Dan Meyer’s recent post on “fake world” math tasks has me thinking about many of the openers and games I have used in my classroom. I have written about The Take-Away Game before, and I still use it often…until the kids learn how to beat me and the strategy is revealed. This next one is not so much a game, but more of a task, similar in some ways to the Locker Problem.
THE HOT SEAT
In this task, chairs are placed in a circle. Chairs will be removed from the circle using the following rules:
- Chair #1 is removed first.
- The next remaining chair is skipped, and the next chair removed.
- This continues, with chairs skipped and removed until only one chair remains.
- Once a chair is removed, it is “out” of the circle
- Whoever is sitting in the last remaining chair “wins”
Here’s a brief Doceri video which shows some game playings:
Like the “Take-Away Game”, I can’t recall where I first encountered this problem. They have both been sitting in my files for over a dozen years. If anyone can name a source, I’d be happy to award some credit.
Why I enjoy this problem:
- It’s not intimidating. We have a chance to draw, get out blocks, magnets….whatever we want to use to model the problem. Great for working in teams.
- I can let the problem marinate. On one day, I may ask the class “Where should I sit if there are 8 chairs?”, and come back the next day with “How about 24 chairs?” If it seems like discussion is flowing, I can put my foot on the gas.
- I can use this problem with all levels of students. If we need to create a data table and look for a pattern as a class, that can happen. If my honors kids want to fly with it, that can also happen.
- The answer is not obvious, but a clear pattern eventually emerges if you model enough circles. And there will be some nice vocabulary opportunities as the payoff.
There are a number of ways to express the solution. Later this week, I will post the “answer”. Until then, have fun moving around the furniture.