CCSS.Math.Content.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

CCSS.Math.Content.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

CCSS.Math.Content.HSA.REI.D.11

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.^*

Through this activity students will be challenged to create equations that fit the data. The students will use the Car Edge website to collect data then input those values into Desmos to determine which function type fits the data best. This allows students to use a webpage and a graphical calculator to see these relationships.

Within the notes portion of this task has students build their understanding of linear and exponential by comparing rates of change. Many students struggle to see the multiplicative pattern involved within exponential functions. Beyond this students will struggle to take advantage of Desmos capabilities for functions. They often do not connect that f(15) is the value of the function at 15 years.

To modify the assignment to make it simplified, the cars could be selected for the students such that they were only modeling linear regressions. As a way of extending the activity for advanced students, you could have them created an example of model that would not follow these forms of regression. Asking them questions such as: "could a car ever lose value then gain value?" or "Could a car ever just gain value?"