When you need to tell someone the time, German gives you two options: a formal, digital-clock style, as in Es ist vierzehn Uhr dreißig (14:30), and a more conversational everyday style built from the words halb (half), Viertel (quarter), nach (past), and vor (to).
Here lies the biggest trap for many learners. In some languages, saying "three and a half" means the third hour has already passed and you're adding another half hour on top — 3:30, counting forward from the hour that just ended. German thinks the opposite way: halb drei does not mean half past three, it means halfway toward three — so halb drei equals 2:30, not 3:30! German always looks ahead to the coming hour and measures the distance toward it, rather than counting from the hour just finished. To avoid the trap, use this trick: whenever you hear halb with a number, subtract one from that number to get the real time — halb vier means 3:30, and halb neun means 8:30.
Viertel is more straightforward: Viertel nach drei means 3:15 (a quarter past three), and Viertel vor vier means 3:45 (a quarter to four) — just like saying "quarter to four" in English.
The second focus of this lesson is how prepositions attach to time expressions. Many languages use one all-purpose preposition for everything — on Monday, in January, at nine o'clock — but German distinguishes carefully by the type of time unit: am is used with days of the week and dates, as in am Montag and am 15. März; im is used with months and seasons, as in im Januar and im Sommer; and um is used exclusively with a clock time, as in um neun Uhr and um halb zehn. These three are never interchangeable, and this is a fixed rule to memorize rather than something you can guess by translating.
The most common mistake is reading halb the intuitive way, as "half past," assuming halb drei means 3:30 when it actually means 2:30 — a mix-up that can genuinely cause missed appointments, so repeat the rule until it becomes automatic.