
anschreiben
to write to
To contact someone in writing, for example by letter, email, or message.
Ich muss den Kundenservice anschreiben, weil meine Bestellung nicht angekommen ist.
I have to write to customer service because my order hasn't arrived.
to write to / put on account
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to write to
To contact someone in writing, for example by letter, email, or message.
Ich muss den Kundenservice anschreiben, weil meine Bestellung nicht angekommen ist.
I have to write to customer service because my order hasn't arrived.

to write up
To write something on a visible surface so that others can read it, for example on a blackboard or whiteboard.
Die Lehrerin schreibt die Hausaufgaben an die Tafel an.
The teacher writes the homework up on the board.

to put on account
To buy goods or services without paying immediately, with the amount owed being recorded so it can be paid later.
In dem kleinen Dorfladen kann man seine Einkäufe noch anschreiben lassen.
In the small village shop, you can still have your purchases put on account.

to be in someone's bad books
To have left a bad reputation or impression with someone; to have fallen out of favor.
Seit er das Projekt vergessen hat, ist er beim Chef schlecht angeschrieben.
Ever since he forgot the project, he's been in the boss's bad books.
'Anschreiben' (to write to / write up) is a separable verb. The prefix 'an' separates in a main clause and comes at the end. In a subordinate clause or infinitive with 'zu', the verb stays together.
Die Professorin schreibt die Termine an.
The professor writes up the dates.
When you contact someone in writing, the person or institution you are contacting is in the accusative. No preposition is needed.
Schreiben Sie bitte die Personalabteilung an.
Please write to the HR department.
When something is written onto a surface, you use the structure 'etwas (Akkusativ) an etwas (Akkusativ) anschreiben' (to write something onto something). The preposition 'an' indicates direction.
Der Trainer schreibt die Taktik an das Whiteboard an.
The coach writes the tactics up on the whiteboard.
The expression 'etwas anschreiben lassen' (to have something put on account) means to buy on credit. It is often used in small, personal shops such as a kiosk or bakery.
Kann ich die Brötchen anschreiben lassen? Ich habe mein Portemonnaie vergessen.
Can I have the rolls put on account? I forgot my wallet.
The idiom 'bei jemandem [gut/schlecht] angeschrieben sein' (to be in someone's good/bad books) is a fixed structure. It uses the past participle 'angeschrieben' with the verb 'sein' and the preposition 'bei'.
Seitdem er zu spät zur Besprechung kam, ist er bei der neuen Chefin schlecht angeschrieben.
Ever since he came late to the meeting, he's been in the new boss's bad books.
to describe
Beschreiben and anschreiben can both involve writing on a visible surface. Beschreiben emphasizes covering a surface with writing or drawings, while anschreiben usually means writing specific information where others can see it. Use beschreiben for the design or marking of the surface and anschreiben for information that needs to be communicated.

Der Lehrer schreibt die neuen Wörter an die Tafel.
The teacher writes the new words on the board.
Die Kinder beschreiben die Tafel mit bunten Zeichnungen.
The children cover the board with colorful drawings.