Exercising the Young Mind

I have posted another problem set in my website. The first one on exponents was successful. I got a few questions from Paulina, but she was able to do most of the problems. At least, I was successful in getting her to sit down on her own to think hard for a while.

I made this one a little harder. I wanted Paulina to think carefully about:

1. the determinants of dimension
2. how measurements change when enlarging along one, two, or three dimensions
3. the relationship between volume and area

The last item can get quite complicated. In fact, there is a whole area of research into isoperimetrical inequalities. However, young kids can answer simple questions about the surface area of a solid when the dimensions are changed. For example, how does the surface area of a unit cube change when we double its dimensions?

This problem set is #2 in http://perezhortinelafamily.us/MathProblemSets/Main_Frame.htm. I recommend using Lego blocks with this problem set.