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New York Standards

New York 8th Grade Math Standards

All 27 New York math standards for 8th grade, each explained in plain English. The official wording is one click away under each one.

27 standards

The Number System

2 standards
Know that there are numbers that are not rational, and approximate them by rational numbers.
NY-8.NS.1
Explain informally that every number has a decimal, show a rational number's decimal eventually repeats, like 1/3 = 0.333 repeating, and call the rest irrational.
Official wording
Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion eventually repeats. Know that other numbers that are not rational are called irrational.
NY-8.NS.2
Estimate irrational numbers with nearby rational ones, like √2 as about 1.4, to compare them, place them on a number line, and estimate expressions.
Official wording
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.

Expressions, Equations, and Inequalities

8 standards
Work with radicals and integer exponents.
NY-8.EE.1
Use the rules for integer exponents to rewrite numerical expressions, like 3² × 3⁻⁵ = 3⁻³ = 1/27.
Official wording
Know and apply the properties of integer exponents to generate equivalent numerical expressions.
NY-8.EE.2
Solve equations like x² = 49 and x³ = 64 with root symbols, know perfect square roots to 225 and cube roots to 125, and know roots like √2 are 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. Know square roots of perfect squares up to 225 and cube roots of perfect cubes up to 125. Know that the square root of a non-perfect square is irrational.
NY-8.EE.3
Estimate very large or very small amounts as a single digit times a power of 10, and compare them, like 3 × 10⁸ being 75 times as much as 4 × 10⁶.
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.
NY-8.EE.4
Multiply and divide in scientific notation alongside standard form, choose sensible units for huge or tiny amounts, and read scientific notation shown by calculators.
Official wording
Perform multiplication and division with numbers expressed in scientific notation, including problems where both standard decimal form and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology.
Understand the connections between proportional relationships, lines, and linear equations.
NY-8.EE.5
Graph proportional relationships and read the unit rate as the slope, and compare two such relationships shown in different ways, like a table and 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.
NY-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.
Common Core 8.EE.6
Analyze and solve linear equations and pairs of simultaneous linear equations.
NY-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.aRecognize when linear equations in one variable have one solution, infinitely many solutions, or no solutions. Give examples and show which of these possibilities is the case by successively transforming the given equation into simpler forms.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
NY-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. Recognize when the system has one solution, no solution, or infinitely many solutions.bSolve systems of two linear equations in two variables with integer coefficients: graphically, numerically using a table, and algebraically. Solve simple cases by inspection.cSolve real-world and mathematical problems involving systems of two linear equations in two variables with integer coefficients.
Common Core 8.EE.8

Functions

5 standards
Define, evaluate, and compare functions. Note: Function notation is not required in Grade 8.
NY-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.
Common Core 8.F.1
NY-8.F.2
Compare two functions given in different forms, like an equation and a table, by their rates of change or starting values.
Official wording
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
NY-8.F.3
Recognize y = mx + b as a linear function that graphs as a straight line, and tell linear functions from non-linear ones, like y = x² making a curve.
Official wording
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. Recognize examples of functions that are linear and non-linear.
Use functions to model relationships between quantities. Note: Function notation is not required in Grade 8.
NY-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.
Common Core 8.F.4
NY-8.F.5
Describe how two quantities relate by reading a graph, like where it rises or levels off, and sketch a graph to match a described real situation.
Official wording
Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described in a real-world context.

Geometry

9 standards
Understand congruence and similarity using physical models, transparencies, or geometry software.
NY-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.aVerify experimentally lines are mapped to lines, and line segments to line segments of the same length.bVerify experimentally angles are mapped to angles of the same measure.cVerify experimentally parallel lines are mapped to parallel lines.
Common Core 8.G.1
NY-8.G.2
Know shapes are congruent when matching sides and angles are equal, or when slides, flips, and turns map one onto the other, and describe those moves on a grid.
Official wording
Know that a two-dimensional figure is congruent to another if the corresponding angles are congruent and the corresponding sides are congruent. Equivalently, two two-dimensional figures are congruent if one is the image of the other after a sequence of rotations, reflections, and translations. Given two congruent figures, describe a sequence that maps the congruence between them on the coordinate plane.
NY-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.
Common Core 8.G.3
NY-8.G.4
Know shapes are similar when angles match and sides are in proportion, or when slides, flips, turns, and a dilation map one onto the other, and describe those moves.
Official wording
Know that a two-dimensional figure is similar to another if the corresponding angles are congruent and the corresponding sides are in proportion. Equivalently, two two-dimensional figures are similar if one is the image of the other after a sequence of rotations, reflections, translations, and dilations. Given two similar two-dimensional figures, describe a sequence that maps the similarity between them on the coordinate plane.
NY-8.G.5
Give informal arguments about triangle angle sums, exterior angles, angles formed when a transversal crosses parallel lines, and similarity from two matching angles.
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.
NY-8.G.6
Make sense of why the Pythagorean Theorem is true and why its converse holds, like showing a² + b² = c² with squares drawn on a right triangle's sides.
Official wording
Understand a proof of the Pythagorean Theorem and its converse.
NY-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.
Common Core 8.G.7
NY-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.
Common Core 8.G.8
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
NY-8.G.9
Use the given volume formulas for cones, cylinders, and spheres to solve problems, like finding how much a cylindrical can holds.
Official wording
Given the formulas for the volume of cones, cylinders, and spheres, solve mathematical and real-world problems.

Statistics and Probability

3 standards
Investigate patterns of association in bivariate data.
NY-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.
Common Core 8.SP.1
NY-8.SP.2
Explain that straight lines often model two related variables, draw a line that fits a scatter plot by eye, and judge the fit by how close the points fall.
Official wording
Understand 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.
NY-8.SP.3
Use a linear model's equation to solve problems about paired data, explaining what the slope and starting value mean, like each hour of study adding 5 points.
Official wording
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

The official New York documents

New York State Next Generation Mathematics Learning Standards, Copyright 2017, New York State Education Department, used with permission.

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.