"Das Mädchen mag deinen Schuh."
Translation:The girl likes your shoe.
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No, it's not normal in German. As you said, in most real-life situations, you would use the plural. The sentence is grammatically correct though and - theoretically - there might be situations in which you would use the singular. E.g. if a little girl is playing with one of your shoes.
Thanks for your answer. One of the shortcomings of Duo is using grammatically correct learning sentences which are not very plausible. If it takes a exaggerated hypothetical situation to justify its usage, then it would be better to use a more reasonable construction. Like, in this case, Jacke, Mantel, Hemd, Haus, etc. Or, using the plural.
Like the articles, the possessive determiners (my, your, his, etc.) agree in gender/number (masculine, feminine, neuter OR plural) and case with the noun they refer to. In this sentence, "your" refers to "shoe" (Schuh), which is:
2) accusative (it's the direct object and almost all direct objects are in the accusative case)
The ending for masculine accusative possessive determiners is -en: deinen. See this table (it's for "my", but the endings are the same):