Handshake Blog

Part A

This problem took some thinking. I first decided that I would multiple 19X20, because there are 20 people and they will each shake 19 hands. However, then I decided to break it down and make sure that this was correct. First, I did it with 3 people which would be 3X2=6, but when I drew a picture of each person shaking a hand it was only 3 handshakes. Next, I tried 5 people. The multiplication problem would be 5x4=20 and when I drew a table to check it there were only 10 handshakes. I recognized a pattern each was half of the multiplication problem because each person is only shaking every person’s hand once and not twice. Person A is shaking person B’s hand, but then person B is not going to shake person A’s hand again. In the first multiplication problem you are accounting for AB and BA. This is not the case.

When I charted it out it looked like this.

1-2          2-3          3-4          4-5

1-3          2-4          3-5

1-4          2-5

1-5

4+3+2+1= 10

5x4=20/2= 10

I then decided to start with one less than is in the group (19) and add all the numbers up.

19+18+17+16+15+14+13+12+11+10+9+8+7+6+5+4+3+2+1= 190

Which is also the same as 20x19=360/2=190

Part B

Manuel is not correct. I do understand what he is trying to do, but like I explained above he is accounting for everyone shaking each other’s hand twice. His strategy alone does not work for this problem. His reasoning is not correct. He does try to explain himself. I think that when Manuel sees a chart or a picture he will understand why his thinking alone does not solve this problem.

Beatriz is very much on the right track. I like the way she drew a picture. Her strategy does work, but she made a mistake and did not get the correct answer. Beatriz drew a great chart and justified her answer well. Yes we can fix her mistake. At number 15, she was supposed to add 15, which would be 15+105= 120 and she recorded it as 130. This mistake caused her to get the wrong answer.  Yes, we could use her reasoning for other problems.

I enjoyed Carmel’s reasoning because I did not come up with anything close to this! It was a great pattern that I did not see at all. I am not sure if you could use this strategy for other problems. He did a great job explaining and showing his work. I can see that he arrived at the correct answer.

Katia’s way is very similar to the way that I chose to solve the problem and the way that I checked Beatriz’s work. We used different charts. I did understand what she did and it does work for this problem. Her reasoning is correct and she did a good job explaining it. I do not see any mistakes that she made and I think we could use her chart to solve other problems.