I <3 Tom Lehrer. I only wish I could have attended one of his math classes. Him and Rudy Rucker.
Actually if we used base 8, it would make for an easier conversion of things to binary, since each octal number (0-7) would correspond directly to a triple of binary digits. Hex is similar in that way, but octal is a little easier for humans to grasp, since you don't have to deal with 'extra' digits (A-F).
Although, if anyone remembers Schoolhouse Rock, there was the one Math Rock piece called Little Twelvetoes that introduced the idea of base 12. I've caught my little one making lists of base 12 numbers using the 'dek' and 'el' characters from the video.
(Seven, and she already knows her multiplication tables)