A Fold-and-Punch Item With Four Holes and Three Options
The item reads: 'A square sheet of paper 8 cm on each side is folded so that the left half lies exactly on the right half, then folded again so that the bottom half lies exactly on the top half. The packet is now one quarter of the original size. A single hole is punched through all the layers, 1 cm from the top edge and 1 cm from the right edge of the packet. The paper is unfolded. Which picture shows the holes?'
Option A: four holes, each near a different corner of the sheet. Option B: two holes, near the two top corners of the sheet. Option C: four holes forming a small square near the centre of the sheet.
Five teachers review the item. Two prefer C, arguing that the punch is close to the middle of the folded packet, so the holes must end up close to the middle of the sheet. The team also wants a second item in which the punch is made exactly on the folded edge, 3 cm from the top of the packet.
1. State the correct option and justify it from layer count, edge mapping and symmetry.
Read the worked answer
Option A.
Layers. Each fold doubles the layers: two folds give 4 layers, and a punch through all of them gives four holes - not one, not two.
Edge mapping. After the first fold the packet's left edge is the vertical crease; after the second, its bottom edge is the horizontal crease. The top and right edges are the open edges, and they carry the original sheet's top and right edges. So a punch 1 cm from the top and 1 cm from the right of the packet is 1 cm from the top-right corner of the unfolded sheet.
Symmetry. Unfolding mirrors each hole across each crease. Across the horizontal centre line the top-right hole produces a bottom-right partner; across the vertical centre line each produces a partner on the left. Four holes, one near each corner.
Option C would be correct only if the punch were near the packet's bottom-left corner - the corner where the two creases meet, which is the centre of the sheet.
2. Diagnose the misconception behind each distractor and rank them by how tempting they are for a Grade 3 child.
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Option B (two holes, top corners). The fold sequence and the mirror across the vertical crease are tracked, but the layer count is not: the horizontal fold doubles the pattern without creating a new position. This usually means the child is simulating the folds visually and loses track of the second one.
Option C (four holes, near the centre). The count is right and the arrangement is attractively symmetric, but the punch is located relative to the wrong corner. The packet's creases become the sheet's centre lines, so the fold corner maps inward and the open corner maps outward.
Ranking: C is the more tempting. It satisfies hole count and symmetry, so the only thing wrong is the packet-to-sheet mapping - exactly the step Grade 3 children most often skip. B is easier to reject once a child counts layers. If only three options are needed, keep C and replace B.
3. The team wants a second item with the punch made exactly on the folded edge. Predict the unfolded result and explain why the item is hard to score.
Read the worked answer
The packet is about 4 cm tall after folding. A punch exactly on the vertical crease (the packet's left edge) does not open into two separate holes when that fold is released: it produces one hole centred on the sheet's vertical centre line, twice as wide as the punch. The horizontal fold still mirrors it, so the unfolded sheet shows two elongated holes on the vertical centre line, one above and one below the horizontal centre line.
It is hard to score for three reasons. The count depends on the convention: two wide holes, or four half-holes? The shapes are not circles, so a child drawing two circles, two capsules or four semicircles could all be described as correct. And if the punch is made close to the fold corner, the two elongated holes merge into one, which changes the answer entirely.
Use it as a discussion item, or rewrite the stem as 'how many separate holes are there after unfolding?' and place the punch far enough from the corner that merging cannot occur.