"The little girl plays on the big drum."
Translation:Das kleine Mädchen spielt auf der großen Trommel.
Attributive adjectives, i.e. those in front of the nouns they refer to, always get a proper ending/declension. It would be klein without an ending only if it would be a predicative adjective, that is an adjective connected by verb like ist/sind/wird, for example "Das Mädchen ist klein und spielt auf der Trommel, die groß ist". Regardless of the gender der/die/das.
I should have learned this already but I'm still confused. Why is it 'kleine' and 'grossen'?
Have a look here: https://deutsch.lingolia.com/en/grammar/adjectives/declension
Das kleine Mädchen is the subject of the phrase, so it's in the nominative case, while "die große Trommel"(nominative) becomes an object in the dative case (due to the usage with "spielen auf") and turns to "auf der großen Trommel".