My high school required at least one year of a foreign language for graduation.
I don’t have the gift for foreign languages and being that at least half of the student population in my school spoke fluent Spanish, I figured that I’d never be able to beat the bell curve going that route. Instead I chose French figuring that I had at least an “average” chance of pulling a middle of the road score.
I received a final grade of “D” for my efforts.
While I lacked any talent in the linguistic arts, I was more at home in the logical science of mathematics. The unambiguous rules of geometry, algebra, and trigonometry were more my speed.
So last week I found myself in a 5th grade classroom reviewing the math lesson for the day: Page 453: Area of Parallelograms.
This should be a cinch!
“The area of a parallelogram is the base times its height.”
There you have it. We’re done. How much more simple can it be? Well, as it turned out all I got were a bunch of blank stares and “We don’t get it!” comments.
“Ok, let’s back up for a moment.”
“Everyone knows what the area of a square is (multiply base x height)? Yes!
“Everyone knows what the area of a rectangle is (multiply base x height)? Yes!
Now, everyone get out a piece of graph paper and draw a rectangle of 8 squares on the bottom and 5 squares tall. Now, what is the area of that rectangle?”
Most of them responded 40. A few came back with 26.
After explaining the difference between area and perimeter a few more times, I believed that I convinced the “26” crowd that the “area” was, indeed, 40 square units.
I then had them draw a line from the top left corner to any point of the line on the bottom and cut out the resulting triangle as I demonstrated on the doc-camera.
“Ok, now slide your triangle piece to the right until the vertical sides line up. What is the figure now?
Response: “A parallelogram!”
“What is the area of that parallelogram?”
“Remember, all we did was cut the rectangle into two pieces and move them around. The area of the two pieces is exactly the same as the original rectangle. Got it?
Now, what is the area of the new parallelogram that we made from the old rectangle that is 40 sq units?”
Yes, now repeat after me:
“All rectangles and squares are parallelograms. The area of any parallelogram is the base times it’s height.”
They started in working some of the exercises until recess. I could tell by the number of hands up and requests for individual help that at least a third still “didn’t get it”. I just didn’t know how to explain it or demonstrate it more clearly.
Having some of them repeat the mantra while writing down the numbers helped a few but clearly, I wasn’t getting through to everyone.
After recess they were supposed to continue math exercises. I hoped the repeated mantra was still embedded in a few memory cells, so I decided to see.
Me: I have a prize for the first person who can tell me what the area of a parallelogram is!
Kid #1 Response: 40!
Kid #2 Response: 26!
Oy Vey!... (pardon my French)