Nine Dots

It's a new school year and a second year of Creative Problem Solving/Design Thinking. We started out with some of the same activities last year's class did, from the CPS book Big Tools for Young Thinkers. The class enjoyed the activities, made a strong start on collaborative brainstorming, and dipped their toes into out of the box ideas.

Then I read a reference to the classic Nine Dots puzzle, which I was already familiar with,  and decided it would be a valuable learning experience for my students. If you haven't come across this wonderful little nudge to thinking literally outside the box, here it is:

The challenge is to connect all nine dots with four straight lines or fewer, without lifting the pencil from the paper.

I first asked if anyone had ever done this puzzle, since 4th graders have a habit of bursting out with what they know, even if you don't want them to tell everyone else at that particular moment. One boy had done it before, so I had prepared in advance with some hands-on puzzles. He very happily took on a brick arrangement challenge, using variously shaped bricks and following a design challenge on cards.

As soon as I put the nine dots up on the Smart Board and explained the parameters and the goal, one boy said, "I see how to do it already." I answered, "Great! Show me on paper." I handed out a sheet with three copies of the nine dots, so students could easily try more than once. There was a lot of excited discussion, and quite a few questions for me as I walked around, mostly clarifications of the rules. No, a curved line is not allowed; no, you may not pick up your pencil; yes, ALL the dots have to be included on one of the lines, when you turn the corner that is the start of a new line.

After 10 minutes or so, none of them had succeeded. (And my young man working with the bricks had been paying interested attention but not saying a word!) It was time for a clue, so I referred to our CPS "rules," which include "think outside the box." This created a buzz, but no actually  going outside the box around the dots that each of them had created in their minds. The student who said he knew how to solve it at the beginning still had not succeeded.

Running out of time, I told them I would give them the solution. The young man already in the know asked if he could put it up on the board, and so we all watched as he drew lines, continuing outside the box, to connect all nine dots in four continuous lines. There were many gasps and "oh!"s.

On to the next challenge, reminding my class to Think Outside the Box!

If you would like the solution to this puzzle, Wikipedia has an article about it.