Summer SAVY 2019: Session 1, Day 2 – Puzzles and Problem Solving (Rising 5th/6th)
We began class today by delving deeper into the problems studied yesterday. Each day will begin with two questions designed to have the students apply the knowledge learned in the previous day to a new scenario. Today’s questions dealt with the 21-card game and ZipZap, and both questions led to interesting discussions about factors, multiples, and divisibility rules. Students learned that there actually is a divisibility rule for 7! We also got to discuss negative numbers in the process of working through a few examples.
Another problem we investigated today involved determining how many ceiling lights out of 20,000 would be on after one person pulls every chain, another pulls every other chain, the next every 3, and so on until finally the last person just pulls the 20,000th chain. A common theme to several problems we have solved thus far is the creation of a similar but simpler problem to see what patterns develop. Students used playing cards to model these lights and noticed several patterns, some of which led nowhere and others led somewhere but very slowly. Ultimately, we determined that all lights that are perfect square numbers are on. We then delved into why that was the case.
We then simulated working through the Monty Hall Problem (https://en.wikipedia.org/wiki/Monty_Hall_problem). Each partnership got to play twenty games while sticking and twenty games while switching in order to understand the seemingly counterintuitive mathematics. In our simulation, stick won 32% of the time (slightly below the theoretical 33.3%) and switch won an astounding 73% of the time (a good bit above the theoretical 66.7%).
In the afternoon, we started investigating my favorite puzzle: the nonogram. It was awesome to see student enthusiasm grow as they learned more tricks for solving these puzzles. There was a good collaborative spirit in the room as they worked through the more challenging 15×15 puzzle. We will investigate some other types of puzzles as well over the rest of the week. This website contains nonograms of various sizes: http://www.puzzle-nonograms.com/. I even encouraged students to try to create their own, and I hope I will have a chance to solve one!
All in all, it was another successful day in Puzzles and Problem Solving. There was some mathematical frustration, and there was some mathematical celebration. There will be plenty more of each the next three days. We wrapped up the day with some more ZipZap. We’ve managed to count to 37 as a class and hope we can surpass that mark later in the week. Tomorrow we will begin tackling perhaps my favorite all-time math problem. I’m excited!