Engaging students: Approximating data by a straight line

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission again comes from my former student Caroline Wick. Her topic, from Algebra: approximating data to a straight line.

B1. Curriculum

How can this topic be used in your students’ future courses in mathematics or science?

Though approximating data by a straight line is a subject that is brought up in Algebra 2, it is something that students will need to use in a number of subjects down the line. Probably the most obvious subject would be statistics. Finding an approximate trend line is extremely important for a statistician so that they can predict future, unobserved data. Another example that might not be as readily noticeable would be anthropology. Anthropology is the study of humans in various parts of life. In this case, according to Brian Hopkins, anthropology can be used by stores to figure out what types of products they should stock on their shelves during different types of the year. They do this by collecting the data, then approximating the trend lines to predict how the product will sell during the same season of the next year. For example, Orange Juice and tissues are known to be sold more often during the winter seasons, so stores know that they want to stock up on orange juice and tissue during the colder season each year.

A1: Applications

What interesting (i.e., uncontrived) word problems using this topic can your students do now?
Using the data given below:
(a) plot the points on a graph
(b) Then, using a ruler, do your best to approximate a trend line that fits the points
(c) Write an equation (y=mx+b) that best fits the trend line
(d) Approximate the next four numbers on the line using the equation you created.

Population growth in squirrels in TX from 1950-1980 (in millions)*
Year (x) 1950 1955 1960 1965 1970 1975 1980
Pop. (y) 12 12.7 13.1 13 13.6 13.7 14

From here the student would create his/her graph with the plotted points, find a line that best fits the points with equal numbers over and under the line. They would then use the data and the line to find an equation that best fits the scatter plot data that they graphed. They would then find the approximate squirrel population for 1985, 1990, 1995, and 2000.

This could be either an assignment or it could turn into a project for students with different sets of data. Students could even collect their own data to formulate the graph and equation.

*not real data, fabricated for this problem specifically.

Culture
How has this topic appeared in pop culture (movies, TV, current music, video games, etc.)?

The approximation of data through trend lines has been used in pop culture since the birth of popular culture in the mid twentieth century. More relevantly, it is used to map certain cultural trends. When a new movie is coming out, statisticians use previous data from people who watched/reviewed the movie before its release to map out how they believe it will be appreciated by the public. A movie that did will before its release will likely have a positive trend line that continues upward at a somewhat steady rate. It will get more tickets at the box office than a movie that was not as well liked that might have a less-steep slope. Statisticians use this same trend approximation with TV shows and whether they should run another season, or in music when it hits the top of the charts. The more people listen to a song, the more likelihood it has to be listened to other people, thus the trend continues upward until is slowly dies off.

Take for instance, Taylor Swift’s “Look What You Made Me Do” that was released August 25th of this year. From its release and popularity, statisticians were able to track the data and predict that the song would be number 1 on the top 100 just a few weeks after its release.

References:

B1: https://www.cio.com/article/2372429/enterprise-architecture/the-anthropology-of-data.html
C1: http://www.billboard.com/articles/news/7949029/taylor-swift-look-what-you-made-me-do-timeline-reputation