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 29 children, find the number of handshakes.
- If there are 253 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 29 children
= (29 - 1) x 29 ÷ 2
= 28 x 29 ÷ 2
= 406
(c)
Guess & Check
253 = (Number of children - 1) x (Number of children) ÷ 2
253 x 2 = (Number of children - 1) x (Number of children)
506 = 22 x 23
Number of children = 23
Answer(s): (a) 15; (b) 406; (c) 23