Math PhD here. You're a fantastic dedicated parent and you did no harm. First, as to the merits of your approach --- I think of multiplication as scaling mysel

Math PhD here. You're a fantastic dedicated parent and you did no harm. First, as to the merits of your approach --- I think of multiplication as scaling myself. That's totally valid. Second, whether it's even possible to do harm here --- worst case scenario, the metaphor doesn't make sense to your kid and she doesn't use it in her own thinking about mathematics. Everyone has to develop their own intuitions --- like you had your epiphany --- and she'll develop hers even if you set her on a track that doesn't work, just as part of her learning and doing mathematics.