Overview
Over the course of a few weeks, we did worksheets and activities in class to understand finding volume and area of different shapes. This would be simple, but then get more complicated as the shapes we found the volume for became more complex. We experienced with finding the equations for how to find the volume and area for the shapes, which in my opinion, was very hard to do. Good thing we were able to work with people on brainstorming equations or else I would have been forever stuck. We did worksheets that dealt with this content in a group of three or four people, and had to turn them in after a few benchmarks. The more activities we did, the more comfortable with the content we got. We had to use the collaborate and listen habit of a mathematician in able to work with our group members and come up with a good solution. We started by working with the Pythagorean Theorem to find the distance formula. This brought us to finding the equation of a circle. Then we used this to find point of a circle using right triangles. Using these methods helped us have a better understanding of trigonometry for right triangles. On the calculator, we found missing angles or side lengths using sine, cosine, and tangent. After learning this content, we used our knowledge to find the area of different polygons. For example, I had to find the area of a heptagon, a seven sided shape. This was a long yet fulfilling experience that made me feel more confident in my work. To do this, we split the shape into triangles using the taking apart and putting back together habit of a mathematician. After this segment, we moved onto volume. We tried to find the volume equations or different 3D shapes, which was harder than finding area equations. The we did a project where we designed a complex problem on finding the area of volume of something that would challenge us.
|
Project Design
Started out with finding how many mac n cheese boxes can fit in a fridge, but was then shut down by Dr. Drew. After a while, we came up with a simpler yet complex problem of finding the volume of our school's flagpole. To do this, we used tools such a a protractor, Mr. Brower's long measuring tape, and a ruler. We thought we were doing everything right until we ended with a giant volume and a very tall pole. Redoing the math we got a much more logical answer, and my partner and I were proud of finally getting the answer right and were able to present our work in class.
We started out with a measurement of 30 feet from the bottom of the flagpole and out to the field. From the end of that, we took a protractor from two feet high and took a string to find the angle from the bottom to the top of the flagpole. The angle we got was 55 degrees, and when we did the math to find the height of the pole, we found it was 70 feet tall. This seemed a little outrageous, so we went back outside to redo the math with our teacher, Dr. Drew, and he believed it was 30 feet tall. We found the angle his way, but still got 55 degrees. Sooner or later we did the math and found that if we created a rectangle out of our triangle, we got the outer angle. Meaning the right angle to use is 35 degrees, not 55. After this we found that the height of the flagpole is actually 48 feet tall. We found that the diameter of the flagpole is 6 inches, meaning the radius is 3, and if you plug in the height and those measurements into the formula, "V=πr(squared)*h". Even though a cylinder (the flagpole) is not really a prism, it shares qualities of one. Just like prisms, the volume is found by multiplying the area of one end of the cylinder's base by its height. In the end, we calculated that the High Tech High's flagpole's volume is 1,357.17
We started out with a measurement of 30 feet from the bottom of the flagpole and out to the field. From the end of that, we took a protractor from two feet high and took a string to find the angle from the bottom to the top of the flagpole. The angle we got was 55 degrees, and when we did the math to find the height of the pole, we found it was 70 feet tall. This seemed a little outrageous, so we went back outside to redo the math with our teacher, Dr. Drew, and he believed it was 30 feet tall. We found the angle his way, but still got 55 degrees. Sooner or later we did the math and found that if we created a rectangle out of our triangle, we got the outer angle. Meaning the right angle to use is 35 degrees, not 55. After this we found that the height of the flagpole is actually 48 feet tall. We found that the diameter of the flagpole is 6 inches, meaning the radius is 3, and if you plug in the height and those measurements into the formula, "V=πr(squared)*h". Even though a cylinder (the flagpole) is not really a prism, it shares qualities of one. Just like prisms, the volume is found by multiplying the area of one end of the cylinder's base by its height. In the end, we calculated that the High Tech High's flagpole's volume is 1,357.17
Reflection
These are all of the Habits of Mathematician I used in this project. It's a lot, but they all tied into what I was doing.
Stay Organized-I somehow fit all my math onto only two pages, and I can read my handwriting. I tried my best to space out everything evenly or at least to where you can read it.
Be systematic- I had to be simple and organized with my work so I could read it and understand it. I kept it in the same place in my backpack, and made sure to not lose them.
Start small-We started small with weird ideas and grew into a bigger/hands on problem that was fun yet frustrating to do.
Conjecture and Test-We had to test new methods such as measuring out what a seventy foot flag pole would look like, and it most deifnetly looked taller than what it actually looks like.
Take Apart and Put Back together- We had to redo about all of our math because we came out with the opposite angle of what we were supposed to use. With this knowledge, we calculated the right answer, meaning a much smaller height, and a much more logical volume.
Seek Why and Prove- Since Dr. Drew disagreed with our first few calculations, we needed to find out why he thought it didn't make sense, and had to remeasure our flag. Seeing it from a different perspective and just as numbers on a paper helped us realize that it was actually ridiculous that we thought the flagpole was taller than our actual school.
Collaborate and Listen (with Modesty)- My partner wasn't always with me, so when she was, we had to be patient with each other and collaborate on what our plans were to do next. We needed to use our time as wisely as we could in able to complete our project.
Stay Organized-I somehow fit all my math onto only two pages, and I can read my handwriting. I tried my best to space out everything evenly or at least to where you can read it.
Be systematic- I had to be simple and organized with my work so I could read it and understand it. I kept it in the same place in my backpack, and made sure to not lose them.
Start small-We started small with weird ideas and grew into a bigger/hands on problem that was fun yet frustrating to do.
Conjecture and Test-We had to test new methods such as measuring out what a seventy foot flag pole would look like, and it most deifnetly looked taller than what it actually looks like.
Take Apart and Put Back together- We had to redo about all of our math because we came out with the opposite angle of what we were supposed to use. With this knowledge, we calculated the right answer, meaning a much smaller height, and a much more logical volume.
Seek Why and Prove- Since Dr. Drew disagreed with our first few calculations, we needed to find out why he thought it didn't make sense, and had to remeasure our flag. Seeing it from a different perspective and just as numbers on a paper helped us realize that it was actually ridiculous that we thought the flagpole was taller than our actual school.
Collaborate and Listen (with Modesty)- My partner wasn't always with me, so when she was, we had to be patient with each other and collaborate on what our plans were to do next. We needed to use our time as wisely as we could in able to complete our project.