Learn Hardcore Russian: Я считаю этот урок интересным.

To count (do arithmetic):
- Я считаю деньги. – I am counting the money.
To consider / to regard / to think of something as:
- Я считаю этот урок интересным. – I consider this lesson (to be) interesting.

In your sentence it has the second meaning: you are expressing an opinion/judgment about the lesson, not doing math.

Why is этот урок in the accusative case?

Этот урок is in the accusative because it is the direct object of the verb считать in the meaning “to consider.”

Structure:

Я – subject (nominative)
считаю – verb
этот урок – direct object (accusative)
интересным – what you consider the object to be (predicate in instrumental)

This pattern is standard:

Я считаю его хорошим учителем. – I consider him a good teacher.
- его – accusative (object)
- хорошим учителем – instrumental (what you consider him to be)

Why is it интересным and not интересный?

Because after считать (in the meaning “to consider”) Russian normally uses the instrumental case for the thing you consider someone/something to be.

Pattern:

Я считаю [кого? что?] [кем? чем?]
- Object – accusative
- Predicative (adjective or noun) – instrumental

So:

урок – masculine, singular
Instrumental singular masculine adjective ending is -ым / -им
интересный → интересным (masc. sg. instrumental)

Other examples:

Я считаю этот фильм скучным. – I consider this film boring.
Мы считаем её талантливой. – We consider her talented.
Они считают его своим другом. – They consider him their friend.

Using интересный (nominative) here would be wrong in standard Russian.

What is the grammatical pattern of this whole sentence?

The pattern is:

[Subject (Nom)] + считать + [Object (Acc)] + [Predicative (Instr)]

Applied to your sentence:

Я – subject, nominative
считаю – verb
этот урок – object, accusative
интересным – predicative, instrumental (adjective describing the object)

Meaning: “I consider this lesson (to be) interesting.”

Could I say Я считаю, что этот урок интересный instead? What’s the difference?

Yes, you can say:

Я считаю, что этот урок интересный.

This is also correct and natural. The difference is:

Я считаю этот урок интересным.
- More compact, a bit more formal / “bookish.”
- Uses the object + instrumental construction.
- Feels like a clear evaluation: I regard this lesson as interesting.
Я считаю, что этот урок интересный.
- Literally: I think that this lesson is interesting.
- Uses a subordinate clause with что.
- Very close in meaning to English I think that…
- Slightly more conversational / neutral.

Both express an opinion. In many contexts they are interchangeable.

Why is there no word for “is” (like “is interesting”) in Russian?

In Russian, in the present tense, the verb “to be” (быть) is usually omitted:

Этот урок интересный. – This lesson is interesting.
(Literally: This lesson interesting. No explicit “is.”)

You only see forms of быть:

in the past: был, была, было, были
in the future: буду, будешь, будет…
in some special constructions, for emphasis, etc.

So when you say:

Я считаю, что этот урок интересный,
the “is” is understood but not spoken.

Can I change the word order? For example, Этот урок я считаю интересным or Я считаю интересным этот урок?

Yes, Russian word order is flexible, and both of these are possible:

Этот урок я считаю интересным.
- Emphasis on этот урок (“This lesson, I consider (it) interesting”).
- Often used when contrasting with other lessons:
  - Этот урок я считаю интересным, а тот — скучным.
Я считаю интересным этот урок.
- Grammatically possible, but less neutral and more “stylistic.”
- The focus shifts slightly to интересным, then clarifies what you consider interesting: этот урок.

The most neutral order is still:

Я считаю этот урок интересным.

Is считать here more like “to think” or more like “to consider/regard”? Could I just use думать?

Считать here is closer to “to consider / to regard”—it suggests a judgment or evaluation, not just any random thought.

Compare:

Я думаю, что этот урок интересный.
- I think this lesson is interesting. (neutral opinion)
Я считаю этот урок интересным.
- I consider this lesson (to be) interesting.
- Slightly more evaluative or confident, sometimes with a shade of “this is my considered opinion.”

Both will be understood as an opinion; the nuance is subtle. Думать is broader (“to think”), while считать is often used for evaluated opinions.

Can I use a noun instead of an adjective after считать in the same way?

Yes. The same pattern works with nouns, and the noun will also be in the instrumental:

Я считаю его другом. – I consider him (to be) a friend.
Они считают это ошибкой. – They consider this (to be) a mistake.
Мы считаем её хорошим специалистом. – We consider her a good specialist.

Pattern is the same:

[Object (Acc)] + [Noun/Adj in Instrumental]

Can I replace этот урок with a pronoun? How would that look?

Yes. If the lesson is already known from context, you can say:

Я считаю его интересным. – I consider it interesting.
- его – masculine singular pronoun, accusative (refers back to урок)
- интересным – still instrumental, agreeing in gender/number/case with the implied урок.

The grammar of the predicate интересным doesn’t change; only the object (этот урок → его) changes.