Researchers have proposed that children’s understanding of arithmetic concepts is related to executive function (working memory, inhibition, switching, and updating) but this relation has been rarely investigated (Bull et al., 2001). Three arithmetic concepts were examined on a problem-solving task: inversion (i.e., addition and subtraction are inverse relations, 3+14-14), associativity ( i.e., addition and subtraction can be solved in any order, 3+14-12), and equivalence ( i.e., both sides of an equation have to be equal, 3+14+12=3+?). We hypothesized that (1) inversion would be the best understood concept, (2) there would be few grade differences in concept understanding, and (3) executive function tasks would be positively associated with the arithmetic concepts. Twenty-one Grade 1-3 children solved arithmetic concept problems and completed executive function tasks. Contrary to the first hypothesis, equivalence was the best understood concept. The second hypothesis could not be tested due to a small number of participants. Contrary to the third hypothesis, no relations were found between the arithmetic concepts and the executive function tasks. Equivalence may have been the best understood because problems could not be accurately solved without using it as a conceptually-based strategy. Understanding inversion and associativity is not necessary for successful problem solving. Children are used to solving problems from left-to-right and may not utilize more efficient problem-solving strategies. Data collection continues to determine whether the second and third hypotheses will be supported with a larger sample size. Overall, investigating the understanding of arithmetic concepts continues to be critical as it is considered essential for developing later mathematical skills (National Mathematics Advisory Panel, 2008).