Tables, graphs, and equations all represent models. We use terms such as “symbolic” or “analytic” to refer specifically to the equation form of a function model; “descriptive model” refers to a model that seeks to describe or summarize phenomena, such as a graph. In Topic B, students expand on their work in Topic A to complete the modeling cycle for a real-world contextual problem presented as a graph, a data set, or a verbal description. For each, they *formulate* a function model, perform *computations* related to solving the problem, *interpret* the problem and the model, and then, through iterations of revising their models as needed, *validate*, and *report* their results.

Students choose and define the quantities of the problem (**N-Q.A.2**) and the appropriate level of precision for the context (**N-Q.A.3**). They create 1- and 2-variable equations (**A-CED.A.1**,** A-CED.A.2**) to model the context when presented as a graph, as data and as a verbal description. They can distinguish between situations that represent a linear (**F-LE.A.1b**), quadratic, or exponential (**F-LE.A.1c**) relationship. For data, they look for first differences to be constant for linear, second differences to be constant for quadratic, and a common ratio for exponential. When there are clear patterns in the data, students will recognize when the pattern represents a linear (arithmetic) or exponential (geometric) sequence (**F-BF.A.1a**, **F-LE.A.2**). For graphic presentations, they interpret the key features of the graph, and for both data sets and verbal descriptions they sketch a graph to show the key features (**F-IF.B.4**). They calculate and interpret the average rate of change over an interval, estimating when using the graph (**F-IF.B.6**), and relate the domain of the function to its graph and to its context (**F-IF.B.5**).