Teacher Notes
X
TIMS Challenge
This problem can be used as a Problem of the Week.
There are 10 handshakes among 5 people.
To solve this problem, students can act out the handshaking. Have one person shake everyone's hand (4 handshakes). Since the next person already shook the first person's hand, he or she will only have to shake 3 other people's hands; the next only 2, etc. The total is 4 + 3 + 2 + 1 = 10 handshakes.
An incorrect answer that is often given is 20: 5 people each shake hands with 4 others, and 5 × 4 = 20. However, every handshake involves 2 people, so this answer counts each handshake twice.
Meeting Individual Needs
Challenge students to complete DPP Item BB by acting out the problem and keeping track of the number of handshakes. Then they can organize the information they collect in a table or diagram and look for patterns. Remind students that you expect them to explain their thinking so someone outside their classroom will understand what they did to solve the problem and why it worked.
BB. Handshakes 
Five people arrive at a party. They all shake hands with each other. How many handshakes are there in all? It might help to draw a picture, make a table, or act out the handshaking. Show or tell how you solved the problem so someone else can understand your thinking. Answer the same problem for 8 people.
Explain your thinking.
