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Elvis and PEMDAS

Any math teacher who teaches the Order of Operations is familiar with the phrase, "Please Excuse My Dear Aunt Sally".  For the life of me, I don't know who Aunt Sally is or what she has done, but apparently we are to excuse her for the offense.  In my math classes, I use "Pale Elvis Meets Dracula After School".  Of course both of these examples are mnemonics or acronyms; so, the first letter of each word stands for something.  P = parenthesis, E = exponents, M = multiplication, D = division, A = addition, and S = subtraction

I have always taught the Order of Operations by just listing which procedures should be done first and in the order they were to be done.  But after viewing a different way on Pinterest (originally posted on Math = Love by Sara Hagen), I have changed my approach. Here is a chart with the details and the steps to "success" listed on the right.

Since multiplication and division as well as addition and subtraction equally rank in order, they are written side by side. What I like about this chart is that it clearly indicates to the student what they are to do and when.  To sum it up:

When expressions have more than one operation, follow the rules for the Order of Operations:
  1. First do all operations that lie inside parentheses.
  2. Next, do any work with exponents or radicals.
  3. Working from left to right, do all the multiplication and division.
  4. Finally, working from left to right, do all the addition and subtraction.
Failure to use the Order of Operations can result in a wrong answer to a problem.  This happened to me when I taught 3rd grade.  On the Test That Counts, the following problem was given.

The correct answer is 11 because you multiply the 4 x 2 and then add the 3, but can you guess which answer most of my students chose?  That's right - 14!  From that year on, the Order of Operations became a priority in my classroom.  Is it a priority in yours?  Should it be?


I have a new product that I recently added to my store entitled: Order of Operations - PEMDAS, A New ApproachThis ten page resource includes a lesson plan outline for introducing PEMDAS, an easy to understand chart for the students, an explanation of PEMDAS for the student as well as ten practice problems.  It is aligned with the fifth grade common core standard of 5.OA.1. Just click on the words under the cover page if it is something you might like.

O-H-I-O and Octagons

An octagon is any eight sided polygon.  We often use a stop sign as an example of an octagon in real life.  But in a actuality, a stop sign is a regular octagon meaning that all of the angles are equal in measure (equiangular) and all of the sides have the same length (equilateral).  For an eight sided shape to be classified as an octagon, it needs to have only eight sides.

I got to thinking about this since fall is just around the corner, and our family are BIG Ohio State football fans.  Being raised in Ohio and having relatives who taught at Ohio State has fueled this obsession, but so has doing graduate work there.  If you aren't familiar with the Ohio State Buckeyes, here is your opportunity to learn something new.

On the right you will see one of the many symbols for THE Ohio State University.  The red "O" is geometric because it is an octagon (just count the sides). Even the beginning of the word Ohio is an octagon. (I just adore mathematics in real life!)

The Ohio Stadium, a unique double-deck horseshoe design, is one of the most recognizable landmarks in all of college athletics. It has a seating capacity of 102,329 and is the fourth largest on-campus facility in the nation. Attending football games in the Ohio Stadium or watching the game on television is a Saturday afternoon ritual for most Ohio State fans.  The stadium is even listed in the National Registry of Historic Places. Anyone (and we have) who has been to a game in the giant horseshoe understands why. There are few experiences more fun or exciting!  In the middle of the football field is the octagonal O as seen in the picture below. (Another example of math in real life!)

And then there is the Ohio State Marching band which I love!  Their half times programs are awesome, and many are posted on You Tube.  The signature formation of the band, which is performed before, during halftime or after home games, is Script Ohio. Each time the formation drill is performed, a different fourth or fifth year band member who plays the sousaphone has the privilege of standing as the dot in the "i" in "Ohio." The crowd always goes wild!  (If you don't believe me, click here to see a video and be sure to check out the "O" on the drums.)  Once, when we were at a game, the band formed a double script Ohio. Even though this "O" is not an octagon since it is written in cursive, I still had to mention this distinctive and unique half time tradition.

Before I continue this posting, I must answer the age old question, "What is a buckeye?"  Since I grew up in Ohio, this question is easy for me to answer, but for everyone else, a buckeye is a nut. (I bet many of you thought it was candy.) Buckeye trees grow in many places in Ohio. The trees drop a "fruit" that comes in a spiked ball with a seam that runs around it. If you crack the seeds open, you can remove the "buckeye." When the nut dries, it is mostly brown in color but it has a light color similar to an over-sized black-eyed pea on one end. This coloration bears a vague resemblance to an eye hence the name, buckeye. 

Then there is Brutus Buckeye, (a student dressed in a costume) the official mascot of THE Ohio State University; so, you might say, since I was born and raised in Ohio, I am a nut!  Brutus (as seen on the left) wears a headpiece resembling a buckeye nut, a block O hat, (another octagon), a scarlet and gray shirt inscribed with the word "Brutus" on the front and the numbers "00" on the back.  Brutus also wears red pants with an Ohio State towel hanging over the front, and high white socks with black shoes. Both male and female students may carry out the duties of Brutus Buckeye as long as they are a committed Ohio State fan.

Finally, if you ever are lucky enough to see four people with their hands in the air, forming letters of the alphabet, it is most likely four Ohio state fans spelling out O-H-I-O!  That's how our grandchildren learned how to spell it! (The picture on the right is of our youngest son with his four groomsmen on the day of his wedding.)

And it is so-o-o easy to remember.  Just use this riddle:  What is round on the ends and high in the middle?  You guessed it - OHIO!