Hun skriver små noter med en rød kuglepen, når læreren taler hurtigt.

Both skriver and taler are in the present tense.

Danish often uses the present tense for habits, routines, and repeated situations, just like English does in sentences such as She writes notes when the teacher speaks quickly. So this sentence describes what she typically does in that situation.

Danish usually does not need a separate progressive form like English is writing.

So hun skriver can mean either she writes or she is writing, depending on the context. Here, the sentence naturally means a repeated or ongoing action, so the simple present is enough.

Noter is the plural form of note.

The adjective små is the plural form of lille. So:

• en lille note = a small note
• små noter = small notes

This is a useful adjective to remember because it is irregular.

Because kuglepen is a common-gender noun in Danish, so it takes en, not et.

With a singular indefinite common-gender noun, the adjective stays in its basic form, so you get rød:

• en rød kuglepen
• et rødt brev
• røde kuglepenne
• den røde kuglepen

So en rød kuglepen is the correct form here.

Here med means with, in the sense of using something.

So med en rød kuglepen means she writes using a red ballpoint pen.

Because Danish usually writes compound nouns as one word.

Kuglepen is made from kugle + pen. Danish does this very often, much more consistently than English. So when two nouns form one idea, they are usually written together.

In Danish, the definite article is often attached to the end of the noun.

So:

• lærer = teacher
• læreren = the teacher

This is one of the most important noun patterns in Danish.

Når is used for when in a general, repeated, or habitual sense.

This sentence means that whenever the teacher speaks quickly, she writes small notes. That is exactly the kind of situation where når is used.

Compare:

• når = when / whenever
• da = when, for one completed event in the past
• hvis = if

Because this is a subordinate clause.

In Danish main clauses, the finite verb usually comes in second position. But subordinate clauses do not follow the same verb-second pattern. So the normal order here is:

• når læreren taler hurtigt

You can compare:

• Main clause: Hun skriver små noter
• Subordinate clause: når læreren taler hurtigt

If the subordinate clause came first, the main clause would change word order:

• Når læreren taler hurtigt, skriver hun små noter med en rød kuglepen.

Because hurtigt is the adverb form of hurtig.

Many Danish adjectives add -t when they are used as adverbs:

• hurtig = fast, quick
• hurtigt = quickly, fast

So læreren taler hurtigt means the teacher speaks quickly.

It depends on the comma style being used.

In modern Danish, many writers do put a comma before a subordinate clause like this, and this is very common in teaching materials. You may also see the sentence written without that comma.

So both versions can occur:

• Hun skriver små noter med en rød kuglepen, når læreren taler hurtigt.
• Hun skriver små noter med en rød kuglepen når læreren taler hurtigt.

For a learner, using the comma is a safe and common choice.