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!
Click here for the next strategy! 🙂