Classroom Resources (3) |

View Standards
**Standard(s): **
[MA2015] AL1 (9-12) 5 :

[MA2019] AL1-19 (9-12) 11 :

5 ) Define appropriate quantities for the purpose of descriptive modeling. [N-Q2]

[MA2019] AL1-19 (9-12) 11 :

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.**

[MA2019] AL1-19 (9-12) 12 : 12. Create equations in two or more variables to represent relationships between quantities in context; graph equations on coordinate axes with labels and scales and use them to make predictions. **Limit to contexts arising from linear, quadratic, exponential, absolute value, and linear piecewise functions.**

[MA2019] AL1-19 (9-12) 28 : 28. 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. *Note: Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; symmetries; and end behavior.* **Extend from relationships that can be represented by linear functions to quadratic, exponential, absolute value, and linear piecewise functions.**

Module 5, Topic A focuses on the skills inherent in the modeling process: representing graphs, data sets, or verbal descriptions using explicit expressions (F-BF.A.1a) when presented in graphic form in Lesson 1, as data in Lesson 2, or as a verbal description of a contextual situation in Lesson 3. They recognize the function type associated with the problem (F-LE.A.1b, F-LE.A.1c) and match to or create 1- and 2-variable equations (A-CED.A.1, A-CED.2) to model a context presented graphically, as a data set, or as a description (F-LE.A.2). Function types include linear, quadratic, exponential, square root, cube root, absolute value, and other piecewise functions. Students interpret features of a graph in order to write an equation that can be used to model it and the function (F-IF.B.4, F-BF.A.1) and relate the domain to both representations (F-IF.B.5). This topic focuses on the skills needed to complete the modeling cycle and sometimes uses purely mathematical models, sometimes real-world contexts.

View Standards
**Standard(s): **
[MA2015] AL1 (9-12) 4 :

[MA2015] AL1 (9-12) 5 :

[MA2015] AL1 (9-12) 6 :

[MA2019] AL1-19 (9-12) 11 :

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. [N-Q1]

[MA2015] AL1 (9-12) 5 :

5 ) Define appropriate quantities for the purpose of descriptive modeling. [N-Q2]

[MA2015] AL1 (9-12) 6 :

6 ) Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. [N-Q3]

[MA2019] AL1-19 (9-12) 11 :

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.**

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 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).

View Standards
**Standard(s): **
[MA2015] AL1 (9-12) 4 :

[MA2015] AL1 (9-12) 5 :

[MA2015] AL1 (9-12) 6 :

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. [N-Q1]

[MA2015] AL1 (9-12) 5 :

5 ) Define appropriate quantities for the purpose of descriptive modeling. [N-Q2]

[MA2015] AL1 (9-12) 6 :

6 ) Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. [N-Q3]

In Module 1, Topic A, students explore the main functions that they will work with in Grade 9: linear, quadratic, and exponential. The goal is to introduce students to these functions by having them make graphs of situations (usually based upon time) in which the functions naturally arise (A-CED.2). As they graph, they reason abstractly and quantitatively as they choose and interpret units to solve problems related to the graphs they create (N-Q.1, N-Q.2, N-Q.3).