# Sort By Grade

Expressions & Equations

8ee1
Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^{2} × 3^{–5} = 3^{–3} = 1/3^{3} = 1/27.
8ee2
Use square root and cube root symbols to represent solutions to equations of the form x^{2} = p and x^{3}= p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
8ee3
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. For example, estimate the population of the United States as 3 × 10^{8} and the population of the world as 7 × 10^{9} , and determine that the world population is more than 20 times larger.
8ee4
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. Understand the connections between proportional relationships, lines, and linear equations.
8ee5
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
8ee6
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. Analyze and solve linear equations and pairs of simultaneous linear equations.
8ee7a
Solve linear equations in one variable.
8ee7b
Solve linear equations in one variable.
8ee8a
Analyze and solve pairs of simultaneous linear equations.
8ee8b
Analyze and solve pairs of simultaneous linear equations.
8ee8c
Analyze and solve pairs of simultaneous linear equations.
Functions

8f1
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.
8f2
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
8f3
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 = s 2 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.
8f4
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.
8f5
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 verbally.
Geometry

8g1a
Verify experimentally the properties of rotations, reflections, and translations:
8g1b
Verify experimentally the properties of rotations, reflections, and translations:
8g1c
Verify experimentally the properties of rotations, reflections, and translations:
8g2
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.
8g3
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
8g4
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 twodimensional figures, describe a sequence that exhibits the similarity between them.
8g5
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.
8g6
Explain a proof of the Pythagorean Theorem and its converse.
8g7
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
8g8
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
8g9
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.