Translation:Yesterday this girl was not at school.
Even better would be just having a skill called "past tense" or any appropriate version thereof. Including different tenses like this into exercises, when we've only been taught in present tense so far, is VERY bad course design.
Strongly disagree. This is how children learn a language: randomly. It's up to the learner to mentally organize accordingly.
Why is this not Девочки in genitive but Девочка? I thought that when X is/was not at Y, it needs genitive. As in another example sentence in this course: Меня вчера тут не было, and not Я вчера тут не был.
So are both nominative and genitive possible in sentences like these? I also noticed that if it's genitive, был/была became neutr. было regardless the actual gender. Correct?
Yes, exactly. If you switch to the Genitive structure of "absence", the agreement will be neuter regardless of the "subject". In both Russian and English "to be" is a curious verb because it can mean mere presence—but can also mean a more active "visiting", "going", "attendance". This use is somewhat more pronounced in Russian.
The Genitive use focuses more on absence thus being a bit more passive—the emphasis is on a person not being at that place rather that choosing not to or going to a different place. The Nominative structure focuses on the active action. Sometimes the implied meaning can change more than a little. Here is a glaring example:
- Там никого не было. = Nobody was there (the place was empty; maybe the people you expected did not come).
- Там никто не был. = Nobody was/has been there (no one has ever been to that place)
The agreement is also neuter for some uses with numbers, especially if these are objects ("There were 3 chairs in the room"). For people it depends on whether you want the action to be perceived as passive and "combined" rather than active an separate.
- В комнате было два окна/пять диванов. ~ The room had two windows/five settees. (были два окна would sound really odd)
- Тест сдавали сорок студентов. = 40 students took the test (a bit of an emphasis on their actively writing a test, each on their own).
- На лекцию пришло сорок студентов. = 40 students came to the lecture (the speaker is more concerned with the number than the action of "coming")
- Персонажей озвучивали двадцать актёров. = 20 actors provided voices for the characters (probably, each character only had one voice talent assigned, so clumping them all together with the neuter "озвучивало" would feel more than a bit confusing)
We do not explore it in detail, just be aware than you are going to encounter such combinations in Russian. It all boils down to the fact that the combination of a number and a noun cannot be easily assigned a grammatical number in Russian (in fact, numerals do not have a grammatical number), so the agreement is a handful of tricks that cover all uses you might ever need.