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:

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!

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**here**for the next strategy! 🙂

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.

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.

Students have a hard time with the explanation of the greater the denominator the smaller the piece therefore it greater than which really messes with their heads and mine🤪

Exactly! That’s why it SO important that they get lots of hands-on, visual experiences!

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?

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! 🙂

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.

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

Here are a couple related blog posts: Adding Up Fractions; Skip Counting…It Ain’t Just 2s, 5s, and 10s; and The Evolution of a Number Bond.

Thanks so much!

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!

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.