## Making Connections

Today Katie spent a long time in the bathtub, mostly doing math :-).  It started out with me giving her the following problem that I got from Zvonkin’s book:

You are standing on the first floor.  You climb to the fourth floor and then climb up as many floor as before.  What floor are you on?

After protesting that she was on the second floor and that our house did not have four floors, she accepts that this is just make-believe.  She then gives the expected answer of “eighth floor.”

I proceed to give her the analogous problem where she initially climbs just to the second floor.  After making the same mistake again and me telling her to think about it for a moment, she comes up with the correct answer.  We then go back to the original problem.  I once again tell her to think about how many floors she climbs initially and she quickly figures out the answer.

After a brief digression on a completely unrelated topic, I ask Katie how many cuts it would take to cut a stick into five pieces.  She immediately says four.  Just to check that it wasn’t an accident, I ask her the same question with seven, and again receive the correct answer.

Me: Did you think of the problem with the floors when solving this one?

Katie: Yes, because you always start out with one piece.  See, you shouldn’t have told me about the other problem.

I smile and explain to her that my goal in giving her the problem was not to stump her and in fact, I was hoping that she would make the connection.