Summer SAVY 2019: Session 1, Day 1 – Puzzles and Problem Solving (Rising 5th/6th)
The Puzzles and Problem Solving class first investigated the Ultimatum Game (http://en.wikipedia.org/wiki/Ultimatum_game) and the Prisoner’s Dilemma (http://en.wikipedia.org/wiki/Prisoner’s_dilemma). After this introduction to game theory, the students then played a 2-player card game, attempting to determine the winning strategy. The problem goes like this:
“Given a deck of 21 cards, players alternate turns by taking one, two, or three cards (that is, you must take at least one but cannot take more than three). The winner of the game is the person who takes the final card. Is there a strategy you could use that would guarantee you would win?”
Students played this game several times and noticed patterns and important situations as they arose. Once the initial problem was solved, we changed the problem in multiple ways (including introducing some abstract concepts!) to continue to develop our understanding of the prompt. Some of these extensions remained elusive for many today, although the students were making progress!
In the afternoon, we looked a dice game called “Petals Around the Rose.” It involves being able to decipher a riddle through understanding various rolls of the dice. This proved challenging for many, but we made some headway as we struggled. We learned what the roses were, and gradually we had built enough knowledge to be able to solve the riddle. Later in the week, we will look at a slightly more complicated dice game. Today’s game can be played here if you are interested: http://www.freeworldgroup.com/games/roses/
Near the end of the day, we worked on a couple of puzzles where one has to successfully transport people or objects across barriers given certain restrictions. After initial exclamations of “That’s not possible!” (I heard this on multiple occasions!), students ended up being very successful in getting a wolf, goat, and cabbage over to the other side of the river. We still haven’t figured out how to get the Beatles to their concert on time, but I bet we’ll solve that soon!
At the very end of the day, we had a brief introduction to the game of ZipZap, a counting game with strange rules that will often be our wrap-up to a long day of class. We were just practicing counting today, and students were getting the hang of it as we went along.
Students should be bringing home a manila folder with them. It should have the three handouts from today if you are interested in puzzling along with the students or asking them to explain what they learned in class. I ask that students bring this folder back with them each day, as we will continue to add fun puzzles and problems to the mix!
I am looking forward to the rest of the week!