## Building Numbers

My daughter recently had her second birthday, so during her birthday dinner I ran through the litany of second birthday facts:

Famous people that were once two: Mozart, Mother Theresa, Einstein,…

Fascinating facts about the number two: $2+2=2\times2=2^2$, It’s the only even prime,…

At which point my 6-year-old asked what an even prime is. He knows what an even number is, so I told him that when we got home I would show him what a prime number is with blocks.
That evening as our family was sitting in the kitchen eating birthday cake I was startled by the sound of blocks hitting the table. I looked up. There was my son, two blocks in front of him on the table and inquisitiveness in his eyes. “Show me,” he said. I sent him back for more blocks.

I showed him that with some numbers, you can take that many blocks and make rectangles.  Like with 6 blocks you can make a 2 by 3 rectangle, but with others you are stuck with only one kind of rectangle: a long skinny one.  For instance, with 7 blocks you can only make a 1 by 7 rectangle: 7 is prime!  I also showed him square numbers and triangular numbers.

After my explanations he invented building numbers.  A number is a building number if (and only if) you can make a building with that many blocks.  For instance, setting one block on the table does not make a building, but stacking two blocks up does!  I asked him whether ever number bigger than one is a building number.  He said yes.

Are building numbers trivial?  Yes!  Silly?  Yes!  But he had fun with it and he had an experience creating something in the realm of mathematics.  Maybe I’ll come up with a demo and activity along these lines that I can do in his classroom.  Hmmm…