From: Carol 
To: Teacher2Teacher Public Discussion
Date: 2000081813:17:18
Subject: Grouping students

I spent all afternoon playing with this problem, first with the
cylinders.
Then I tried listing all possible combinations of 4, then 6, then 8,
then 10 students by writing all possible ways students could be
paired.
Example for 4 studednts A, B, C, and D
AA  AB  AC  AD
BA  BB  BC  BD
CA  CB  CC  CD
DA  DB  DC  DD
I eliminated the AA - DD diagonal along with the pairs above the
diagonal.

BA
CA CB
DA DB DC

Then tried to find patterns with the remaining pairs. What I found was
the following:
Round 1  		Round 2  		Round 3
DA			BA			CA
CB  			DC  			DB

If you were to circle round 1 in one color, round 2 in a second color,
and round three in a third color, you could see that they are in a
symmetric
pattern.

When you do the same thing with 6 students A,B,C,D,E,F,G you can
select
pairs for each round by picking student pairs that are in a physical
pattern, but not always exactly symmetric in itself, but symmetric
with another round.
If I could demonstrate this in color, it would be clearer. It is very
hard to describe the patterns in words.

As I tried to do this with 8 students it was more difficult to find
the
patterns, but I was able to do it.

But 10 students was nearly impossible--or maybe I was getting tired.

I think you are correct about looking for a computer program to do
this.
There should be a way to write a computer or graphing calculator
program that could do this for any even number of students.
I still want to think about it some more.
Carol

















 - Carol

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