The author investigated the relationship between aspects of student motivation and performance on mathematical tasks varying in cognitive demand relevant to meeting the expectations of the Common Core State Standards for Mathematics (CCSS-M). A sample of 479 primarily Latino middle school students completed established survey measures of motivation and a constructed response assessment of two facets of mathematical competence. The assessment measured students' progress toward performing a procedure and demonstrating understanding by providing a written critique of a peer's work, a more cognitively demanding facet. As predicted, higher interest and efficacy in mathematics, lower performance-avoidance goals, and fewer experiences of negative emotions related to performance levels for both facets, while utility and mastery-approach goals (i.e., focusing on understanding mathematics) related only to the more cognitively demanding facet. Implications of these findings for preparing students to be successful mathematical learners, especially in the many states implementing the CCSS-M, are discussed.