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Composing and Decomposing Fractions

Written by Donna Boucher

Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.

CCSSM 4.NF.3b reads as follows:

Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation.  Justify decompositions, e.g., by using a visual fraction model.  Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

Here’s a little fraction activity that can move your kiddos in the right direction toward that understanding. Be sure to provide manipulative support (concrete) and have students record their work with a model (representational). A suggestion for how to draw the model is shown below. Click here to grab your freebie!  As always, I love to hear how you use this in the classroom.  🙂

14 Comments

  1. Katie

    Thanks for this! I will be starting my CCSS unit on fractions after Christmas…and just reading the standards makes my head hurt! I like the way you explained this one.

    Reply
    • Donna Boucher

      Ha ha! I totally understand. Glad this helps. 🙂

      Reply
  2. Dondee

    Thank you so much for this!

    Reply
    • Donna Boucher

      You’re welcome!

      Reply
  3. Cindy in Wisconsin

    Thanks so much! I know this will be a help to my students; I look forward to using it!

    Reply
    • Donna Boucher

      My pleasure, Cindy! 🙂

      Reply
  4. Rhonda Griswold

    This is just the latest download I have and I will use for summer school. Glad to have the freebie and I appreciate all the work you do. thanks for making it possible to not have to reinvent the wheel so to speak.

    Reply
    • Donna Boucher

      I need a t-shirt: “Will work for sweet comments!”. Thanks so much, Rhonda. 🙂

      Reply
  5. Adrienne

    I’m looking for a concrete way to introduce and work with composing and decomposing fractions. Any suggestions?

    Reply
  6. Chrissy

    We have been sharing this activity with teachers in our Fractions training (I am a K-5 math consultant) this year! We model it with connecting cubes, a different color for each addend. With one missing addend, sometimes we play a version of “I wish I had”… I wish I had 7/8. Right now I have 3/8 (built with 3 cubes, each with a unit of 1/8). What do I have behind my back? (4/8)

    The equations with two missing addends have been especially powerful in generating great mathematical discourse. When my 10/12 looks different than your 10/12, we have lots to talk about!

    Thanks for this awesome activity!

    Reply
    • Donna Boucher

      Love it, Chrissy! I like the idea of using linking cubes. Thanks for sharing.

      Reply
  7. Maria

    For Texas, which TEKS does this activity cover? You have so many awesome activities and sometimes with the TEKS I get confused.
    Thanks,
    maria

    Reply
    • Donna Boucher

      Maria, it is 4.3(B), Decompose a fractions in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations.

      Reply
  8. Penny

    Donna,
    I absolutely LOVE your work and insight into all the various areas you share with us! I always say “I want to be like you when I grow up!!” You’ve helped me and my teachers understand the TEKS / SE’s … thanks for that!

    Reply

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