Are they related?

The following mathematics activity was originally written for middle school learners. It was intended to introduce  this  seventh grade, Michigan Grade Level Content Expectation: "Create and interpret scatter plots and find line of best fit; use an estimated line of best fit to answer questions about the data." While lessons on this expectation typically include middle schoolers measuring things like their own arm span and height to see if they are related, my experiences with adolescents suggest that they are often self-conscious about their bodies and uncomfortable with such activities. Instead, I came up with the idea for them to measure dolls and action figures to see if certain relationships fit what we know about the human body. Here is the activity using the Connected Math Project's Launch-Explore-Summarize learning plan format.
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Needs: One hour; learners in groups; The Da Vinci Code; The Vitruvian Man handout; something that measures distances; set of dolls or action figures (preferably one for every pair of students); and a method for collecting and graphing data


Launch: The Divine Proportion
Read "The PHI Section" from Dan Brown's The Da Vinci Code. Here is a paragraph to give you a taste:

Despite PHI’s seemingly mystical mathematical origins, Langdon explained, the truly mind-boggling aspect of PHI was its role as a fundamental building block in nature. Plants, animals, and even human beings all possessed dimensional properties that adhered with eerie exactitude to the ratio of PHI to 1. 

Test out the theory on The Vitruvian Man (modified for seventh graders)

Explore Data from Dolls
Assign each expert group to explore a relationship described in "The PHI Section"

• Total height to belly button height
• Distance of shoulder-fingertip to elbow-fingertip
• Distance of hip-floor to knee-floor

Here is the data collected from one set of dolls using Fathom:

Summarize Jigsaw
New groups will be formed that include one person from each expert group. Learners will share what they found during their exploration. Teacher walks around gathering information to summarize the activity with the whole group.
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In the Common Core State Standards, this topic is found in the high school statistics section:
Summarize, represent, and interpret data on two categorical and quantitative variables
6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.