Summer SAVY 2017, Session 1/Day 2- Puzzles and Problem Solving (Rising 4th/5th)
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 looked a dice game today called “Petals Around the Rose.” It involves being able to decipher a riddle through understanding various rolls of the dice. This proved challenging for the students, but we made some headway as we struggled. We learned that the answers were always even. 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. The game can be played here if you are interested: http://www.freeworldgroup.com/games/roses/
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. Figuring out how many of those there were out of 20,000 proved to be a challenging exercise for us!
In the afternoon, we started investigating my favorite puzzle: the nonogram. Student reactions to nonograms were consistent with the spirit of the day, which I could best paraphrase as “This is so hard! I don’t get it! I want to do something else! Oh! Wait, that makes sense! I love these! I want to do more of them!” 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/. We mostly worked with 5×5 and 10×10 nonograms today, but some students worked on a 15×15 near the end. I even encouraged students to try to create their own; I would love to try to solve one of these student creations!
We wrapped up our day with our first full-fledged ZipZap contest. We still haven’t managed to count past 34 as a class. It is difficult! I hinted that we might add in “Zop” by the end of the week, and I loved hearing from so many students who made connections to the opening question I asked today by trying to identify the first potential ZipZapZop
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. Tomorrow we will begin tackling perhaps my favorite all-time math problem. I’m excited!