This unit was filled with geometric equations and problem-solving. I never knew that a simple question like What's the ideal configuration of a honeycomb? Could actually include so much geometry. I learned a lot of myself in this unit. Mainly how I can problem solve, both by myself and with others. I would ask other peers how they would find the answer and compare their way of finding it to mine. This would open up a lot of possibilities to me, I would be able to start over, but also using steps that I've already gotten an answer out of. All the problems and tasks offered this for me and this built my academic understanding and openness as well as social understanding.
I was able to build understanding for every problem that was set my way, through trial and error, and brainstorming. I would find myself a little confused to start, but I would usually go back and think of what I've learned and how that can help me start solving this problem. Problems that this really showed in were the Bigger Corral problems, where we had to find the perimeter and area of differently sized corrals. We would switch the shapes between rectangles to triangles. We had to split each side up, to sum up to either 300 or 900. These gave me a lot of practice in finding an area in both shapes.
There would be some occasions where I had to find the height of a triangle so that added another step to the problems. You had to find it by splitting the bottom side in half. You would then use the Pythagorean Theorem backward. Instead of a squared + b squared = c squared, it would be a squared - c squared = b squared. The problem Leslie’s Flower was the problem that introduced this concept. I got the process and question wrong the first time. However, after going through it again and receiving the help I was able to understand and solve it correctly. It really grew my understanding and the rhythm of finding the height of a triangle then using that to find the area.
My overall knowledge of the different equations grew. Examples of these include area, surface area, and volume. In order to find the surface area you would divide how much the sides add up to and divide it by the number of sides there are, then you would know the exact length of each side. Next, you would multiply the length of the sides by how many sides there are and you would be given your surface area. The Back on the Farm problem centered on finding the different surface areas of different polygons such as an octagon (8 sides), a decagon (10 sides), and a Dodecagon (12 sides). This problem gave me a lot of time to practice with different shapes and get the process down.
Geometry includes two important factors, Trigonometry, and the Pythagorean Theorem. Last year we touched the Pythagorean Theorem a little bit, but didn't really dive into it and use it, mix it with Trigonometry can find a way to make all these steps combine together to find the final answer. Because this unit was focused on those two topics we learned and practiced them a lot. Each problem that we faced included one of the two and we had to investigate multiple ways that they could fit into the problem. It was really fun to explore the different possibilities and continue wanting to work. This is rare for me and I feel like because we kept learning as we worked with our peers it kept bringing me back to the problem, trying to problem solve. This started in one of our first assignments in this unit, Make the Lines Count. This assignment took me a little while to complete because there were so many ways that you could make a triangle, it was very interesting to me and kept me hooked, and motivated to finish it. I think from there my curiosity grew. This unit was very beneficial to me and I hope that we have more units like this in the future.
This mini project was all about cars! In this project, each student got to generate a question of their own that was about cars. However, the question had to be answered using math. There was a system our question had to follow. We had to ask a good question, make it specific, answerable, and clear. It had to create a mathematical framework. We had to do the math and reflect on our result.
For example: “What car is the best?” would not work as a specific and mathematically answerable question. However, if we changed it to “What car has the best gas mileage, and has the best speed to drive 300 miles?” would be a better question to create.
The question I created for this unit was “ Are lighter cars better for gas mileage, fuel efficiency, and economy?”
I researched the lightest cars as of 2017 and collected my data. I collected the weight, HP, Gas Milage, Price, 0-60 time, and fuel capacity of every vehicle. In the end, I found the average of every component and compared them all with each other. It was a project mainly about compare and contrast.
This project was a different change of pace and I really enjoyed it. It was great that we had the freedom to research our own question and we could use any type of math we wanted.
To the side is my final product for the project: