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Now we’ve hit upon the major struggle that my students seem to have.
One big difference is that multiplicative thinking is “relative.” I think students think of counting and additive thinking as very concrete (whether or not they actually are) but struggle when they have to think in a more relative term.
“The wand is 6 units long” seems pretty concrete. But, “The wand is three times as long as the other” is now a relationship that causes them to rethink their “counting” strategies. If they don’t successfully make this switch to a comparative relationship, I believe they get stuck here.