user8751: I teach chess to children and a colleague of mine told me of this position to show to the kids. Black plays and gives mate in two. It seems an easy position but the children I teach had difficulties with it because they think that the only way to mate is capturing as much pieces of the opponent as possible in the process. 
[fen "7r/8/8/5k2/4q3/8/6PR/r5RK b - - 0 1"]

Black plays and gives mate in two. What should Black do?

user9840: A quiet move: 1... Qa8, keeping the pawn pinned, and white will be mated next move.
When teaching kids is important do show MATE IN ZERO FIRST, so MATE IN ONE and so on.
Never give a child a problem she can not solve. Because success is stimulating and a failure is depressing and could be mortal.

user8860: [Corrected: most of the alternative solutions I suggested fail to g4+]
There must be some mistake in the diagram, because R(either)xR+
is a non-quiet move that forces mate in 2.  Quiet moves don't work
because of the defense Rc8+ or Rxh8.  Except that the FEN indicates
that the wP is on g2, not b7 as it seems, and that makes Qa8! a quiet
solution (Zugzwang: if RxR(either) then QxR is mate; other Rook moves
are captured by a Rook for mate; and the pawn is still pinned).
To make this unique the Queen can be put elsewhere on the diagonal,
like d5: 
[fen "7r/8/8/3q1k2/8/8/6PR/r5RK b - - 0 1"] 

I see that Dag Oskar Madsen already suggested this fix in a comment.
Possibly of interest: while trying to Google this position I ran across
this mate-in-2 problem,
credited to T.A.L.Herlin 1852, which might have been the inspiration
for the present problem though its solution is not as nice or as quiet:
[fen "kr5R/rp6/8/8/4Q1K1/8/8/8 w - - 0 1"] 

Solution:

 1 Qe8! (threat 2 QxR#) Rxe8/Ra4+ 2 Rxe8/Qxa4#!


8751: <p>I teach chess to children and a colleague of mine told me of this position to show to the kids. Black plays and gives mate in two. It seems an easy position but the children I teach had difficulties with it because they think that the only way to mate is capturing as much pieces of the opponent as possible in the process. </p>

<pre><code>[fen "7r/8/8/5k2/4q3/8/6PR/r5RK b - - 0 1"]
</code></pre>

<p><strong>Black plays and gives mate in two. What should Black do?</strong></p>
 9840: <p>A quiet move: 1... Qa8, keeping the pawn pinned, and white will be mated next move.</p>

<p>When teaching kids is important do show MATE IN ZERO FIRST, so MATE IN ONE and so on.</p>

<p>Never give a child a problem she can not solve. Because success is stimulating and a failure is depressing and could be mortal.</p>
 8860: <p>[<em>Corrected</em>: most of the alternative solutions I suggested fail to g4+]</p>

<p>There must be some mistake in the diagram, because R(either)xR+
is a non-quiet move that forces mate in 2.  Quiet moves don't work
because of the defense Rc8+ or Rxh8.  Except that the FEN indicates
that the wP is on g2, not b7 as it seems, and that makes Qa8! a quiet
solution (Zugzwang: if RxR(either) then QxR is mate; other Rook moves
are captured by a Rook for mate; and the pawn is still pinned).
To make this unique the Queen can be put elsewhere on the diagonal,
like d5: </p>

<pre><code>[fen "7r/8/8/3q1k2/8/8/6PR/r5RK b - - 0 1"] 
</code></pre>

<p>I see that <strong>Dag Oskar Madsen</strong> already suggested this fix in a comment.</p>

<p>Possibly of interest: while trying to Google this position I ran across
<a href="https://www.reddit.com/r/chess/comments/2k1913/white_to_mate_in_two_moves_by_theodore_adrien/" rel="noreferrer">this mate-in-2 problem</a>,
credited to T.A.L.Herlin 1852, which might have been the inspiration
for the present problem though its solution is not as nice or as quiet:</p>

<pre><code>[fen "kr5R/rp6/8/8/4Q1K1/8/8/8 w - - 0 1"] 
</code></pre>

<p>Solution:</p>

<blockquote class="spoiler">
  <p> 1 Qe8! (threat 2 QxR#) Rxe8/Ra4+ 2 Rxe8/Qxa4#!</p>
</blockquote>
