Link to a brief video showing how it works.
Link to a Facebook Reel showing how it works.
This post outlines an activity to introduce linear functions (or scatter plots). The students are tasked with shopping for a used car – a specific make and model. They go to Carmax.com to find mileage and price for 10 cars for sale. They have to find a make and model that has at least 10 cars and can change the search radius to include all locations of Carmax as necessary.
They enter the data for each car into a table on a Google Doc. They are not to include the “k” or the “$” or “,” for price. This allows easier transfer of data. I do not use 0s for the mileage as the slope is more meaningful per thousand miles. For example, -$104 per thousand miles vs $.104 per mile.
Before they graph, you can provide them a common set of data to guide them through a trial run. This way you can show them your graph of the data to allow them to verify that they did it correctly. The data sets shown below are linked at the bottom of this post. (This can be useful for introducing systems of equations as Mustangs typically have a higher intercept and a steeper slope, which allows for a cluster of dots from both in an intersection.)
They copy and paste the mileage and price into a Google Sheet and attempt to graph. You can provide a link to a YouTube video on graphing a scatter plot to free you up to help individuals. The title of graphs should have the variable(s) and the individuals under study. A subtitle can be included to show when data was collected or a data set was accessed. The variables should include units.
A next step would piggy back off of this activity with a Jamboard addressing mileage and price to help students interpret scatter plots.
Here are links to items used for this activity.
I present the scatterplot of used Ford Mustangs on a Jamboard (image above) with ads for two used Mustangs along with a cutout of each car. The cutouts are used to help the students understand the reasoning behind the position of each point. Here is a FB Reel and a YouTube video showing how the Jamboard can be used. To access the Jamboard, you must make a copy. See image at bottom of post.
First, I take the cutout of the first car and “drive it” along the x-axis (top 3 photos in gallery below). This helps them understand the horizontal axis placement. Then I move the car up to the appropriate price (bottom row left). Finally, I replace the car cutout with the bigger blue dot that was placed by the ad with the car. We then discuss that a dot can be used to represent that car and the location on the scatterplot is based on the two values in the ordered pair (which can be typed into the ( , ) in the Jamboard next to each car.
The same steps are used for the other Mustang (see it “driving” along the x-axis below).
The next step would be to identify additional points on the scatterplot. I then revisit driving the cars and show that driving the car more miles results in a lower price and driving the car less miles results in a higher price.
Finally, we discuss that this is a general trend but that it is not always true for each car. I highlight a couple points where one of the cars has more miles and a higher price (below). This leads into a discussion about additional factors influencing price.
An related I have used is having students create their own scatterplot for mileage and price of used cars. They shop on Carmax.com. This allows them experience the scatterplot from a data and context point of view.
Make a copy to access Jamboard.
When our 3rd child was born, we decided to buy a used Honda Odyssey as 3 young kids were not fitting into a sedan. Being the stats geek I am (master’s in statistics at the University of South Carolina – total geek) I collected mileage and price data for all the used Odysseys for sale on dealer sites throughout South Carolina. I then created a the scatterplot shown below. I went to a dealer, showed an agent my graph, and he immediately exclaimed “Where did you get that? We create graphs like that every week!”
It was this experience that led me to the idea of using used car data to introduce linear functions. Shopping for a used car has proven to be a relevant, real life activity the students enjoy.
Here is a link to a comprehensive activity that walks students through various components I use for introducing students to linear function topics.
The activity is presented on a WORD document (feel free to revise). It shows screenshots to walk student through the Carmax website (subject to Carmax revising their website). The screenshots make it easy for the student to navigate, which increases independence. (NOTE: there is an ample number of Youtube videos on using Google Sheets for this activity.)
The end product looks like this. Note the importance of using 1000s of miles as the slope is more meaningful, -$140.64 per thousand miles, as opposed to 14 cents per mile. I would start with the scatterplot alone to unpack the variables, the relationship between the variables, and the ordered pairs. Then the line and equation can be introduced to show a meaningful use of the line and the equation. The y-intercept has meaning with “0 miles” equating to a new car (I do not explain that new cars have miles already accumulated until we unpack the math).