or “How Many Clinks?”

If you’ve never tried to solve the Handshake Problem before, I’d highly advise trying it now.

*Marcia is at an OWP Summer Institute with X students. On the first day of class, her teacher asks everyone to shake hands and introduce themselves to each other. How many handshakes were there? Brainstorm some ways you could find an answer.*

Recently I was a demi-facilitator for the Oakland Writing Project Summer Institute 2015. I used a this problem as an example of a rich task with multiple entry points. What phenomenal mathematical discourse erupted from a room of K-12 ELA teachers! So many “aha moments” and so many great discussions came out of our brief time together.

They must’ve had an awesome teacher.

Thanks to Barb, my math friends and I solve a version of this problem every time we go out to dinner, or at least every time we have drinks. Instead of everyone shaking hands, Barb has us all clink each other’s glasses. Instead of counting handshakes, we count clinks.

Same concept; much more fun application.

2 people? 1 clink. 3 people? 3 clinks. 4 people? 6 clinks.

The trick is to clink everyone individually. You can’t simply do a group toast; you have to take the time to clink everyone else’s glasses. It only gets better with more people (said the math teacher).

The next time you get together with friends, don’t be afraid to propose this toast: “n x (n-1) / 2, where n = the number of friends!” Then count the clinks and compare your number to the algebra.

Cheers!

–Monie

#xmath #handshakeproblem #clinks