Paper Cutting — Unfolding the Pattern

🎯 Learning Objective

Visualise the full pattern formed when cuts made on a folded paper are opened out.

💡 Concept

• A cut made on folded paper repeats as a MIRROR image across every crease when opened
• A half-shape cut ON the crease opens into one full symmetric shape: half-circle on fold → full circle
• A shape cut at the corner where two creases meet opens at the CENTRE of the sheet
• Number of fold lines = number of symmetry axes in the final pattern
• Fold vertically then horizontally → final design is symmetric about both centre lines
• A diagonal fold makes the pattern symmetric about that diagonal

✏️ Easy Example

Q. A sheet is folded in half and a semicircle is cut with its flat side on the fold line. What appears on opening?

1. The cut mirrors across the crease
2. Two half-circles join along the fold

Answer: One full circle sitting on the centre fold line

🇮🇳 Real-Life Example

School craft snowflakes and Sankranti paper torans work on this — a few small cuts on folded paper open into a big symmetric design.

📝 Exam-Level Example

Q. A square is folded left onto right, then top onto bottom. A small quarter-circle is cut at the corner where the two folded edges (creases) meet. What is seen on opening?

1. That folded corner is the CENTRE of the original sheet
2. Quarter-circle mirrors across both creases: 4 quarters join

Answer: One full circle at the exact centre of the sheet

📝 Exam-Level Example

Q. A sheet folded once (vertical crease) has a triangle cut from the OPEN edge, away from the crease. How does the opened sheet look?

1. Cut is away from the crease, so it stays a separate shape
2. It mirrors across the vertical crease

Answer: Two identical triangles, one on each side, at equal distance from the centre line

🪄 Memory Trick

Ask two questions: was the cut ON the crease (opens into ONE bigger joined shape) or AWAY from it (opens into TWO mirrored copies)? That single check eliminates most wrong options.

⚠️ Common Mistakes

• ❌ Opening the folds in the same order as folding instead of reverse order
• ❌ Rotating the cut shape while unfolding — unfolding MIRRORS shapes, never rotates them
• ❌ Forgetting that the final pattern must be symmetric about every fold line

🏆 Exam Tips

• ✅ First fix the crease positions on the answer sheet mentally, then place mirrored shapes
• ✅ Check every option against symmetry: any option not symmetric about the fold lines is wrong

📌 Summary

• Cuts mirror across each crease on opening
• Cut on crease → one full joined shape; cut away → mirrored pair
• Corner at meeting creases → shape opens at sheet centre
• Fold lines = symmetry axes of the final pattern