I am working on a differentiated lesson for a course I am taking - the topic is dividing by one-digit. As a remedial math teacher I am struggling to come up with an enrichment activity for division - any thoughts or ideas you could share would be appreciated.

I'm not sure what grade you are working with but what about

divisibility rules
interpretting the remainder in problem solving situations
division problems with missing digits like 9_ dividied by _ = 24 r1
remainder riddles (my number divided by 1 has no remainder, my number divided by 2 has a remainder of 1, etc.)

Start with an answer (some with remainder, some with a decimal, some with a fraction, some just a straight up whole number)...have the students determine an appropriate word problem using division. Makes them interpret how/why remainders can be written in different ways, when they are needed, etc.