Isma'il was Ibrahim's son, left with his mother Hajar as an infant in a valley where nothing grew. Water was given there, and people settled around it. Years later he helped his father raise the foundations of the Kaaba, and the Quran records him as true to his promise.
A valley with nothing in it
The Quran records the du'a Ibrahim made when he left his family in that place: Our Lord, I have settled some of my descendants in an uncultivated valley near Your sacred House — our Lord, that they may establish prayer. So make hearts among the people incline toward them and provide for them from the fruits (14:37).
Everything a child needs is in that verse: where they were, that there was nothing there, why they were left, and what was asked for. The story of the water at Zamzam and of Hajar going between the two hills is preserved in hadith rather than in the Quran, and is worth telling as such — it is what the sa'y in Hajj commemorates to this day.
Building the House
Years later, father and son are shown working together: And when Ibrahim was raising the foundations of the House and Isma'il, saying, Our Lord, accept this from us. Indeed, You are the Hearing, the Knowing (2:127).
They are building the most important building in the story, and what the Quran records them saying is a request that it be accepted. Not a claim about what they had achieved. That contrast is worth pointing at, especially against the people of 'Ad and their monuments a few stories earlier.
True to his promise
Surah Maryam describes him in two lines: And mention in the Book, Isma'il. Indeed, he was true to his promise, and he was a messenger and a prophet. And he used to enjoin on his people prayer and zakah, and was to his Lord pleasing (19:54-55).
Of everything that could have been said about him, the Quran leads with keeping his word. For a child that is a usable standard, and it is the thing to attach to his name.
And in the account of the dream in Surah as-Saffat, the son's answer is: O my father, do as you are commanded. You will find me, if Allah wills, of the steadfast (37:102). The Quran does not name the son in that passage, though most scholars have held it was Isma'il.
The one idea to leave a child with
He kept his word. Out of everything that could have been recorded about him, the Quran opens with true to his promise — and that is something a six-year-old can start doing this week.
What age is this story for?
Six for the valley, the water and the building. The dream in Surah as-Saffat is a nine or ten year old's story, and should be told with the son's own answer, which is what makes it bearable to a child.
Quran, hadith, or neither
Three sources get blended in most retellings of this story, and separating them is genuinely useful for a child.
The valley, the du'a and the building are Quranic. The detailed account of Hajar running between Safa and Marwah and the water appearing is preserved in hadith, in Sahih al-Bukhari — strong, but a different kind of source, and worth naming as such.
Beyond those, a good deal of description — ages, conversations, precise geography — comes from later material. Where you do not know, say so; it is a better lesson than the detail would have been.
Who was Prophet Isma'il?
Ibrahim's son, left as an infant with his mother Hajar in a barren valley near the Sacred House. He later helped his father raise the foundations of the Kaaba (2:127) and is described in 19:54 as true to his promise.
Is the story of Zamzam in the Quran?
The valley and Ibrahim's du'a are in the Quran (14:37). The detailed account of Hajar and the water is preserved in hadith, in Sahih al-Bukhari, rather than in the Quran.
Who built the Kaaba?
The Quran describes Ibrahim raising the foundations of the House with Isma'il, and records their du'a: “Our Lord, accept this from us” (2:127).
What is Isma'il best known for in the Quran?
Keeping his word. Surah Maryam introduces him with “he was true to his promise” (19:54), before mentioning that he was a messenger and a prophet.