By Matt Haber, posted August 17, 2015 –

I read a blog on this site that stated an expectation of any pre-K–grade 6 mathematics experience is the development of a sense of number. Firmly establishing and maintaining flexibility with number is simultaneously ongoing and foundational to working with operations involving whole numbers and fractions.

Student success in this area does require a strong understanding of fraction equivalency. My research and classroom practice has shown that student success in later elementary grades is greatly determined by a strong understanding of fraction equivalence and becoming flexible with decomposing and recomposing fractions. Many tasks can address fraction equivalence and support students in this journey.

I use fraction manipulatives to aid students as they grapple with equivalency. These manipulatives involve building linear halves, fourths, eighths, sixteenths, and the whole. I ask students to find different ways, let’s say, to make 3/4. Some responses are 1/4 + 1/4 + 1/4, 1/2 + 1/4, 8/16 + 1/4. Connecting the visual to the number representation builds flexible thinking and understandings about equivalence. Modifying this task using pattern blocks (thirds, sixths, halves) or other objects is appropriate.

Another task I use is listing fractions, such as 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8, and allowing students to group or consolidate them. Many students find 7/8 or 1/2 + 3/8. Others find 1/4 + 1/4 + 1/4 + 1/8 and 5/8 + 2/8. Occasionally, I get 1 – 1/8. Tasks such as this give students the opportunity to explore flexibility and efficiency.

Flexibility—with fractions as well as with whole numbers—gives students a strong advantage as they move into subsequent grades that build on fraction concepts. But more important, I believe that when students connect their flexibility with whole numbers to other concepts—such as decimals, fractions, and negative integers—the story of math begins to unravel, sparking meaning and, thus, confidence and excitement.

Matt Haber is the founder of Problem Solved! Innovative Learning for the 21st Century, where he consults with educators, parents, and students with twenty-first–century mathematics, teaching, and learning. For seventeen years, he worked as a teacher and mathematics coordinator for the Los Angeles Unified School District, where he provided districtwide professional development to teachers, principals, and directors.