Units and Scale Discipline
Numbers arrive wearing labels (hours, centimeters, "in thousands," percent, per serving) and the arithmetic is indifferent to all of them. The points leak in the mismatch, a per-hour rate multiplying minutes or meters dividing centimeters, and at the label: an axis scale never applied, a percent multiplied raw, a whole-batch amount treated as one serving's.
These patterns aren't really about conversion factors. They're about whether the conversion happened BEFORE the arithmetic, whether the scale label got applied at the moment of reading, and whether the answer's units were checked against the ask before gridding.
The work
4 ways in · any order
Lesson
Units and Scale Discipline
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Convert to one unit before any multiplication, apply axis scales and percent conversions at the read, find what one serving is worth before scaling batches, and unstack layered scales one line at a time. The lesson works the reflex and the two patterns that break it, and it saves the trap for last: flawless arithmetic on numbers that never spoke the same unit.
Diagnostic
10-item topic check
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Ten items across the two patterns: rate-time mismatches, length conversions, axis scales, percent conversion, batch-to-serving scaling, and stacked scales. 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.