I made this one a little harder. I wanted Paulina to think carefully about:
- the determinants of dimension
- how measurements change when enlarging along one, two, or three dimensions
- 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.