The aim of this research is to devise a cognitive tool for meeting the diverse needs of learners for comprehending new procedural knowledge. A model of affordances on teaching fraction equivalence for developing procedural knowledge for adding/subtracting fractions with unlike denominators was derived from the results of a case study of an initial prototype of a graphical partitioning model. Offering affordances in our model makes available profitable spaces for learners to interact in ways that meet their needs. This model of affordances was evaluated by a pre-test-post-test control group design to study the performance of the experimental group in learning with the model. Results of the study indicated that the model afforded learners, with various abilities for learning, knowledge of fraction equivalence. The key for mediating the generation of procedural knowledge for adding/subtracting fractions with unlike denominators in working with our cognitive tool was the concept of fraction equivalence and the capability of computing this.