Spatial Visualization
What Spatial Visualization asks
These items ask you to manipulate figures mentally: fold and punch paper, rotate or unfold a shape, combine two pieces, or decide what results when shapes overlap. Level G items add steps, so a single mental shortcut is rarely enough.
Working through manipulations
For paper folding, trace the folds in reverse. Each unfold reflects the punched holes across that fold line, and every hole passes through all layers, so the number of holes doubles with each fold. For combining pieces, match notches, tabs, and edge lengths before considering the overall outline. For rotation, pick one asymmetric detail - a notch, a dot, a shorter side - and follow it; rotation preserves handedness, while reflection reverses it.
Worked example
A square sheet is folded in half vertically, right edge onto left edge, then in half horizontally, bottom edge onto top edge. A single hole is punched through all layers near the top-left corner of the folded packet. Unfold the horizontal fold first: the hole reflects across the horizontal centre line, giving two holes, one near the top-left and one near the bottom-left. Unfold the vertical fold: both holes reflect across the vertical centre line, giving four holes near the four corners. An option with two holes on the top edge forgot the second unfold; four holes along a diagonal used the wrong reflection lines; four holes offset from the corners ignored the punch position.
Traps
The costliest mistake is reflecting across the wrong line, especially when a fold is offset rather than central. Another is forgetting that one punch makes a hole in every layer. In assembly items, do not align pieces by their outer silhouette alone; a piece can fit the outline while its internal lines land in the wrong place.