3.14159... Ways to Use Math They Didn't Teach You In 2nd Grade

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Bitmoji ImageWe've all seen them. For a while they were all the rage. Hack videos. You know, "47 Paperclip Hacks You Didn't Know," "12 Ways to Use a Tissue Your Mom Never Taught You," and "23 Ice Cube Hacks You Can Use Today."

None of those are real, but these are; "43 Simply Brilliant Camping Life Hacks," "26 Nail Hacks Every Girl Should Try," and "30 Crazy Food Hacks." [click at your own risk]

I think one of the reasons these types of videos became a thing was because they showcased everyday items doing unusual things. Things most people would not have thought of. In many ways, math classes should be the same way.

There is a difference between learning how to solve math problems and learning how to solve specific math problems. If Algebra 1 students know the steps to solving a variety of two-step equations, but do not understand how to apply the concept of inverse operations in other contexts, they don't really understood the concept that two-step equations are meant to teach. All they've really done is allowed themselves to be programmed like a computer, possibly for the sole purpose of passing a state test.

But as students take more advanced math classes, the ability to solve math problems in general is of far more value than the ability to solve specific types of problems. In Precalculus and Calculus, many of the types of problems students would be asked to solve will require them to apply broader concepts to analyze the problem from a more abstract perspective. There are of course, many problems that can be used to build skills in these areas, but these are not the types of problems that these subjects were meant to address. They are merely skill building problems.

Here is an example.

To the left is the graph of a polynomial function. Just from looking at the graph, it is possible to determine whether the leading coefficient is positive or negative, what the approximate zeros of the polynomial function are, along with their minimum possible multiplicity, the minimum degree of the polynomial which produces this graph, and ultimately the factors of the polynomial.

This is a great deal of information we can determine about the polynomial function just from the graph, and we haven't done any calculations of any kind yet.

We can determine whether the degree of the polynomial is even or odd by looking at the end behavior of the graph. As x approaches either positive or negative infinity, y approaches positive infinity. This tells us that the degree is even. Being able to describe the end behavior of a graph and being able to understand what it tells you are different skills. By completing this type of analysis prior to doing any calculations, we can actually get a much better understanding of what calculations we need to do. This allows us to be more judicious making decisions about how to continue.

This is hacking math; taking those individual, isolated skills we often ask our students to learn and having them use them in new and creative ways.

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