How should teachers handle late assignments

When a student hands in an assignment late, there should be a consequence.  Currently it is up to the individual teacher, and school, for what the consequence will be.  In my opinion the current way of taking 10% off once it is late, is good, but the teachers should give the students the full day to hand it in, in case they forgot it at home, or, depending on the assignment, didn't transfer it over to the school computer.  I also think that it is a good idea to have the cut-off date for assignments be a week from when they are due, and if it isn't handed in before then it will be marked a 0.  I do like the current way that late assignments are handled but there should be a standard that the entire school follows.  Instead of some teachers having a shorter cut-off date, which can confuse students, it should all be the same.