"We are in the big restaurant."
Translation:Wir sind in dem großen Restaurant.
From Wiktionary (https://en.wiktionary.org/wiki/im#German): "... im is usually not applicable when the definite article has an indicative function. This includes contexts in which English would use a demonstrative pronoun (“this” or “that”) but also some others."
So I guess the original sentence is "Wir sind in dem großen Restaurant", which can be translated as "We are in the big restaurant" ("over here") or "We are in that big restaurant". Here just the former translation is used.
"Wir" is the subject of the sentence and so "wir" is the nominative case. "sind" is the verb and has no case. "im Restaurant" or "in dem großen Restaurant" is in dative.
As long as you have a sentence with the verb "sein"(to be) without any preposition or other verb, then the case is nominative for all words. Here you have the preposition "in". "in" can lead to accusative or dative (Wechselpreposition). The sentence does not describe a movement --> dative: Wir sind in dem großen Restaurant. Wir sitzen in dem großen Restaurant. With movement we use accusative: Wir gehen in das große Restaurant.
In case we walk around in the restaurant, we use dative because there is no movement in relation to the restaurant. We stay in the restaurant = no movement. --> Wir gehen in dem großen Restaurant.
ok, so is it right that, the sentence is in "Dative", ~ yes and no. The sentence contains "in dem Restaurant" and "dem Restaurant" is dative. A sentence does not get one case, but some words of a sentence get cases.
A short visualization: Ich gebe dem Opa den Wein. (I give [the] grandpa the wine.) "Ich" is in nominative. "dem Opa" is in dative. "den Wein" is in accusative. Both words "Wein and "Opa" are masculine words in German.
..., therefore we use "grossen", ~ We use "großen" because of Dative - right. :-) You will need to have a look to grammar tables. There are more facts than only the case and the word gender which rule the endings of the adjectives and articles. Have a look there: https://en.wikipedia.org/wiki/German_adjectives
but "restaurant" is  neuter, ~ yes, it is.
--> so the neuter article "das" turns to "dem" in dative.
Yes, you have to conjugate the adjective based on the noun's grammatical gender and the case in use. Restaurant is a neuter noun (das Restaurant) and so "großes Restaurant" in nominative becomes großen Restaurant in dative. If the adjective comes later (The restaurant is big), the adjective remains in its original form (Das Restaurant ist groß).
Has the weak vs strong inflection been taught on Duo till this stage? I don't get it from the comments below. Großen can either be Male>Akkusativ or Dativ>Plural, in this case it appears to be neither with someone below commenting "Dativ>weak inflection" (I don't get the weak part).