Translation:The white hat is not for my grandmother.
I think that the idea of register applies here. That one can speak or write with various levels of formality, ranging from being very formal to extremely informal. I think that DuoLingo tries to keep us somewhere in between, so that we can be easily understood by everyone, but at the same time, learning and developing informal speech. If they really wanted us to learn a lot of informal expressions, we might take longer to absorb the material, since these expressions can be unclear for the beginner. And it is a two way street- if the Italian is a semi-formal register, then the English translation should also be, meaning that words like granny, daddy, sonny, mommy, auntie, and such would not be allowed.
In England we also use gran, nan, and sometimes nanna which is very close to the Italian nonna. For grandfather we usually use grandad. Granddaughters or very young children affectionately use grandaddie.
Having English as my first language but being of Italian descent, it feels really odd to translate 'Nonna'. My nonna is my nonna! I understand it would be different for people of different backgrounds though.
Why is it not "la mia nonna" for the "my" part rather than "mia nonna" without the definite article "la" ?
For singular family members, the definite article is not required in a possessive statement.
Perfect answer. But it should be expanded a little to what constitutes 'a family member.' e.g. step-daughter, father-in-law etc (ecc)