You don't have to apologise! It's great that you checked because there might be other people with the same question.
Here is a bit more information on words ending in -chen. In German, you can make diminutives by adding -chen to a noun. So for instance, you can take 'der Mann' (the man) and turn it into 'das Männchen' (the little man). But you aren't just adding the -chen. You also need to add an umlaut for a change in sound: Baum > Bäumchen, Haus > Häuschen, Hahn > Hähnchen. Words ending in -chen are either neuter or plural.
The meaning of Mädchen is a bit of an exception. Its origin lies in Magd, but Mädchen is now the standard word for girl. Hope that helped.
Of course, I am trying to say that: when you change the definite or indefinite article, you follow those rules of these cases: accusative, dative, nominative; so far that I learned. So, if you say "Dem Mädchen spielt mit die Katze" you know that who is the predicate and, the subject, right? or in other case you know who is suffering the action and who is doing the action, got it?
If you want to say that there is only one of them you can say that the word is "singular". When there are more than one, the noun is "plural". "Katze" is a singular female noun which is why it receives the definite article "die" in Nominative and Accusative. The plural noun is "Katzen".
Die Katze > the cat; die Katzen > the cats.
Das Mädchen > the girl; die Mädchen > the girls.
Why "dem" and not "den"?
The previous question was, "The Jungen rennen mit den Madchen." This question is "Die Katze spielt mit dem Madchen."
Both sentences contain a verb and then the dative "mit" followed by an accusative pronoun… so what then is the difference between "den" and "dem"?
So confused! :(
Simply memorizing the most common ACCUSATIVE (Direct Object) prepositions (bis, durch, für, gegen, ohne, um), alerts that the Direct Object article will always change to the respective Accusative case: DER becomes DEN, DIE (feminine)remains DIE, DAS (neut.) remains DAS, and DIE (plural) remains DIE.
Similarly, the most common Dative (Indirect Objects) propositions (aus, außer, bei, mit, nach, seit, von, zu) shows that the Indirect Object (receiver of the action) article will always change to the Dative case: DER becomes DEM, DIE (fem) becomes DER, DAS (neut) becomes DEM, and DIE (pl) will ALWAYS be DEN regardless of the gender of the Indirect Object.
Finally, the "Doubtful Prepositions" (don't worry about these yet) can change cases depending upon whether there is movement or not, ("Place where"(DATIVE), or ("Place which"(ACCUSATIVE). Taking a few minutes learning the prepositions will make this MUCH easier! Viel Glück!