Comparing Fractions: One Unit Fraction from a Whole

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.

Students should have flexible strategies for comparing fractions, and the strategies should be based on reasoning and fractions sense. In the first article of this series, we looked at comparing fractions with like numerators or denominators. You’ll also find the vertical alignment of fraction comparison standards from 2nd through 4th grade in that post.

The next comparison strategy involves fractions that are one unit fraction from a whole. A unit fraction is a fraction with a numerator of 1, for example 1/8 or 1/12. Examples of fractions that are one unit fraction from a whole are 7/8 or 11/12. The key to this type of comparison is to think about, and visualize, the distance each fraction is from one whole. For example, 7/8 is 1/8 from a whole and 11/12 is 1/12 from a whole. Since 1/12 is smaller than 1/8, 11/12 is closer to one whole, so it is the greater fraction.

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To really understand this strategy, students need lots of hands-on practice and they need to understand the meaning of the denominator–the larger the denominator, the smaller the piece. Take a look at this graphic:

One Unit Fraction
By using the visual, you can see that 11/12 is closer to the whole, because 1/12 is smaller than 1/8.

After we had practiced comparing fractions one unit fraction from a whole using fraction tiles, we played a good, old-fashioned game of War. I made two copies of this sheet for each pair of students on cardstock, laminated them, and cut them out. Each player turned over one card, and the player with the greater fraction had to explain why theirs was greater. Students had the fraction tiles handy to refer to, if they needed them.  Check out this video of my students in action!


Click here for the next strategy! 🙂

10 Comments

  1. Lori Martensen

    I am also working to deepen fraction sense. Comparing fractions with “one missing piece” is challenging for students to grasp. I love how you have the fraction tiles to scaffold learning with purposefully fraction cards to emphasize that they are one unit fraction from a whole. Note: In your blog post the description of a unit fraction should read “with a numerator of 1”. I love your fractions posts! Thanks for sharing.

    Reply
    • Donna Boucher

      Oh good grief! Thanks for catching my typo, Lori. And I agree that this strategy is difficult for students to wrap their mind around. So important that they see it with concrete materials.

      Reply
  2. Lisa

    I am curious about John voicing the rule incorrectly. Several times he says, “The smaller the denominator, the smaller the piece.” However, he clearly understands the rule. It seems he is struggling to speak up and that is why the girl is beating him. So if his issue is with voicing the rule rather than understanding the rule, when is the appropriate time to correct him? I wonder if giving him the language again would help him overcome his hesitancy or hinder him?

    Reply
    • Donna Boucher

      It might help to give him the language again, Lisa. I think he was in competition mode and not thinking through exactly what he was saying. He also might have been a little nervous since I was videoing them! 🙂

      Reply
  3. Debbie Krueger

    I call these “missing piece” fractions. Once we have moved to the abstract I have them visualize the size of the missing piece to determine which fraction is larger.

    Reply
  4. Amber Cunningham

    Do you have any ideas or resources for mixed numbers and improper fractions?

    Reply
  5. Dawn Hirsh

    This is a great and fun way to teach. I think here in Israel we just use workbooks, and my ld child is lost in the woods. Coronavirus has been a blessing for us because I can teach her using manipulatives, hands-on, and games. However, I wish she was in a learning environment where more collaborative learning and math talks could take place. Even if she goes back to school, I don’t think we do that here. Thank you for sharing your knowledge. Teaching fractions can be tricky!

    Reply
    • Donna Boucher

      Thank you so much for your comment, and I’m glad you find my content useful for your child! It’s a silver lining from COVID that you’ve been able to bond with your child over math. Even if she doesn’t get it at school, I hope you’ll continue to celebrate the joy of math at home! Best of luck to you.

      Reply

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