slope, and compare two shown in different ways, like a table versus an equation for speed.
Official wording
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
M.8.R.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.
Common Core 8.EE.6
Analyze and solve linear equations and pairs of simultaneous linear equations.
M.8.R.EE.7
Solve one-variable linear equations with fraction or decimal coefficients and the distributive property, and give examples with one, no or infinitely many solutions.
Official wording
Efficiently, flexibly, and accurately 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 where solution paths may require using the distributive property and combining like terms.
M.8.R.EE.8
Solve systems of two linear equations by graphing, algebra or tables, knowing the solution is where the lines cross, and use them for real-world problems.
Official wording
Analyze and efficiently, flexibly, and accurately solve pairs of simultaneous linear equations.aUnderstand the solution to a system of linear equations is the point of intersection, because the intersection is a solution to both equations.bSolve systems of linear equations using a variety of strategies (algebraically, graphically, numerically in tables, verbally, etc.)cSolve real-world and mathematical problems leading to two linear equations in two variables.
Apply and extend previous understandings of arithmetic to algebraic expressions.
M.8.R.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.
Common Core 8.F.1
M.8.R.F.2
Compare features of two functions shown in different ways, like a table and 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).
M.8.R.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.
Common Core 8.F.3
Use functions to model relationships between quantities.
M.8.R.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.
Common Core 8.F.4
M.8.R.F.5
Read a graph to describe in words how two quantities relate, such as where it rises, falls or curves, and sketch a graph from a story, like a bike ride with a rest stop.
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 informally.

Spatial Reasoning

9 standards
Understand congruence and similarity using physical models, transparencies, or geometry software.
M.8.SR.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.aLine and segment lengths are preserved in rotations, reflections, and translations.bAngles are taken to angles of the same measure.cParallel lines are taken to parallel lines.
Common Core 8.G.1
M.8.SR.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.
Common Core 8.G.2
M.8.SR.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.
Common Core 8.G.3
M.8.SR.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.
Common Core 8.G.4
M.8.SR.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.
Common Core 8.G.5
Understand and apply the Pythagorean Theorem.
M.8.SR.G.6
Explain why the Pythagorean Theorem holds using a proof, like rearranging squares, and why sides that fit a^2 + b^2 = c^2 always form a right triangle.
Official wording
Efficiently, flexibly and accurately explain a proof of the Pythagorean Theorem and its converse.
M.8.SR.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.
Common Core 8.G.7
M.8.SR.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.
Common Core 8.G.8
Solve real-world and mathematical problems involving area, surface area, and volume.
M.8.SR.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.
Common Core 8.G.9

The official Washington documents

Washington State Learning Standards for Mathematics by the Office of Superintendent of Public Instruction are available under a Creative Commons Attribution License (CC BY 4.0).

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.