Is there a figurative term equivalent to the German idiom "Fingerübung"?
Just recently I was wondering on how to best translate the figurative German word 'Fingerübung'
In particular I am referring to the second meaning in the authorative German dictionary duden1, which translates to
b) small/easy piece of an exercise (translation: me)
In my research, I stumpled upon the verbatim translation finger exercise, however it only seems to be valid for the first meaning in German, i.e. its meaning being limited to music2.
I also encountered the phrase apprentice piece but I was not able to find water-proof resources or a confirmative entry of the dictionaries I know of.
So my question remains, is there an equivalent idiom (preferably a single word, if there is one for this purpose) in the English language that can be used figuratively in the sense that it refers to a small, easy exercise which neither needs much time nor effort to solve or complete3?
Footnotes & References:
1 https://www.duden.de/rechtschreibung/Fingeruebung
2 vide, e.g. https://www.lexico.com/definition/finger_exercise or https://www.collinsdictionary.com/dictionary/english/finger-exercises resp.
3 To give an example for the use of the word in the German language. For instance, one can refer to small, i.e. not out-of-the-oridnary tricky, calculus problems such as solving an integral or computing the derivative of a well-behaved function as a 'Fingerübung' (when the student itself attends a lecture on 'Mathematical Methods in Physics', in which tasks like integrals or derivatives are seen as preliminaries.)
I'd say "warm-up problem" or "warm-up exercise" might be a good translation if you're using it in school or college courses.
From Merriam-Webster:
Warm-up: a preparatory activity or procedure.
"Toy problem" or "toy example" might work, and is often used in academic contexts. It's often used to describe a demonstration (such as in a textbook or something presented by a professor), not necessarily something that students would work on themselves, but I think it can be used for either situation.
As I said in a comment under Nobody's answer I think the figurative use of Fingerübung is idiomatic and expressive, even though the Duden entry (b) is not describing it (but a piece of music written or played for the purpose of exercise, an étude).
It turns out that there is an exact English equivalent, the five-finger exercise, which can be used figuratively as well.
Other suggested translations like child's play or easy-peasy miss the learning or preparatory aspect which is usually present when Fingerübung is used. And if one wanted to express child's play one could use the exact German counter-piece Kinderspiel instead of Fingerübung.
I'll submit child's play as a term that means an easy exercise or task in the context you've given in part 3.
Example: That calculus problem was child's play compared to the functions we're studying in advanced physics.
It also came up on Reverso for Fingerübung with this example:
Mit diesem, auf dem m2webalizer basierenden Produkt von mquadr.at wird die erfolgreiche Einrichtung des Internetzuganges zur lockeren Fingerübung.
With this service product, based on the technology of mquadr.at's m2webalizer, a successful internet setup becomes childsplay [sic].
In English, this term is two words, child's play, referring to something so simple, a child could do it.