Improper representations are frowned upon in school, but they have their place. Once, a niece of mine in kindergarten told me she knew what 3 times 11 was: 33.

Improper representations are frowned upon in school, but they have their place. Once, a niece of mine in kindergarten told me she knew what 3 times 11 was: 33. I asked "Well then, what's 7 times 11?" "It's seventy-seven." "Okay, I bet you don't know what 12 times 11 is." "Twelvety-twelve", she gleefully replied. We agreed that twelvety-twelve is a perfectly good number, we know what it is, but if we were talking to other people we would tell them one hundred and thirty two – for us, twelvety-twelve is just fine. – Bill Thurston, Groups, Tilings and Finite State Automata