SammieStage1

=Stage 1 Identify Desired Results=
 * **Establish Goals:** **(G)** ||
 * === ** Common Core State Standards ** ===

** Cluster: **

 * F-LE.1. Distinguish between situations that can be modeled with linear functions and with exponential functions.
 * Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
 * Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
 * Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
 * F-LE.2. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
 * F-LE.5. Interpret the parameters in a linear or exponential function in terms of a context. ||

//What understandings are desired?//

 * //Students will understand that:// **(U)** ||
 * * Choosing the appropriate mathematical model for a given situation requires examining the data from more than one perspective.


 * principal, interest and time are factors that impact financial outcomes in unique, yet critical ways.


 * exponential functions grow by equal factors over equal intervals, not by equal differences over equal intervals. ||

//What essential questions will be considered?//

 * **Essential Questions:** **(Q)** ||
 * * Why is it important to view data from more than one perspective when modeling a given situation?


 * Why is it important to consider the exponential relationship that exists between principal, interest and time when making financial decisions?


 * How do the rates of change of linear functions compare to the rates of change of exponential functions? ||

//What key knowledge and skills will students acquire as a result of this unit?//
data, exponential growth/decay, prinicipal, interest, ammoritization, regression coefficient •critical Ideas: prinicipal, interest and time are the three factors that influence pay off amounts for loans. data requires critical evaluation in order to model appropriately with a mathematical representation. •formulas: A = Pe rt, y = mx+b || •(1) model exponential functions for given parameters and use their models to predict outcomes. •(3) evaulate the rates of change of linear and exponential functions. •(3) test the regression coefficient of linear and exponential functions. •(1) analyze data to determine what type of function would best fit the data. •(2) assume the role of a perspective college student with given financial resources and career plans. •(2) reflect on the cost-to-benefit ratio of post-secondary decisions. ||
 * //Students will know:// **(K)** || //Students will be able to:// **(S)** ||
 * •vocabulary:


 * 2004 ASCD and Grant Wiggins and Jay McTighe**