TEA: Activity-amati- -- Whoisaverage

Who Is Average?

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Peter M. Amati, Jr.
Holliston High School
Holliston, Ma. 01746
School Phone 508-429-0677
amati@tea.rice.edu

Overview
In this activity students will discuss what constitutes an average sized female and average sized male. This concept will be critical when looking at a number of features when designing the insulated underwear, namely: heat lost per unit area , cost per set of underwear and mass per set of underwear. Once a consensus as to what constitutes an average sized female and average sized male has been established then a protocol to measure (estimate) that, can be arrived at.

The students will:

establish what is meant by an average sized female and male.
discover that there are parameters (limits) and that must be worked within (There are giants and midgets; but under these conditions we must work within limits.)
design a protocol that will lead to determining the averaged sized female and male in the class.
employ that protocol to determine the average sized female and male in class.
use the above determined average to calculate the average amount of cloth needed to cover an average size male and female.

Grade Level/Discipline
Grades 9-12, but may be adapted to middle school Physical science and general science classes.

National Standards

Benchmarks:

State Standard: Massachusetts' frameworks

Strand 1 Inquiry #'s 1 - 34
Strand 3 Technology #'s 2, 6, 10, 15, 16, 18, 19, 27, 31, 32, 34, 37, 38, 39, 40, 41, 42, 53, 54, 56, 60, 61, 62, 63, 65, 78
Strand 4 Science Technology and Human Affairs #'s 2, 3, 10, 11, 15, 16

Pre-activity set-up

role of twine
meter sticks
two large sheets of paper , at least 3' wide and 7' long. (back side of gift wrap or paper used for mailing packages, is good)
straight edge 6' long (A straight piece of wood is good. Shop classes are an excellent source.)
marking pens

Materials

role of twine
meter sticks ? two large sheets of paper , at least 3' wide and 7' long. (back side of gift wrap or paper used for mailing packages, is good)
straight edge 6' long (A straight piece of wood is good. Shop classes are an excellent source.)
marking pens

Time Frame
Two class periods (approximately 55 minutes per period)

Engagement and Exploration (Student Inquiry Activity)
Have largest and smallest kids come to the front of the room. (Know your kids. Make sure they are comfortable with having their size being looked at by the entire class.) Ask "Do you think it would take the same amount of material to make a set of underwear for each of these kids?" Discussion can be very exciting since extremes are being looked at. Eventually discussion should be brought back to what constitutes an average.

Have the PIs take charge of the research teams, there have to be leaders. PIs should lead a discussion as to why average sizes have to be determined.

There will be undoubtedly a discussion of the large, medium and small categories, as opposed to averages. The rationale as to why averages must be found is that no one knows who will be on the expedition and that average costs of materials and masses must be looked at in budgetary and logistic planning. The idea of working within certain parameters; with the average being just that, must be conveyed to the kids.

Have PIs , using a consensus of groups, lay out one protocol that is to be followed by all groups in determining the average sized male and female in class.

There is no real right answer. A protocol that has worked well is:

list on the board measurement that should be looked at in get sizes. These should include height, waist, chest and inseam. Make sure these are done in the metric system. (Great location for extensions e.g. What is precision? Significant numbers.)
create a data table reflecting these quantities.
twine can be used to get the various lengths and then measured with a meter stick. N.B. Always have girls work with girls and guys with guys; for obvious reasons. Level of maturity will determine which measurements can be taken. (If someone is really concerned about the height measurement (or whatever,) of a classmate they will then have to convert to inches so that they can "understand" the number. Great motivational tool to learn conversions.) If maturity level is such that this cannot be used ,average height, waist, chest and inseam measurement can be supplied. Avoid giving data if at all possible.
using above data determine which female and which male, from that parcticular class, best represent the average female and male person.
using large sheets of paper marked off into 5 or 10 cm squares trace outline of your class's average male and female respectively. Grid system should be drawn by kids, using straight edge. Hands on; besides it reinforces that feeling of ownership in the lab (project).
share with the kids the idea of a "sandwich pattern" (the using of a front and back pattern, with the assumption that the edges will be sewn together) to determine how much material must be use in making a typical set of underwear.
counting the number of squares that are enclosed by the outline (any part of a square is counted as a full square) of the average male and female will give the total area of cloth needed for the average sized female and male .
calculate the amount of cloth that is needed to make a set of underwear for the average female and average male.

Explanation (Discussing)
Discuss with students, based on THEIR observations and THEIR calculations, how much material is needed for the average female and average male explorer. Put the averages on the board , there should be a gross difference between the typical female and male. This should help in stressing that averages must be looked at, at least initially, in ascertaining probable costs and masses of underwear sets in working with budgetary and logistic planning.

Elaboration (Polar Applications)
Set the scene by explaining that students will be role-playing the parts of clothing designers developing long underwear for a sea ice research team taking ice cores from the Weddell Sea.

Ask students to read about Peter Amati's research in the Weddell Sea on the Teachers Experiencing Antarctica and the Arctic web site../../tea_amatifrontpage.html

In parcticular, note the journal entry from June 6, 1992../../amati/6.5.1992.html In this entry, Peter describes the extreme cold and dryness of Antarctica.

Another interesting reference can be found on the GLACIER web site at../../expedition/2_trainingcamp.html

Exchange (Students Draw Conclusions)
Student PIs present tabulated data acquired from all research teams and lead discussion that will lead to a consensus as to what the average area to be covered in the average female and male are.

Evaluation (Assessing Student Performance)
Rubric dealing with formal lab report and graphed data sets.

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