Against the background of neuroimaging studies on how the brain processes numbers, there is now converging evidence that numerical magnitude representations are crucial for successful mathematics achievement. One major drawback of this research is that it mainly investigated mathematics performance as measured through general standardized achievement tests. We extended this research by investigating the association between numerical magnitude representations and children's strategy use during single-digit arithmetic. Our findings reveal that children's symbolic but not nonsymbolic numerical magnitude processing skills are associated with individual differences in arithmetic. Children with better access to magnitude representations from symbolic digits retrieve more facts from their memory and are faster in executing fact retrieval as well as procedural strategies. These associations remain even when intellectual ability, digit naming, and general mathematics achievement are additionally controlled for. All this indicates that particularly the access to numerical meaning from Arabic symbols is key for children's arithmetic strategy development, which suggests that educators and remedial teachers should focus on connecting Arabic symbols to the quantities they represent. (Contains 4 tables and 1 figure.)