Dividing Fractions

My 6th graders have been working with dividing fractions for the last two weeks. We explore these four ways, in this order:

  1. Number line
  2. Rectangles — I wrote about this here.
  3. Dividing by one
  4. Common denominator

It’s completely intentional that we work with the number line and rectangles first. I want my kids to see the answer and that it should match their intuition and understanding.


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  1. Elaine Watson
    Posted June 1, 2016 at 8:18 am | Permalink

    This is a great post! Sweet and to the point. I work with adult learners and a big focus is getting them to understand fractions and their operations. I had forgotten the #3 and #4 examples. I work a lot with the “magic one” for changing the appearance of, but not the value of, a fraction. I use the Magic One for renaming a fraction in order to add or subtract, but I never thought to use it for dividing. This is such an improvement on “just flip the second one and multiply” with no understanding.


  2. zenxbear
    Posted July 1, 2016 at 3:17 am | Permalink

    I was confused about method 3. How one would convince them with manipulating fraction with fractions as numerators and denominators. And I am multiplying top and bottom with a fraction not a mere integer. So I let it simmer in the back of my head, for a day. It occurred to me (while looking at some pow) that maybe while teaching rates, one can naturally show use of rates with decimals/fractions components. It is still amazing to see a teacher do this with 6th grader.
    I am planning of passing teacher recruitment exams in France, and temping for a while. And fraction division is on the curriculum of 8th grader not 6th grader. Although they divide decimals by writing the euclidean division. And use proportionality tables with decimals on the rows.
    Teaching trivial things is so complex.

  3. Posted August 13, 2016 at 1:25 pm | Permalink

    On method 4, do you tell them to divide both numerators (and ignore denominators), or do you show them some kind of method, then agree to skip showing that step?

    • Marti Newman
      Posted August 13, 2016 at 1:52 pm | Permalink

      For method 4 in my classroom, we write it the same way because kids come to understand the common denominator as a common unit. You have 10 of something being divided by 9 of that same something, so 10 / 9 . Here, that same something is twelfths. When kids use this understanding, there’s no need to divide the denominators to one.

      • marti newman
        Posted September 26, 2016 at 8:52 pm | Permalink

        Hey Fawn,

        I appreciate your posts and your love of rectangles. :)

        I’m curious: why do you teach common denominator method after dividing by 1? I do the opposite. I build, trying to help kids feel the progression, from modeling to common denom. to dividing by 1.

        Maybe I’m missing something…


  4. Kirstyn Martin
    Posted August 28, 2016 at 5:34 pm | Permalink

    Hi Fawn! Love your blog! Do you show them the algorithm for dividing fractions at the end of the 10 days?

    • Maia
      Posted February 7, 2018 at 9:26 pm | Permalink

      Hi Kirstyn,
      Isn’t the traditional algorithm basically technique #3 “Dividing by 1”. I don’t think you would need anything beyond these methods for kids to be able to approach any situation with confidence.

2 Trackbacks

  • By #MTBoS – mbrunnermath on August 25, 2016 at 5:51 pm

    […] this post again about Dividing Fractions from Fawn Nguyen. I saw it early in the summer, but I’m glad to have it pop up again in my […]

  • By Shortcut Found – mbrunnermath on September 14, 2016 at 4:37 pm

    […] classes we were talking about dividing fractions, and we were modeling them with rectangles, á la Fawn Nguyen. My second period is full of awesome students, and they were doing such good work and were keyed […]

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