# Labeling the Number Line

by Lisa Bush, Vice President of Professional Learning
November 02nd, 2016

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Why are fractions on the number line so hard for students to understand, and what can teachers do to help students reason their way through them?

In this clip from Beyond Pizzas & Pies, Mr. Seay demonstrates for students how to label the number line after the unit interval has been partitioned into thirds. How does Mr. Seay’s explicit use of the chart and the large number line help students’ understanding?

Mr. Seay’s use of the chart and number line serve two important purposes for his third-grade students. First, the chart helps students see the relationship between the number of rods needed to partition the unit interval (in this case, 3) and the name of one of the rods (1/3). The second purpose addresses how to label the fractions on the number line. When students first transition from using materials like fraction kits to representing fractions on the number line, they may need explicit instruction on how and where to write the fractions. While it is true that in this context any one of the purple rods could be labeled 1/3 (and that label could be written anywhere on the rod) this is not the case when labeling the fractions on the number line. The number line is a distance model, meaning that as the rods are iterated on the number line, the label for 1/3 goes at the end of the first rod, the label 2/3 goes at the end of the second rod, and the label 3/3 goes at the end of the third rod.

What questions do you use to help students reason about fractions as numbers? Share your ideas with us.

Lisa Bush is Senior Director of Professional Learning for Math Solutions, and a conference speaker. Lisa has created and provided numerous professional development opportunities for educators. She authored the curriculum and resources for a math capstone course and an elementary math methods course for Grand Canyon University. Her coaching experience includes beginning teachers, mentor teachers and career classroom teachers. Lisa has taught mathematics in classrooms ranging from kindergarten to calculus. Find Lisa on Twitter at @lBush11.