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On the linked explanation, I’m looking for thoughts on canceling for fraction reduction which is not in the standards for good reason (first page), yet wondering if related thought processes could connect with and reinforce other important prior topics (second page). My question is, “Would it be worth venturing into activities like page 2, that would evolve into mostly mental math, to develop a sense for fraction reduction.” https://dl.dropboxusercontent.com/u/7405693/public%20responses/Tools%20fraction%20reduction.pdf
I’m not sure I completely understand the question, but here are some reactions. On the one hand, I think the activity on page 2 might strike students as a little weird: “we already know that 2/3 of 15 is 10, why are we doing this the hard way?” On the other hand, it is illuminating in showing a connection between previous knowledge and general rules that have now been developed for operations on fractions. My general feeling about reducing fractions is that there will be situations where it is clearly beneficial to replace a fraction with an equivalent simpler one, and this is one of them. So I’m not opposed to reducing fractions, just to the idea that it is always a necessary thing to do. We want students to know how to find equivalent fractions and choose useful ones in cases where there is one that is clearly useful.
My examples were ambiguous. I explain here: https://dl.dropboxusercontent.com/u/7405693/public%20responses/crosscancel.avi
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