Title: 
Algebra I Module 5, Topic B: Completing the Modeling Cycle 
URL: 
https://www.engageny.org/resource/algebraimodule5topicboverview 
Content Source: 
EngageNY

Type: 
Lesson/Unit Plan

Overview: 
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 Module 5, Topic B, students expand on their work in Topic A to complete the modeling cycle for a realworld 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 (NQ.A.2) and the appropriate level of precision for the context (NQ.A.3). They create 1 and 2variable equations (ACED.A.1, ACED.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 (FLE.A.1b), quadratic, or exponential (FLE.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 (FBF.A.1a, FLE.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 (FIF.B.4). They calculate and interpret the average rate of change over an interval, estimating when using the graph (FIF.B.6), and relate the domain of the function to its graph and to its context (FIF.B.5). 
Content Standard(s): 
Mathematics MA2015 (2016) Grade: 912 Algebra I  4 ) Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. [NQ1]
Alabama Alternate Achievement Standards
 Mathematics MA2015 (2016) Grade: 912 Algebra I  5 ) Define appropriate quantities for the purpose of descriptive modeling. [NQ2]
Alabama Alternate Achievement Standards
 Mathematics MA2015 (2016) Grade: 912 Algebra I  6 ) Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. [NQ3]
Alabama Alternate Achievement Standards
 Mathematics MA2019 (2019) Grade: 912 Algebra I with Probability  11. Create equations and inequalities in one variable and use them to solve problems in context, either exactly or approximately. Extend from contexts arising from linear functions to those involving quadratic, exponential, and absolute value functions. Unpacked Content
Alabama Alternate Achievement Standards



Tags:

arithmetic sequence, descriptive modeling, domain, equations, Exponential function, expression, formulas, geometric sequence, graph, inequality, input, linear function, units 
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Comments  There are six lessons in this topic.
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