Forensic scientists need to be able to identify the physical characteristics of a victim of a crime. The length of several bones can be used with a particular equation to find a person's height. In this activity, students will collect data to establish the equations that relate the length of several bones and the height of the individual.
This activity is adapted from an activity written by George Knill and published in the February 1981 issue of Mathematics Teacher.
Before the Activity
If you are using the TI-Navigator System with the TI-73 you will need the attached .pdf file.
Students should be familiar with using the TI-Navigator™ system to submit lists and equations to the teacher.
The teacher should be familiar with using the TI-Navigator system to send lists to the students.
Students should be familiar with linear relationships, linear functions, domain, range, independent variable, and dependent variable.
During the Activity
Match students into pairs of the same sex.
Have the students determine the independent and dependent variables in the relationship between height and the lengths of the individual bones.
The students begin by measuring their height and the length of the humerus (both in centimeters) using the measuring tape.
In L1, students should input the length of their humerus and in L2, students should input their height. The teacher should collect the girls data using TI-Navigator. Then, the teacher should send these lists to all girls. The girls should develop an equation that could be used to find the height given the length of the humerus. The same process should be done with the boys data.
After the linear regression equations have been found, the students should use the TI-Navigator system to contribute the point that represents their height and the length of the humerus.
Then, place the graphs of the linear regression equations on the graph of the points to see how the points correlate to the line. The two equations that forensic scientists use to determine height from the length of the humerus are h = 73.570 + 2.970H (males) and h = 64.977 + 3.144H (females).
You can compare the models found in the class to the actual equations used.
The same process can be followed for the femur, tibia, and radius. The actual equations used for each bone are as follows:
FEMUR: h = 69.089 + 2.238F (males) and h = 61.412 + 2.317F (females)
TIBIA: h = 81.688 + 2.392T (males) and h = 72.572 + 2.533T (females)
RADIUS: h = 80.405 + 3.650R (males) and h = 73.502 + 3.876R (females)
After the Activity
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary