Mathematics Subject Enrichment Activity
Class: VI
Chapter: Geometry – Angles (NCERT Ganita Prakash, Pages 37–40)
Activity Title: Make Your Own Protractor
Topic
Construction and measurement of angles using a paper-made protractor.
Aim
To construct a semicircular protractor using simple paper folding and use it to understand equal angle divisions (30°, 45°, 60°, 90°, etc.).
Materials Required
A sheet of paper
Compass or circular object (to draw a circle)
Pencil, ruler, eraser
Scissors
Protractor (for verification)
Procedure
Draw a circle of convenient radius on paper using a compass (or trace around a round object).
Cut out the circle carefully.
Fold the circle into two equal halves → semicircle. Mark the crease as the diameter. Write “0°” at the right end of the diameter.
Fold the semicircle again into two equal halves. The new crease divides 180° into two parts of 90° each. Mark 90° at the top of the semicircle.
Fold the semicircle into three equal parts. Each division = 180° ÷ 3 = 60°. Mark 60° and 120°.
Further fold into six equal parts. Each part = 30°. Mark all points: 30°, 60°, 90°, 120°, 150°, 180°.
Open out the semicircle, draw lines through the creases, and write the angle measures.
Your paper protractor is now ready!
Observations (with Solutions)
A full circle = 360°
A semicircle = 180°
Folding gives equal angle divisions:
2 parts → 180° ÷ 2 = 90° each
3 parts → 180° ÷ 3 = 60° each
6 parts → 180° ÷ 6 = 30° each
By combining folds, we can also get 45°, 15°, etc.
Measured Angles with Paper Protractor:
Right angle = 90°
Straight angle = 180°
Acute examples = 30°, 45°, 60°
Obtuse examples = 120°, 135°, 150°
Reflections
Folding paper provides a hands-on understanding of how angles are formed and measured.
A protractor’s equal markings come from repeated halving and dividing of 180°.
This activity shows that geometry tools are not magical – they are based on mathematical logic of circles and symmetry.
It improves skills of angle construction, estimation, and verification.
Higher Order Thinking Skills (HOTs)
If you fold the circle into 12 equal parts, what will each angle measure?
✅ 360° ÷ 12 = 30°.How will you mark 45° on your paper protractor?
✅ By folding the semicircle (180°) into 2 → 90°, then folding 90° into 2 → 45°.Can you make a paper protractor for 15° markings?
✅ Yes, fold 90° into 6 equal parts → each = 15°.Why is it impossible to get every single degree marking (like 37°) by folding?
✅ Because folding divides angles into equal halves/thirds, not arbitrary measures. Exact 1° markings require instruments (protractor/divider).
