Following the Recipe

      I like to bake.  Actually, I really really like to bake.  It's one of my only hobbies that finds me indoors now that I think about it.  I'm not one of those bakers, though, who can just whip up something delicious without a recipe in front of me.  I like recipes.  I know several women who can rattle off the recipes for their favorite treats off the top of their head with 100% accuracy.  I have always marveled at that ability because I do not have it.  I've been using the same chocolate chip cookie recipe since I first learned to bake about thirty years ago and I am not even close to having it memorized.  I wouldn't even try.  I get that little recipe card out and follow it each and every time.  Maybe the recipe card is my security blanket.  I don't know.
   What I've realized this summer while taking these math classes is that math is a lot about knowing the recipe.  In the language of mathematics, the "recipe" is called a "formula," but it's really the same thing.  If you don't happen to have the formula memorized, you simply need to remember that there is in fact a formula and then use it.
   There have been many times over the course of these past several weeks that I have read and then reread a homework problem, wondering how in the world to even begin solving it.  I've started scratching out some preliminary guesses as to how to plug in the information that's given and then realized, "Hey, there's a formula for this!"  It's amazing how even the most difficult of problems can be solved with the formula that was designed specifically for that purpose.
   If you want to figure out the volume of a pyramid or cone, you'll want to know that V=1/3 bh.  If you want to be able to figure out the value of each interior angle of a polygon, you'll want to know that the formula (n-2) x 180/n is the one that you need.  The "n" is where you plug in the number of sides of the polygon that you are working with.   For example, if you are figuring out the interior angles of a square, you'd plug the number 4 for the four sides into the spot in the formula where the "n" is.  (4-2) x 180/4 will give you the answer of 90 degrees.  Pretty neat.  Try it for a hexagon, an octagon, or even a 22-gon and you'll soon have your answers.  Try it without the formula and you won't get very far very fast.
   Do you remember hearing the formula for slope: "rise over run?"  That's an easy one to remember.  How about that area of a rectangle is "length times width?"  Could you memorize the formula for the equation of a line from two points, though?  What about the distance formula show below?

   Not only do we need to know these formulas in order to "know" math, but we also need to understand the order of operations.  We again need to follow the recipe.  When solving an algebraic equation, which part do we start on?  Here's a handy little tool courtesy of coolmath.com for that:

   If you don't know to do the part of the problem that's in parentheses first and to do all multiplication and division before you do any addition or subtraction, you'll just make a big mess of the problem and end up with the wrong answer.  Like I said, it's a lot like baking.
   I have found that knowing the formulas is empowering.  Knowing that there is a formula to plug the numbers into is empowering.  Solving the problem with a correct answer at the end is satisfying much like biting into that warm perfectly baked chocolate chip cookie is satisfying.  If I'm being honest, I enjoy the cookie a little bit more than the math problem, but you get my drift.

 photo courtesy of www.meals.com