So, Petals Around the Rose (the name is really important!) is a game/puzzle which, if you followed that link just now, is likely making you really frustrated (sorry about that). Five dice are rolled, and you have to predict what score those dice make (and I promise that there is logic to how the computer decides the scores). If you use the site I linked to, you enter your prediction before seeing what the actual score was.
For the last couple of days, I've been using the puzzle in the last 5 minutes of my lessons with Year 7. One student has already seen the puzzle before (and is taking great pleasure in keeping the solution a secret), but as of yet, none of the others have figured it out.
They are trying, though. My students are very determined to find out what the answer is, and keep suggesting their own theories, unprompted. Because of how the game works, it's easy to get them to test their theories - roll the dice again, and get them to give the score. Even if they manage to be right that time, it doesn't take long to find a roll where their theory fails. But this is what mathematics is, right? Noticing patterns, coming up with conjectures, testing those conjectures, and going back to the drawing board if it doesn't hold up.
This is their score as it stands now:
I'm not sure how we'll proceed with this now. I might wait until next week to bring this out again, but I do want to keep playing the game with the class until they figure it out. We'll see how long that takes.
The question I've been leading to is this: How do I get students to display this same determination and persistence to finding actual mathematical patterns and theorems? I guess this is what every maths teacher spends their entire career trying to answer.