While the Perfekt dominates spoken German for most verbs, the Präteritum is essential in writing and is actually preferred in speech for a small group of very common verbs. The auxiliaries sein and haben are almost always in the Präteritum: ich war, er war and ich hatte, er hatte. The same applies to the modal verbs: ich konnte, ich musste, ich sollte, ich wollte, ich durfte. Saying Ich bin müde gewesen or Ich habe nicht gekonnt sounds unnatural; Ich war müde and Ich konnte nicht are the standard forms. This is why learners should drill these Präteritum forms first.
Beyond the auxiliaries and modals, several strong verbs also have stem-vowel changes in the Präteritum that must be memorized individually. Common patterns include: gehen → ging, kommen → kam, geben → gab, finden → fand, wissen → wusste, and denken → dachte. The Präteritum of wissen is especially useful because it differs sharply from its present tense: ich weiß (present) versus ich wusste (past). Building a strong mental list of these frequent strong-verb stems is one of the most efficient ways to improve both written and spoken fluency at B1.
The Präteritum is the tense of narration, biographies, news reports, and formal storytelling. Whenever you want to describe a sequence of past events smoothly, as in Er ging nach Hause, und dann kam seine Schwester, the Präteritum is the right choice. Combined with the Konjunktiv II forms you have already learned, it also unlocks more elegant hypothetical constructions: Wenn ich Zeit gehabt hätte, wäre ich ins Kino gegangen. Treating Präteritum as the "written and narrative past" and Perfekt as the "spoken past" (except for the high-frequency verbs above) is a reliable strategy.