This study investigated the fluency with which first-graders with strong, moderate, or weak mathematical abilities apply the decomposition-to-10 and tie strategy on almost-tie sums with bridge over 10. It also assessed children's memorized knowledge of additions up to 20. Children's strategies were analysed in terms of Lemaire and Siegler's model of strategic change, using the choice/no-choice method. Results showed that the children applied both the decomposition-to-10 and the tie strategy efficiently and adaptively. Furthermore, the first-graders had already memorized the correct answer to more than half of the tie sums. Finally, children with strong mathematical abilities applied the different strategies more efficiently but not more adaptively than their mathematically weaker peers. [For complete proceedings, see ED489597.]