Der Lehrer schreibt an die Tafel.

Breakdown of Der Lehrer schreibt an die Tafel.

schreiben
to write
an
on
der Lehrer
the teacher
die Tafel
the board
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Questions & Answers about Der Lehrer schreibt an die Tafel.

Why is there an article before Tafel, while in English we often say “on blackboard” without one?
German nouns almost always need a definite or indefinite article when used generally. Here die Tafel literally means the board. In English you can drop the article in some set phrases (“at school,” “on blackboard”), but in German you normally say an die Tafel, an der Tafel or auf die Tafel – always with an article.
What case is die Tafel, and how do I recognize it?
die Tafel here is in the accusative case. You know it’s accusative because an is a two‑way (Wechsel‑) preposition that takes accusative when there is movement toward something (writing onto the board). Even though feminine die looks the same in nominative and accusative, the preposition tells you which case it really is.
When would I use an der Tafel instead of an die Tafel?

Use an die Tafel (accusative) for motion onto the surface: “writes onto the board.”
Use an der Tafel (dative) for location at the surface: “is standing at the board” or “looks at the board.”

Could I say auf die Tafel instead of an die Tafel, and does it change the meaning?

Yes. Both mean “onto the board.”
an often implies writing on a vertical surface.
auf stresses the surface itself (“on top of”).
In practice teachers use them interchangeably:
Der Lehrer schreibt an die Tafel.
Der Lehrer schreibt auf die Tafel.

Is schreibt here a separable verb like anschreiben?
No. Here schreiben is the simple main verb, and an is just a preposition. The separable verb anschreiben means things like “to record somebody’s name” or “to write a note to someone.” In schreibt an die Tafel the verb is simply schreiben (“to write”).
Why doesn’t the sentence mention what the teacher writes?

German can leave out the direct object if it’s clear or not the focus. The emphasis here is on the action/location (writing on the board). If you want to specify what is written, add a direct object in the accusative before the prepositional phrase:
Der Lehrer schreibt die Hausaufgaben an die Tafel.

Can I start with An die Tafel for emphasis?

Yes. German allows you to front a prepositional phrase for emphasis or style. You then keep verb‑second order:
An die Tafel schreibt der Lehrer.
(verb schreibt remains in second position, subject follows it).

Why don’t we translate Der Lehrer schreibt an die Tafel as “The teacher writes to the board”?
In English “write to” usually means addressing a person or sending a letter. German an with a surface often has the sense “onto.” So although it literally reads “writes at/to the board,” in natural English you say writes on the board.