Reasoning · Grade 4-1 Overlapping, Folding, and Cutting Paper
Problem
In the Example the two points on the crease stay put.
Folding along a line is exactly the line-of-symmetry idea from Grade 4: the fold matches the flap onto its mirror image, so the crease behaves like a mirror standing on the paper.
4.G.A.3Solve An Easier Related ProblemA corner moves like a mirror image, the same distance across.
This is the one fact a reflection gives you: same distance, straight across, nothing stretched. With paper in your hand you can check it by pressing the crease and holding the sheet up to the light.
8.G.A.1Create A Physical RepresentationA folded corner lands the same distance from the crease, straight across it, with nothing stretched.
The crease behaves as a mirror, so the corner and its landing spot are equally far from it on opposite sides.
Folding is a flip, and a flip keeps every length and every angle, so the folded flap is an exact copy of what it came from.
In (a) the flap lands inside, giving a 4-sided outline.
When both ends of the crease are already corners or edge points, only one corner is left to track, so a single mirror measurement settles the whole picture.
8.G.A.1Visualize Spatial RelationshipsIn (b) one corner meets the top edge and one juts out: 6-sided.
The hint is doing measuring work for you: being told a corner lands on the top edge fixes that point without any calculation, and then only one corner is left to place.
8.G.A.1Visualize Spatial RelationshipsIn (c) the diagonal fold pushes a tab right: 5-sided.
This is the case worth pausing on: a diagonal fold only makes the two halves match up perfectly for a square. On a taller rectangle the folded half slides past, and that is precisely why a piece hangs over the edge.
8.G.A.1Visualize Spatial RelationshipsIn (d) the hint pins the crease and a tab goes left: 5-sided.
"Fold so that these two points meet" always names one particular crease — the one that has both points the same distance away on opposite sides — so the hint replaces guessing with a single drawn line.
4.G.A.3Draw A DiagramReal paper confirms 4, 6, 5, 5 corners.
Comparing the number of corners you drew with the number you feel on the folded paper catches almost every mistake in this kind of question.
4.G.A.1Create A Physical RepresentationA crease is a mirror: follow the corners across it one at a time, and the ones that overshoot the edge are exactly the bumps in your outline.