This study investigates linguistically diverse elementary mathematics classrooms, focusing on potential for dialogic discourse (constructing meaning through dialogue) and alignment with Common Core Standards for Mathematical Practice (SMPs). Constant comparative methods and discourse analysis of field notes, video recordings, and transcriptions examine verbal moves, exchanges, sequences, and episodes of discourse from elementary dual language (Spanish/English) mathematics classrooms. Analysis demonstrates that specific verbal moves (e.g., exploratory talk, accountable talk, and generative assessment/feedback may shift discourse toward dialogic and support SMPs. Other supporting moves (e.g., think time, visuals, and code-switching) are identified. Models of teaching are built from relationships among moves, exchanges, sequences and episodes within mathematics lessons. Implications for teaching and research in linguistically diverse mathematics classrooms are shared.