This week I gave a presentation to grade 3-5 teachers from around my district. One of the points I wanted to drive home to them is that number sense does not apply to only whole numbers. Students can (and should!) have number sense with regards to fractions and decimals as well.

One area where I see teachers frequently take shortcuts and/or avoid number sense is with comparing fractions. Some teachers teach their students to use cross multiplication to verify whether two fractions are equal. Others teach their students to use one and only one strategy for comparing fractions: find common denominators. This strategy works, don’t get me wrong. However, it develops one skill, not number sense.

When comparing fractions, students should be mentally choosing from a variety of strategies. Why? Because students might notice they can make a comparison quickly and mentally. Why go to the trouble of creating common denominators, which likely involves making some notes on paper, if you can mentally make a comparison based on your understanding of fractions?

To that end, I put together three “books” that teachers could use to prompt some discussion and reasoning among their students. I’d love for their students to start realizing that fractions are something they can make sense of.

- John’s Pizza
- Lunch With Friends
- Eating Half (1/29/2015 Fixed page 4 so final fraction is 3/6, not 2/4.)

Each book focuses on comparisons around a particular strategy, but the strategy is never spelled out for the students. Instead, my hope is that by noticing, wondering, questioning, reasoning, and communicating, a class of students can make sense of the strategy in each book.

By no means are these books intended to fully develop students’ number sense with regards to comparing fractions. Additional experiences and practice are likely required. However, if you’re a teacher who wants a place to start this work with your students, give these a try and let me know how it goes.