Subject Enrichment Activity – Mathematics QUADRILATELS (Class 8)

 

Subject Enrichment Activity – Mathematics QUADRILATELS (Class 8)

Topic:

Exploring Quadrilaterals through Paper Folding – “Which Quad?”

---

Aim:

To understand and identify different types of quadrilaterals (square, rectangle, rhombus, kite) formed by folding paper and observing the shapes of creases.

---

Materials Required:

• One square sheet of coloured paper
  
  

• Ruler
  
  

• Pencil
  
  

• Scissors (optional)
  
  

• Glue (if students wish to paste their work in notebook)
  
  

• Geometry box
  
  

---

Procedure / Steps:

1. Fold the sheet into half — observe that you get a rectangle.
   
   

2. Fold it again into a quarter — you now have a smaller rectangle or square depending on your paper.
   
   

3. Make a triangular crease at the middle corner of the folded sheet.
   
   

4. Open the sheet and observe the pattern of creases. Identify the shapes formed by the intersecting lines.
   
   

5. Repeat the folding differently to form multiple creases (as shown in the image).
   
   

6. Try different types of folds (diagonals, half folds, triangles) to explore how each fold changes the pattern of quadrilaterals formed.
   
   

---

Observation Table:

Type of Fold	Shape of Paper After Folding	Crease Pattern Observed	Type of Quadrilateral Formed
Half fold (vertical)	Rectangle	1 vertical line	Rectangle
Quarter fold	Square	1 vertical + 1 horizontal line	Square
Triangular fold from middle corner	Square	Diagonal lines crossing	Rhombus / Kite
Multiple folds (as shown in activity)	Square	Concentric diagonals	Combination of Squares and Rhombi

---

Result / Conclusion:

By folding and unfolding the paper in different ways, various quadrilaterals such as rectangles, squares, rhombi, and kites are formed through creases.
This shows that a single square sheet can generate many types of quadrilaterals depending on the folds made.

---

Mathematical Concept Involved:

• Properties of quadrilaterals (sides, angles, diagonals)
  
  

• Lines of symmetry
  
  

• Relationship between diagonals in different quadrilaterals
  
  

• Visualisation and geometry through paper folding (origami approach)
  
  

---

Extension / Higher-Order Thinking (HOTs):

1. 🔹 If you fold the paper into 8 equal parts, what kind of symmetrical shapes do you observe?
   Answer: The shapes formed are smaller rectangles or squares with multiple lines of symmetry.
   
   

2. 🔹 How can you prove that the shape formed after folding twice is a square and not a rectangle?
   Answer: By measuring sides and diagonals — all sides are equal and diagonals are equal, confirming a square.
   
   

3. 🔹 What happens if you fold the paper along both diagonals and both midlines?
   Answer: You get multiple intersecting creases forming smaller squares, rectangles, and rhombi — showing symmetry across both axes.
   
   

4. 🔹 Can we find the ratio of sides of rectangles formed after each fold?
   Answer: Yes, every fold halves the side length, so the ratio becomes 1:21:21:2, 1:41:41:4, etc., illustrating proportional reasoning.
   
   

---

Reflection / Student’s Note:

📝 Folding paper helped me visualize how different quadrilaterals are related. I discovered that folding along diagonals forms rhombi and folding along midlines forms rectangles. I also noticed the symmetry and equal lengths in squares and rectangles. This activity made abstract geometry concepts more concrete and fun!