Project Overview
Throughout this project, we explored many different mathematical concepts, all relating to the over-arching topic of measurement. We began with a basic review of Pythagorean Theorem, which led into a study of right triangles and their properties. This then expanded into a full overview of right triangle trigonometry, with a specific focus on sine, cosine, and tangent. From there, we applied our knowledge of trigonometry into a unit fixated on two-dimensional space. We learned to take apart shapes, specifically by dividing them into triangles, and from there discover new techniques for finding the areas of more complex two-dimensional shapes. Next, we dove into the third-dimension, where we studied volume, from the most basic rectangular prisms to spheres. We finally wrapped up our measurement unit with a personalized mini project, in which we used all the skills gained throughout our mathematical adventure.
"Design Your Own Project"
For this "design-your-own" project, my partner and I decided to find the volume of a cylindrical cake. We used a bundt cake pan, which creates a final product shaped vaguely like a ring- one smaller cylinder was taken out from the center. We also created another layer to our volume exploration by choosing to find the volume of the cake before and after baking. Our final product included the cake itself, a project sheet we created containing our plans, and a presentation containing a detailed description of the math used to solve our problem.
(Click through slideshow to view math solution/process)
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Reflection:This was especially interesting, because it allowed me and my partner to take creative license and design a project that we could connect to and feel engaged with. We were also able to have fun while practicing our newfound volume skills. My partner and I found this process relatively simple overall, but did face some challenges along the way. For example, we failed to apply the habit "Stay Organized," and ended up leaving out some ingredients. While we did manage to catch our mistake and fix it before baking, we can't be sure whether or not it affected the rise and resulting volume of our cake.
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Overall Reflection
Throughout this unit, I feel as if I've experienced major academic growth, and well as achieving a higher level of confidence in my skills as a mathematician. Instead of simply learning formulas, we dove deep into the logic behind them, completed proofs, and only moved on once the class was completely confident in a topic. While I'm a relatively fast learner, meaning that I can sometimes find such a style slightly tedious, I felt that this mix of practice and math exploration was extremely beneficial. I also appreciated how we were able to use real-world examples and connect them to the math we were learning. A habit I felt that I utilized the most during this whole unit was "Start Small," because that was essentially how the entire project was run. We began with a basic concept of measurement, and expanded that into a much more complicated one. By doing this, we were able to feel more comfortable with new content and accepting challenges. Overall, I believe that this unit has been a substantial one, and I look forward to continuing on in math class and facing new challenges as they come.