Spatial reasoning for pipe trades aptitude tests: folding, rotation and cubes

Spatial reasoning is the ability to picture shapes in your head — turning them, folding them, seeing them from another side. Some UA locals list it by name: Local 342's test covers math, spatial relations and mechanical aptitude. Prep providers also describe a paper-folding section in the battery many locals use. Not every local tests it, so check your local's notice. If yours does, it is worth practising: it is the section applicants are least likely to have seen before, and it improves fast.

Paper folding

A square of paper is folded once or more, a hole is punched through every layer, and you choose what the sheet looks like opened out.

• Unfold in reverse. Start with the last fold. Each time you open a fold, every hole gets a mirror-image partner on the other side of that fold line.
• Count first. One fold doubles the holes, two folds make four, three make eight. Any answer with the wrong number of holes is out.
• Check the mirror lines. Holes are always symmetric about the fold lines. An answer with holes off those lines of symmetry is wrong.

Rotation: turned or flipped?

You see a shape and four options. One is the same shape turned on the page; the others are mirror images — the shape flipped over. No amount of turning makes a mirror image match.

• Pick one distinctive feature, such as a stub sticking out, and note which side of the long part it is on.
• Turn the option in your head until its long part lines up with the original, then check whether the stub is on the same side.

Counting cubes

A stack of cubes is drawn in three dimensions and you count them, including the ones you cannot see that hold up the ones you can.

• Go column by column. For each top face you can see, count how many cubes high it is.
• Add the columns up. The common mistake is to count only the faces you can see.

Cube nets

A flat pattern of six squares folds into a cube, and you are asked which face ends up opposite another.

• Squares that share an edge on the pattern end up next to each other, never opposite.
• In a straight row of squares, the two squares either side of a middle one are opposite each other.
• For bent patterns, pick one square as the floor and fold the others up around it, one at a time.

Why it matters on the job

Pipe work is three-dimensional. Fitters read isometric drawings, picture a rolling offset that moves up and sideways at once, and lay out runs around obstacles they cannot see yet. That is presumably why some locals test it. Our spatial reasoning practice has over a hundred questions of these four kinds, with a free timed sample.