A map, not a picture
Nobody found this stated in a verse. It's what you're left holding when you refuse to drop any of five claims that each have their own footing in the text. The diagram below is the oldest attempt to draw that shape — it's from the 1200s, and it still works.
Now break it — drop one claim and watch the shape fail
Each one is load-bearing. Every historic error is just the shape of letting go of one.
There is one God.
The hardest constraint — everything else bends around it. Watch what Paul does in 1 Cor 8:6: he takes the two words of the Shema, God and Lord, and splits them across the Father and Jesus. That is a Jew doing something startling to his own creed while insisting he hasn't broken it.
Deut 6:4Isa 45:51 Cor 8:6
The Father is God.
The only one nobody has ever contested. Worth stating anyway, because the argument needs it as a fixed point to measure the other two against.
assumed everywhere
The Son is God.
John 1:1 does distinction and identity in one sentence — with God, and was God. Thomas says "my Lord and my God" and is not corrected. Philippians applies Isaiah 45:23 to Jesus, and in that passage the speaker is YHWH insisting there is no other. But the strongest evidence isn't a verse — it's the practice. Marana tha in 1 Cor 16:22 is Aramaic, so it predates the Greek-speaking church: they were praying to him within a couple of decades, and these were people who would die before praying to anyone but God.
John 1:1John 20:28Phil 2:10–11 ← Isa 45:231 Cor 16:22
The Spirit is God.
Honestly the thinnest strand, and I'd rather say so than pretend. There's no single declarative verse. It rests on how the Spirit is spoken of — lying to the Spirit counts as lying to God; the Spirit searches God's own depths the way your spirit knows your thoughts; the Spirit speaks, forbids, decides, grieves. That's why this piece took until 381 to settle.
Acts 5:3–41 Cor 2:10–11Acts 13:2Eph 4:30
The three are genuinely distinct.
Not three names for one actor. Jesus prays to the Father rather than to himself, and Gethsemane is unintelligible otherwise. All three are present at once at the baptism — voice, body, dove — which is a hard scene to stage with one character.
Matt 3:16–17Luke 22:42John 17:5
All of these get taught. Each one is a named error with a date attached. Worth knowing which, because a sharp twelve-year-old will push on them.
One substance in three states, and never in more than one at a time. That's exactly the claim the baptism scene rules out.
No part of an egg is the egg. But the Father isn't a third of God — he is God, entirely.
Same failure, better PR. A leaf is a piece of a plant, not the plant.
Those are roles he holds toward other people, not distinctions within him. He never talks to himself in any of them.
Light and heat are effects the sun throws off — later than it, lesser than it, dependent on it. That's the exact thing the Nicene fight was about.
Every analogy fails, and they fail in the same place. Everything in creation is either one thing or several things. The claim is that God is not an instance of either.
So the failure isn't a gap in your teaching that a better illustration would close. It's the content. Probably the most useful thing you can do with a class this age is hand them the water-ice-steam analogy, let them like it, and then ask who Jesus was talking to in the garden.