# Could These Bones Be Amelia Earhart's? (Modeling Module)

### Author: Marsha Davis

In this module, students create models for predicting human stature from bone lengths. The goal for the development of these models is to determine whether a set of bones found on Nikumaroro Island might be Amelia Earhart's. In Activity 1, students work with a model developed by Dr. Mildred Trotter for predicting height from tibia length. Since students will not be able to directly measure their own bone lengths, they collect height and forearm length measurements from the class. They compare heights of male students to female students. In Activity 2, students make a scatterplot of height versus forearm length from the class data. Based on their scatterplot, they discuss the direction, form, and strength of the relationship between height and forearm length. Then they create their first model by drawing a line (by hand) on their height-forearm scatterplot that they think summarizes the pattern in the data.

In Activity 3, students are given data from the Forensic Anthropology Data Bank at the University of Tennessee on height and bone lengths. In order to investigate the direction and form of the height-radius data, students use technology to make a scatterplot of height versus radius length. After sharing their Activity 2 models for predicting height from forearm length and discovering that different students created different models, students are introduced to the leastsquares criterion for picking the "best" model. Then they fit a leastsquares (regression) line to the data and use this model to predict the height of the person whose bones (including a radius) were found on Nikumaroro Island.

In Activity 4, students are introduced to the coefficient of determination, r^{2}, a measure of the strength of a linear relationship. They determine leastsquares equations for the relationships between:

(1) height and radius,

(2) height and tibia, and

(3) height and arm (arm= radius + ulna)

Then they use r^{2} to select which of these relationships is the strongest. Using their chosen model, students use the bone lengths found on Nikumaroro Island to determine whether the bones might be Amelia Earhart's.

This module was adapted from Chapter 3 of Mathematics: Modeling Our World, Course 1, 2nd edition (2010), COMAP, Bedford MA.

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