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Real-World Applications of Math February 25, 2014

Posted by Media4Math in algebra, math, media.
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Why Problem Solving Matters

Until students can demonstrate the ability to apply the math skills they have learned, they are merely memorizing and reciting algorithms. Students may be able to complete a worksheet of skills-based problems, yet be completely stumped by applications of those skills. Relying on textbooks to be the main source of real-world applications of math can also prove frustrating for student and teacher alike.

Problem solving is not a textbook activity, nor should it be limited to the contrived word problems that characterize so much of what is called problem solving. An effective strategy for getting students more engaged in math is to have them gather data, organize it, analyze it, and draw their own conclusions about it. There are endless sources of real-world data. In this blog posting we provide a case study.

Case Study: Movie Data

Background

Gathering data related to movies is a way to get students motivated about a subject that is part of their world. The-numbers.com has tons of data on movies. You should bookmark this site, since it is the source of endless data that can be used for exploration. Before starting an activity, here is how to gather data from the site and use it in a spreadsheet.

Suppose you want to gather the box office data for the movie Gravity.

1. Go to the site: The-numbers.com.

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2. Search for the movie.

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3. At the search results select the item that includes the box office data.

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4. You’ll see the following tabs. Click on Box Office.

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5. You’ll see a graph and, if you scroll down, daily and weekly box office data for that movie.

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6. Suppose you want to capture the weekend box office data. Scroll down and highlight the entire data table. Copy it to the clipboard.

Screen Shot 2014-02-24 at 7.54.08 PM7. Open a spreadsheet and paste the data in the spreadsheet.

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Once you have the data in a spreadsheet, you can begin manipulating it.

Problem Solving Assignment

Once you have shown students how to access the site and how to copy and paste data, they can begin their assignment. (Alternatively, you could gather the data for the students.) Here is the problem solving scenario:

Gather box office data for a movie that premiered at least three months ago. Gather at least 12 weekends worth of box office data in a spreadsheet. Create a line graph. Describe the shape of the graph and what it says about how the movie did.

Repeat this with at least two other movies. What do you notice about the line graphs you constructed? What conclusion can you make that would apply to all movies?

Students should put together a report that shows spreadsheet data, graphs, and an analysis of their results. Here is a sample project. We’ll be using the data we gathered for Gravity.

From the data gathered, highlight two columns (Date and Gross receipts). You could also copy and paste those columns into a new spreadsheet.

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Create a line graph using your spreadsheet (the sample shown was done with Microsoft Excel).

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The graph clearly shows that the first few weekends after Gravity premiered account for the vast majority of its potential revenue.

Now let’s look at two other movies: Despicable Me 2 and Avengers. These graphs summarize the results.

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All the graphs (and your students would provide data for other movies) show that a movie’s revenue is almost entirely dependent on its first two or three weeks. After that, the revenue drops off significantly.

A student who does this activity and comes up with similar conclusions has shown some problem solving prowess. Gathering the data, analyzing it, and drawing conclusions about it are the kinds of problem solving skills that are important. Simply constructing a line graph from given data is a far cry from the kind of analysis that can, and should, be done.

This activity also has some clear extension possibilities:

  • Describe how these data graphs are examples of decreasing functions.
  • Find a nonlinear regression model for a data set using a graphing calculator. Test the equation with other data sets.
  • Investigate the graphs of Date-vs.-Cumulative Gross (column G of the spreadsheet). Describe any patterns you see.
  • Look at the Percent Change (column D of the spreadsheet) in the data. Develop a geometric series that models the data.
  • Research an upcoming movie and try to develop a predictive model of how it will do over a three-month period. What information do you need?

Conclusion

This activity includes a number of mathematical skills:

  • Gathering data
  • Graphing data (line graphs)
  • Analyzing graphs
  • Making predictions
  • Nonlinear functions, regression models (as extension activities)

These skills are combined into a rich problem solving activity, with data that is of relevance to students. This activity goes beyond using math skills in isolation and presents an interesting challenge to students, but one well within their abilities, especially if done as a group activity.