Answering the Question Actually Asked
The most expensive mistake on the test costs nothing mathematically: the work is right and the reported number is not the one the question named. The points leak at the stop, the solved variable or an intermediate value (a width, a total, one evaluation) gridded as if it were the destination, and at the name: the other person's share, the other variable of a system, or the smallest of a set standing in for the quantity the question actually asked about.
These patterns aren't really about algebra at all. They're about whether the ask got reread after the solving, whether every intermediate value got treated as fuel rather than as an answer, and whether the number that went in the grid matches the words at the end of the question.
The work
4 ways in · any order
Lesson
Answering the Question Actually Asked
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Solve, then substitute into the expression the question named; underline the asked quantity before starting; treat widths, totals, and single evaluations as fuel; and spend two seconds rereading the ask before gridding. The lesson works the habit and the two patterns that break it, and it saves the trap for last: perfect work reported for the wrong quantity.
Diagnostic
10-item topic check
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Ten items across the two patterns: expressions built from the variable, named quantities in splits and systems, multi-step geometry and averages, and comparison asks. Take it cold to surface the ones still catching you, or after the lesson to confirm they are gone.
Grid-in Check
Student-produced response
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About a quarter of SAT math answers are typed, not chosen, with no options to react to. These grid-in items diagnose by the value you enter, then route into the same drills the multiple-choice check feeds.
Targeted Practice
Drill a single pattern
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Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the pattern and you move on.