I argued (again) today with my students. One of them told me I’m really picky. I am. I think this particular definition for improper fractions isn’t enough. It only tells me what an improper fraction *looks like*. I want to know more importantly, what does it mean to be improper? What does it tell me about my fraction if the numerator is larger than or equal to the denominator?

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I usually fight against the term “bigger” and propose “greater.” I always wonder why kids consistently return to bigger? Is there a natural math “terminalogyphobia?”

Hmmm….I think it’s because as babies and toddlers we use the words bigger/smaller to compare the size of objects. Then when we want to talk about numbers, we can make a”bigger” pile of blocks with a greater number of blocks. Along the same lines, “great” is used to describe something good/fantastic–not related to size.