Schmierpapier=jotting or scratch paper (Am.) and scribbling-paper (Br.)
In America "scratch paper" ("scratch
pad" for "Schmierblock) is the more
commonly used one.

As in: "Do you have any scrap paper?" which is more commonly heard in the American classroom.

Commonly used in Canadian schools .
Reference: my four children!

After looking at the other answers above and the following references, there seems to be no 100% right choice for (UK) English or for (NA) English, let alone both. For the first time I would be forced to go against majority search engine results and majority dictionary results and choose:

"scribbling paper"

because:

1. "to scribble" has the same meaning in English everywhere and is widely used, so everyone would understand it even though they themselves might use "scrap paper" or "scratch paper". The readers of your translations will not look in dictionaries to see if you chose the right word, they will just understand it or misunderstand it.

2. "scrap paper" sometimes means "waste paper", that is, something to be disposed of. There could be both "Schmierpapier" and "Altpapier" in a classroom.

3. "to scratch" meaning to "to scribble" or "to write in rough" is not so widely used as scribble and might therefore not be understood everywhere in the world.

4. You can quote three dictionaries if anyone does ask.

Kl. Muret-Sanders Langenscheidt: "scribbling paper" = "Schmierpapier"

Duden/Oxford: "scrap paper" = "Schmierpapier"

LEO Online = "scribbling paper" and "scratch paper" = "Schmierpapier"

Uni Clausthal = "scribbling paper" = "Schmierpapier"

AUTODICAUTOM: no listing for "Schmierpapier"

"Altpapier" = "waste paper" but also often "scrap paper"

PONS: "Schmierpapier = "rough paper" or "scrap paper"

NODE: "scratchpad" = "notepad" = (computing) small fast memory for short notes

NODE: no listing for "scratch paper"

NODE: no listing for "scribble paper"

NODE: "scrap paper" = odd bits of paper used for making rough notes

Webster: "scratch paper" = paper suitable for casual writing

Webster: "scrap paper" not listed

Webster: "scribble paper" not listed

Northern Light, AltaVista and Google results were inconclusive for "scrap paper" versus "scratch paper" because of the use of "scrap paper" to mean "waste paper". Both versions received over 5000 hits on all of the three search engines though. "scribbling paper" never received more than 50 hits.
- HTH - Dan

even though the answer above which rejects this selection is quite impressive, I'd go for the easy and obvious translation here.

Scrap paper seems to me to be the right choice simply because that is the word used in an equivalent context by the same group of people, e.g. students/pupils at a school. Other people can use scrap paper, of course, but among students in a German school you would hear Schmierpapier in the same context and with just about the same mental picture behind it as when American/English students say scrap paper.

HTH, Sibyl