Page 33 - Ganit Kaushal

Activities

Activity 1

Objective: To construct the shape sequence of Koch snowflakes starting with an equilateral triangle of side 9 cm.

Material Required: White paper sheets and scissors.

Procedure: Do as asked in the following:

1. Start with an equilateral triangle of side 9 cm. Follow the steps given for the construction of the Koch
snowflake sequence.
2. Make four iterations.

3. Count the total line segments in each shape of the Koch snowflake.

4. Write them as a sequence of numbers. Yes, you got it right. It’s 3, 12, 48 …
5. Observe the pattern and explain it.
Correct. It is three times the powers of 4 starting with the power 0, i.e.,

T = 3 × 4 n – 1 ; n = 1, 2, 3 …….
n
6. What is the 4th term of this sequence?
Right. It is 192.

Project/Activity 2

Objective: To recognise the pattern in the given number sequence.
Do as asked in the following:

1. Recognise and write the pattern name in each of the following sequences given below from (a) to (j)
in your notebook.

2. Rewrite each of the following sequences in your notebook, along with the next three terms in each
sequence.

3. In each of the following sequences, write in your own words the rule for forming the numbers in the
sequence.
(a) 1, 1, 1, 1, 1, 1, 1, ...... (b) 1, 2, 3, 4, 5, 6, 7, ......

(c) 1, 3, 5, 7, 9, 11, 13, ...... (d) 2, 4, 6, 8, 10, 12, 14, ......
(e) 1, 3, 6, 10, 15, 21, 28, ...... (f) 1, 4, 9, 16, 25, 36, 49, ......

(g) 1, 8, 27, 64, 125, 216, ...... (h) 1, 2, 3, 5, 8, 13, 21, ......
(i) 1, 2, 4, 8, 16, 32, 64, ...... (j) 1, 3, 9, 27, 81, 243, 729, ......

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