Page 12 - Maths Skill - 6

10 Maths

3. Patterns in Division
Observe the following patterns.

� 14 ÷ 7 = 2 � 11 ÷ 11 = 1
140 ÷ 7 = 20 121 ÷ 11 = 11
1400 ÷ 7 = 200 1221 ÷ 11 = 111
14000 ÷ 7 = 2000 12221 ÷ 11 = 1111
140000 ÷ 7 = 20000 122221 ÷ 11 = 11111

4. Patterns in Square Numbers
Observe the following,
1 × 1 = 1; 2 × 2 = 4; 3 × 3 = 9; 4 × 4 = 16
A number when multiplied by itself is called a squared number. Geometrically, these numbers form a square as
shown here.
4

3

4

2 3

2

1 dot 4 dots 9 dots 16 dots
Hence, we can make a sequence of square numbers 1, 4, 9, 16, 25, 36, ............. . This sequence can be extended
infinitely. We may also find some more interesting facts and patterns within the square numbers.
1 × 1 = 1 = 1
2
2
2 × 2 = 2 = 4 = 1 + 3 [Sum of the first two odd numbers]
2
3 × 3 = 3 = 9 = 1 + 3 + 5 [Sum of the first three odd numbers]
2
4 × 4 = 4 = 16 = 1 + 3 + 5 + 7 [Sum of the first four odd numbers]
2
5 × 5 = 5 = 25 = 1 + 3 + 5 + 7 + 9 [Sum of the first five odd numbers]
If you observe the above pattern carefully, each square number is the sum of consecutive odd numbers. Can you
guess the next step in the pattern?

5. Patterns in Triangular Numbers
Observe the following shapes made by dots.

Each of the given shapes is a triangle. Count the numbers of dots. These are 1, 3, 6, 10, 15,.... The numbers that
form a triangle are called triangular numbers.