Kennarinn sýnir okkur þolfall á töflunni.

Because -inn is the definite article attached to the end of the noun.

• kennari = teacher
• kennarinn = the teacher

Icelandic usually puts the at the end of the noun instead of using a separate word like English does.

So:

• kennari = a teacher / teacher
• kennarinn = the teacher

In this sentence, kennarinn is the subject.

Sýnir is the present tense, 3rd person singular form of the verb að sýna.

The subject is kennarinn = the teacher, which is he/she in grammatical terms, so Icelandic uses the matching verb form:

• að sýna = to show
• ég sýni = I show
• þú sýnir = you show
• hann/hún sýnir = he/she shows

So Kennarinn sýnir... means The teacher shows...

Because okkur is the correct case form of we/us here.

• við = we (subject form, nominative)
• okkur = us (dative/accusative-related object form, depending on the verb)

The verb að sýna usually works with:

• someone in the dative
• something in the accusative

So the pattern is:

að sýna einhverjum eitthvað
= to show someone something

That is why:

• okkur = to us / us
• þolfall = the thing being shown

It is dative.

The verb að sýna commonly takes:

• the person receiving the information in the dative
• the thing shown in the accusative

So in:

Kennarinn sýnir okkur þolfall á töflunni.

• kennarinn = subject, nominative
• okkur = indirect object, dative
• þolfall = direct object, accusative

This is a very useful pattern to remember:

sýna einhverjum eitthvað
= show someone something

Þolfall is the noun meaning accusative case.

So the sentence is talking about grammar: the teacher is showing the accusative.

A learner might notice something funny here: þolfall is itself in the sentence as a noun, and at the same time it names the accusative case.

In this sentence, þolfall is the direct object of sýnir, so grammatically it is in the accusative as well. Since þolfall is a neuter noun, the nominative and accusative singular forms are the same, so you do not see any change.

Because it is being used in a general, subject-name sense, like talking about a concept.

Compare English:

• The teacher is showing us the accusative on the board.
• The teacher is showing us accusative on the board.

English strongly prefers the accusative, but Icelandic often uses case names and school-subject terms without the definite article, especially when speaking generally.

So þolfall here means the grammatical topic accusative case, not necessarily one specific physical thing.

Because á takes different cases depending on whether there is location or motion.

• á + dative = on something, location
• á + accusative = onto something, motion toward a surface

Here the meaning is on the board, a static location, so Icelandic uses the dative:

• á töflunni = on the board

If there were motion, you could get:

• skrifa á töfluna = write onto the board

So this sentence uses dative because the teacher is showing something on the board, not moving it onto the board.

Because it is:

1. in the dative singular
2. definite = the board

The base noun is:

• tafla = board

In this sentence, after á with location, it must be dative singular, and with the definite article attached it becomes:

• töflunni = the board in dative singular

So:

• tafla = a board
• á töflu = on a board
• á töflunni = on the board

The vowel change from a to ö is part of the noun’s inflection.

The basic order here is:

Subject – Verb – Indirect Object – Direct Object – Prepositional Phrase

So:

• Kennarinn = subject
• sýnir = verb
• okkur = indirect object
• þolfall = direct object
• á töflunni = prepositional phrase

That gives:

Kennarinn sýnir okkur þolfall á töflunni.

This is a very natural and straightforward Icelandic sentence order.

Yes, Icelandic word order is somewhat flexible, but the verb usually stays in the second position in main clauses.

For example, you could move á töflunni to the front for emphasis:

Á töflunni sýnir kennarinn okkur þolfall.

This still means essentially the same thing, but now the sentence starts with On the board. Because Icelandic is a verb-second language, the verb sýnir still comes second.

So yes, word order can change, but it follows rules, not random rearrangement.

A lot of the meaning is shown by case endings, not just position.

In this sentence:

• kennarinn is nominative, so it is the subject
• okkur is dative, so it is the person being shown something
• þolfall is the direct object
• á töflunni is a location phrase

Because Icelandic marks nouns and pronouns with case, it can allow more flexible word order than English while still keeping the roles clear.

That is one of the big differences English speakers have to get used to.