Sample response: About 123 centimeters (around 4 feet). I measured the humerus and height of several classmates and created a scatter plot. I used a plot of the residuals and found that a linear model seemed to be appropriate. I then found the line of best fit to be about $y = 5.1 x + 0.2$, where $y$ is the height in centimeters and $x$ is the length of the humerus in centimeters. Using 24 centimeters for $x$, I found that $5.1 \boldcdot 24 + 0.2 = 122.6$, which I rounded since this is a rough estimate.

The purpose of this discussion is for students to communicate how they used mathematics to justify their findings.

Ask students:

• “How confident are you in your answer? What information helped you determine your confidence?” (Not very confident. Since the correlation coefficient is near 0.6, there is only a moderate relationship between height and humerus length. Additionally, this ancient human ancestor may have a different anatomy—for example, apes tend to have proportionally longer arms than humans do.)
• “How did you use mathematics to estimate the height of the ancient human?” (First, I collected data on the height and the approximate length of the humerus of my classmates. I then made a scatter plot to determine whether or not a linear model was appropriate and then computed a line of best fit. I substituted 24 centimeters into my line of best fit and obtained my answer.)
• “Do you think that the way you measured the humerus of your classmates impacted your choice of linear model? Explain your reasoning.” (Yes, I think that I probably overestimated the bone length because I was measuring from the outside and not the inside. I think that my model likely overestimates height.)