Ég þarf reiknivél í kennslustundinni í dag.

þarf is the 1st person singular present tense of the verb að þurfa = to need / to have to.

So:

• ég þarf = I need
• þú þarft = you need
• hann/hún/það þarf = he/she/it needs

Unlike English, Icelandic verbs change less by person in the present tense, but the subject pronoun is still usually stated.

The dictionary form is að þurfa.

In this sentence, þarf is the present tense form used with ég:

• að þurfa = to need
• ég þarf = I need

This verb can also mean have to / must, depending on context. Here, with a noun object (reiknivél), it clearly means need.

Because Icelandic does not have an indefinite article.

English says:

• a calculator

Icelandic simply says:

• reiknivél

So Ég þarf reiknivél literally looks like I need calculator, but it means I need a calculator.

If Icelandic wants to say the calculator, it usually adds the definite article to the end of the noun instead.

It literally breaks down as:

• reikni- = calculating / calculation-related
• vél = machine

So reiknivél is literally something like calculating machine, i.e. calculator.

This kind of compound noun is very common in Icelandic.

It is the direct object of þarf, so it is in the accusative case.

The verb að þurfa normally takes an accusative object:

• Ég þarf reiknivél. = I need a calculator.

In this particular noun, the nominative and accusative singular look the same, so you do not see a visible change here.

Because í means in / during / in the course of, and after it the noun must appear in a case form.

Here, í is used in a location/static sense, so it takes the dative:

• í kennslustundinni

Also, kennslustundinni includes the definite article, so it means in the lesson / in class rather than just in a lesson.

Because several pieces are packed into one word:

• kennslustund = lesson / class period
• -in- = the definite article (the)
• -ni = part of the dative singular ending

So kennslustundinni means the lesson / the class period in the dative singular after í.

This is very normal in Icelandic: instead of using a separate word for the, Icelandic often adds it to the end of the noun.

A very common rule in Icelandic is:

• í + dative for location / being in
• í + accusative for motion into

Here the meaning is not going into class, but being in class / during class, so Icelandic uses the dative:

• í kennslustundinni = in class / during the lesson

Compare the idea:

• location: í skólanum = in the school
• motion: í skólann = into the school

It usually means something like in class or during the lesson.

Icelandic often uses í in contexts where English might say:

• in class
• during class
• in the lesson

So the phrase is natural even though the English wording may vary.

Because the sentence is treating the two nouns differently:

• reiknivél = a calculator (indefinite, non-specific)
• kennslustundinni = the class / the lesson (definite, a specific class period, or class as a known context)

So the speaker needs some calculator, but is referring to the class period they are in today.

In Icelandic, the is often attached to the end of the noun.

So instead of a separate word like English the, Icelandic has forms like:

• kennslustund = lesson
• kennslustundin = the lesson
• kennslustundinni = to/in the lesson, depending on the case context

The exact form changes with:

• gender
• number
• case

That is why the article does not always look the same.

í dag is the normal Icelandic expression for today.

Literally, it is in day, but you should learn it as a fixed expression:

• í dag = today

It stays as two words. This is just how Icelandic expresses the idea.

Because Icelandic word order is fairly flexible, and time expressions often come later in the sentence.

So:

• Ég þarf reiknivél í kennslustundinni í dag.

is perfectly natural.

You could also move í dag earlier for emphasis, for example:

• Ég þarf í dag reiknivél í kennslustundinni.
• Í dag þarf ég reiknivél í kennslustundinni.

But the original version is a very normal neutral sentence.

Yes. That would mean:

• I need a calculator today.

Adding í kennslustundinni makes the situation more specific:

• Ég þarf reiknivél í kennslustundinni í dag.
• I need a calculator in class today.

So the longer sentence gives both:

• when: í dag
• in what context: í kennslustundinni

kennslustund means lesson, teaching period, or class period.

It is a compound word:

• kennsla = teaching
• stund = period / moment / session

So kennslustund is basically a teaching session.

Depending on context, English might translate it as:

• lesson
• class
• class period

It is completely natural and neutral.

A speaker might also choose simpler or more conversational alternatives depending on context, but this sentence is standard and idiomatic. In everyday speech, someone might also say something like:

• Ég þarf reiknivél í tíma í dag.

where í tíma can also mean in class.

But í kennslustundinni is perfectly correct and clear.

Yes.

For example:

• Ég þarf reiknivél. = I need a calculator.
• Ég þarf að fara. = I have to leave.

So:

• þurfa + noun often means need
• þurfa að + verb often means have to / need to

In your sentence, because the object is reiknivél, the meaning is need.

Þarf ég... would usually be a question:

• Þarf ég reiknivél í kennslustundinni í dag?
• Do I need a calculator in class today?

For a normal statement, Icelandic uses:

• Ég þarf ...
• I need ...

So the word order helps signal whether the sentence is a statement or a question.