Commentary: Finding Fractions Between Other Fractions

 

            There are lots of ways to find a new fraction between two non-equivalent fractions.  Asking students to do so is a good measure of their understanding of fractions  when we had a placement exam, we used to ask students to find two fractions between a quarter and a half, and over half our incoming students didn’t answer the question correctly.  Many of these students did remember fraction algorithms, albeit without understanding (of course, there is a very simple algorithm for finding a fraction between two fractions, but students don’t know it, and hence can’t apply it rotely; I don’t teach the algorithm if the emphasis is on new understanding). 

            This handout includes many methods, some are incorrect, and some have correct reasoning but incorrect language, etc.  I’ve used this handout as both a paper assignment and as an in-class activity.  8/05

 

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