Sign and Boundary Discipline
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalSigns and boundaries fail at a short, predictable list of posts, and the test writes a distractor for each. The points leak at the posts, minus-a-negative collapsing to subtraction, a distributed minus stopping at the first term, a squared negative coming out negative, a negative divisor leaving the inequality unflipped, and at the boundary: at least and at most pointing the wrong way, or an endpoint counted against the wrong symbol.
These patterns aren't really about being careful. They're about knowing exactly WHERE the care goes: the four sign-bearing moments and the two boundary decisions, checked deliberately, in place of a vague instruction to watch the negatives.
The work
4 ways in · any order
Lesson
Sign and Boundary Discipline
›
Name the four sign posts and slow down at exactly those; translate at least and at most before the algebra; judge each endpoint by its own symbol; and let the problem's words decide whether the boundary itself is allowed. The lesson works the checkpoints and the two patterns they guard, and it saves the trap for last: the flip that never happened.
Diagnostic
10-item topic check
›
Ten items across the two patterns: all four sign posts, direction-word translation, endpoint-aware counting, absolute-value branches, and budget boundaries. 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
›
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
›
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.