extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers
order a set of real numbers arising from mathematical and real-world contexts
use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y2 - y1)/ (x2 - x1), is the same for any two points (x1, y1) and (x2, y2) on the same line
graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship
use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems
identify functions using sets of ordered pairs, tables, mappings, and graphs
write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations
write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants
write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants
model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants
identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations
generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation
use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with the origin as the center of dilation
solve problems involving the volume of cylinders, cones, and spheres
use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders
use the Pythagorean Theorem and its converse to solve problems
determine the distance between two points on a coordinate plane using the Pythagorean Theorem
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, and the angle-angle criterion for similarity of triangles
generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane
differentiate between transformations that preserve congruence and those that do not
explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90°, 180°, 270°, and 360° as applied to two-dimensional shapes on a coordinate plane using an algebraic representation
contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation
use a trend line that approximates the linear relationship between bivariate sets of data to make predictions
determine the mean absolute deviation and use this quantity as a measure of the average distance data are from the mean using a data set of no more than 10 data points
solve real-world problems comparing how interest rate and loan length affect the cost of credit
calculate and compare simple interest and compound interest earnings
estimate the cost of a two-year and four-year college education, including family contribution, and devise a periodic savings plan for accumulating the money needed to contribute to the total cost of attendance for at least the first year of college
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