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).
I recently worked with a student on an online grocery shopping activity – finding ingredients for mac and cheese. We had the ingredients listed in a column on a Google Doc (allows both of us to edit the doc simultaneously) and then he cropped and pasted a photo of each ingredient (see photo below). The goal was for him to identify the total he need and the total cost in planning for actual shopping or to continue with the online shopping. Note: he wasn’t actually buying anything at this point but this was a step in preparing him to do so.
This activity is dense with math tasks and shopping related tasks. The math tasks include the following:
Identify the price (vs quantity of the item or unit price).
Interpret the quantity for the ingredient.
Identify the units (oz and cups)
Compare amount in box with amount needed.
Determine how much more is needed, if any.
Compare choices before selecting the item, (Barilla Pasta vs another brand).
To convert units, the “mathy” approach can be used or the student may simply use an app. For this student we chose an online unit converter (see below). This is more complicated that it appears. The student must choose the units and the order (in this case convert cups to ounces or vise versa), distinguish between imperial and US cups, understand that you enter the quantity (the search results in 1 US ounce appearing by default), and then interpret the decimal (keep in mind the ingredient quantities are in fractions).
Life skills math is more complex and challenging that parents and educators may realize. As a result, the planning for developing these skills should begin much sooner rather than later – not to mention the actual logistical tasks of shopping, e.g. finding an item in the grocery store.