Working in Subgroups
How to ensure every student works with every other student by using subgroups
Getting everybody to work with everyone else in subgroups is one of those tasks you think should be easy to arrange, but when you try to work out the groupings, the combinations never quite seem to work.
The composition of the subgroups should match the course objectives. Diverse groups allow people to learn about other departments, while homogeneous groups permit delegates to share knowledge and experience.
Be careful if you use race, age, gender, religion or nationality as criteria for creating diverse subgroups. You must have a good training reason for using these criteria. “Let’s split the girls up” is not a good reason. Giving people practice in managing diversity is a better reason. The safest selection criteria are experience, location, and the delegate’s job.
Mixing the sub-groups
A good way to have a nervous breakdown is to change the sub-group composition for each exercise. For an even better nervous breakdown, try arranging the groups so that every student has worked with every other student by the end of the course.
After a few hours of brain-bashing, you will come to the conclusion that only certain combinations of group and subgroup size provide a complete solution.
The number of subgroups required for a solution is:
N/n(Where N is the size of the group, and n is the size of the subgroup.)
The number of sessions required to ensure that everyone meets everyone else is:
(N-1)/(n-1)The main conditions for a perfect solution are:
The number of subgroups and
the number of sessions must be integers.
When you have an imperfect solution:
Use a plan for a larger number of people and insert blanks. This may reduce group size too much.
Use a plan for a larger group size and substitute blanks to reduce the group size.
Use a plan for a smaller number of people and add in the extras.
Some example plans
N=4, n=2
1 AB CD
2 AC BD
3 AD BCN=6, n=2
1 AB CD EF
2 AC BE DF
3 AD BF CE
4 AE BD CF
5 AF BC DEN=8, n=2
1 AB CD EF GH
2 AC BD EG FH
3 AD BC EH FG
4 AE BF CG DH
5 AF BE CH DG
6 AG BH CE DF
7 AH BG CF DEN=9, n=3
1 ABC DEF GHI
2 ADG BEH CFI
3 AEI BFG CDH
4 AFH BDI CEGN=10, n=2
1 AB CD EF GH IJ
2 AC BD EG FI HJ
3 AD BC EH FJ GI
4 AE BF CG DJ HI
5 AF BE CH DI GJ
6 AG BH CJ DF EI
7 AH BI CF DG EJ
8 AI BJ CE DH FG
9 AJ BG CI DE FHN=15, n=3
1 ABC DEF GHI JKL MNO
2 AEH BDG CLN FKJ IJO
3 ADO BIL CEM FGJ HKN
4 AIN BEJ CDK FHO GLM
5 AJM BKO CFI DHL EGN
6 AGK BFN CHJ DIM ELO
7 AFL BHM CGO DJN EIKN=16, n=2
1 AB CD EF GH IJ KL MN OP
2 AC BD EG FH IK JL MO NP
3 AD BC EH FG IL JK MP NO
4 AE BF CG DH IM JN KO LP
5 AF BE CH DG IN JM KP LO
6 AG BH CE DF IO JP KM LN
7 AH BG CF DE IP JO KN LM
8 AI BJ CK DL EM FN GO HP
9 AJ BK CL DM EN FO GP HI
10 AK BL CM DN EO FP GI HJ
11 AL BM CN DO EP FI GJ HK
12 AM BN CO DP EI FJ GK HL
13 AN BO CP DI EJ FK GL HM
14 AO BP CI DJ EK FL GM HN
15 AP BI CJ DK EL FM GN HON=16, n=4
1 ABCD EFGH IJKL MNOP
2 AHJO BGIP CFLM DEKN
3 AGLN BHKM CEJP DFIO
4 AFKP BELO CHIN DGJM
5 AEIM BFJN CGKO DHLPN=21, n=3
1 AHO BIP CJQ DKR ELS FMT GNU
2 ANS BFK CGL DOT EIU HJP MQR
3 AGK BNL CET DPS FOR HIQ JMU
4 AEM BOQ CFS DHN GJR ILT KPU
5 ACI BUT DJL EPR FGQ HKS MNO
6 AFL BDM COP EJK GHT INR QSU
7 APT BCR DGI ENQ FHU JOS KLM
8 ADQ BEH CKN FIJ GMP LOU RST
9 ABJ CDU EGO FNP HLR IMS KTQ
10 ARU BGS CHM DEF IKO JNT LPQN=25, n=5
1 ABCDE FGHIJ KLMNO PQRST UVWXY
2 AJNRV BFOSW CGKTX DHLPY EIMQU
3 AILTW BJMPX CFNQY DGORU EHKSV
4 AHOQX BIKRY CJLSU DFMTV EGNPW
5 AGMSY BHNTU CIOPV DJKQW EFLRX
6 AFKPU BGLQV CHRMW DINSX EJOTY