By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 10 children, find the number of handshakes.
- If there are 23 children, find the number of handshakes.
- If there are 276 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 10 children
= (10 - 1) x 10 ÷ 2
= 9 x 10 ÷ 2
= 45
(b)
Number of handshakes for 23 children
= (23 - 1) x 23 ÷ 2
= 22 x 23 ÷ 2
= 253
(c)
Guess & Check
276 = (Number of children - 1) x (Number of children) ÷ 2
276 x 2 = (Number of children - 1) x (Number of children)
552 = 23 x 24
Number of children = 24
Answer(s): (a) 45; (b) 253; (c) 24
