Ms. Beyer's first graders have been working for several weeks on solving problems that encourage the use of such multiple representations as ten frames and number lines. The class is using Math Trailblazers, a National Science Foundation-supported elementary school math curriculum developed to reflect recent reform efforts in mathematics education. Mathematical representations are words, pictures, drawings, diagrams, graphical displays, and symbolic expressions. Each category is characterized by its own rules of use and relationships. Many educators and researchers argue that multiple representations are important for fostering understanding and should be an integral part of instruction. Teachers should help students understand that representations are tools to model and interpret mathematical phenomena, represent aspects of situations in mathematical terms, and emphasize the importance of representing mathematics ideas in a variety of ways. Three specific instructional strategies create opportunities that may support students' development of representational competence: (1) Engaging in dialogue about the explicit connections between representations; (2) Alternating directionality of the connections made among representations; and (3) Encouraging purposeful selection of representations. (Contains 5 figures.)