Reasoning · Grade 4-2 Figure Puzzles
Problem
Overlap corners are corners inside plus side crossings.
The outline of the shared part can only be built out of the two squares' own edges, so it can only turn a corner where an edge stops — at a square's own corner, or where two edges cut across each other.
4.G.A.1Create A Physical RepresentationA triangle needs 1 corner inside.
Reading the picture backwards, an apex made of two slanted edges has to be a corner of a square, and a flat cut-off base has to be a side of the other square slicing that corner off.
3.G.A.1Work BackwardsA triangular overlap needs exactly three corners, made of one square's corner sitting inside plus two crossings of the edges.
Every corner of the overlap is either a corner of one square lying inside the other, or a point where two edges cross.
The two kinds of corner never overlap and nothing else can make one, so their counts simply add to the number of sides.
Let just one corner poke into the other square.
Pushing the tilted square down until only one corner is still inside leaves the smallest possible overlap, and the only shape a single poking-in corner can make is a triangle.
4.G.A.2Draw A DiagramA quadrilateral needs one corner from each.
A four-sided overlap with two sides coming from each square needs each square to poke one corner into the other, so the squares must be offset from each other along a diagonal.
3.G.A.1Work BackwardsOverlap the two squares at a slant.
Overlapping the squares corner-to-corner along a diagonal always leaves one corner of each square inside the other, and that is the ordinary four-sided overlap.
4.G.A.2Draw A DiagramA pentagon needs 3 corners inside in total.
A full, uncut side showing up in the overlap is a strong clue — it means the other square swallowed that side whole, so both of its endpoints are corners hiding inside.
3.G.A.1Work BackwardsPush in far enough for two corners of one square.
Once one square has swallowed a whole side of the other, that side stays in the overlap, and the single corner poking in from the left adds the bend that turns four sides into five.
4.G.A.2Draw A DiagramAll three drawings match their cases.
Counting the sides of the shaded piece is the whole question, so counting them again at the end is the natural check.
4.G.A.2Create A Physical RepresentationEvery corner of the shared part is either a corner that slipped inside or a place where two edges cross — count those and you know how many sides the overlap will have.