Me mostre frases de exemplo com schreiben an die Tafel oder an der Tafel ?notieren auf ein Blatt oder auf einem Blatt ? .Me diga o maior numero de expressões diárias possíveis.

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There are some german verbs (and prepositions), that do not really change their meaning, whether they're used with Akkusativ or Dativ. schreiben and notieren are two of those.
Try to think about the basic meaning of Dativ and Akkusativ. While Akkusativ refers to the direct object something is inflicted upon, Dativ, at least in this case, fulfills a "local" kind of role.

Ich schreibe an die Tafel (I'm writing on the board)
Ich schreibe an der Tafel (I'm writing in front of the board, most likely still writing on the board itself)

Ich notiere auf einem Blatt (local again, "ontop of a paper")
Ich notiere auf ein Blatt (noting something while utilizing a sheet of paper)

THos topic is pretty complicated, even for Germans. Most germans do not tend to think about the cases at all, they know them naturally. On the other hand, when it comes to cases like those, many are at a loss on which one is correct. In most cases, the maning does not really change, but there are some cases where it matters:

verteilen (to distribute/to split (into groups))

Die Schüler verteilen sich in ihren Klassen (The pupils are "spreading out" in their classrooms (a test kind of situation))
Die Schüler verteilen sich in ihre Klassen (The pupils split up and enter their respective cassrooms)

Although the difference is only one letter, those sentences mean different things. This is a more or less artificial sentence though because it is purposely fabricated to not differ in almost any way.