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German prepositions are notoriously slippery: some always take one case, the two-way prepositions take either, and many have meanings that don't map cleanly to English. The free games here practice the prepositions with a fixed case, where the preposition alone decides between accusative and dative. Two-way prepositions need a complete sentence, so they are explained below rather than drilled in the games.
Fixed accusative: durch, für, gegen, ohne, um. Fixed dative: aus, bei, mit, nach, seit, von, zu. Two-way (Wechselpräpositionen): an, auf, hinter, in, neben, über, unter, vor, zwischen - accusative when the phrase answers Wohin? (a change of location: ich gehe in die Küche), dative when it answers Wo? (a location: ich bin in der Küche). Movement alone is not the test - Ich laufe im Park takes the dative because the park is where the running happens. Genitive (mostly formal): während, trotz, wegen, statt.
Prepositions are hard to learn from a chart alone because so many uses are idiomatic. What tends to work best is high-volume contextual exposure, which the game format above compresses into a few minutes a day.
The fixed-accusative prepositions are durch, für, gegen, ohne, um (memorise as DOGFU or 'durch-für-gegen-ohne-um'). They consistently take the accusative.
The fixed-dative prepositions are aus, bei, mit, nach, seit, von, zu (often memorised as 'aus-bei-mit-nach-seit-von-zu'). They consistently take the dative.
Nine prepositions - an, auf, hinter, in, neben, über, unter, vor, zwischen - take the accusative when the phrase answers Wohin? and describes a change of location (ich gehe in die Küche), and the dative when it answers Wo? and describes a location (ich bin in der Küche, ich laufe im Park). You need the whole sentence to decide, not the preposition on its own.