One step in reading and analyzing scatterplots is simply identifying what the dots on the graph represent. If students do not understand the dots (including the position) how can they analyze. An approach I have used is start by having students create their own scatterplot for mileage and price of used cars they shop for on Carmax.com. This allows them experience the scatterplot from a data and context point of view.

Then 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 goal is to help the students understand the reasoning behind the position of each dot.

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.

The scatterplot above is an approach I use to introduce systems of equations. Here is the process I use. (Note: I have found that students like math associated with buying a car – relevant, real life application for them.)

In my class, students would have seen a scatterplot with mileage and price for a single car. I explain that we will now compare two cars.

To review, in a do now or initiation at the start of class I would have one group generate a scatterplot for the Toyota Camry data and the other groups, Mustang (Excel sheet for all of this note: this data is old). Then they would share with each other

We would revisit the relationship shown and revisit the idea of depreciation.

I show a Camry and Mustang and ask two questions: Which car do you think costs more brand new? Which do you think depreciates faster and why?

Then I show them the scatterplot above and ask which car has higher dots at the far left? Explain what this means (Mustangs start off with a higher price). Then I ask about the dots at the far right.

The students are then asked to estimate when the cars have approximately the same value.

Then I present scatterplot below, with lines of best fit (trend lines) and they are asked the same question. We estimate the specific mileage and price and write as an ordered pair.

Finally, I explain that this is known as a system of equations and the ordered pair is the THE solution. The entire unit will focus on finding an ordered pair as a solution.