# How Much for a Used Car?

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## Objective

SWBAT create scatterplots to explore the relationship between age or mileage and the selling price of a used car. SWBAT draw a line of best fit, determine an equation for the line, and interpret the correlation coefficient.

#### Big Idea

How can you determine a fair selling price for a used car? Students use scatterplots, lines of best fit, and correlation coefficients to predict an appropriate selling price.

## Opening

10 minutes

Today's class is designed to be an introduction to scatterplots for my students. Students worked briefly with scatterplots in the Multiple Representations unit, but at the time we looked more at Line of Best Fit as a linear representation, without much statistical context. This introduction is meant to lead to work involving correlation coefficients and residuals.

I begin class by showing them a video that gives an overview of how to represent data on two quantitative variables on a scatter plot and how to look for correlation. The video I like most on the this topic is on Apex Learning Common Core tutorials which is not available publicly. This video is fairly similar (in terms of the content covered).

The key points I want to highlight to students are:

• They will be looking to see if there is a relationship between two variables.
• The suspected cause variable will go on the x-axis and the suspected effect variable will go on the y-axis.
• Positive, negative, and zero correlation.
• Perfect, strong, or weak correlation.
• Drawing a line of best fit.
• Using the line to make predictions.

## Investigation

40 minutes

The bulk of today's class will be spent on the Illustrative Math task, Used Subarus I.  We read the problem aloud together and talk a little bit about the context. I find students are interested in thinking about looking up the prices of used cars on Craigslist, so this task often seems relevant to them.  I tell students that they will be looking to compare price and age and price and mileage today to see if there might a relationship between either or both of those variables.  I try to elicit from students that they will need to make two separate graphs:

• Price vs. Age Comparison
• Price vs. Mileage Comparison

We review the idea of independent and dependent variables and I introduce the idea of suspected cause and suspected effect as representing the two axes.

I let students work through most of the class making their graphs (by hand) and then call them back together for a whole group discussion.

## Discussion + Closing

10 minutes

Once students have constructed both graphs by hand, I'll project two different examples of student work on the Smartboard.  Now based on what students learned in the opening video, we'll spend some time talking about the direction, strength, and form of the relationships.  In this case, both of the relationships show a strong, negative correlation. I want to elicit this idea from students and ask them what happens as they age of the car and/or the mileage of the car increases.

Next, if there's time, we draw a line of best fit up at the Smartboard.  I remind students that there is no exact right answer for a line of best fit and ask for students to share different strategies for drawing an appropriate line.

This usually brings us to the end of class, but if there is more time, we can talk about finding an equation for this line and I might introduce students to the regression line, which we will later see using technology.

## Citations

S-ID Used Subaru Foresters I

S-ID Used Subaru Foresters I is licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License

Source http://www.illustrativemathematics.org/standards/hs