Percentages
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalEvery percent is a percent OF something, and that something is where the test hides the trap. The arithmetic is a multiplication. The points leak in the base, a change undone against the new value instead of the original, in the handling, a percent added or subtracted like a plain number, and at the end, the wrong family member: the discount reported as the price, the change as the total.
These patterns aren't really about whether you can find ten percent of something. They're about whether you named the base before computing, whether the percent scaled its base instead of joining it, and whether the number you reported answers the exact question, the new value, the change, or the rate.
The work
4 ways in · any order
Lesson
Percentages
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Scale the base instead of adding the percent, undo an increase by dividing, measure percent change against the starting value, and stack successive percents by multiplying. The lesson works the method and the three patterns that derail it, and it saves the trap for last: the right computation with the wrong family member reported.
Diagnostic
10-item topic check
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Ten items across the three patterns: taking the percent of the wrong base, treating a percent like an absolute number, and reporting the change when the value was asked. A mix of discounts, reverse percents, percent change, and stacked changes. 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.