Recently there have been calls to study and apply critical theory and tools around social justice, and intersectional approaches of race, anti-racism, gender, sexuality, disability and accessibility, and class in Library and Information Studies (LIS). But applying lasting techniques in the LIS classroom require pedagogies that are intersectional, assessable, and apply lasting change for the student. This article argues for impactful approaches to intersectionality -- the inclusion of multiple identities and subjectivities such as race, gender, sexuality, and class -- to LIS in three parts: (1) Teaching critical theories alongside traditional LIS texts, (2) using systems of assessment for cultural competencies and analysis, and (3) classroom activities that implement metacognitive change. These approaches in the LIS classroom can demonstrably move LIS students into a deeper critical analysis of power in libraries that will be applied throughout their careers.