"He eats an apple every day at quarter to one."
Translation:O her gün bire çeyrek kala elma yer.
MoDan, i think it depends on what you want to put the focus, what you want to emphasize. Duolingo doesn't give all the alternative sentences. I have found a super web-site on this topic: https://en.wikipedia.org/wiki/Turkish_grammar#Word_order. Enjoy it! But i'm not Turkish native, i can't appreciate the value of the content. Anyway, enjoy it!
It depends on whether you are talking about the minutes before the hour or after the hour. So 12.45 "quater to one": "bire (=dative) ceyrek" 10.55 "five to eleven": "on bire bes"
and for minutes past the hour you use the accusative 1.15 "quarter past one": "biri ceyrek" 11.05 "five past eleven": "on biri bes"
The tips and notes are quite helpful for this session: https://www.duolingo.com/skill/tr/What-time-is-it%3F/tips-and-notes
ZandraL.Le, i find in my note-book the explanations of Ektoraskan, in lesson 2, level 2, very clear, who gave 4 examples: 2 for a time between One o clock and 1h30 and two for time between one thirty and Two o clock. Firstly: "BIRI on geçiyor"=IT IS ten PAST one and "BIRI on gece"="AT ten PAST one", "bir" with the accusative case ending "i". Let see the two examples with "BIRE": "BIRE on var"="IT IS ten TO one" and "BIRE on kala"=AT ten TO one" , "bir" with the dative case suffix "e".