Kennarinn sýnir okkur verkefnið.

Icelandic doesn’t use a separate word for “the”. Instead, it sticks a definite article ending onto the noun.

• kennari = a teacher (indefinite)
• kennarinn = the teacher (definite, nominative singular masculine)

So -inn is the masculine definite ending in the nominative singular. The sentence needs “the teacher”, so it uses Kennarinn.

The infinitive (dictionary form) is að sýna = to show.

Icelandic verbs change their ending according to the subject. For að sýna in the present tense:

• ég sýni – I show
• þú sýnir – you (sg.) show
• hann / hún / það sýnir – he / she / it shows
• við sýnum – we show
• þið sýnið – you (pl.) show
• þeir / þær / þau sýna – they show

The subject Kennarinn is 3rd person singular, so the verb must be sýnir.

Icelandic has different forms for subject and object, like English we vs. us, but with more case marking.

• við = we (subject, nominative)
• okkur = us (object; used for both accusative and dative)

In this sentence, we are not the subject; we are the people being shown something. That means we are an object, so the form must be okkur, not við.

The verb sýna takes two objects:

• the person you show something to → dative
• the thing that is shown → accusative

In the sentence:

• Kennarinn – the teacher
  
  • Subject, nominative singular.
• okkur – us
  
  • Indirect object (the people shown to), dative plural.
• verkefnið – the assignment / project
  
  • Direct object (the thing shown), accusative singular.

So the pattern with sýna is:
subject (nom) + sýna + person (dat) + thing (acc).

The basic noun is verkefni (neuter) = assignment, project, task.

Neuter nouns have the same form in nominative and accusative. The definite ending in the singular is -ið:

• verkefni – an assignment (nom/acc sg, indefinite)
• verkefnið – the assignment (nom/acc sg, definite)

In the plural:

• verkefni – assignments (nom/acc pl, indefinite)
• verkefnin – the assignments (nom/acc pl, definite)

So -ið here is the neuter singular definite ending.

The most natural neutral order in Icelandic is:

Subject – Verb – Indirect object (dative) – Direct object (accusative)

So:

• Kennarinn (subject)
• sýnir (verb)
• okkur (indirect object, dative)
• verkefnið (direct object, accusative)

You can say “Kennarinn sýnir verkefnið okkur”, but it sounds less neutral and usually adds emphasis or a different rhythm. The default everyday order is “sýnir okkur verkefnið”.

Yes. If we are the ones doing the showing, we become the subject, so we use við (nominative), and the teacher becomes an object:

• Við sýnum kennaranum verkefnið.
  We show the teacher the assignment.

Here:

• við – subject, nominative plural
• kennaranum – to the teacher, dative singular (indirect object)
• verkefnið – direct object, accusative singular definite

The past tense of sýna is sýndi (3rd person singular).

So the sentence becomes:

• Kennarinn sýndi okkur verkefnið.
  The teacher showed us the assignment.

Pattern:

• present: hann / hún sýnir
• past: hann / hún sýndi

Icelandic often uses the “er að + infinitive” construction to express a continuous action (similar to English is doing).

So:

• Kennarinn er að sýna okkur verkefnið.
  The teacher is showing us the assignment (right now).

You can also use the simple present (Kennarinn sýnir okkur verkefnið) for a general statement or habitual action.

The normal position for ekki (not) here is after the indirect object:

• Kennarinn sýnir okkur ekki verkefnið.
  The teacher does not show us the assignment.

Order:
Kennarinn (S) – sýnir (V) – okkur (IO) – ekki (NEG) – verkefnið (DO).

You just make verkefnið plural definite → verkefnin:

• Kennarinn sýnir okkur verkefnin.
  The teacher shows us the assignments.

Plural pattern for verkefni (neuter):

• sg definite: verkefnið – the assignment
• pl definite: verkefnin – the assignments

Very roughly (not strict IPA):

• Kennarinn ≈ KEN-na-rin
  
  • stress on the first syllable; nn is doubled (short vowel before it)
• sýnir ≈ SEE-nir
  
  • ý is like a long ee, but tenser
• okkur ≈ OK-kur
  
  • short o (like in off), double kk gives a strong k sound
• verkefnið ≈ VER-kev-nith
  
  • fnið cluster is tricky; ð is a soft th like this, often very weak

So the whole thing roughly: KEN-na-rin SEE-nir OK-kur VER-kev-nith (with main stress on KEN, and each word’s first syllable stressed).