Arithmetic is an important skill for people of all ages, and increases education and career opportunities. In particular, arithmetic concepts focus on the relationships, principles, and properties within addition, subtraction, multiplication, and division. Three concepts are of particular interest because there is little research on individual variation and the relationship between these concepts. These concepts are: inversion, associativity, and equivalence. These concepts were measured via immediately retrospective reports of problem-solving strategies. This study focused on those individual variations in the form of a longitudinal design. Fortythree participants were asked to solve 24 mathematical problems twice a year for 3 years. Children were studied from Grades 4 to 6. Accuracy and solution data were analyzed using two mixed model ANOVAs and a Pearson correlational analysis. The children had the greatest accuracy on inversion problems, followed by associativity, and then equivalence. They displayed the highest concept usage on equivalence problems, followed by inversion, and then associativity. Overall, children had higher accuracy on the addition and subtraction problems, compared to the multiplication and division problems. Children used the concepts more often on the addition and subtraction problems, compared to the multiplication and division problems. Overall, this study provides evidence that more research needs to be conducted on children's understanding and use of these three concepts on multiplication and division problems, as well as to identify individual variations and patterns.