Partitioning of Natural numbers

Today in my grade 7 I introduced the idea of partitioning of numbers. We talked about how different ways one can partition natural numbers. The simplest one are {1,prime,composite} and {even,odd} but one can also partition natural numbers as {even factors, odd factors} and this classification is equal to {square numbers, non square numbers} The one example which brings to life this concept is the celebrated problem of locked and unlocked rooms.