8: Grade 8

Grade 8

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Linear equations, exponents and scientific notation, and proportional relationships form the number and algebra core. Functions are introduced: students define, interpret, and compare linear and non-linear functions. Congruence, similarity, the Pythagorean theorem, and volume, alongside scatter plots and linear regression, round out the grade.

8.1Define the real number system as composed of rational and irrational numbers.8.10Compare proportional and non-proportional linear relationships represented in different ways (algebraically, graphically, numerically in tables, or by verbal descriptions) to solve real-world problems.8.11Solve multi-step linear equations in one variable, including rational number coefficients, and equations that require using the distributive property and combining like terms.8.12Solve systems of two linear equations in two variables by graphing and substitution.8.13Determine whether a relation is a function, defining a function as a rule that assigns to each input (independent value) exactly one output (dependent value), and given a graph, table, mapping, or set of ordered pairs.8.14Evaluate functions defined by a rule or an equation, given values for the independent variable.8.15Compare properties of functions represented algebraically, graphically, numerically in tables, or by verbal descriptions.8.16Construct a function to model a linear relationship between two variables.8.17Analyze the relationship (increasing or decreasing, linear or non-linear) between two quantities represented in a graph.8.18Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities, describing patterns in terms of positive, negative, or no association, linear and non-linear association, clustering, and outliers.8.19Given a scatter plot that suggests a linear association, informally draw a line to fit the data, and assess the model fit by judging the closeness of the data points to the line.8.2Locate rational approximations of irrational numbers on a number line, compare their sizes, and estimate the values of the irrational numbers.8.20Use a linear model of a real-world situation to solve problems and make predictions.8.21Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects, using relative frequencies calculated for rows or columns to describe possible associations between the two variables.8.22Verify experimentally the properties of rigid motions (rotations, reflections, and translations): lines are taken to lines, and line segments are taken to line segments of the same length; angles are taken to angles of the same measure; and parallel lines are taken to parallel lines.8.23Use coordinates to describe the effect of transformations (dilations, translations, rotations, and reflections) on two-dimensional figures.8.24Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them.8.25Analyze and apply properties of parallel lines cut by a transversal to determine missing angle measures.8.26Informally justify the Pythagorean Theorem and its converse.8.27Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane.8.28Apply the Pythagorean Theorem to determine unknown side lengths of right triangles, including real-world applications.8.29Informally derive the formulas for the volume of cones and spheres by experimentally comparing the volumes of cones and spheres with the same radius and height to a cylinder with the same dimensions.8.3Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions.8.30Use formulas to calculate the volumes of three-dimensional figures (cylinders, cones, and spheres) to solve real-world problems.8.4Use square root and cube root symbols to represent solutions to equations.8.5Estimate and compare very large or very small numbers in scientific notation.8.6Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.8.7Determine whether a relationship between two variables is proportional or non-proportional.8.8Graph proportional relationships.8.9Interpret y = mx + b as defining a linear equation whose graph is a line with m as the slope and b as the y-intercept.
Example Problems
Express 1.2 as a mixed number.
Function A is defined by the equation:
Function B is defined by the table:
xy
0-3.5
1-1
21.5
34


Which function increases faster?
Solve for x:
How many solutions does this system of equations have?
Evaluate:

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