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 us

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.