Hún tók stóra matskeið og hrærði í sósunni á meðan sósan sauð.

Because matskeið is a feminine singular noun here, and it is the direct object of tók, so it is in the accusative singular.

The adjective stór has to match that:

• nominative feminine singular: stór
• accusative feminine singular: stóra

So:

• stór matskeið = wrong here
• stóra matskeið = correct for a large spoon / tablespoon as the object of tók
• stóru matskeið would be a weak form and would not fit this indefinite phrase

A useful comparison:

• Hún tók stóra matskeið = She took a large spoon
• Hún tók stóru matskeiðina = She took the large spoon

Icelandic normally does not use an indefinite article like English a/an.

So a bare noun phrase such as stóra matskeið can mean:

• a large spoon
• a large tablespoon

Indefiniteness is usually understood from context.

By contrast, definiteness is often shown by attaching the article to the noun:

• matskeið = spoon / a spoon
• matskeiðin = the spoon

It can mean tablespoon as a unit or a large spoon as an object, depending on context.

In cooking:

• ein matskeið af sykri = one tablespoon of sugar
• taka matskeið can literally mean take a tablespoon/spoon

In this sentence, because she then stirred the sauce, many learners will naturally understand it as a large spoon used for stirring. But the Icelandic word itself is still matskeið.

Because Icelandic commonly uses the expression að hræra í einhverju, literally to stir in something, when talking about stirring food in a pot or bowl.

So:

• hræra í sósunni = stir the sauce

The preposition í is part of the pattern here, and it requires the dative case, which is why you get sósunni.

This is one of those verb patterns you mostly have to learn as a chunk:

• hræra í súpunni
• hræra í grautnum
• hræra í sósunni

Because the noun has different grammatical roles in the two clauses.

1. í sósunni

   • after the preposition í
   • with hræra í
   • so the noun is in the dative
   • sósunni = the sauce in dative singular

2. sósan sauð

   • here sósan is the subject of the verb sauð
   • subjects are normally in the nominative
   • sósan = the sauce in nominative singular

So it is the same noun, but different case forms:

• nominative: sósan
• dative: sósunni

Here á meðan means while or during the time that.

So:

• á meðan sósan sauð = while the sauce was boiling

It introduces a time clause that tells you when the stirring happened.

You can think of it as linking two actions happening at the same time:

• she stirred
• the sauce boiled / was boiling

Sauð is the past tense singular of the verb sjóða, which means to boil.

Some useful forms:

• infinitive: sjóða
• present singular: sýður
• past singular: sauð
• past plural: suðu

So:

• sósan sýður = the sauce is boiling
• sósan sauð = the sauce boiled / was boiling

It is an irregular verb, so it is worth memorizing separately.

Because Icelandic simple past often covers meanings that English splits into:

• simple past
• past progressive

So sósan sauð can mean:

• the sauce boiled
• the sauce was boiling

In this sentence, because of á meðan and the overall cooking context, English usually prefers:

• while the sauce was boiling

That sounds more natural than while the sauce boiled, even though the Icelandic form itself is just simple past.

The dictionary form is taka, meaning to take.

Tók is the past tense singular:

• infinitive: taka
• present singular: tekur
• past singular: tók
• past plural: tóku
• past participle: tekið

It is also an irregular verb, so learners usually memorize it early.

In this sentence:

• Hún tók stóra matskeið = She took a large spoon

Because the same subject applies to both verbs.

The structure is:

• Hún tók ... og hrærði ...

This works the same way as English:

• She took a spoon and stirred the sauce

You do not need to repeat she unless you want special emphasis or a different structure.

Most likely for clarity.

If the second clause said:

• á meðan hún sauð

that would sound ambiguous, because hún could refer to:

• she
• or the sauce (since sósa is feminine)

By repeating sósan, the sentence makes it completely clear that it is the sauce that was boiling.

It is in the accusative singular.

That is because it is the direct object of tók:

• Hún tók stóra matskeið

The verb taka usually takes a direct object in the accusative.

Since matskeið is feminine singular, the adjective also matches that accusative form:

• stóra matskeið

It is normal subordinate-clause word order.

The clause begins with the conjunction á meðan, and then you get:

• sósan = subject
• sauð = verb

So:

• á meðan sósan sauð

That is a normal and straightforward pattern for a subordinate time clause in Icelandic. The main thing to notice is not the word order itself, but that á meðan introduces the clause while the sauce was boiling.