The "remembered success effect" (Finn, 2010) refers to the finding that challenging academic tasks that start or end with extra opportunities for success are preferred to challenging tasks that do not include these opportunities. Work on remembered success has primarily been done with adults. We assessed (in a preregistered study) whether the remembered success effect could be detected in two school-aged groups of students (281 third-graders and 289 sixth-graders). We examined the effect in terms of students' future activity choices and task evaluations, as well as their expectancies for success, task values, and perceived costs, key motivational constructs from expectancy-value theory. More specifically, we tested whether students would prefer an "extended" difficult math task that began or ended with a set of moderately difficult problems (i.e., that included experiences of relative success) over a shorter task that contained the same number of difficult problems, but none of the moderate problems. Results showed that students in both grades preferred the extended task. In addition, students' expectancies and subjective task value were higher, and perceived costs lower, in the "extended" condition than in the short condition. Results were generally stronger for the older students. Adding experiences of remembered success to challenging math tasks could turn out to be a straightforward, cost-effective way to increase the likelihood that students will choose to engage in and persist at such tasks, even as early as Grade 3. [This is the online version of an article published in "Journal of Educational Psychology."]