Know that there are numbers that are not rational, and approximate them by rational numbers.
NC.8.NS.1 Understand that every number has a decimal expansion. Building upon the definition of a rational number, know that an irrational number is defined as a non-repeating, non-terminating decimal.
NC.8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers and locate them approximately on a number line. Estimate the value of expressions involving:
NC.8.NS.2.a Square roots and cube roots to the tenths.
NC.8.NS.2.b π to the hundredths.
NC.8.EE Expressions and Equations
Work with radicals and integer exponents.
NC.8.EE.1 Develop and apply the properties of integer exponents to generate equivalent numerical expressions.
NC.8.EE.2 Use square root and cube root symbols to:
NC.8.EE.2.a Represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number.
NC.8.EE.2.b Evaluate square roots of perfect squares and cube roots of perfect cubes for positive numbers less than or equal to 400.
NC.8.EE.3 Use numbers expressed in scientific notation to estimate very large or very small quantities and to express how many times as much one is than the other.
Analyze and solve pairs of simultaneous linear equations.
NC.8.EE.8 Analyze and solve a system of two linear equations in two variables in slope-intercept form.
NC.8.EE.8.a Understand that solutions to a system of two linear equations correspond to the points of intersection of their graphs because the point of intersection satisfies both equations simultaneously.
NC.8.F.3 Identify linear functions from tables, equations, and graphs.
Use functions to model relationships between quantities.
NC.8.F.4 Analyze functions that model linear relationships.
NC.8.F.4.a Understand that a linear relationship can be generalized by y = mx + b.
NC.8.F.4.b Write an equation in slope-intercept form to model a linear relationship by determining the rate of change and the initial value, given at least two (x, y) values or a graph.
NC.8.F.4.c Construct a graph of a linear relationship given an equation in slope-intercept form.
NC.8.F.4.d Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of the slope and y-intercept of its graph or a table of values.
NC.8.F.5 Qualitatively analyze the functional relationship between two quantities.
NC.8.F.5.a Analyze a graph determining where the function is increasing or decreasing; linear or non-linear.
NC.8.F.5.b Sketch a graph that exhibits the qualitative features of a real-world function.
Understand congruence and similarity using physical models, transparencies, or geometry software.
NC.8.G.2 Use transformations to define congruence.
NC.8.G.2.a Verify experimentally the properties of rotations, reflections, and translations that create congruent figures.
NC.8.G.2.b 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.
NC.8.G.2.c Given two congruent figures, describe a sequence that exhibits the congruence between them.
NC.8.G.3 Describe the effect of dilations about the origin, translations, rotations about the origin in 90 degree increments, and reflections across the x-axis and y-axis on two-dimensional figures using coordinates.
Investigate patterns of association in bivariate data.
NC.8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Investigate and describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.