A Lesson Learned in 5th Grade That Has Stuck . . .
When I was in 5th grade, my teacher sent us (the students) home with a
math question, wanted us to "think it out" before we gave our answers.
(For you folks that hate math, I’ve simplified)
The question went as follows:
You have a jar that starts with one fly in it at 10:00 AM. The fly doubles every 5 minutes. If the jar is full at 4:00 PM, when is the jar half full?
(Some of you may want to stop reading for a moment and see if you can answer. You may use your fingers if you wish)
Now my mind went to simple division – the time in the middle or half way between 10 AM and 4 PM equals 1 PM, reasoning there are 6 hours between 10 and 4. 6 divided by 2 equals 3 hours. 10 AM plus 3 hours equals 1 o’clock. I thought it was rather simple, but questioned why we had been sent home with this equation to “think about.” So I asked my mom.
She immediately looked at my answer, and said, it appears right, but she also questioned why the teacher would give us this much time to think about it.
After thinking it through for a few minutes, she laughed and said, 3:55. I questioned what she meant by that, thinking it strange. How is that possible?
“Well, she said, “if the jar is full at 4 PM, 5 minutes earlier it would have been half full.
I considered the answer, although my 5th-grade math skills said to me, I don’t get it.
The next day in class, the teacher asked the class what answers we had come up with. Some of the “ambitious” students immediately raised and waved their hands. As the teacher picked them one by one, they all replied “1 PM.”
The teacher asked, “Does anyone have a different answer?”
I recall one kid yelled, was it like a peanut butter jar, or like a big pickle jar? I remember the class went silent for a moment, perhaps questioning if the size of the jar was relevant. The teacher eyed him for a moment, slightly shook her head, took a deep breath and said, “The jar size has nothing to do with it. Does anyone else have a different answer?”
I didn’t raise my hand assuming my mother was confused, and all the “smart kids” that immediately responded couldn’t be wrong. Rather than embarrassing myself and trying to explain the “different answer,” I had been told by my mom, I kept my hands on my desk.
At that point, the teacher said, “3:55 PM.”
I probably would have exclaimed, Ahh shit, if it had been a part of my vocabulary at the time. However, I just sat there and watched her explain to everyone; how if the jar is full at 4 PM it would have been half full (doubling every 5 minutes) at 5 minutes to 4 – even drawing a graph on the board (perhaps for the pickle jar kid).
Now that I have bored you with this little story, or perhaps, sent some of the mathematically challenged into a heightened state of anxiety – what is the point? What did I learn from this little math question?
A LOT . . .
• I learned to listen to my mother's wisdom more often.
• Sometimes the people that think they know the answers are blinded by their own personal arrogance and ambition.
• People do not recognize exponential doubling until it is right on top of them. And people often do not think things completely out.
I also, often equate the growth in population to this little math question. My concerns being its doubling effect and possible consequences And I see Global Warming sneaking up on us very quickly – maybe it is already 3:55 PM. . . but then again, I've heard that is just a rumor.
You can come to your own conclusions.
Just some food for thought. Enjoy your minutes.
The question went as follows:
You have a jar that starts with one fly in it at 10:00 AM. The fly doubles every 5 minutes. If the jar is full at 4:00 PM, when is the jar half full?
(Some of you may want to stop reading for a moment and see if you can answer. You may use your fingers if you wish)
Now my mind went to simple division – the time in the middle or half way between 10 AM and 4 PM equals 1 PM, reasoning there are 6 hours between 10 and 4. 6 divided by 2 equals 3 hours. 10 AM plus 3 hours equals 1 o’clock. I thought it was rather simple, but questioned why we had been sent home with this equation to “think about.” So I asked my mom.
She immediately looked at my answer, and said, it appears right, but she also questioned why the teacher would give us this much time to think about it.
After thinking it through for a few minutes, she laughed and said, 3:55. I questioned what she meant by that, thinking it strange. How is that possible?
“Well, she said, “if the jar is full at 4 PM, 5 minutes earlier it would have been half full.
I considered the answer, although my 5th-grade math skills said to me, I don’t get it.
The next day in class, the teacher asked the class what answers we had come up with. Some of the “ambitious” students immediately raised and waved their hands. As the teacher picked them one by one, they all replied “1 PM.”
The teacher asked, “Does anyone have a different answer?”
I recall one kid yelled, was it like a peanut butter jar, or like a big pickle jar? I remember the class went silent for a moment, perhaps questioning if the size of the jar was relevant. The teacher eyed him for a moment, slightly shook her head, took a deep breath and said, “The jar size has nothing to do with it. Does anyone else have a different answer?”
I didn’t raise my hand assuming my mother was confused, and all the “smart kids” that immediately responded couldn’t be wrong. Rather than embarrassing myself and trying to explain the “different answer,” I had been told by my mom, I kept my hands on my desk.
At that point, the teacher said, “3:55 PM.”
I probably would have exclaimed, Ahh shit, if it had been a part of my vocabulary at the time. However, I just sat there and watched her explain to everyone; how if the jar is full at 4 PM it would have been half full (doubling every 5 minutes) at 5 minutes to 4 – even drawing a graph on the board (perhaps for the pickle jar kid).
Now that I have bored you with this little story, or perhaps, sent some of the mathematically challenged into a heightened state of anxiety – what is the point? What did I learn from this little math question?
A LOT . . .
• I learned to listen to my mother's wisdom more often.
• Sometimes the people that think they know the answers are blinded by their own personal arrogance and ambition.
• People do not recognize exponential doubling until it is right on top of them. And people often do not think things completely out.
I also, often equate the growth in population to this little math question. My concerns being its doubling effect and possible consequences And I see Global Warming sneaking up on us very quickly – maybe it is already 3:55 PM. . . but then again, I've heard that is just a rumor.
You can come to your own conclusions.
Just some food for thought. Enjoy your minutes.
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