Kennarinn metur svarið.

Because Icelandic usually adds the definite article to the end of the noun instead of using a separate word like English the.

• kennari = teacher
• kennarinn = the teacher

The ending -inn here is the masculine singular definite article in the nominative.

For the same reason: Icelandic is using the suffixed definite article.

• svar = answer
• svarið = the answer

The ending -ið is the definite article for a neuter singular noun like svar.

The dictionary forms are:

• kennari = teacher
• svar = answer

When you look words up, you normally search for the indefinite singular form, not the form with the attached article.

Metur comes from the verb meta, which means to assess, evaluate, judge, mark depending on context.

In this sentence:

• meta = dictionary form, to assess
• metur = assesses / evaluates (present tense, third person singular)

So Kennarinn metur svarið means that the teacher assesses the answer.

Because meta is the infinitive, while metur is the conjugated present-tense form used with he/she/it or a singular noun.

Here the subject is kennarinn = the teacher, which is third person singular, so the verb is:

• ég met = I assess
• þú metur = you assess
• hann/hún/það metur = he/she/it assesses

So kennarinn metur = the teacher assesses.

• Kennarinn is the subject: the one doing the action.
• Svarið is the object: the thing being assessed.

So:

• Kennarinn = the teacher
• metur = assesses
• svarið = the answer

This follows the very common Icelandic word order subject + verb + object.

Kennarinn is in the nominative case, because it is the subject of the sentence.

The nominative is the case typically used for the doer of the action.

It is the accusative object of the verb meta.

A useful detail: for the neuter noun svar, the nominative singular definite and accusative singular definite are both svarið. So even though it is functioning as an accusative object here, the form looks the same as nominative.

That is very common with neuter nouns in Icelandic.

You know from the sentence structure and from the verb’s meaning.

In Kennarinn metur svarið:

• kennarinn comes first and is the natural subject
• metur is a transitive verb here, so it takes an object
• svarið is what gets assessed, so it is the object

Even though the form svarið could also be nominative, in this sentence its role is clearly object.

Yes. This is the most straightforward neutral word order:

• Kennarinn — subject
• metur — verb
• svarið — object

So it matches normal English order quite closely here.

Icelandic can move elements around more than English can, but this sentence is plain and standard.

Not as a normal neutral sentence meaning the same thing.

Icelandic does allow fronting, but main clauses follow a verb-second pattern, so if you move the object to the front, the verb normally comes next:

• Svarið metur kennarinn.

That kind of order is possible only in special contexts and sounds marked. It would usually emphasize the answer.

For a beginner, the safest pattern is the one in your sentence:

• Kennarinn metur svarið.

Usually the definite article is attached to the noun, as in this sentence:

• kennarinn = the teacher
• svarið = the answer

There is also a separate demonstrative/article-like word hinn, but that is used in more special or formal situations. In ordinary sentences like this one, the suffixed article is the normal choice.

You would remove the suffixed article endings:

• Kennari metur svar.

That means A teacher assesses an answer or Teacher assesses answer, depending on context.

Compare:

• kennari = a teacher
• kennarinn = the teacher
• svar = an answer
• svarið = the answer

A rough English-friendly guide would be something like:

• Kennarinn ≈ KYEN-na-rin
• metur ≈ MEH-tur
• svarið ≈ SVA-rið

A few useful notes:

• kk in kennari is pronounced with a strong k sound.
• e in metur is like e in bet.
• sv at the start of svarið is pronounced together.
• ð is a soft sound like th in this, though at the end of words it can be weaker.

Not always. Meta is broader than just school grading.

Depending on context, it can mean:

• assess
• evaluate
• judge
• estimate
• sometimes grade/mark

So in a classroom sentence like this, assesses or evaluates is often a very good translation.