By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 6 children, find the number of handshakes.
- If there are 37 children, find the number of handshakes.
- If there are 91 handshakes, how many children are there?
(a)
Pattern for the number of handshakes
1 child: 0
2 children: 0 + 1 = 1
3 children: 0 + 1 + 2 = 3
4 children: 0 + 1 + 2 + 3 =6
Number of handshakes = (Number of children - 1) x (Number of children) ÷ 2
Number of handshakes for 6 children
= (6 - 1) x 6 ÷ 2
= 5 x 6 ÷ 2
= 15
(b)
Number of handshakes for 37 children
= (37 - 1) x 37 ÷ 2
= 36 x 37 ÷ 2
= 666
(c)
Guess & Check
91 = (Number of children - 1) x (Number of children) ÷ 2
91 x 2 = (Number of children - 1) x (Number of children)
182 = 13 x 14
Number of children = 14
Answer(s): (a) 15; (b) 666; (c) 14
