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My 5-year old daughter played through Dragonbox pretty quickly and afterward I went through some concepts with her like x/x = 1 or 1x = x.

When shown to her using fractions of a drawn circle or simple multiplication of real objects, she seemed to understand the concept in the abstract.

However, once I introduced something like ayx/yx = a, it seemed to trip her up, even though the motions in Dragonbox made sense to her.

That said, I'm not sure I understood why x/x = 1 until much after 5 years old, so maybe there's something to be said about going through the motions of computation before truly understanding the general concept.

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