Ella has been feeling quite fractious over her fractions, with little reason for it. She said she had the sense that she's going too slowly, but that's not actually true, she's progressing just fine.
But yesterday, she had a major CLICK moment where she understood, really understood, how fractions are related to division and multiplication. She got the "breaking it up into parts" idea, finally. I think she got that glimmer that "A Whole" is not one static thing, that the definition can switch depending on the thing you're investigating.
Take a pizza, that's easy, and divide it into 8 parts. Each piece is 1/8 of a whole. Ella has never had a problem with this.
But it wasn't until we *started* with the parts (in this case, a drawing of a bunch of fruits and vegetables...carrots, apples, and pears), made them into one big "group" in our minds, and then identified each type of thing as a fraction of the big group, that she really got it.
I LOVE that startled look on their faces when they finally say "Oh!" And then that gratified, proud, slow smile that follows the exclamation, as they *realize* they understand something that they didn't a moment before. I live for that. Nothing else like it in the world.
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