Measuring Your World
Do Your Own Project
Project Description
This project was overall an exploration of different topics in math. The topics we covered were the Pythagorean Theorem, right triangle trigonometry, the area of polygons and circles, and different dimensions of volume. The Pythagorean Theorem is when the equation a^2 + b^2 = c^2 is put into place to solve the length of the hypotenuse in a right triangle. Right triangle trigonometry is for finding the angle of the missing sides with trigonometry. The area of polygons and circles is complex and takes a lot of practice to remember how to use the angles from inside the circle or in the case of a polygon the lengths on the outside of the shape in order to get the area of the polygon or circle. The different dimensions we studied were 2D and 3D. This was through a series of worksheets that explored the area of each of the different dimensions of polygons. Some of the worksheets included were the Corral Problem, which was a series of problems pertaining to finding the area of a different shaped polygon each time. Another worksheet we worked on for one of these topics was called Exploratory. This worksheet was focused on finding the angles of x1 and y1 in a circle.
In this project, we were asked to explore one of the covered topics by measuring something through math. I chose to further explore volume. My group decided to calculate the height of a large tree that is located in the front of our campus. We did this by measuring the shadow because we are not allowed to simply measure the tree. We understand that shadows are not an exact representation of what the measurements of the tree are, so we will be using proportions. Since we know my height and the length of my shadow, we are able to measure the height of the shadow.
In this project, we were asked to explore one of the covered topics by measuring something through math. I chose to further explore volume. My group decided to calculate the height of a large tree that is located in the front of our campus. We did this by measuring the shadow because we are not allowed to simply measure the tree. We understand that shadows are not an exact representation of what the measurements of the tree are, so we will be using proportions. Since we know my height and the length of my shadow, we are able to measure the height of the shadow.
Math
We first started by measuring the length of the shadow of the tree, which we did by taking a measuring tape from the end of the shadow to the root of the tree. Then we measured my height and my shadow by repeating what we did with the tree for me. After we had all of the measurements, we divided the length of my shadow, which is 103 inches, by my height which is 67 inches, in order to get the proportion. Tis resulted in a proportion of 1.539 inches. After that, we took the proportion, which is 1.539 inches, and divided it by the shadow of the tree to get the height of the tree, which is 257.64 inches. This means that from our calculations the tree is 21 feet and 47 inches. The math my group did was not as challenging as we could have made it, but we did not know until we learned about how the rest of our class had completed the project.
Reflection
Overall, this project furthered my knowledge in many important topics in math. Learning trigonometry was hard at first, but once I used the Habit of a Mathematician that worked best for solving the problem, I easily learned what steps I could take in order to better my understanding. For example, I used the habit of Being Systematic and that helped me experiment more but with an understanding of what I was doing. I also used the habit of Staying Organized all throughout this project because if I wasn't organized with my notes, I would not have been able to use them as a reference in case I struggled with a problem or topic. During the portion of the project where I worked with my group on the math, the Habit of a Mathematician I used was Look for Patterns. I used this habit to find the connection between both shadows, which is that they are both right triangles so they are similar triangles. A way my group could have improved this project and made a better fit for us would be solving our problem with trigonometry instead of solving it with similar triangles. Our original thought was to use a hula hoop, but we believed that would be too simple, therefore we tried to challenge ourselves to do something we could physically measure without doing so.