Foundation Mathematics Unit 2

Foundation Mathematics Unit 2

Sample assessment task – bones and bodies

Forensic anthropology is the examination of human skeletal remains for law enforcement agencies to determine the identity of unidentified bones. A forensic anthropologist can assist investigators by assessing characteristics such as age; sex; height (calculations of length of bones can be used to predict height); ancestry; disease and trauma. The focus of this activity will be to use bone lengths, in particular the femur (upper leg), tibia (lower leg) and humerus (upper arm) to calculate the height of an individual.

Part 1

The following table provides formulas for calculating heights of males and females from bone lengths:

Bone / Male / Female
Femur (Upper leg) / femur length ´ 2.238 + 69.089 / femur Length ´ 2.317 + 61.412
Tibia (Lower leg) / tibia ength ´ 2.37 + 80.97 / tibia Length ´ 2.6) + 65.63
Humerus (Upper arm) / humerus Length ´ 2.99 + 72.42 / humerus Length ´ 3.22 + 61.32

a. A tibia measures 42 cm, approximately how tall, in centimetres, is the person to whom the tibia belongs?

b. The femur of a 25-year-old male measured 49.7 cm. What was the height of the person?

c. The tibia of a 32-year-old female measured 33.5 cm. What was the height of the person?

d. After the age of thirty, the height of a person begins to decrease at the rate of approximately 0.06 cm per year. Re-caclulate d. above taking this into account.

e. The decomposed remains of a 20 year old person were found. The humerus was 30 cm long and the body was 160 cm. Is the body likely male or female?

f. A building company was beginning a construction of a new subdivision in the outskirts of Epping when workers discovered two bones that appeared to be human. The bones were recovered and analysed in a local forensic lab. Forensic anthropologists examined the two bones and determined one was a humerus measuring 40 cm long and the other was a tibia measuring 35 cm long. Four people in the area had been reported missing in the past year.

Reported missing / Height (cm) / Age (years)
Ryan Wegener / 190.5 / 25
Cheryl Hartmann / 160 cm / 18
Chelsea Moll / 177.5 cm / 29
Robbie Graber / 180 cm / 22

Who might the bones belong to?

Part 2

How do you measure up? How accurate are your bones at predicting your height?

a. Measure your own bones and use these measurements with the relevant formula to predict your height.

b. Calculate the difference actual height – predicted height for each bone measurement, and state whether ach prediction is an over-estimate or an under-estimate.

c. Which bone provided the best prediction for you?

Part 3

Comparing individual results to mean class results.

a. Use class data to determine the mean of the absolute values of differences for male students and or female students in your class for predictions of height for each bone.

b. Calculate the percentage error for your individual results and the class results.

c. Compare the class results with your individual results.

Areas of study

The following content from the areas of study is addressed through this learning activity.

Area of study / Content dot point
Patterns and number
Data
Measurement / 1, 3, 4
1, 3, 4, 5
1, 3

Outcomes

The following outcomes, key knowledge and key skills are addressed through this task.

Outcome / Key knowledge dot point / Key skill dot point
1 / Patterns and number
1, 4
Data
1, 5, 6, 7
Measurement
1, 4, 5 / Patterns and number
2, 3, 4, 5
Data
2, 3, 4
Measurement
1, 3, 4
2 / 2, 3 / 1, 2, 3, 4, 5
3 / 1, 2, 3 / 1, 2, 3