The real world is really messy and difficult to model exactly which is the beauty of data. The simple act of making that graph is really all students need to answer the question using the tools they know and feel comfortable with – algebra and some quadratics maybe. A few others alluded to the idea that simplicity is sometimes as good or better than reality when it comes to modeling. I think students need to appreciate the complexity, but not get bogged down in it.

I think looking for the perfect formula and the exact solution in situations like this actually does the opposite of the problem’s original intention (although fun for the teachers to explore!). I’ve run into a few situations where a problem looked really interesting and the class and I got really invested in it only to discover that it was rediculously detailed and required things that they weren’t able to do. Talk about your ultimate let down after a hard day’s work!

There is a definite skill needed in picking those perfect problems that are developmentally appropriate within the scope and sequence of the curriculum being taught, can be differentiated over various levels of complexity while still being able to provide some kind of real tangible answer at the end in a relatively neat and manageable way. Not an easy task, but so worthwhile when it happens!