Adding and Subtracting Rational Numbers on the Number Line

byAaron Bingea

When students are asked to operate with unfamiliar rational numbers they cling to previously learned algorithms without a conceptual understanding of what is actually happening with the numbers. Their insufficient grasp of foundational number and operation concepts are major contributors to an overall intolerance and avoidance of working on any task that contains these unfamiliar numbers. Although this issue is glaring, it is increasingly difficult to address when the middle school curriculum assumes and requires a fundamental and flexible understanding of numbers. This unit will boldly aim to formally and methodically address the fundamental issue of my students’ limited number and operation sense via the use and study of the number line.

This unit is an extension and will be used in succession with Jeff Rossiter’s unit, Placing Rational Numbers on the Number Line, which focuses on the realization and placement of rational numbers on the number line. From this prerequisite unit, students will gain a unified understanding of what rational numbers are and how they can be represented on the number line and then move on to adding and subtracting of rational numbers, the focus of this unit.


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