Imagine 50 closed lockers in a hallway.
One student goes by and opens every one.
Another students goes to every second locker and closes it.
A third student goes to every third locker and if it is open, closes it, and if it is closed, opens it.
A fourth student then does the same but for every fourth locker.
A fifth student does the same but for every fifth.
And so on.
At the end, which lockers will be open and which will be closed? Why these numbers?
I think there is merit in analyzing the best way to deliver the problem. Case in point, the students did question the words 'And so on.' "Do you mean forever?", "How far should we go?", "When do we stop?" were fairly common.
But here, I want to emphasize something that totally surprised me. About how the students solved the problem, and what they chose as their method. The options were wide open. I'm defining wide open here as 7 different ways of solving this.
1) Pen and paper (immediately popular when they were reading the problem)
2) Chart paper (the response was, muted)
3) A long roll of mural paper (the rolling, intriguing, but not much commitment from the crowd)
4) The white board (notable enthusiasm)
5) Cube Links (crickets)
6) 2-sided plastic counters (aha moments for most groups, interest was building)
7) Sticky Notes (game over...close the door...the kids are getting rowdy)
But I didn't close the door. Instead, I offered two groups of students (per class) to take the problem outside, into the hallways, with their sticky notes. Inside the classroom, 2-sided counters were popular, followed by some independent pen and paper enthusiasts.
Having given some time for the groups outside to get going while I watched students inside, I wandered out the door to check on the progress. And there was the surprise. I thought, Sticky Notes outside the class, was one option. My misconception was that I could imagine how students outside were using those Sticky Notes. It wasn't one option. And I had no idea the students were going to do all of this:
Lay numbered Stickys on the Floor
Using O's and C's
Only OPEN Stickys without using Close Stickys
Choosing to skip lockers instead of all being labelled.
Tally Marks on each Sticky as needed.
Moving Stickys up and down, for Open and Closed
How long will 50 remain OPEN?
24 has been through some changes:
Some inside highlights can be seen here:
Here come the counters,
Some planning with Paper and Pencil.
I thought I knew what I was going to see. Today was a pleasant surprise. This is good.
At the end of the day, I still have these questions:
How could I have widened their options (choices) before starting?
Logistics and timing were an issue. How can I manage this better?
What prompting questions, if any, are needed here?
How can I better word the question, "Which lockers will be open and which will be closed"?
An attempt at answering that last one: Can I just say, "What will happen?"