Shmoop's (Natural) Resources for Teachers
Math and modeling? Do mathematicians secretly want to parade down runways and have photoshoots in chic makeup and feathered hair, wearing the latest and greatest that contemporary fashion has to offer? Honestly though, who wouldn't want all that?
The truth is that math and modeling have a lot in common. The angle made by a stiletto's heel will affect how much reinforcement it will need. The speed at which supermodels stride down the catwalk can be described using functions. The maximum number of diamonds that can fit onto a jacket depends on the area of that jacket (and on the supply of diamonds available).
Actually, mathematical modeling isn't limited to the world of haute couture exclusively. Anytime students look at real-world scenarios through math-tinted glasses, they're modeling. Probably not what Tyra Banks is looking for in America's Next Top Model, but still. Take what you can get, we say.
The Common Core State Standards guide defines modeling as "the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions." Since different topics apply to different contexts, it's difficult to dissect modeling into distinct and isolated standards. Instead, modeling a specific subject (i.e. functions, geometry, algebra, etc.) can be taught along with the subject itself.
When given a problem, students should first be able to discern what kind of mathematics they will need to apply. For instance, balancing the budget of the Fashion Extravaganza in Milan might require knowledge of matrices and statistics, but probably not imaginary numbers or trigonometry.
As they start to focus more on the specifics of the problem, they might try tactics such as identifying the information at their disposal, recognizing the unknown quantities, and understanding exactly what the question is asking of them. They can then begin to create and apply mathematical structures (equations, shapes, diagrams, graphs, etc.) that describe the problem.
A model might be very photogenic in a studio setting, but can't walk in heels. Exactly how photogenic is the model, and how dangerous would a walk down the runway be? Is it even important? (If we're talking about a supermodel then probably, but we're guessing a male hand model won't be parading around in pumps too often.) Likewise, students must also be able to recognize a mathematical model's strengths, weaknesses, and precision.
After constructing and applying their model to the problem, students must also interpret the answer in terms of its context. Which budget makes more sense for the Fashion Extravaganza: $3.26 or $3.26 million? If the answer is incorrect or inaccurate, students should investigate why their model produced such a result. That way, they can fix the model accordingly and get an answer that actually makes sense.
Since most students probably aren't clued in to the realm of high-end fashion, it may be better to relate mathematical concepts to issues that concern them. For instance, students could calculate the average MPG of their old '91 Toyota Corolla, find the maximum number of texts they can send per month without being charged extra, and design a dance hall that can fit the entire student body.
Modeling allows students a deeper and more in-depth understanding of the mathematical concepts they're working with. In applying math to realistic situations, they will understand not only the relevance of math in everyday life, but also how to use their mathematical chops to solve their own real-world problems. Like how to become America's Next Top Model.