Our group was responsible for proving the area of the volume of a pyramid to be ⅓ * base * height. One of our more difficult tasks was finding information on how Ancient Egyptians solved the problem. The conclusion we came to, an estimation method calculating and adding the volume of each layer of the pyramid, was a reminder for me of how the basic building blocks of math like multiplication and addition have such practical applications. This question may not be interesting for students learning modern mathematics, but it held such great importance for the Ancient Egyptians and the construction of the pyramids and think this is a good example showing the importance of contextualizing mathematics problems for math learners.
My main takeaway from this project is the universality and importance of geometric visualization. In EPSE 308, we’ve learned about the importance of engaging different senses to aid in memory, retention, and learning. Reflecting on my own mathematics education in elementary and high school, I find that there was a significant lack of visualization, which is why I appreciate the changes in curriculum in BC to include representation of math algebraically, pictorially, and symbolically.
Our extension involved splitting a right-angle triangular prism and a general triangular prism into three triangular pyramids of equal volume. The following is not a complete proof, but it shows the geometric intuition required to visualize and prove our extension problem.
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