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\\October 8, 2025 3:15 PM Bharat Arora P-9 Reader _________________________ Date: ___________________74

We can see many patterns in this triangle. 1 TeSSellaTioNS
Š The first diagonal is ‘1’. 1 1 2 1 1 Tessellation is the tiling pattern resulting from the repeating arrangement of a particular

Š The next diagonal has the counting numbers, that 1 3 3 1 shape to cover a plane without leaving any gaps or overlapping. Observe the following
is, 1, 2, 3, ... 1 4 6 4 1 tessellations.
Can you find any other pattern? 1 5 10 10 5 1
FACTS
Knowledge Desk A famous Dutch artist, M.C. Escher, was

Pascal’s triangle is a special arrangement of numbers named after Blaise Pascal, a famous a master of tessellations. He created
amazing art where interlocking shapes
French mathematician and philosopher. In this arrangement, the numbers are arranged in a of birds, fish, and lizards would cover
triangular array such that the number 1 is there at the end and the beginning of all the rows the entire page with no gaps.
and the remaining numbers are the sum of the nearest two numbers in the row just above.

Some More Number Patterns Think Tank Logical Thinking
Let us observe the following number patterns and try to write the missing numbers. Check which among the following shapes provides tessellation.

1. 1 4 9 16 25 2. 0 2 6 12 20 30 1. 2. 3. 4. 5. 6.

+3 +5 +7 +9 +2 +4 +6 +8 +10 +12 +14 +16

3. 4. 5.
1 × 1 = 1 1 × 9 + 2 = 11 1 × 8 + 1 = 9 Practice Time 7C

11 × 11 = 121 12 × 9 + 3 = 111 12 × 8 + 2 = 98
111 × 111 = 12321 123 × 9 + 4 = 1111 123 × 8 + 3 = 987 1. Identify the pattern and find its next two terms.
1111 × 1111 = 1234321 1234 × 9 + 5 = 11111 1234 × 8 + 4 = 9876 (a) (b)

___________=________ ___________=_______ ___________=______ Pattern made with a ______ turn Pattern made with a ______ turn
___________=________ ___________=_______ ___________=______
(c) (d)
Multiplication tables also show some beautiful patterns.
Look at the tables of 6 and 8 given below:

Table of 6: Pattern made with a ______ turn Pattern made with a ______ turn
1
6 12 18 24 30 36 42 48 54 60 2. Make patterns of the following objects by giving them a turn every time.
4
(a) (b)
The ones digits repeat themselves after the fifth multiples.

Table of 8:
8 16 24 32 40 48 56 64 72 80 (c) (d)

The ones digits repeat themselves after the fifth multiples.
1
3. Make patterns of the following shapes by giving them a turn every time.
2
Think Tank Logical Thinking
(a) (b) +
Write down your family member’s mobile numbers in your notebook. Can you observe ÷ –
or establish any pattern in them? ×

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