Ich schreibe die Telefonnummer auf den Zettel.

Because aufschreiben is a separable verb.

The full verb is aufschreiben, meaning to write down. In a normal main clause, the conjugated part goes to the usual verb position, and the prefix moves to the end:

• Ich schreibe ... auf.

So:

• ich schreibe auf = I write down / I am writing down

In other forms, the verb stays together:

• Ich will die Telefonnummer aufschreiben. = I want to write down the phone number.
• Ich habe die Telefonnummer aufgeschrieben. = I wrote down / have written down the phone number.

schreiben means to write in a general sense.

aufschreiben means to write down, often with the idea of noting something so you do not forget it.

Compare:

• Ich schreibe einen Brief. = I am writing a letter.
• Ich schreibe die Telefonnummer auf. = I am writing down the phone number.

So aufschreiben is more specific than schreiben.

Telefonnummer is the direct object of the sentence — it is the thing being written down.

The noun Telefonnummer is feminine, so its article is die in the nominative and also die in the accusative.

That is why you get:

• die Telefonnummer

Also, Telefonnummer is a compound noun:

• Telefon = telephone
• Nummer = number

In German compounds, the last noun decides the gender, and Nummer is feminine, so Telefonnummer is feminine too.

Because auf is a two-way preposition. It can take either:

• accusative for direction / movement toward a place
• dative for location / position in a place

Here, the idea is that the phone number is being written onto the piece of paper, so German treats it as a kind of direction or placement. That is why it uses the accusative:

• auf den Zettel

Compare:

• Ich schreibe die Telefonnummer auf den Zettel. = I write the phone number onto the note.
• Die Telefonnummer steht auf dem Zettel. = The phone number is on the note.

So:

• auf den Zettel = onto the paper
• auf dem Zettel = on the paper

Zettel usually means a note, slip of paper, or small piece of paper.

In this sentence, auf den Zettel suggests writing the number down on a specific note or piece of paper.

Depending on context, English might translate it as:

• on the note
• on the paper
• on the slip of paper

It is a very common everyday word.

Den is the accusative masculine definite article for der Zettel.

It suggests that the speaker means a specific piece of paper — one that is already known in the situation.

• auf den Zettel = onto the note / the piece of paper

If you wanted to mean onto a note / onto a piece of paper, not a specific one, you could say:

• Ich schreibe die Telefonnummer auf einen Zettel.

So both are possible, but they mean slightly different things:

• den Zettel = a specific note
• einen Zettel = some note / a note

Because German very often forms compound nouns by joining words together.

So instead of writing telephone number as two separate words, German makes one noun:

• Telefonnummer

This is completely normal in German. A few similar examples are:

• Hausnummer = house number
• Handynummer = mobile phone number
• E-Mail-Adresse = email address

A useful rule: in German compounds, the final part is the main noun, and it determines the gender and plural.

Den Zettel is accusative singular masculine.

The basic noun is:

• der Zettel = the note

After the two-way preposition auf, German uses:

• accusative for motion/direction
• dative for location

Since the sentence expresses writing something onto the paper, it uses accusative:

• auf den Zettel

You can also see the masculine article change clearly:

• nominative: der Zettel
• accusative: den Zettel
• dative: dem Zettel

German present tense can cover several meanings that English expresses differently.

So Ich schreibe die Telefonnummer auf den Zettel can mean:

• I write down the phone number
• I am writing down the phone number
• sometimes even I will write down the phone number, if the context makes that clear

Usually the context tells you which English translation is best.

Yes. You can simply say:

• Ich schreibe die Telefonnummer auf.

That already means I’m writing down the phone number.

Adding auf den Zettel just gives extra information about where you are writing it.

So:

• Ich schreibe die Telefonnummer auf. = I’m writing down the phone number.
• Ich schreibe die Telefonnummer auf den Zettel auf. = also possible, but stylistically a bit heavier because auf appears twice
• Ich schreibe die Telefonnummer auf den Zettel. = a natural way to express it with the location included

Because in German, all nouns are capitalized.

So in this sentence:

• Ich is capitalized because it starts the sentence
• Telefonnummer is capitalized because it is a noun
• Zettel is capitalized because it is a noun

This is a standard rule in German spelling and one of the first things learners notice.