Overview

**Performance Task Overview**

__**Topic: Algebra - Fitting Models to Data - Social Media and Student Performance**__ Students will collect and analyze data to determine a function that most closely relates student use of social media technology with performance in school. This task is designed to draw students in with a discussion regarding modern technology which plays an important role in their lives. Students will have to decide what data to collect, how to collect it, and will then have to determine how to analyze it and create a mathematical model which most closely represents the data. They will use this data to draw conclusions regarding student use of technology for social purposes and how this relates to performance in school. These conclusions will be reported to the class, principal, and school at large.


 * __Essential Questions__:**
 * How can we use mathematics to predict human behavior?
 * How do we know our data will allow us to make a reasonable inference?
 * What are the limitations of mathematical modeling?


 * __Enduring Understandings__:**
 * Variables can be related in many different ways.
 * Representing data in multiple forms allows individuals to better draw conclusions from that data.
 * Different functions can be used to model real life situations, but the resulting models must be carefully interpreted.


 * __NCTM Standards__:** The following are relevant NCTM Standards for Grades 9 - 12. Students in these grades should:

//** Understand patterns, relations, and functions ** //
 * understand relations and functions and select, convert flexibly among, and use various representations for them;
 * analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior;

** Represent and analyze mathematical situations and structures using algebraic symbols **
 * use symbolic algebra to represent and explain mathematical relationships;
 * judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.

** Use mathematical models to represent and understand quantitative relationships **
 * identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships;
 * draw reasonable conclusions about a situation being modeled.

** Analyze change in various contexts **
 * approximate and interpret rates of change from graphical and numerical data.

//The following facets of understanding are evident in the work throughout the performance task and the final product.//
 * __Facets of Understanding__:**


 * **Explanation:** Students will explain the methods used to analyze data and create mathematical models and the mathematical reasoning behind their conclusions.
 * **Interpretation:** Students will interpret the data they collect and the results of their attempts to create lines of best fit and other models in order to create their conclusions and report their confidence in those conclusions.
 * **Application:** Students will have to draw upon their general knowledge of functions in order to decide what kind of data to collect and will need to draw upon knowledge of individual types of functions as they attempt to create lines of best fit and appropriate mathematical models.
 * **Perspective:** Students will assume the perspective of researchers and reporters as they collect and analyze data and then present that to the community at large.
 * **Empathy:** While this facet is covered to a lesser extent, students will need to consider the point of view of those who will complete their surveys and polls. They must decide what types of questions to ask, how to ask them, and how anonymous the records will be. They must also consider the best medium through which to report their conclusions to the general public.
 * **Self-Knowledge:** While not explicitly covered, the students may come across some important revelations as they draw conclusions about the data they have collected. They may find that their research confirms or denies their expectations, or may simply look at the information they read about in real-life studies with a more critical eye.