# Teacher Resources

## Which Model Models Best?

On this page you will find lesson objectives, standards, instructional notes and UDL opportunities.

Estimated Time:  45 - 60 minutes

### Lesson Objectives:

• Students will gather and analyze data to determine a model of best fit.
• Students will apply their understanding of residuals and behaviors of functions to justify the model.

Key Common Core State Standards:

S.ID.6 Represent data on two quantitative variables on a scatter plot and describe how the variables are related.

1. Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

Supporting Common Core State Standards:
F.IF.4 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.

F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

## Instructional Notes:

In this lesson, students will analyze contextual situations and determine which type of function should serve as the best model for a data set.  Students will consider which function family may best model the data given the contextual situation.  Students will apply their understanding of function families and residuals to justify the model selected.

Students need to complete the “Exploring Other Function Models” lesson reflection prior to the start of this lesson.  Students should be comfortable with multiple function families including logarithmic functions, polynomial and power functions, and sinusoidal curves prior to the start of this lesson.

> Go to Which Model Models Best? lesson

## Sample Responses

For sample responses to the Algebra II Journal questions, visit the Algebra II Journal in the Teacher Resources.

## Which Model Models Best? Page - 10

Solutions for this data set will vary based on the institution criteria selected.  Multiple functions may be selected and justified as the model of best fit.  Focus more on the justification provided rather than the function selected.  Consider providing options for students to present their findings, such as group presentations, gallery walk, etc.

> Go to lesson, page 10

## UDL Opportunities:

Checkpoint 3.1: Activate or supply background knowledge.
Checkpoint 3.2: Highlight patterns, critical features, big ideas, and relationships.
Checkpoint 3.4: Maximize transfer and generalization.
Students will need to understand key features and behaviors of different function families to determine which function best models a data set.  Students will have to justify why the model selected is the best model for the data set.

Checkpoint 4.1: Vary the methods for response and navigation.
Checkpoint 5: Provide options for expression and communication.
Checkpoint 8.3: Foster collaboration and community.
Students have options to use an online applet and/or graphing calculator to analyze the data sets.  The end of lesson reflection may be submitted to the teacher.  Alternatives may include having students or groups present their findings to the class or having students do a gallery walk of final models.

Checkpoint 7.2: Optimize relevance, value, and authenticity.

The scenarios in this lesson are based on real-world data in order to optimize relevance and authenticity.