Class 6 NCERT bridge course Answers Activity W1.7 Matchstick Triangle Patterns

  Class 6 NCERT bridge course Answers Activity W1.7

Activity W1.7  

Matchstick Triangle Patterns

Matchstick activity: 

 Ask the students to make shapes using equilateral triangles with the help of matchsticks as given below: 

 Let them make more such chains by adding equilateral triangles. 

 Ask them to find out the number of matchsticks required in each step. 

Let them come up with a pattern. 

Some interactions through activities will expose students to the properties of shapes such as squares and rectangles.  

Activity W1.7 – Matchstick Triangle Patterns

Objective:

To explore patterns and geometry using equilateral triangles formed by matchsticks. Students observe how shapes grow and identify a numerical pattern.

Instructions for Students:

1. Use matchsticks to make a chain of equilateral triangles as shown in the image.

2. Begin with 1 triangle, then add more triangles by sharing sides where possible.

3. Count the number of matchsticks required at each step.

4. Identify and describe the pattern.

5. Predict how many matchsticks will be needed for more triangles.

Step-by-Step Shape Formation:

From the image:

Step	No. of Triangles	Matchsticks Used
1	1	3
2	2	5
3	3	7
4	4	9

Pattern Observation:

• First triangle = 3 matchsticks

• Every new triangle shares one side with the previous one, so we add only 2 more matchsticks for each new triangle.

Formula:

$$\text{Matchsticks} = 3 + 2 \times (\text{No. of triangles} - 1)$$

or simply,

$$\text{Matchsticks} = 2n + 1 \quad \text{where } n = \text{number of triangles}$$

Examples:

• For 5 triangles:
  $2 × 5 + 1 = 11$ matchsticks

• For 10 triangles:
  $2 × 10 + 1 = 21$ matchsticks

• For 20 triangles:
  $2 × 20 + 1 = 41$ matchsticks

Conclusion:

This activity helps students:

• Understand patterns in geometric growth.

• Practice counting and reasoning.

• Learn properties of equilateral triangles, side-sharing, and efficiency in design.

Image Explanation:

The provided image clearly illustrates the chain pattern:

• The triangles are equilateral and connected side-by-side.

• Each new triangle reuses a side, reducing the total number of matchsticks needed.