# Creating Linear Functions to Model State Population Data

## Objective

SWBAT write functions that describe the relationship between two variables of interest. SWBAT calculate and interpret average rate of change over specified intervals.

#### Big Idea

Using online data, students analyze US State population trends and create linear models to represent the data!

## Entry Ticket: Introduction to Google Public Data

15 minutes

For today's Entry Ticket: Point Slope Review Modeling State Population I have students review the point-slope form of linear functions. I give time for this review to activate prior knowledge and because the point-slope form will be useful in the class activity on modeling state population change.

After reviewing the entry ticket, I have students log on to the website for Google Public Data and explore the site. I ask students to explore the site and see some of the interesting data sets and representations/tools available on the site.

The reason for this activity is it gets students comfortable with the data tools that they will be using in today's lesson. Students will need to navigate the Google Public Data website to select data to compare changes in population over time for different states.

After about 5-7 minutes of allowing students to explore the website, I reconvene the attention of the class, and walk through how to get to the state population data and begin to introduce the main activity for the class on creating linear functions to model state population growth.

Video Narrative on Using Google Public Data:

## Activity: Creating Linear Functions to Model State Population Data

40 minutes

The class then turns to the meat and potatoes of the lesson - the Class Activity: Creating Functions to Model State Population Data.

I like to have students work in pairs rather than groups of 3 or 4. Pairs lend itself to working well in a computer lab - one partner primarily works on the computer and the other works on writing out the work on the assignment sheet. In this way each student has a role and a clear task to be working on during the structured activity.

Since the entry ticket focused on using Google Public Data, students should be familiar enough to begin using the technology. I focus my energy on being sure each pair of students are setup and are on the website in the first few minutes of this section.

The 40 minutes for this section may seem a bit long. The reason for the time allotted to this activity is I always want to try and provide students enough time to get a context for the activity, get used to the new technology and have time to process and engage in the activity. Worse case scenario is if a pair(s) completes the activity I would have them shift to the reflection questions and then the homework so that all students remain busy and on task during the entirety of the class.

Students are working on the activity during this 40 minutes. I am rotating among pairs checking in and asking probing questions dependent on where each group is in terms of thinking about the problem.

For the Pulling It All Together Question (Question #6) I am looking for students to compare and contrast the actual data with the function they created. My goal is for students to understand functions do not always perfectly fit data. I also am looking for students to analyze the population change over time and identify whether or not it is best modeled by a linear function. At this point in the year students are not expected to be able to generate an exponential function, but I would like to see students being able to identify the population change as something other than linear.

## Reflection on State Population Activity

20 minutes

After completing the state population activity, I have students write out some responses to the Reflecton Questions: Comparing State Population Data. Reflecting back on work is an important skill for students to develop, and once that many students are not yet developmentally or cognitively ready to engage in on their own. Providing explicit instruction in how to reflect on learning is one way to help develop those skills for students During this sections students are working independently and I am rotating to students and checking in on their progress.

Another reason for this activity is it provides a buffer for students who need additional time to complete the creating functions activity. If any group of students does not finish the activity from the previous section, I would suggest that those students continue working on the activity and complete the reflection responses for homework or for their exit ticket. This is one straightforward way to provide more access and Differentiated Instruction to engage more students in learning.

## Exit Ticket and Homework: Creating Linear Functions to Model State Population Data

15 minutes

For the Exit Ticket and Homework: Comparing State Population Data, students complete an Idea Organizer  to consolidate and integrate the concepts learned in today's lesson. Students complete this exit ticket for homework as it is a continuation of the work done in class and gives students a chance to take the time they need to develop well-written responses outside of school.

This Exit Ticket asks students to go beyond a summary of the different linear functions they created to model data. The assignment pushes students to critically analyze the choice of creating a linear function to fit the data and determine if another type of function (exponential, quadratic) could be a better fit and why.