Learn Hardcore Norwegian: I dag gjør vi lekser fra norsktimen. - Today we do homework from the Norwegian lesson.

Norwegian main clauses usually follow the verb-second rule (V2): the finite verb (here: gjør) comes in the second position in the sentence, no matter what comes first.

I dag gjør vi lekser fra norsktimen.
1st element: I dag
2nd element: gjør (verb)
3rd element: vi (subject)

You can absolutely say:

Vi gjør lekser i dag fra norsktimen.
Vi gjør lekser fra norsktimen i dag.

These are also correct. Putting I dag first simply emphasizes today (the time) more strongly. All versions are grammatical; the nuance is about what you want to highlight.

What exactly does gjør mean here? Why not a verb that directly means do homework?

Gjør is the present tense of å gjøre (to do / to make). In Norwegian, just like in English, you do homework; you do not normally read homework or have homework when you mean to work on it.

So:

å gjøre lekser = to do homework
I dag gjør vi lekser = Today we are doing homework.

It is a fixed, idiomatic combination: gjøre lekser is the natural expression for doing homework in Norwegian.

The English meaning is Today we are doing homework… but the Norwegian is just gjør. How does Norwegian express the -ing form?

Norwegian usually does not have a separate continuous/progressive tense like English am doing / are doing.

vi gjør lekser can mean:
- we do homework (in general), or
- we are doing homework (right now / today), depending on context.

In I dag gjør vi lekser fra norsktimen, the time expression I dag makes it clear that it is about what is happening today, so in natural English you translate it as Today we are doing homework from the Norwegian lesson.

Why is it lekser (plural) and not lekse (singular)? Isn’t homework uncountable in English?

In Norwegian, lekse (singular) / lekser (plural) is typically used in the plural when meaning school homework:

Jeg gjør lekser. = I am doing homework.
Har du gjort leksene dine? = Have you done your homework?

En lekse is more like a single homework task or lesson, but in normal school talk lekser (plural) is the standard way to talk about homework as a whole.

So even though English uses uncountable homework, Norwegian uses plural lekser.

Why is there no article before lekser? Why not gjør vi noen lekser or gjør vi leksene?

Bare plural lekser (without article) is used in a general sense: doing homework, not referring to a specific set.

Vi gjør lekser. = We are doing homework (in general).

If you mean specific homework previously mentioned or understood from context, you use the definite plural:

Vi gjør leksene. = We are doing the homework (the specific assignments we have).

Noen lekser (= some homework assignments) is possible but sounds more like an emphasis on some rather than all:

Vi gjør noen lekser i kveld, og resten i morgen.
We will do some homework tonight, and the rest tomorrow.

In your sentence, the focus is just on doing homework today, so lekser without article is normal and natural.

Why is it fra norsktimen and not i norsktimen?

The preposition changes the meaning:

fra norsktimen = from the Norwegian class / lesson
→ the homework comes from that class (it was assigned there).
i norsktimen = in the Norwegian class / lesson
→ something happens during the class.

Your sentence:

I dag gjør vi lekser fra norsktimen.
= Today we are doing homework from the Norwegian class.
(Homework that was given in that class.)

If you said:

I dag gjør vi lekser i norsktimen.
= Today we are doing homework in the Norwegian class.
(We are sitting in the Norwegian lesson and doing homework there.)

So fra indicates origin/source, i indicates location/time.

What exactly is norsktimen made of? Why is it one word and why the ending -en?

Norsktimen is a compound noun + definite ending:

norsk = Norwegian (language / subject)
time = lesson, class, hour (here: a school lesson)
norsktime = Norwegian class / Norwegian lesson
norsktimen = the Norwegian class / the Norwegian lesson

In Norwegian, compounds are almost always written as one word:

norsk + time → norsktime
In definite singular, time → timen, so: norsktimen.

The -en at the end is the definite singular article for masculine nouns: en time → timen.

Why is norsktimen not capitalized, while Norwegian in English would be?

In Norwegian:

Language and nationality words (norsk, engelsk, tysk) are not capitalized.
School subjects formed from them are also lowercase.

So:

norsk (the language)
norsktime / norsktimen (Norwegian class / the Norwegian class)

In English you write Norwegian with a capital N, but in Norwegian you write norsk, norsktime, norsktimen with a lowercase n.

Could the word order be I dag vi gjør lekser fra norsktimen?

No, that word order is incorrect in standard Norwegian.

Because of the verb-second rule, after I dag the finite verb must come next:

I dag gjør vi lekser fra norsktimen. ✅
I dag vi gjør lekser fra norsktimen. ❌ (verb in 3rd position)

The subject vi must come after the verb when something else (like I dag) comes first.

How do you pronounce gjør and what sound is ø?

Gjør is pronounced approximately like [jyør] in many accents:

gj-: often just a y-like sound [j] in this word.
ø: a rounded front vowel, somewhere between e in bed and u in burn, but with rounded lips.
r: a trilled or tapped r, depending on dialect.

So a rough English approximation is “yur” but with rounded lips on the vowel.