The youngest in the army
Talut led an army out against Jalut. The Quran records the moment: those who were certain they would meet Allah said, How many a small company has overcome a large company by permission of Allah (2:249).
Then, in a single verse: So they defeated them by permission of Allah, and Dawud killed Jalut, and Allah gave him the kingship and wisdom and taught him from that which He willed (2:251).
The Quran spends one line on the fight. The famous details — the sling, the stones, the size of Jalut, the refusal of armour — are not in it. Children can still be told the story is about a young man who was not the obvious choice, because that much the Quran does support: the army was small, and he was the one who did it.
A voice the mountains joined
What follows is strange and beautiful, and children love it. And We subjected the mountains to exalt Allah with him, and the birds (21:79). Again in Surah Saba: O mountains, repeat Allah's praises with him, and the birds (34:10).
In the same verse: And We made the iron soft for him — and then the practical instruction, Make full coats of mail, and calculate precisely the links (34:11). He was taught a trade, and the Quran records the technical detail of getting the rings right.
That combination is the whole point of him. Mountains joined his praise, and he still sat and made armour properly. The Quran mentions both in adjacent lines without treating it as a contrast.
The two men who came over the wall
In Surah Sad, two men climb the wall into his private chamber. They startle him. One says his brother has ninety-nine ewes and he has one, and that his brother has pressed him to hand it over (38:21-23).
Dawud answers immediately: he has certainly wronged you. And then the Quran says he realised he was being tested, asked forgiveness of his Lord, and fell down bowing (38:24-25).
What was he corrected for? Not for a crime. For deciding before hearing the other side. In the verses just after, he is addressed directly and told to judge between people in truth and not follow desire (38:26).
For a child, this is one of the most usable passages in the whole Quran. A prophet, a king, given a book and a voice the mountains answered — and the thing he was pulled up on was answering too fast.