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Professional Development & Resources

Freaky Fraction Splitting

Resource MAA

Take a pile of nine pebbles, nine coins, or nine cucumbers (but you can't use zucchini!) and split it into two piles. Then, split each of those piles into two piles. Keep doing this until you have nine piles, each with one object.

What could be mathematically astounding about such a process? There is a scary, tremendous amount of astonishing mathematical stuff! But in this video, I present a particularly freaky invariant related to fractions. Can you figure out what is going on?