Ratio Part 2

1. Ratio Part 2 On a Dig

2. Teacher notes Provide ulna bones (models, cardboard cutouts or paper) to students to measure or have students excavate these bones out of sand or dirt, different groups can do this different ways based on your class structure and needs The bones provided in this lesson measure 20, 23, 26, 30.5, 32, 36 (in centimeters)

3. Teacher Notes - 2 Differentiate through difficulty of the calculations if desired The project can be bigger, you work from a larger pool of missing persons bones and collaborate as a team

4. Pack your bags! • We’re traveling to Uromi, Edo State, Nigeria! • Background - • One of the larger cities in its area • Primarily Farming and Trading economy • Ruled by a monarch

5. History A 2007 study of 109 individuals found that there is a very specific ratio between the length of the ulna bone and the height of an individual in the community of Uromi, Edo State

6. Formula Researchers worked to calculate at formula that would allow them to estimate the height of an individual based solely on knowing the person’s gender and the length of the ulna bone. They measured over 100 ulna bones and the heights of individuals from Uromi Estimated stature (cm) = Ulna length*Height ulna ratio+/-0.10 (if male) +/-0.21(if female)

7. Estimate • Scientists created the formula and a chart which allows researchers to measure an ulna bone and quickly estimate the height of that individual • Teacher Note – this is a good place to differentiate, the heights on the chart can be removed so that students who need a challenge can do the calculations, and students who struggle with the concepts can have the benefit of the chart with the calculations done for them, or the students can create the chart on their own based on the formula

8. Ratios

9. Scenario 10 people disappeared from Uromi on June 3, 2009 We have located a sandy dumpsite outside the village that has a number of ulna bones. We must measure the ulna bones and determine if these bones could have come from the missing persons, and which persons they could be from. We must excavate the site and recover the bones

10. Instructions 2 We will measure each bone in centimeters We will calculate the man and woman’s height the bone would have come from (using the formula or the chart) We will compare that information to the missing persons data and determine whose, if any, these bones could be We will prepare a report for the community law enforcers

11. Preparation to collect Create a table with columns labeled, bone letter, bone length, Female height, Male height, Name of possible matches, Notes

12. Handling the bones Collect each bone Label each bone with a piece of tape and a specific letter Measure the bone at its longest points – in centimeters Record your data in the prepared table

13. Draw conclusions Compare the heights of the bones collected with the data on the missing persons report Determine if any bones could match the persons on the report Fill in information on the table you prepared Think of explanations

14. Assessment Activities • Prepare a report for the local LEOs (law enforcement officials) Include the following • The time, date, location, your name, and title. • The label and description of each bone recovered including the length in centimeters • A summary of which bones could belong to which individuals listed in the report – include the table and a written explanation • If necessary, an explanation of why any bones recovered do not match any individuals on the missing persons report • Why is it useful to know the ratio between an individuals’ bone length and their height? • Is this method an individualizing or class finding • (have we identified the individual or is this data just consistent with known information about the individual) • Why not just use DNA to identify the origin of the bones?

15. References http://en.wikipedia.org/wiki/Uromi http://www.ispub.com/ostia/index.php?xmlPrinter=true&xmlFilePath=journals/ijfs/vol3n1/ratio.xml