He could do the hard questions.
He just never got to them.
On the second module he answered the easy and medium questions well and got nothing at all on the hard ones — not because they were beyond him, but because the module ended first. His ceiling was set in the opening minutes, by pacing, not by knowledge.
So the score was never a measure of what he knew. It was a measure of how far into the test he got.
Four minutes on question one, then a sprint, then fourteen minutes left on the table.
He spent a fifth of module one on its first question, panicked through the back half at eight to seventeen seconds each, and still handed it in with 14:17 unused. In the other module he did the reverse and ran right to the buzzer. Nobody had ever shown him the clock, so the clock was running him.
So the first thing I changed was not algebra. It was when he is allowed to give up on a question and move on.
Twelve questions got under twenty seconds.
Ten of them were wrong.
That is not a knowledge problem and it is not bad luck; it is a habit, and habits are what a plan can actually be written against. The write-in answers were worse still: one right out of eleven, and seven of the misses were a number already printed in the problem. He was reading the question, finding a number, and writing it down.
So he got two rules before he got a single new topic: nothing goes down under twenty seconds, and on a write-in he writes what he is solving for before he starts solving.
Five of the twenty-seven misses were a gap in knowledge.
Twenty-two were something else.
The largest group was the one that stings: he did the mathematics correctly and then reported the wrong number. Below are two of them, reconstructed. In the first he found the angle at the center and doubled it when the question wanted it halved. In the second he squared one side of the equation and not the other. Both students who make these errors know the rule perfectly well.
So five of them became lessons, and the other twenty-two became a checklist he runs on every question. That is the difference between a tutor teaching topics and a plan built from evidence.