Make Your Own Protractor Mathematics Subject Enrichment Activity

 

Mathematics Subject Enrichment Activity

Class: VI
Chapter: Geometry – Angles (NCERT Ganita Prakash, Pages 37–40)
Activity Title: Make Your Own Protractor

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Topic

Construction and measurement of angles using a paper-made protractor.

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Aim

To construct a semicircular protractor using simple paper folding and use it to understand equal angle divisions (30°, 45°, 60°, 90°, etc.).

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Materials Required

• A sheet of paper
  
  

• Compass or circular object (to draw a circle)
  
  

• Pencil, ruler, eraser
  
  

• Scissors
  
  

• Protractor (for verification)
  
  

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Procedure

1. Draw a circle of convenient radius on paper using a compass (or trace around a round object).
   
   

2. Cut out the circle carefully.

3. Fold the circle into two equal halves → semicircle. Mark the crease as the diameter. Write “0°” at the right end of the diameter.
   
   

4. 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.
   
   

5. Fold the semicircle into three equal parts. Each division = 180° ÷ 3 = 60°. Mark 60° and 120°.
   
   

6. Further fold into six equal parts. Each part = 30°. Mark all points: 30°, 60°, 90°, 120°, 150°, 180°.
   
   

7. Open out the semicircle, draw lines through the creases, and write the angle measures.
   
   

8. Your paper protractor is now ready!
   
   

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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°
  
  

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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.
  
  

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Higher Order Thinking Skills (HOTs)

1. If you fold the circle into 12 equal parts, what will each angle measure?
   ✅ 360° ÷ 12 = 30°.
   
   

2. How will you mark 45° on your paper protractor?
   ✅ By folding the semicircle (180°) into 2 → 90°, then folding 90° into 2 → 45°.
   
   

3. Can you make a paper protractor for 15° markings?
   ✅ Yes, fold 90° into 6 equal parts → each = 15°.
   
   

4. 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).