"grote" is always used after definite articles, regardless of gender or number of objects.
- De grote hond
- Het grote huis
- De grote huizen
"groot" is used as a predicate adjective and after indefinite articles that come before "het" words:
- Het huis is groot.
- Ik woon in een groot huis.
I realize it's somewhat archaic, but the phrase, "the great dog," can actually have the same meaning as "the large dog" or "the big dog." This term would most commonly be used today in regard to a room--the great room--where the meaning would be "large," but it could still be applied to any other object.