Patterns - Making Rules
Aarav and Meera were making human faces using black stickers for eyes. Each face they created required two black stickers. As they continued adding more faces, their friend Rohan joined them and asked:
"How many black stickers will be needed for 8 faces?"
Observing the Pattern
- For 1 face → 2 black stickers
- For 2 faces → 4 black stickers
- For 3 faces → 6 black stickers
- For 4 faces → 8 black stickers
From this, they noticed a pattern: Number of black stickers = 2 x Number of faces
Finding the Stickers Needed for 69 Faces:
Using the pattern: Black stickers required = 2 x 69 =
Thus, to make 69 faces, they need 138 black stickers.
To make a triangle , 3 match sticks are used.
If we want to make two triangles we need
The Following table gives the number of match sticks required and the number of triangles to be formed:
| Number of triangles to be formed | 1 | 2 | 3 | 4 | 5 | 6 | ... |
|---|---|---|---|---|---|---|---|
| Number of match sticks required | .... | ||||||
| Observation(pattern) | 3 × 1 | 3 × 2 | 3 × 3 | 3 × 4 | 3 × 5 | 3 ×6 | ... |
To make a square, 4 match sticks are needed.
If we want to make two squares we need
If we want to make three squares we need
Let us arrange
| Number of squares to be formed | 1 | 2 | 3 | .... |
|---|---|---|---|---|
| Number of match sticks required | ... | |||
| Observation(pattern) | 4 × 1 | 4 × 2 | 4 × 3 |