Abstract
At the primary level, the equivalence of two fractions is generally thought of in terms of equal quantities that share a common whole as a reference. It is understood as an expression of absolute size rather than as a ratio. In addition, given the challenge of taking multiplicative relationships into account when comparing fractions, techniques for tackling these complexities are in high demand, with teachers seeking them out as much as students. It therefore seems pertinent to examine the didactic conditions that can be relied on to enable students to gain a thorough understanding of equivalent fractions. In our research, we used a teaching sequence that covered various interpretations of fractions in order to foster an understanding of fractions as a multiplicative structure. This article presents three scenarios from our sequence, showing how equivalence was worked out in accordance with the particular interpretation (or interpretations) of fractions at play for each. The variety of scenarios proposed promotes the development of strategies that differ according to the constraints inherent in each scenario, thus offering multiple starting points for comprehending the notion of equivalence.
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