Javier and Bob had a terrific time visiting Tséhootsooí Middle School, Round Rock Elementary/Junior High School, Tsaile Public School, and Kayenta Middle School. We shared the following activities with students at those schools:
- The Friends and Enemies Game – Participants secretly pick one person in the room to be a friend and one person to be an enemy. When Javier shouted, “Go!” students would move around the room so that their friend was between them and their enemy. We examined questions like, “How many people are needed to play the game?” and “If we think of people as points and connected segments between those points, which shapes are possible if everyone in has their friend between them and their enemy?”
- Liar’s Bingo – (link to article PDF describing it, pp.18-19) – Look at the cards (PDF). What do you notice? Then Bob does a magic trick and everyone in the room figures it out.
At Diné College, we shared the following activities with the teachers who gave us their time:
- The Handshake Problem – How many handshakes in a group of size n? What if we care about the order in which people shake hands? In a group of size five, how many ways can every person shake only two hands? We got a hand(le) on many other questions related to the simple act of a bunch of people shaking hands.
- Musical Pigeonholes – In a typical game of musical chairs, you start with one fewer chair than people. The people dance around to the music and when the music stops, people scramble to the chairs. The person without the chair is kicked out of the game, one chair is removed and the game repeats. In our version, EVERYONE must sit down in a chair and each time we remove one chair but keep everyone playing. What can we say about the number of people in each chair each time? What patterns arise?
- The Cookie Jar Problem – (link to PDF) – Numbered cups and same number of chips in each cup. What questions can we ask? We asked and asked some more. The surprise is that we were toying with the same algorithm used to help guide the appropriate dosage of “intensity moderation radiation therapy” for patients with cancer. This is a great example of how asking questions leads people to see patterns which leads to theories. Those theories, in turn, find application in beneficial and sometimes very useful ways. Thanks to Gabriella Pinter for showing Bob this activity!
Our gratitude to our hosts, our participants, and to the National Science Foundation for funding our trip. – Bob & Javier