Translation:I am at the table with the lunch.
No, it is not at all common in English. Obviously a non-native English speaker translated it--all too common on Duolingo.
Yes, I knew immediately what this meant. Clearly you folks have never traveled with mulitiple Morris teams distributed between lots of little cars (as one does at a Morris ale when moving from stand to stand).
This is clearly lunchtime at a stand (a site at which one dances) at a public park. All the cars have come in through different entrances, and the only person who knows what is happening with lunch is Natalie, who very likely got there before us all with the lunch. So we call her up on someone's cell phone, and she says "Ich bin am Tisch mit dem Mittagessen," and then explains where that is.
Only problem is, I don't think Natalie knows German.
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"I am at the lunch table", doesn't give the information that you have the lunch. You might just be at the table. But, the sentence, "I am at the table with the lunch." Gives the information that you have the lunch with you. Moreover, the given sentence doesn't specifically say that it's a lunch table, it could be any table.
"With the lunch" is not considered to be time, manner nor place. This is a physical item that is with the person "at the table" which is the place and the place must go first. Say you had the plate of pasta and you are at the table and want everyone to come and eat now. "I am at the table with the lunch." We are not talking here about "going to lunch" or "at lunchtime".
Yes, there are many prepositions that take Dative Case for their objects. There are two prepositional phrases here that both take Dative. Someone gave us this song to learn the prepositions that always require Dative.: http://www.deutsch-leichter.de/dativ.mp3 http://german.about.com/library/blcase_dat2.htm
I get the frequently made point that these sentences are slightly eccentric now and again in order to challenge us to translate what's there rather than what we think should be there - but this is just irritating; I'm bound to try to 'correct' sentences that simply have no meaning whatsoever - like this one - and getting marked wrong for giving an answer that's plainly much better than the required answer is a pain in the a**e. Just for the record.
"I'm at the table having lunch" was not accepted. This is one way (of many) we would say it here in UK. I'm at the table with lunch does not sound natural though it's meaning is clear. Please Duo, it is time for someone to read over 'the report it' comments and take action. This level is hard enough to get through without unnecessary obstacles thrown in our path.
As others have pointed out, this only makes sense unless in a very very specific case. Even then, it would make more sense to say "I am at the table that has the lunch." or "I am at the table with the food." Or "I am at the table and I have brought the lunch." There are many ways that are more natural to an english speaker. If it is for a very specific case then it has very little real world value to those who are learning. Please fix Duo.