Reasoning · Grade 4-1 Transformations of Figures
Problem
A turn cannot change side count or side length.
This is the whole reason the puzzle is fair: it guarantees that a fingerprint made only of counts and lengths will survive whatever turn was used.
8.G.A.1Visualize Spatial RelationshipsA turn cannot change how many sides a piece has or how long they are, so those counts survive whatever rotation was used.
Rotating lays the piece onto a copy of itself, so every side keeps its length and every corner keeps its angle.
Any piece whose counts differ from the template can therefore be thrown out at once, without ever being turned.
Give each template an identity card of sides and notches.
Counting sides and counting notches needs no ruler and no protractor, yet those two numbers alone already split the pieces into groups that can never mix.
8.G.A.2Make A Systematic ListThrow out every piece with the wrong counts.
Two cheap counts do almost all the searching, so the slow work of mentally rotating a shape only has to be done a few times instead of two dozen.
8.G.A.2Eliminate Possibilities5 sides and 1 notch makes C the left-of-centre piece.
Starting with the template that has the most lopsided side lengths is smart order-of-work: it is the one a young solver can lock on to by eye alone.
8.G.A.2Visualize Spatial Relationships6 sides and 1 notch makes A the right piece.
Once you have decided which piece it must be, checking is quick: put a fingertip on the notch of each and see whether the sides going out from the notch have matching lengths.
8.G.A.2Visualize Spatial Relationships8 sides and 2 notches makes B the bottom-left corner piece.
A piece pressed into a corner of the square has two of its sides forced to be straight and at right angles, which is a strong extra clue once the side count has narrowed things down.
8.G.A.2Visualize Spatial RelationshipsAll three match by turning alone, never mirroring.
Finishing the sweep instead of stopping at the first plausible piece is what turns a guess into an answer.
8.G.A.2Eliminate PossibilitiesTurning a shape never changes how many sides or notches it has — count those first and most of the puzzle disappears.