extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers

approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line

convert between standard decimal notation and scientific notation

order a set of real numbers arising from mathematical and real-world contexts

generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation

compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane

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

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

represent linear proportional situations with tables, graphs, and equations in the form of y = kx

represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0

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

solve problems involving direct variation

distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0

identify functions using sets of ordered pairs, tables, mappings, and graphs

identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems

write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations

describe the volume formula V = Bh of a cylinder in terms of its base area and its height

use the Pythagorean Theorem and its converse to solve problems

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

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

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

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 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

model the effect on linear and area measurements of dilated two-dimensional shapes

construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data

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

explain how small amounts of money invested regularly, including money saved for college and retirement, grow over time

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