Back in November I gave a presentation about logic puzzles to a group of math educators. I wrote about it here. One of the things I was asked at this presentation was whether I had used this lesson with students. Answer: no…until now!
More recently, I wrote about demo lessons… Well, put two and two together, and TA-DA! You get a demo lesson about logic puzzles. [and much rejoicing was had by all.]
I had half an hour alloted for my lesson, so I had to pick one puzzle to share with my students-for-the-day. I chose the first one: Shikaku. Because it is the simplest one to describe, and these students had been doing work with area & perimeter. So: rectangle area; in puzzle form. Seemed like a good match.
The lesson went really well. The sixth graders dove right in and seemed to be enjoying themselves. They were able to articulate right away what the goal of the puzzle was, and they were really eager to work on them. Some wanted to work by themselves, but I got most of them talking to a partner without too much trouble. The hardest part was getting them to stop and share their strategies. Actually, they had a difficult time verbalizing what they were doing beyond “top to bottom”, “bottom to top” type comments. One pair said they started with the small rectangles, but then they decided to do the big rectangles first and then “fill in the rest” with the smaller ones.
The best conversations happened next, after I gave them the last five minutes to go back and continue working on the puzzles some more. I overheard one girl say to another student that “the prime numbers have to be 1 [by whatever prime #]”. Pretty sophisticated for a sixth grader. I heard another pair talking about how starting with the numbers “right next to each other” was a good strategy, and why “because there are less possible ways to do it.”
Overall, it was a success! I even had one student ‘discover’ the 4-color problem. And the teacher whose class I was stealing told me that he planned on using it with his other class later in the day. So, I must have gotten something right.
Further thoughts: There were one or two students who asked me if you could make some shape that was non-rectangular…I responded by asking them if the shape they were drawing was a rectangle and then they answered their own question (no, we can’t) based on the rules that the class had come up with. So, the follow-up is “What if you changed the rules? What if you could use non-rectangular shapes? How would that change the puzzle?” I also had the thought of making students work on creating other puzzles in the same “family” as Shikaku, but using other shapes (triangles, parallelograms, etc.) and learning from creating those.
In case you can’t tell, I love this lesson. It has officially become my go-to demo lesson.