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).
   
   

Origami Bunny Mathematics Subject Enrichment Activity

 

Mathematics Subject Enrichment Activity

Class: VI
Chapter: Geometry – Angles & Paper Folding (NCERT Ganita Prakash, Page 43)
Activity Title: Exploring Angles through Paper Folding (Origami Bunny)

Topic

Origami Bunny Understanding angles, symmetry, and crease geometry using paper folding.

Aim

To explore how folding a square sheet of paper creates creases that form different angles, and to measure and classify these angles after unfolding.

Materials Required

• Square sheet of coloured paper
  
  

• Ruler
  
  

• Protractor
  
  

• Pencil & eraser
  
  

• NCERT Textbook (Page 43, Activity 8 for reference)
  
  

Procedure

1. Take a square sheet of paper.
   
   

2. Follow the steps shown in the textbook: fold along the given dotted lines to create the paper bunny (Steps 1–8).
   
   

3. After completing, unfold the paper completely.
   
   

4. Observe the creases formed on the square.
   
   

5. Mark the creases with a pencil.
   
   

6. Use a protractor to measure the angles formed at the intersections of creases.
   
   

7. Record the angle measurements and classify them as acute, right, obtuse, or straight.
   
   

Observations (with Solutions)

Make the paper craft as per the given instructions Then, unfold and open the paper fullyDr aw lines on the creases made and measure the angles formed.

When unfolded:

• Step 1 fold → Diagonal crease divides 90° into two 45° angles.
  
  

• Step 2 fold → Horizontal crease forms 180° straight line.
  
  

• Step 3 fold → Vertical crease forms 90° with horizontal.
  
  

• Step 4 & 5 folds → Small diagonal creases form 30°, 45°, 60° angles depending on symmetry.
  
  

• Step 7 fold → Bottom triangle crease forms an isosceles triangle with angles approx. 45°, 45°, 90°.
  
  

Thus, the unfolded paper shows:

• Right angles (90°)
  
  

• Acute angles (30°, 45°, 60°)
  
  

• Obtuse angles (120°, 135°)
  
  

• Straight angles (180°)
  
  

Reflections

• Folding creates lines of symmetry.
  
  

• Creases represent angle bisectors and triangular subdivisions.
  
  

• We can discover geometry in art (origami) – a real-life connection.
  
  

• This activity improves measurement skills, visualization, and reasoning.

Higher Order Thinking Skills (HOTs)

1. If you fold the square paper along both diagonals, how many equal angles are formed at the center?
   ✅ 4 equal angles of 90°.
   
   

2. Can you prove that folding always creates angle bisectors?
   ✅ Yes, because folding aligns one side over the other, dividing the angle into two equal halves.
   
   

3. Create another origami model (boat, house, etc.) and unfold – what new angles and shapes are formed?

1) If you fold the square along both diagonals, how many equal angles are formed at the centre?

Answer: Four right angles (90° each).
Why: In a square, the diagonals are perpendicular and intersect at the centre. Each diagonal is an angle bisector of a 90° corner, so around the centre you get 360∘=4×90∘360^\circ = 4\times90^\circ360∘=4×90∘.

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2) Prove that a fold (crease) is an angle bisector.

Answer/Proof (superposition):
Let ∠AOB\angle AOB∠AOB be the angle at O. Fold along line lll so that ray OAOAOA falls exactly on ray OBOBOB. Folding is a reflection in lll, which is a distance-preserving isometry. Hence every point on OAOAOA maps to an equally distant point on OBOBOB. Therefore ∠AOl=∠lOB\angle AOl=\angle lOB∠AOl=∠lOB; i.e., line lll splits ∠AOB\angle AOB∠AOB into two equal angles. So every crease made by matching two edges/rays is an angle bisector.

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3) Create another model and state the angles/shapes formed on unfolding.

Example model (easy & symmetric): Fold both diagonals and both midlines (horizontal & vertical). Unfold.

• Angles at centre: The two midlines are perpendicular (90°) and each is at 45° to each diagonal. With the four creases together you get 8 equal central angles of 45∘45^\circ45∘ (since 360∘/8=45∘360^\circ / 8 = 45^\circ360∘/8=45∘).
  
  

• Shapes formed: The square is partitioned into 8 isosceles right triangles meeting at the centre; each has angles 45∘,45∘,90∘45^\circ,45^\circ,90^\circ45∘,45∘,90∘. Along edges you also see symmetrical kite/triangle regions confirming line-symmetry in both axes and both diagonals.

• (Students may present any other symmetric fold—e.g., “blintz” fold (all four corners to centre). On unfolding, creases again act as angle bisectors and typically produce many 45∘45^\circ45∘, 90∘90^\circ90∘, 135∘135^\circ135∘ angles with multiple isosceles right triangles.)