Anecdote #2 – Panic Attack at the Deli! What Happens When the Customer Wants 1/3 of a Pound of Salami?
When I was a young mom, on my way to a picnic with my two small children, I stopped at the deli and ordered a 1/3 of a pound of salami. I suppose that seems absurd, but ½ a pound was too much and ¼ pound wasn’t enough, so there you have it.
It occurred to me that it was taking a long time to get my order and I wondered where the clerk was. I found her standing in front of the electronic scale in a daze.
In the olden days, when televisions had knobs and phones had dials, the scales at the deli were marked with ounces and fractions of pounds. The clerk would put slices of meat on the tray until the correct number of ounces or the correct fraction of a pound was indicated. (Back then, I would wager that most clerks knew that 1/3 of a pound was close to 5 ½ ounces or thereabouts, but that is the topic for a different post).
Back to the deli clerk… She was standing in front of the relatively new digital scale, frozen in a mild panic attack. It took me a moment to realize that she didn’t know the decimal equivalent of 1/3 and was too embarrassed to ask anyone. So, I helped her out with 0.33 (or so), and we were on our way.
Anecdote #3 - How Does One Make a ½ Sandwich?
Fast-forward twenty years into the future. I was teaching high school one summer and a student of mine, who coincidentally worked in that very same deli from the last anecdote, shared the following story:
One day a customer came into the store and ordered half a roast beef sandwich and half a turkey sandwich (the deli sold half-sandwiches). So, the teenage, soon-to-be-off-to-college coworker of my student made a whole turkey sandwich, and a whole roast beef sandwich, cut them in half, and gave one of each half to the customer.
My student told this story in class and got the desired laughs from most of his classmates, especially when he told the part about asking his coworker what she was planning to do with the left-over halves. Apparently, having been embarassed by the question, she told him exactly where she thought they should go and included some colorful explatives. The class thought that was hilarious.
Both of these stories have several points in common. The problems involve parts of wholes. They, when juxtaposed with each other, illustrate the importance of numeracy, particularly with fractions and decimals, as well as mathematical thinking. It is striking to realize that one young woman was a recent high school graduate and the other, would be off to college within a year. The skills involved in the deli tasks should have been mastered by the 6th grade, and that is a generous estimate.
In his recent testimony before the Congress, Dr. Skip Fennell, member of the National Mathematics Advisory Panel, stated the following regarding conceptual understanding of mathematics:
"As students learn mathematics they need to have the mutually reinforcing benefits of conceptual understanding, procedural fluency, and the opportunity to solve problems applying and extending the mathematics learned."
Regarding fractions he stated:
Some would argue that fractions may be the most critical of the Panel's Critical Foundations for algebra. Fractions are defined here as fractions, decimals, and percent, leading to work with ratio and proportion. Several of the Panel's task groups, as well as the Panel's teacher survey, substantiated that difficulty with fractions is pervasive and an obstacle for far too many students to success in algebra."
And on the abysmal state of our cultural thinking (actually Dr. Fennell called the section "Effort Matters"):
"So, once and for all, we need to stop the parent conference that begins with the phrase, 'Well, you know I was never good in math either.' Math is important - for our children and for our country."
Anecdote #4 – The Geometry Teacher has the Last Laugh
If you don’t teach math, try for a moment to put yourself back in your high school fill-in-the-blank math class. One of the questions students repeatedly ask is, “What am I ever going to use this for?” This particularly happens in Geometry class. I was delighted to see one such student behind the counter of the carpet store, using geometry everyday no less, only several years after he had left my class. Ironic!
The moral to these stories is that it is a good idea to pay attention in math class. One probably does not have 20/20 foresight to know whether or not he/she will need to know given mathematical concepts at some point in the future.
Wednesday, June 11, 2008
Tuesday, June 10, 2008
Anecdote #1 – The Curtain Ring Problem
A couple I knew, college educated I might add, needed to make a curtain for a closet opening. Curtain rings come in packages of 12. This might seem very practical, 12 being a dozen and all.
So, the couple divided the fabric into 12 spaces, easily done by folding in halves and thirds. When they attached the rings, they found that they were one ring short, thus no ring for the end. They discovered that they needed 13 rings when the curtain has 12 spaces. Alas, they just left the curtain flapping. See the diagram.
Clearly they were using a mathematical approach, but unfortunately, it wasn’t the best one.
Using 12 rings means the curtain needs to be folded into 11 spaces, and 11 is a prime number, meaning it has no other factors except itself and 1. Therefore the folding method to determine the spacing of the rings is impractical. The curtain needs to be measured, then the measurement number needs to be divided by 11 or alternately multiplied by 1/11.
Example: Let us say that the fabric is 5ft. wide.
Yes, I used the frightening "fraction" to help solve the problem. The result: A curtain that doesn’t look ridiculous, lot of money saved. And some say that math isn’t practical and they have no use for it!