Commentary: Fraction Strips

 

            Fraction strips are great; I think they’re probably the best manipulative for giving students a sense of the size of fractions and fraction equivalence.  We usually make them together in class.  We first make halves, then fourths, then eighths.  At each step, we talk about relationships that come up.  For example, , and one of the reasons why fractions are so confusing to kids is that there are different names for the same number.  We talk about why the word “reduce” is confusing.  We look at things like that half of a fourth is equal to a fourth of a half (and what operations are we doing?).  We then make thirds and sixths, which open up good questions like which fraction on the eighths strip is closest to  etc.  

            The handout helps students explore important concepts and patterns.  Just constructing the strips for fifths, sevenths, etc. is a challenge.  I tried teaching students an algorithm for folding these strips (link), but it didn’t work so well.  If students eyeball, or try to measure, they will often make mistakes, but these can lead to interesting conversations.  If it’s more important to have students have more-or-less accurate strips, the instructor can make them, but ultimately, any manipulative is only a start, and students need to abstract from it to examine more complicated fractions.  Nonetheless, if students can get a reasonably accurate set of strips (using 11x17 paper, cut the long way) with denominators up to twelve, it can give them a lot of insight into the size of fractions.  It’s a very different model from the pies and pizzas that most are used to.  7/05