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
use the Pythagorean Theorem and its converse to solve problems
write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants
use a trend line that approximates the linear relationship between bivariate sets of data to make predictions
graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship
solve problems involving the volume of cylinders, cones, and spheres
order a set of real numbers arising from mathematical and real-world contexts
differentiate between transformations that preserve congruence and those that do not
The student applies mathematical process standards to represent and use real numbers in a variety of forms. The student is expected to:
Convert between standard decimal notation and scientific notation; and
calculate and compare simple interest and compound interest earnings
use data from a table or graph to determine the rate of change or slope and y-intercept in 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
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
describe the volume formula V = Bh of a cylinder in terms of its base area and its height
determine the distance between two points on a coordinate plane using the Pythagorean Theorem
identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems
generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane
construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data
extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers
represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠0
The student applies mathematical process standards to use one-variable equations or inequalities in problem situations. The student is expected to:
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; and
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 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
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
compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane
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
identify functions using sets of ordered pairs, tables, mappings, and graphs
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
The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in one's life as a knowledgeable consumer and investor. The student is expected to:
Calculate and compare simple interest and compound interest earnings;
solve problems involving direct variation
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
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