Introduction

Today’s mishnah contains a debate concerning cleaning up after the meal.

Mishnah Four

Bet Shammai says: [after the meal] they sweep the floor is and then they wash their hands.,   But Bet Hillel says: they wash their hands and then they sweep the floor.

Explanation

According to Bet Shammai first they sweep the floor to gather up all the crumbs that might have fallen during the meal.  Evidently these crumbs would be eaten.  Food was quite scarce in those times and when we take into consideration how much work they had to put into making bread, it is no wonder that they didn’t want to waste anything, even a small amount of food.  Only after sweeping up the crumbs would they wash their hands.  This would prevent the crumbs from being ruined by the water. 

Bet Hillel holds that the first thing they should do is wash their hands so that they can bless and say Birkat Hamazon immediately.  In the time of the mishnah it was considered mandatory to wash one’s hands before reciting Birkat Hamazon.  Many Jews still observe this law on Shabbat and holidays.  According to the Talmud the servant would pick up all the pieces of significant size (more than an olive’s worth) before they would wash their hands so that those pieces could be saved.  It seems that to Bet Hillel it was important that they shouldn’t delay Birkat Hamazon any more than is absolutely necessary.