Literature that investigates the factors underlying arithmetic problem-solving achievement extensively evaluates the cognitive components, such as working memory (WM) and processing speed, at the basis of this acquisition. Recently, studies have shown that also the emotional factors, such as math anxiety (MA), could play a crucial role in the resolution of arithmetic problem-solving even during the first years of formal education. In this study, we tested 145 fourth-grade students to evaluate the possible combined effect of cognitive (i.e., WM, processing speed) and emotional (i.e., math anxiety) factors in untimed arithmetical problem-solving achievement. Regression analysis showed that MA contributed significantly to explain arithmetic problem-solving achievement even after having accounted for the cognitive abilities (WM and processing speed). In addition, the comparison between high-MA and low-MA children showed that the former had decreased performance in arithmetical problem-solving and WM tasks. On the whole, data seemed to corroborate the findings concerning the crucial role of math anxiety on math achievement even in untimed math tasks. Findings are discussed in terms of math educational context, and they underline the need to take into consideration also the emotional factors--apart from the cognitive skills--when developing interventions on math achievement.