Student Group Maker Calculator (Even Groups, No Leftovers)

How it works

groups = ⌊N ÷ size⌋, leftover = N mod size · no-leftover mix: find a, b with a × size + b × (size ∓ 1) = N · round-robin pairs: N − 1 rounds (even N) or N rounds (odd) · rotation time = stations × minutes + moves

Dividing a class evenly is a small problem that eats minutes every day, and the arithmetic has a neat answer: any class size can be covered by groups of a chosen size and its neighbour — for fours and threes, every number from 6 upward works — so nobody is left as a fifth wheel and no group is oddly large. The same counting decides whether stations can rotate cleanly (one group per station) and how many rounds it takes for every student to have partnered every other, which is the classic round-robin schedule. Choosing how to assign students is pedagogy — random for breaking cliques, snake-drafted by ability for balanced project teams — but the numbers come first.

Worked example

Twenty-nine students in preferred groups of four: 7 groups of 4 leave one over, so make 5 groups of 4 and 3 groups of 3 (8 groups) — or 6 of 4 and 1 of 5. In pairs that is 13 pairs plus one triple, and 29 rounds for everyone to partner everyone. With 6 stations and 8 groups, two stations need doubled materials; a full rotation of 8-minute stations takes about 53 minutes.

Frequently asked questions