When designing an instructional tool and using it in pedagogical activities, it is essential that designers and users understand what pedagogical affordances and constraints the tool provides to support its successful integration into targeted pedagogical activities. Toward this end, we developed "Pedagogical Affordance Analysis (PAA)." PAA involves analyzing teachers' Pedagogical Content Knowledge and/or Technological Pedagogical Content Knowledge to elicit pedagogical affordances and constraints that are specific to a given instructional goal. Information obtained through PAA can help in designing, refining, and/or evaluating instructional tools. We present a case study in which we used PAA to successfully design a visual representation for middle-school algebra. To the best of our knowledge, PAA is the only available systematic method that leverages teachers' pedagogical knowledge in identifying pedagogical affordances and constraints. PAA can be used across a wide range of existing tools and prototypes of to-be-designed tools. [This paper was published in: "ICLS 2020 Proceedings," ISLS, 2020, pp. 1561-64.]