Learn Hardcore Russian: После третьего урока у нас длинная перемена, и мы выходим во двор. - After the third lesson we have a long break, and we go out into the yard.

третий урок is nominative (dictionary form).
After после, both the numeral and the noun must be in the genitive:
- третий → третьего
- урок → урока

So you get после третьего урока = after the third lesson.

How does третий change to третьего? What is going on grammatically?

Третий is an ordinal numeral and behaves like an adjective. It must agree with the noun in:

gender
number
case

Here:

урок is masculine, singular, genitive.
So третий must also be masculine, singular, genitive → третьего.

Pattern (masculine singular):

Nominative: третий урок
Genitive: третьего урока
Dative: третьему уроку
Accusative: третий урок
Instrumental: третьим уроком
Prepositional: о третьем уроке

Stress stays on the first syllable: ТРЕТЬего.

What does у нас mean here? Why does it mean we have?

Russian often expresses possession with the structure:

у + person (in genitive) + есть / implied есть + thing

Literally it means at / by someone there is something, but it is translated as someone has something.

Examples:

У нас длинная перемена. = We have a long break.
У меня есть книга. = I have a book.
У него завтра экзамен. = He has an exam tomorrow.

In this sentence, у нас = we have in a school schedule context.

What exactly is перемена? How is it different from перерыв?

Both can translate as break, but usage is different:

перемена
- Typical school word.
- Means the break between lessons.
- Strong association with children, school timetable.
- Example: На большой перемене мы идём в столовую.
перерыв
- More general: break, pause, interruption.
- Used for work breaks, meeting breaks, coffee breaks, etc.
- Example: У меня перерыв с двух до трёх.

In a school context, between lessons, перемена is the natural choice.

Why is it длинная перемена and not долгая перемена? Aren’t both “long”?

Both длинный and долгий can translate as long, but their main uses differ:

длинный – about physical length or duration measured in relation to a typical length:
- длинная дорога – a long road
- длинная перемена – a long break (compared to the short ones)
долгий – about duration in time, often with a feeling of it being lengthy, drawn-out:
- долгий разговор – a long (lengthy) conversation
- долгое ожидание – a long wait

For school breaks, Russians very naturally say длинная перемена (a “long” break compared to the usual short ones). Долгая перемена is possible, but sounds less idiomatic in this fixed school phrase.

Why is there a comma before и: …длинная перемена, и мы выходим…?

In Russian, you normally put a comma before и if it connects two independent clauses, each with its own subject and verb.

Here we have:

После третьего урока у нас длинная перемена.
Subject: (implied) we / our class; Predicate: у нас длинная перемена.
Мы выходим во двор.
Subject: мы; Predicate: выходим во двор.

They are two separate sentences joined by и, so Russian punctuation requires a comma before и:
…длинная перемена, и мы выходим во двор.

Why is выходим in the present tense when in English we might say “we go out” or “we go out after the third lesson”?

Russian present tense is often used for:

regular, repeated actions (habitual actions)

So мы выходим во двор here means:

we (usually / always) go out into the yard (at that time)

It describes what typically happens every day after the third lesson. English also sometimes uses present simple this way (we go out into the yard), so the usage is parallel: habitual present, not “right now.”

Why use выходим and not идём? Both seem to mean “go”.

Both verbs involve movement, but the focus is different:

идти / ходить – to go, to walk (movement itself)
- Мы идём во двор. = We are going / we walk to the yard.
выходить / выйти – to go out, come out (movement from inside to outside)
- Мы выходим во двор. = We go / step out into the yard.

In a school context, after a lesson you go out of the classroom/building into the yard, so выходим (во двор) is more precise: it highlights leaving inside space to the outside.

What case is во двор, and why is it used here?

Двор is masculine.

Nominative: двор (yard)
Accusative: двор
Prepositional: во дворе (in the yard – location)

After verbs of motion with a destination (go to, come into), Russian uses the accusative case:

во двор – into the yard (direction / movement to)
во дворе – in the yard (location / where)

Here we have movement to a place, so во двор (accusative, direction) is correct: мы выходим во двор = we go out into the yard.

Why во двор, not в двор?

Russian uses во instead of в mainly for phonetic reasons – to make pronunciation easier and more natural.

Rules of thumb:

во is used before many words starting with:
- в (e.g. во власть, во время)
- some consonant clusters where в
  - consonant is hard to pronounce

In в двор, you would have дв right after в, giving three consonants in a row and sounding awkward. Во двор is smoother and is the standard, idiomatic form.

Could I change the word order, for example say У нас после третьего урока длинная перемена? Is that correct?

Yes, you can change the word order; Russian is flexible. All of these are grammatical:

После третьего урока у нас длинная перемена.
У нас после третьего урока длинная перемена.

The meaning is almost the same: After the third lesson we have a long break.

Nuances (very slight):

Starting with После третьего урока emphasizes the time (“After the third lesson…”).
Starting with У нас emphasizes who has that break (“We have a long break after the third lesson”).

Both sound natural in spoken and written Russian.

What exactly does урок mean here? Is it “lesson”, “class”, or “lecture”?

Урок in a school context usually corresponds to:

a lesson / a class period in a school timetable.

So:

третий урок – the third period / the third class of the day.

Typical usage:

У нас сегодня шесть уроков. – We have six classes today.
На первом уроке у нас математика. – In the first period we have math.

In universities, people more often say занятие or лекция for classes, but урок is the standard word for school lessons.