Dissection in math.
This isn't the type of dissection where you poke around a frog's guts trying to find the heart.
This isn't the type of dissection where you poke around a frog's guts trying to find the heart.
I have no idea who this girl is. But she doesn't seem to be a fan. Frog guts are gross.
Dissection in math is a whole new way to look at shapes. It is mind blowing in a lot of ways, and it has been interesting to research this field of math that I hadn't heard about before.
Wolfram MathWorld helped me a lot with my research, so I can't take the credit for some of these pictures or definitions. Here is the link to my source: http://mathworld.wolfram.com/Dissection.html
Dissection in math is a whole new way to look at shapes. It is mind blowing in a lot of ways, and it has been interesting to research this field of math that I hadn't heard about before.
Wolfram MathWorld helped me a lot with my research, so I can't take the credit for some of these pictures or definitions. Here is the link to my source: http://mathworld.wolfram.com/Dissection.html
Basically, dissection is the theory that any two shapes with a common area can be dissected and folded in to one another. For example, this triangle, when unfolded correctly, or split up into smaller shapes, forms a square of an equal area.
I discovered dissection in class last Friday. We were working on finding the areas to shapes as a class, and sharing our different methods of determining the area of each shape. We discovered that there were many different ways to find the area. But I have a method I've been using since I can remember. With shapes on a grid, I've always tried to match up the partial pieces to form whole squares on the grid and then I count up the squares. Easy enough right? Just like a puzzle. Find the pieces that fit together, and you have your area. Boom. But I didn't know that it was actually a thing! I thought it was just the easy way I tested out of 5th grade geometry without learning any equations. But apparently dissection IS a thing....and its fun! Very addicting, I might add. I love it.
In class on Friday, I spent a long time trying to figure out the area of a complex shape "my way". I'm one of those people who has to finish something they start when I'm really excited about it...or I'm just stubborn. Regardless, I decided to cut apart the shape that I was using to try to reform it, because just drawing it out wasn't helping me. I cut apart the shape and tried to fit the pieces together. And even though it took me a LONG time (yes, I know I spent the remainder of class working on it even after the rest of the class moved on) eventually I did find the area of that darn shape. Using MY method. Taking the shape apart and fitting the pieces together like a puzzle until they formed a shape I could measure the area of easily.
So, what I was doing was very similar to dissection. Essentially, I was cutting the shape apart and fitting the pieces into a different shape. BOOM. Learned something new!
I tried to take pictures of the work I did, but they weren't turning out very well. Sorry!
Reflection:
Through this activity, I definitely learned something new. Before this I hadn't even realized that dissection existed in math. Now I found something that wasn't only new, it was exciting and fun. I wish I had learned more about it earlier on. Like when I was in 5th grade and I thought I had gotten away with cheating because I used a different method than the teacher and tested out of the class anyway. They could have taught me then that what I was doing was another mathematical theme! As I go through my education classes and hear about all of the problems with education, I'm starting to realize the truth in the idea that maybe teaching kids a cut and dry idea and trying to get them to memorize it exactly the way we teach them is wrong. As a student, I discovered this way of doing math on my own without any teacher showing me. And I got the correct answers. I just got in trouble a lot for not showing my work. Sometimes teachers are so worried about cheating that they make kids show their work, and then if the work they show doesn't look like the method the teacher uses, they count it as wrong. That isn't a good way to teach. Its a good way to kill inspiration, excitement, and creativity in students. I was a good student who was curious and found my own way to do math problems. It is frustrating that my curiosity in math was not encouraged, but instead mistaken for cheating. Maybe I would have enjoyed math a lot more if the opposite were the case!
I don't want to end this post on a bitter note. So I'm just going to say, I love dissection in math. I love it a lot more than I wish I did! Math isn't all bad. It can be fun. Like a puzzle. :)
In class on Friday, I spent a long time trying to figure out the area of a complex shape "my way". I'm one of those people who has to finish something they start when I'm really excited about it...or I'm just stubborn. Regardless, I decided to cut apart the shape that I was using to try to reform it, because just drawing it out wasn't helping me. I cut apart the shape and tried to fit the pieces together. And even though it took me a LONG time (yes, I know I spent the remainder of class working on it even after the rest of the class moved on) eventually I did find the area of that darn shape. Using MY method. Taking the shape apart and fitting the pieces together like a puzzle until they formed a shape I could measure the area of easily.
So, what I was doing was very similar to dissection. Essentially, I was cutting the shape apart and fitting the pieces into a different shape. BOOM. Learned something new!
I tried to take pictures of the work I did, but they weren't turning out very well. Sorry!
Reflection:
Through this activity, I definitely learned something new. Before this I hadn't even realized that dissection existed in math. Now I found something that wasn't only new, it was exciting and fun. I wish I had learned more about it earlier on. Like when I was in 5th grade and I thought I had gotten away with cheating because I used a different method than the teacher and tested out of the class anyway. They could have taught me then that what I was doing was another mathematical theme! As I go through my education classes and hear about all of the problems with education, I'm starting to realize the truth in the idea that maybe teaching kids a cut and dry idea and trying to get them to memorize it exactly the way we teach them is wrong. As a student, I discovered this way of doing math on my own without any teacher showing me. And I got the correct answers. I just got in trouble a lot for not showing my work. Sometimes teachers are so worried about cheating that they make kids show their work, and then if the work they show doesn't look like the method the teacher uses, they count it as wrong. That isn't a good way to teach. Its a good way to kill inspiration, excitement, and creativity in students. I was a good student who was curious and found my own way to do math problems. It is frustrating that my curiosity in math was not encouraged, but instead mistaken for cheating. Maybe I would have enjoyed math a lot more if the opposite were the case!
I don't want to end this post on a bitter note. So I'm just going to say, I love dissection in math. I love it a lot more than I wish I did! Math isn't all bad. It can be fun. Like a puzzle. :)
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