8.NS.A Know that there are numbers that are not rational, and approximate them by rational numbers.
8.NS.A.1 Know that numbers that are not rational are called irrational. Understand that every number has a decimal expansion. Write a fraction a/b as a repeating decimal. Write a repeating decimal as a fraction.
8.NS.A.2 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).
8.EE.A.2 Use square root and cube root symbols to represent solutions to equations. Use square root symbols to represent solutions to equations of the form x² = p, where p is a positive rational number. Evaluate square roots of small perfect squares. Use cube root symbols to represent solutions to equations of the form x³ = p, where p is a rational number. Evaluate square roots and cube roots of small perfect cubes.
8.EE.A.4 Perform operations with numbers expressed in scientific notation, including problems where both standard form 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.
8.EE.B Understand the connections between proportional relationships, lines, and linear equations.
8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways (graphs, tables, equations).
8.EE.B.6 Using a non-vertical or non-horizontal line, show why the slope m is the same between any two distinct points by creating similar triangles. Write the equation y = mx for a line through the origin. Be able to write the equation y = mx + b for a line intercepting the vertical axis at b.
8.EE.C Analyze and solve linear equations and pairs of simultaneous linear equations.
8.EE.C.7 Solve linear equations in one variable. Give 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). Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
8.EE.C.8 Analyze and solve pairs of simultaneous linear equations. Find solutions to a system of two linear equations in two variables so they correspond to points of intersection of their graphs. Solve systems of equations in two variables algebraically using simple substitution and by inspection (e.g., 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6). Solve real-world mathematical problems by utilizing and creating two linear equations in two variables.
8.F.A Define, evaluate, and compare functions.
8.F.A.1 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.
8.F.A.2 Compare properties (e.g., y-intercept/initial value, slope/rate of change) of two functions each represented in a different way (e.g., algebraically, graphically, numerically in tables, or by verbal descriptions).
8.F.B Use functions to model relationships between quantities.
8.F.B.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a verbal description of a relationship, two (x, y) values, a table, 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.
8.F.B.5 Describe 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 features of a function that has been described verbally.
8.G.A Understand congruence and similarity using physical models, transparencies, or geometry software.
8.G.A.1 Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length. Angles are taken to angles of the same measure. Parallel lines are taken to parallel lines.
8.G.A.2 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.
8.G.A.3 Given a two-dimensional figure on a coordinate plane, identify and describe the effect (rule or new coordinates) of a transformation (dilation, translation, rotation, and reflection). Image to pre-image, Pre-image to image.
8.G.A.4 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.
8.G.A.5 Use informal arguments to establish facts about: The angle sum and exterior angle of triangles. The angles created when parallel lines are cut by a transversal. The angle-angle criterion for similarity of triangles.
8.SP.A Investigate patterns of association in bivariate data.
8.SP.A.1 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.
8.SP.A.2 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.
8.SP.A.4 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 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.