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The importance of reasoning quantitatively is reflected in both mathematics education research and mathematical standards for K-12 students. In this article, we detail how a quantitative reasoning framework can be used to help differentiate two quantities we have found students often struggle with: arc length and the measure of a central angle. We argue that taking the time to define all four components of a quantity can support students’ understanding of theorems involving these quantities.

Applying Quantitative Reasoning to Clarify Arc Measurements