# Sharks and Science: the Santa Cruz Edition

|## Post by Graduate Student, Victor Perez

Over the past week I had the great pleasure of working with Jason Tovani and his four paleontology classes at Delta High School. Delta is a unique school that accommodates students that did not find success at traditional high schools. Delta gives the students and the teachers the opportunity to pursue non-traditional education methods to motivate student involvement and draw out their potential. This effort closely aligns with my own personal goal, and the goal of PaleoTeach; in which we use real scientific research to give meaning to basic concepts being taught. Although the students had some apprehension towards the lesson at first, I certainly think they all appreciated it by the end.

*Graduate Student, Victor Perez, talks to Delta High School students about Megalodon and helps them calculate the size of the animal by measuring the teeth and participating in a geometry lesson. Photos by Jason Tovani.*

The lesson that we employed used 3D printed *Carcharocles megalodon* teeth in order to estimate the total body length of this extinct behemoth. The thing that made this lesson exceptionally interesting is that the body length estimates that we used had never been tested (to my knowledge) on an associated dentition of Megalodon. The equations we used were based on the research of Shimada (2003), in which he made linear regression lines correlating the tooth crown height to body length in the modern Great White Shark. These equations show that the growth rate of tooth crown in the Great White Shark is proportional to the growth rate of the entire body. Using these equations for Megalodon requires some bold assumptions. Namely, that the same proportional growth rate existed in this extinct shark.

Based on the results that the students got, it seems that we get very different estimates depending on the tooth position within the jaw; despite the fact that all of the teeth came from a single individual. The anterior teeth always provided a lower estimate and the posterior teeth often resulted in significant over estimates. Upon averaging the results of numerous tooth positons we got more realistic estimates (around 65 feet), however this still seems like an overestimate. This suggests to me that the rate at which Megalodon replaced its teeth may not correlate with that of the Great White Shark, especially in the posterior positions. Further, we often find Megalodon teeth with a distinct pathology, in which the cutting edges of the teeth have a wavy profile. This is often thought to be due to the tooth actually outgrowing the jaw. If this is the case, then certainly the growth rate of the teeth is not proportional to the growth rate of the rest of the body. This is a new discovery that come into fruition from the efforts of these students, which further exemplifies the power of bringing real research into the classroom.

This lesson was expanded to include a real life application of basic geometry concepts. Rather than having students solely measure crown height, they were asked to visualize the teeth as a triangle. Subsequently, they measured the dimensions of the triangle and learned the scientific definitions of their measurements (i.e., crown height, crown width, distal edge length, and mesial edge length). This was a very basic application of geometry that could easily be modified to include more advance concepts. This very simple activity has endless possibilities that can accommodate any science class and I look forward to seeing how it progresses.