Reconstructing the unit on the number line: Tasks to extend fourth graders’ fraction understandings

ABSTRACT

This paper shares how fourth grade students solved a unique type of number line task. Instead of giving students the unit and asking them to locate a fraction on the number line, students were given two points on the number line and asked to either find 1, or another number on the number line. This type of task is called “reconstructing the unit” and has been used by others to study students’ understanding of fractions. We wanted to discern how students solved these unique number line tasks and determine ways students applied prior understanding of key fraction ideas to make sense of these tasks. Students generally solved the tasks by first finding a unit fraction which they found in two different ways. We realized that reconstructing the unit tasks on a number line provided a space for students to apply and extend key fraction ideas related to the meaning of numerator and denominator, unit on the number line, partitioning, as well as order and equivalence ideas initially developed with more concrete models. This task type using the number line has the potential for deepening students' fraction understandings.

KEYWORDS:

• Fractions
• models
• number line
• rational numbers
• representations