By considering the diagrams and the pattern developed in the table, answer the following questions.
- If there are 9 kids, find the number of handshakes.
- If there are 22 kids, find the number of handshakes.
- If there are 78 handshakes, how many kids are there?
(a)
Pattern for the number of handshakes
1 kid: 0
2 kids: 0 + 1 = 1
3 kids: 0 + 1 + 2 = 3
4 kids: 0 + 1 + 2 + 3 =6
Number of handshakes = (Number of kids - 1) x (Number of kids) ÷ 2
Number of handshakes for 9 kids
= (9 - 1) x 9 ÷ 2
= 8 x 9 ÷ 2
= 36
(b)
Number of handshakes for 22 kids
= (22 - 1) x 22 ÷ 2
= 21 x 22 ÷ 2
= 231
(c)
Guess & Check
78 = (Number of kids - 1) x (Number of kids) ÷ 2
78 x 2 = (Number of kids - 1) x (Number of kids)
156 = 12 x 13
Number of kids = 13
Answer(s): (a) 36; (b) 231; (c) 13
