Our class today helped us get into the swing of things in a thinking classroom.  We were in random groups, up at the board, tackling a challenging problem.

3 logicians (honest people with perfect logic) each have a hat.  On each hat is a number.  The numbers are positive (non zero) integers.  2 of the numbers add up to the 3rd, and each of the people know this.  Person A looks at person B and C and says “I do not know my number”.  Person B looks at person A and C and says “I do not know my number”.  Person C looks at person A and B and says “I do not know my number”.  After hearing this, person A says “I know my number is 50”.  Our goal is to determine the numbers that B and C are wearing.

We wrote our ideas, and tried to get a handle on what we know and what we don’t know.

We looked at ways to represent relationships between numbers and options.  We used diagrams and drawings and equations
We came across a promising strategy, and followed it through to see if it works.

We ended off by justifying our work to classmates by acting out the possible scenarios.

The question and solution are not straightforward.  Even when we walked through them a few times we really needed to engage our reasoning skills.

It was not always a comfortable feeling to have a problem we were challenged by.  We relied on each other, we looked at what other groups were doing, we tried a few different strategies, and even then the solution seemed so close you could almost touch it.  We experienced struggle today.  We will experience struggle often, in math and in life, and it’s good to recognize that many positive things can come about after struggling and investing time and effort.

Good work today!