Reasoning · Grade 4-1 Overlapping, Folding, and Cutting Paper
Problem
You are holding the bottom-right quarter of the sheet.
Naming which quarter you are holding, and which of its four edges are creases, is the one piece of bookkeeping that makes the rest of the problem straightforward instead of guesswork.
4.G.A.1Visualize Spatial RelationshipsOne cut through four layers opens into 4 holes.
A crease is a mirror: whatever is on one side of it appears flipped on the other, which is exactly what a line of symmetry means.
4.G.A.3Visualize Spatial RelationshipsOne cut through the folded sheet makes four holes, because each crease mirrors whatever sits on one side of it.
A crease sends every cut point straight across to a partner the same distance away, so each crease doubles what the cut produces.
The two creases act one after the other and neither limits the other, so the doublings multiply into four copies.
If unsure, fold and snip a real sheet.
Handling the actual paper turns an imagination task into an observation, and it is the fastest way to check an answer you reasoned out.
4.G.A.3Create A Physical RepresentationThe hole in (1) touches the outer corner, not a crease.
Half of a half is a quarter, so the little corner square is a quarter of the way along each side of the big sheet — easy to mark before drawing.
4.NF.B.4Visualize Spatial RelationshipsOpened out, all four corners go and a cross is left.
Undoing the creases in the reverse order to the folds means only one mirror image has to be pictured at a time, which is much safer than trying to see all four copies at once.
4.G.A.3Work BackwardsThe four corners are 1/4, so 3/4 remains.
Counting up the four equal holes as a fraction of the sheet is a quick numerical test that the drawing is not missing a hole or showing an extra one.
4.NF.B.4Work BackwardsThe triangle in (2) sits at the centre where both creases meet.
Spotting that the corner of the shaded triangle is the centre of the sheet, not a corner of it, is the whole trick — the cut touches both creases, so its copies will meet in the middle instead of scattering to the corners.
4.G.A.1Visualize Spatial RelationshipsOpened out, four triangles make one diamond hole.
Because the cut runs right along both creases, the mirror copies join edge to edge rather than sitting apart, which is why four small triangles turn into one tidy diamond.
4.G.A.3Work BackwardsThe hole is 1/8, so 7/8 remains.
Turning the answer into a fraction of the sheet gives a size to compare against the drawing, catching a hole drawn far too big or too small.
4.NF.B.4Work BackwardsEvery crease is a mirror, so undo the folds one at a time and flip the hole across each crease — a hole touching the raw edges ends up at the corners, a hole touching the creases ends up in the middle.