Represent 3/8 in three different ways with ___________. Of course, it is is important to use MULTIPLE models—not just one model for representing a fractions (e.g., Petit, Laird, Marsden, & Ebby, 2015). However, I have found that my prospective teachers can easily find multiple representations for 3/8 with pattern blocks, yet struggle to find any representations for 3/8 that do not involve eighth pieces or sixteenth pieces. In fact, very rarely in curriculum and other spaces do we find the whole defined as anything other than 1 circle when the circle model is employed.
The whole can be two circles, four circles, eight circles, a piece of a circle. There are an infinite amount of representations. Learning to redefine the unit and clearly identify the whole is a huge conceptual hurdle for understanding fractions.
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I like how redefining the unit creates flexibility in thinking, but I wonder if this flexibility also fuels the debate that exists between people who view ratios as fractions and people who view ratios and fractions as separate ideas/mathematical entities. If I define my unit to be 8 circles, 3/8 is 3 circles out of 8 circles shaded (a ratio of 3 to 8); however, some people would argue that viewing the fraction 3/8 as the ratio 3:8 is wrongly viewing two separate concepts as identical. It makes me wonder...
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Nicole
3/1/2016 08:19:30 am
I agree. This is just one of many activities we will do. And, at the end of the day students do NEED to conceptualize fractions as ratio. Of course, in addition to ratio students need to think about fractions as:
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Nicole M.

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