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TACHS Visual reasoning without guesswork

Teaching notes and examples for focused review. Use the family lessons and annual question bank to practice these methods.

Updated October 3, 2026

5 terms with examples.

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Term / patternMeaning / methodExample
ReflectionA fold maps points across a mirror line.A hole two squares left of a vertical fold appears two squares right after unfolding.
RotationA turn changes orientation while preserving shape.A 90-degree clockwise turn maps an upward arrow to the right.
InvariantTrack a property that stays fixed while others vary.Every example may contain exactly two shaded regions despite different outlines.
Layer count and coincident holesUnfolding reflects punched positions through the layers present; coincident reflected positions count once.A punch away from both creases after two perpendicular folds can yield four holes; a punch on a crease may yield fewer distinct holes.
Row ruleA matrix rule must explain all supplied cells.If a dot shifts right one place per column, verify this in each complete row.

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