Paperclips are quite the issue.
Math is most difficult when the correct answer involves a multitude of correct answers. According to Adam, the correct answer is not what is most important, the way you arrived to your conclusion is what is most important. Although I wholeheartedly agree with that statement, the situation I was put into that week was certainly an excellent example of why mankind is screwed.
The paperclip problem. What a dilemma. The paperclip problem went a little something like this: You have a paperclip; the exact dimensions of this paperclip are unknown, although, you know the paperclip is just over four centimeters long. You have ten meters of wire and it's up to you to determine how many paperclips you could make out of that ten meters of wire. (The problem worksheet can be found here:)
Solving this problem would have been a leisurely and quiet stroll though the park, a stroll through a park that happened to be comprised completely of paperclips. Yet there was one thing that I had overlooked when solving the problem.
I looked at the picture of the paperclip and could make out a half circle of either side of the paperclip. So I employed the equation 2πr, (Two times Pi, times the Radius of the circle.) and divided my result in half because, again, I was trying to find the circumference of half a circle.
The rest was fairly straight forward. There were ten millimeters in a centimeter, and all there was left to do was add up the lengths of all the straight sides of the paperclip. After doing so I proudly marched up to Adam. He looked over my paper and gave me a nod of approval. I returned to my seat, victorious, and began helping out my table mates who had reached different conclusions. Surely they were wrong, right? The teacher's nod of approval was a sure sign that I had gotten the answer right!
Well, this is where that whole multitude of answers thing comes into play. At the end of the period Adam wrote down the problem on the whiteboard, and began asking the class for different answers that people had reached. I of course shared my answer with the class, and by the end of the period there were at least seven different recorded results that everyone agreed were probably the answer. And before he dismissed the class, he was like,
"HAHAHAHA! I HAVE FOOLED YOU ALL. THE REAL ANSWER ISN'T EVEN ON THE BOARD!"
(This isn't what he said, yet that is most certainly how it felt.)
My victory was lie. I went to Adam after class was over and asked him what I did wrong, my method was so precise, so scientific, yet I was wrong? He told me that my answer wasn't wrong, it was simply a variation of an answer that could be considered correct. All of the answers that he had written on the board were AMAZINGLY close to the actual answer, yet all of them strayed slightly off of the bull's-eye. Adam asked me what I did to arrive at my answer. I described my process to him. (Refer to paragraphs four and five.) He thought about it for a second;
"Are you sure that this is a perfect circle?"
I glanced at my paper. It sure looked like a circle. It was round, like circles should be, yet there was a part of me DEEP DOWN in my cerebral cortex that wanted to verify that I was dealing with what was indeed a perfect circle. I whipped out a compass, pinned it on the center point, and lined up the pencil arm with the radius of the circle I had drawn.
The damn thing was off by an unnoticeable amount of degrees.
This is where I made my mistake. While my method was efficient and led me to what was almost a perfect answer, my slight oversight in assuming that the length of the paperclip's curved sides could be calculated using a perfect circle had cost me a lot of time in corrections. It was a slight mistake that could have been apprehended with a little bit of fact checking. I could have asked someone if I was right in assuming what I assumed, I could have checked up on my peers to see if had actually calculated the sides of the paperclip using a compass or protractor, I could have used a compass or protractor in the first place. I learned one thing from that little mistake:
Math is most difficult when the correct answer involves a multitude of correct answers. According to Adam, the correct answer is not what is most important, the way you arrived to your conclusion is what is most important. Although I wholeheartedly agree with that statement, the situation I was put into that week was certainly an excellent example of why mankind is screwed.
The paperclip problem. What a dilemma. The paperclip problem went a little something like this: You have a paperclip; the exact dimensions of this paperclip are unknown, although, you know the paperclip is just over four centimeters long. You have ten meters of wire and it's up to you to determine how many paperclips you could make out of that ten meters of wire. (The problem worksheet can be found here:)
Solving this problem would have been a leisurely and quiet stroll though the park, a stroll through a park that happened to be comprised completely of paperclips. Yet there was one thing that I had overlooked when solving the problem.
I looked at the picture of the paperclip and could make out a half circle of either side of the paperclip. So I employed the equation 2πr, (Two times Pi, times the Radius of the circle.) and divided my result in half because, again, I was trying to find the circumference of half a circle.
The rest was fairly straight forward. There were ten millimeters in a centimeter, and all there was left to do was add up the lengths of all the straight sides of the paperclip. After doing so I proudly marched up to Adam. He looked over my paper and gave me a nod of approval. I returned to my seat, victorious, and began helping out my table mates who had reached different conclusions. Surely they were wrong, right? The teacher's nod of approval was a sure sign that I had gotten the answer right!
Well, this is where that whole multitude of answers thing comes into play. At the end of the period Adam wrote down the problem on the whiteboard, and began asking the class for different answers that people had reached. I of course shared my answer with the class, and by the end of the period there were at least seven different recorded results that everyone agreed were probably the answer. And before he dismissed the class, he was like,
"HAHAHAHA! I HAVE FOOLED YOU ALL. THE REAL ANSWER ISN'T EVEN ON THE BOARD!"
(This isn't what he said, yet that is most certainly how it felt.)
My victory was lie. I went to Adam after class was over and asked him what I did wrong, my method was so precise, so scientific, yet I was wrong? He told me that my answer wasn't wrong, it was simply a variation of an answer that could be considered correct. All of the answers that he had written on the board were AMAZINGLY close to the actual answer, yet all of them strayed slightly off of the bull's-eye. Adam asked me what I did to arrive at my answer. I described my process to him. (Refer to paragraphs four and five.) He thought about it for a second;
"Are you sure that this is a perfect circle?"
I glanced at my paper. It sure looked like a circle. It was round, like circles should be, yet there was a part of me DEEP DOWN in my cerebral cortex that wanted to verify that I was dealing with what was indeed a perfect circle. I whipped out a compass, pinned it on the center point, and lined up the pencil arm with the radius of the circle I had drawn.
The damn thing was off by an unnoticeable amount of degrees.
This is where I made my mistake. While my method was efficient and led me to what was almost a perfect answer, my slight oversight in assuming that the length of the paperclip's curved sides could be calculated using a perfect circle had cost me a lot of time in corrections. It was a slight mistake that could have been apprehended with a little bit of fact checking. I could have asked someone if I was right in assuming what I assumed, I could have checked up on my peers to see if had actually calculated the sides of the paperclip using a compass or protractor, I could have used a compass or protractor in the first place. I learned one thing from that little mistake:
DON'T MAKE ASSUMPTIONS.
Like I said, I could have saved myself a lot of time if I had done something as simple as ask someone. Assumptions are a dangerous thing to make, especially if a more precise method of thought was available. From such a small mistake came some serious repercussions, I lost a bunch of time at home fact checking, time that could have been used to progress a little further in one of my other classes, time that could have been used in LITERALLY any other fashion.
All ranting aside, I made a little mistake by assuming something that wasn't true, and I learned how to avert making assumptions by using a couple of other much more simple methods.
I made a little mistake, learned from it and am now better because of it.
All ranting aside, I made a little mistake by assuming something that wasn't true, and I learned how to avert making assumptions by using a couple of other much more simple methods.
I made a little mistake, learned from it and am now better because of it.