Euclidean Geometry • Equitable Distributing • Linear Optimisation • Set Theory • Nonstandardanalysis • Representations • Topology • Transcendental Numbers • Number Theory • Calculation of Times (Previous | Next)

In life, there is often distribution unfairness. Although the following is not new, equitable distributing is to be demonstrated by examples that occur daily at school:

1. How do we distribute work-results equitably?

2. How do we channel groups equitably through the cafeteria?

3. How do we form equitably groups in physical instruction?

To 1.: The work results are put down first alphabetically, arranged according to the names of the present pupils (in trays, on the table or the like). The names are or will be put down alphabetically in a spread-sheet analysis (except the missing pupils). Behind each name a random number is produced. The names are arranged according to the random number. The pupils are called according to this order (possibly in groups) so that they can receive their work results.

To 2.: At the beginning, groups with members are formed that would like to dine together or are to do this. These groups (-names) become arranged as described under 1. Then for each group (the available output time) * group size/diners is computed. The second group goes into the cafeteria if the time determined for the first group is past. The third group follows if additionally the time for the second group has elapsed and so on. If necessary, the points in time have to be computed rounded. If singular groups can do only to certain time intervals, they are distributed first on the time intervals. Then the procedure continues with the remainder time for the remaining.

To 3.: At the beginning, groups of same capacity are formed and the individual names are written in a firm sequence one below the other and after an assigned group number numbered serially. If group members are missing, they are first filtered, as e.g. the entry "missing" is noted behind their name and afterwards is selected after the empty entries.

The group size should be a multiple of the number of groups that can be formed. The sequence of the names should be firm, for reasons of the probability. Changes of the capacity are considered in changed groups. Behind each name, the numbering is divided by the number of groups. If the numbering does not begin with 0, a number must be subtracted before accordingly. The decimal places of the received values are truncated. This can be attained also by a rounding of the values reduced by 1/2. In a further column, now random numbers are registered.

Whereupon the three columns are only arranged according to the values determined first, then additionally according to the random numbers. In a fourth column, beginning from above, the numbers from 1 to number of groups are registered. After the last value, it is again continued with 1 up to the number of groups and so on. Now the numbers are sorted again according to names. Finally the group assignments can be announced in alphabetical order.

If the number of pupils who can be divided is not a multiple of the number of groups, proxies from the same group should be formed to each name. The names that have the smallest time absent by sitting out are intended for sitting outs. They deputise for their deputies (e.g., if there are several runs in an instruction unit). The time absent is credited accordingly.

A simple procedure with a dice (instead of a computer) functions as follows: The pupils are set up ordered according to their (self-determined or over-directed) capacity on a line. The one with the highest capacity is assigned to one of the groups by throwing the dice. The next one is determined under the remaining groups by the dice and so on. If each group has a member, it is continued as with the one with the highest capacity now with the one with the henceforth highest capacity.

Without considerable aids, groups can be formed also as follows: All pupils are requested to move respectively in a circle after their capacity coincidentally. Couple formation is prevented with the request "A and B apart to the circle line!". After the command "stop!" everyone remains at his place. One of the pupils is now requested to leave its place and move on an approximate circle line around the remaining or around in each case a group.

After a further command "stop!" the pupils are divided by imaginary straight lines into groups. First, the intersection is build the straight line forms through the break point of the one who stands on the circle line and the respective centre of the circle with the group circle line. The groups are defined by parallel straight lines that go parallel to the straight line through the respective intersection and the respective centre of the circle.

These procedures are more equitable than the judging selection by individual pupils. Three capacities are sufficient according to experience.

© 2006-2007 by Boris Haase

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