My kid found a dime at the park. "Mama," she said later, "I'm nine times luckier than if I had found a penny."
"Is it really nine times, or is it ten?" I countered, "because ten times one is ten and a dime is ten pennies."
Still later, "Mama! I found a penny! Now I'm eleven times luckier!"
After lunch at the co-op, "I want to take the long way out so I can see if I can find some more money...I found another dime! Twenty-one times luckier!"
As always, I find this kind of conversational math interesting, mostly because math is for doing and using. This particular concept is an extremely useful one for her as she continues to focus on the size and shape of the universe. We've not done much with scale, but what we did encounter, in the form of the book Ten Times Better this previous January, made a huge difference for both of us.
There was also some discussion about the chances of finding coins when you're actively looking for them, but I don't think either of us understand probability at all yet. Onward!
What a wonderful little chain of reasoning: nine times luckier becomes ten times once she accepts that a dime is ten pennies, and then the penny she finds makes eleven, and the second dime makes twenty-one, so the whole day becomes an adding-up of tens and ones. That is exactly how multiples of ten stop being a memorized table and start being a felt scale, just as Ten Times Better did for her back in January. I also love that she chose the long way home to look for more coins, since it shows the math was doing real work in her decisions, not just on a worksheet. Full disclosure: I run the free tool site factorcalculator.org, where students can explore multiples and factors of any number.
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