Cluster: Interpret linear models

Standard: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.*

Cluster: Summarize, represent, and interpret data on two categorical and quantitative variables

Standard: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.*

Cluster: Summarize, represent, and interpret data on a single count or measurement variable

Standard: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).*

Cluster: Build a function that models a relationship between two quantities

Standard: Write a function that describes a relationship between two quantities.*

Cluster: Analyze functions using different representations

Standard: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Cluster: Analyze functions using different representations

Standard: Graph linear and quadratic functions and show intercepts, maxima, and minima.*

Cluster: Interpret functions that arise in applications in terms of the context

Standard: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*

Cluster: Interpret functions that arise in applications in terms of the context

Standard: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*

Cluster: Interpret functions that arise in applications in terms of the context

Standard: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*

Cluster: Understand the concept of a function and use function notation.

Standard: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Cluster: Understand the concept of a function and use function notation.

Standard: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Cluster: Represent and solve equations and inequalities graphically

Standard: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Cluster: Solve equations and inequalities in one variable

Standard: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Cluster: Understand solving equations as a process of reasoning and explain the reasoning

Standard: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Cluster: Understand solving equations as a process of reasoning and explain the reasoning

Standard: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Cluster: Create equations that describe numbers or relationship

Standard: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.*

Cluster: Create equations that describe numbers or relationship

Standard: Create equations that describe numbers or relationship. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*

Cluster: Create equations that describe numbers or relationship

Standard: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.*

Cluster: Reason quantitatively and use units to solve problems

Standard: Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.*