One step in reading and analyzing scatterplots is simply identifying what the dots on the graph represent. Students who do not understand the meaning of the points, including the position, will struggle to interpret the graph. This post outlines a Jamboard activity to support interpretation of the points.
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.
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.
Used car shopping to collect data on 10 used cars of a single make and model.
Creating a scatterplot for price vs mileage of the used car of choice.
Creating a line of best fit (regression line) to model the data.
Creating a linear bi-variate equation (regression equation) to model the data.
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).
The images shown are excerpts from the latest iteration of a budget project I have used for years. The content addressed in this project can be used as stand alone activities and are relevant real life examples for our students. Even the younger students could benefit, e.g., learning addition by shopping for items online and recording the prices (for older students throw in computing tax). These topics are especially useful for multiplication word problems, rate, single variable equations, and linear functions (slope being rate of change such as car payment per month).
Here is an overview. You graduate from high school and are living on your own. You have a job, but your car is getting old. You need to figure out how to save for a down payment in your budget and for when you must pay a car payment and insurance. (You will have to get your OWN insurance.)
The image below shows the table for all monthly expenses.
The students have imbedded activities such as
estimating monthly food costs by estimating cost for meals for a single day
shopping for disposable household items
shopping for car insurance based on the car they shop for (more on that at the end) NOTE: they do not share personal information other than a school email address (or my email address) to receive the quote
searching for a job with a hourly pay and estimate after tax income
They shop for a car last as the idea is they need to save up for a down payment. The amount they can save is based on how much money is left over after paying all other bills. How much they save will be converted to how much they can spend on a car payment and monthly insurance payment.